ICIC Express Letters

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ICIC Express Letters

Editors-in-Chief Junzo Watada, Graduate School of Information, Production & Systems, Waseda University 2-7, Hibikino, Wakamatsu, Kitakyushu 808-0135, Japan Yan Shi, Graduate School of Science and Technology, Tokai University 9-1-1, Toroku, Kumamoto 862-8652, Japan

Advisory Board Steve P. Banks, UK Tianyou Chai, China Tom Heskes, Netherlands Lakhmi C. Jain, Australia Jerry M. Mendel, USA Masaharu Mizumoto, Japan Witold Pedrycz, Canada Jeng-Shyang Pan, Taiwan Peng Shi, UK Jianrong Tan, China Takeshi Yamakawa, Japan Lotfi A. Zadeh, USA Kaiqi Zou, China

Associate Editors Ramesh Agarwal, USA Jamal Ameen, UK Rawshan Basha, UAE Michael V. Basin, Mexico Yasar Becerikli, Turkey Genci Capi, Japan Ozer Ciftcioglu, Netherlands Joshua Dayan, Israel Vasile Dragan, Romania Kei Eguchi, Japan Keiichi Horio, Japan Chao-Hsing Hsu, Taiwan Xiangpei Hu, China Gerardo Iovane, Italy Karim Kemih, Algeria Dongsoo Kim, Korea Hyoungseop Kim, Japan Huey-Ming Lee, Taiwan Zuoliang Lv, China Magdi Mahmoud, Saudi Arabia Anatolii Martynyuk, Ukraine Tshilidzi Marwala, South Africa Subhas Misra, India Takuo Nakashima, Japan Nikos Nikolaidis, Greece Sing Kiong Nguang, New Zealand Pavel Pakshin, Russia Jiqing Qiu, China Chin-Shiuh Shieh, Taiwan Mika Sato-Ilic, Japan Guifa Teng, China Gancho Vachkov, Japan Edwin Engin Yaz, USA Jianqiang Yi, China Zhong Zhang, Japan Lindu Zhao, China

Sponsored by QinHuangDao YanDa Intelligent Informatics Inc.

2010 ICIC International ISSN 1881-803X Printed in Japan

ICIC EXPRESS LETTERS

Volume 4, Number 5(B), October 2010

CONTENTS

Heuristics for Joint Decisions in Domain Implementation and Verification 1735 Zhiqiao Wu and Jiafu Tang

A First Approach to Artificial Cognitive Control System Implementation Based on the Shared Circuits Model of Sociocognitive Capacities 1741 Alfonso Sanchez Boza and Rodolfo Haber Guerra

Study of Shore-Based AIS Network Link Capacity 1747 Chang Liu and Xinyu Wang

Ontology and Rule Combined Reasoning Framework Design 1753 Guanyu Li, Yi Liu and Buwei Chen

Vulnerability Assessment of Distribution Networks Based on Multi-Agent System and Quantum Computing 1761 Xiangping Meng, Kaige Yan, Jingweijia Tan and Zhaoyu Pian

A New Multiple Kernel Learning Based Least Square Support Vector Regression and Its Application in On-Line Gas Holder Level Prediction of Steel Industry 1767 Xiaoping Zhang, Jun Zhao and Wei Wang

The Parameterization of all Stabilizing Simple Repetitive Controllers with the Specified Input-Output Characteristic 1773 Iwanori Murakami, Tatsuya Sakanushi, Kou Yamada, Yoshinori Ando Takaaki Hagiwara and Shun Matsuura

Image Noise Removal Based on Image Detail Preserving 1779 Yunfeng Zhang, Caiming Zhang and Hui Liu

A Novel Epidemic Model with Transmission Medium on Complex Networks 1785 Chengyi Xia, Junhai Ma and Zengqiang Chen

Output Feedback Switching Controller Design for State-Delayed Linear Systems with Input Quantization and Disturbances 1791 Zhaobing Liu, Huaguang Zhang, Qiuye Sun and Dongsheng Yang

Fuzzy Variable of Econometrics Based on Fuzzy Membership Function 1799 Xiaoyue Zhou, Kaiqi Zou and Yanfang Wang

Applying Image Processing Technique to Radar Target Tracking Problems 1805 Kuen-Cheng Wang, Yi-Nung Chung, Chao-Hsing Hsu and Tsair-Rong Chen

Fault Detection and Diagnosis for Process Control Rig Using Artificial Intelligent 1811 Rubiyah Yusof, Ribhan Zafira Abdul Rahman and Marzuki Khalid

Syntactic Feature Based Word Sense Disambiguation of English Modal Verbs by Naive Bayesian Model 1817 Jianping Yu, Jilin Fu and Jianli Duan

A Robust Adaptive Beamforming Optimization Control Method via Second-Order Cone Programming for Bistatic MIMO Radar Systems 1823 Fulai Liu, Changyin Sun, Jinkuan Wang and Ruiyan Du

(Continued)

2010 ICIC International ISSN 1881-803X Printed in Japan

ICIC EXPRESS LETTERS

Volume 4, Number 5(B), October 2010

CONTENTS (Continued)

Study of Parameters Selection in Finite Element Model Updating Based on Parameter Correction 1831 Linren Zhou and Jinping Ou

Dynamic Modeling of 3D Facial Expression 1839 Jing Chi

Chaos in Small-World Cellular Neural Network 1845 Qiaolun Gu and Tiegang Gao

Evaluating the Quality of Education via Linguistic Aggregation Operator 1851 Ying Qiao, Xin Liu and Li Zou

Collaborative Filtering Algorithm Based on Feedback Control 1857 Baoming Zhao and Guishi Deng

MVC Algorithm Using Depth Map through an Efficient Side Information Generation 1863 Ji-Hwan Yoo, Young-Ho Seo, Dong-Wook Kim, Manbae Kim and Ji-Sang Yoo

Design of Node with SOPC in the Wireless Sensor Network 1869 Jigang Tong, Zhenxin Zhang, Qinglin Sun and Zengqiang Chen

Research on the Sensorless Control of SPMSM Based on a Reduced-Order Variable Structure MRAS Observer 1875 Lipeng Wang, Huaguang Zhang, Zhaobing Liu, Limin Hou and Xiuchong Liu

Production Planning Based on Evolutionary Mixed-Integer Nonlinear Programming 1881 Yung-Chien Lin, Yung-Chin Lin and Kuo-Lan Su

Hiding Secret Information in Modified Locally Adaptive Data Compression Code 1887 Chin-Chen Chang, Kuo-Nan Chen and Zhi-Hui Wang

Genetic Programming Based Perceptual Shaping of a Digital Watermark in the Wavelet Domain 1893 Asma Ahmad and Anwar M. Mirza

A Competitive Particle Swarm Optimization for Finding Plural Acceptable Solutions 1899 Yu Taguchi, Hidehiro Nakano, Akihide Utani, Arata Miyauchi and Hisao Yamamoto

Design and Implementation of a Novel Monitoring System for Container Logistics Based on Wireless Sensor Networks and GPRS 1905 Kezhi Wang, Shan Liang, Xiaodong Xian and Qinyu Xiong

Spatially Adaptive BayesShrink Thresholding with Elliptic Directional Windows in the Nonsubsampled Contourlet Domain for Image Denoising 1913 Xiaohong Shen, Yulin Zhang and Caiming Zhang

Application of Type-2 Fuzzy Logic System in Indoor Temperature Control 1919 Tao Wang, Long Li and Shaocheng Tong

Traffic Flow Forecasting and Signal Timing Research Based on Ant Colony Algorithm 1925 Wenge Ma, Yan Yan and Dayong Geng

Statistical Layout of Improved Image Descriptor for Pedestrian Detection 1931 Ming Bai, Yan Zhuang and Wei Wang

(Continued)

2010 ICIC International ISSN 1881-803X Printed in Japan

ICIC EXPRESS LETTERS

Volume 4, Number 5(B), October 2010

CONTENTS (Continued)

Adaptive Control for Missile Systems with Parameter Uncertainty 1937 Zhiwei Lin, Zheng Zhu, Yuanqing Xia and Shuo Wang

Application of Plant Growth Simulation Algorithm on SMT Problem 1945 Tong Li, Weiling Su and Jiangong Liu

A Controller Design for T-S Fuzzy Model with Reconstruction Error 1951 Hugang Han and Yanchuan Liu

An Analysis for Parameter Configuration to Find a Trigger of Change 1959 Rika Ito and Kenichi Kikuchi

Complexity Reduction Algorithm for Enhancement Layer of H.264/SVC 1965 Kentaro Takei, Takafumi Katayama, Tian Song and Takashi Shimamoto

Modeling of Enterprises Risk Management and Its Robust Solution Method 1973 Min Huang, Yanli Huo, Chunhui Xu and Xingwei Wang

Fundamental Study of Clustering Images Generated from Customer Trajectory by Using Self-Organizing Maps 1979 Asako Ohno, Tsutomu Inamoto and Hajime Murao

Interface Circuit for Single Active Element Resistive Sensors 1985 Amphawan Julsereewong, Prasit Julsereewong, Tipparat Rungkhum Hirofumi Sasaki and Hiroshi Isoguchi

Analytic Solution of Shock Waves Equation with Higher Order Approximation 1991 Valentin A. Soloiu, Marvin H.-M. Cheng and Cheng-Yi Chen

Fuzzy Opinion Survey Based on Interval Value 1997 Lily Lin, Huey-Ming Lee and Jin-Shieh Su

Certificate of Authorization with Watermark Processing in Computer System 2003 Nai-Wen Kuo, Huey-Ming Lee and Tsang-Yean Lee

Weighted Similarity Retrieval of Video Database 2009 Ping Yu

Job Scheduling of Retrieving Dynamic Pages from Online Auction Websites on Grid Architecture 2015 Chong-Yen Lee, Hau-Dong Tsui and Ya-Chu Tai

An Improvement on Li and Hwang's Biometrics-Based Remote User Authentication Scheme 2021 Wen-Gong Shieh and Mei-Tzu Wang

Multiple Robot System Applying in Chinese Chess Game 2027 Song-Hiang Chia, Kuo-Lan Su, Sheng-Ven Shiau and Chia-Ju Wu

Towards a Dynamic and Vigorous SOA ESB for C4I Architecture Framework 2033 Abdullah S Alghamdi, Iftikhar Ahmad and Muhammad Nasir

Joint Multiple Parameters Estimation for Vector-Sensor Array Using Biquaternions 2039 Fei Wang, Hailin Li and Jianjiang Zhou

2010 ICIC International ISSN 1881-803X Printed in Japan

ICIC EXPRESS LETTERS

Aims and Scope of ICIC Express Letters

The Innovative Computing, Information and Control Express Letters (abbreviated as ICIC Express Letters, or ICIC-EL) is a peer-reviewed English language journal of research and surveys on Innovative Computing, Information and Control, and is published by ICIC International bimonthly. The primary aim of the ICIC-EL is to publish quality short papers (no more than 6 printing pages, basically) of new developments and trends, novel techniques and approaches, innovative methodologies and technologies on the theory and applications of intelligent systems, information and control.

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2010 ICIC International ISSN 1881-803X Printed in Japan ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1735–1740

HEURISTICS FOR JOINT DECISIONS IN DOMAIN IMPLEMENTATION AND VERIFICATION

Zhiqiao Wu and Jiafu Tang Department of Systems Engineering Key Lab of Integrated Automation of Process Industry of MOE Northeastern University Shenyang 110004, P. R. China [email protected]; [email protected] Received February 2010; accepted April 2010

Abstract. One of the critical objectives of software product line (SPL) development is minimizing the development cost of software systems. Thus, costs of domain implementation and veriﬁcation, which may involve substantial expenses in SPL development, should be reduced. In addition, both should not be considered individually but in an integrated manner to further reduce development cost. In this paper, an integrated decision model for SPL development is proposed to assist decision-makers in selecting reuse scenarios for domain implementation and in simultaneously determining the optimal number of test cases for domain veriﬁcation. An objective of the model is to minimize SPL development cost while satisfying the required system and reliability requirements. The Lagrange relaxation decomposition (LRD) method with heuristics was developed to solve integrated decision problems. Based on LRD, the non-linear model boils down to a 0-1 knapsack problem for the sub-problem of reuse scenario selection and an integer knapsack problem of the number of tests assignment sub-problem. Keywords: Software product line, Integrated decisions, Lagrange relaxation

1. Introduction. In the past, reuse-based software development has been implementation-centric. On account of increasing scale and complexity as well as decreasing development cost and time of software products for maintaining market competitiveness, it is difficult to develop reliable software products using conventional techniques [1]. There- fore, a tradeoff between cost and quality of reuse-based software products has become a major concern in software product development. To address this issue, various software engineering techniques, such as reuse economics and analysis/design methods, have been developed. Software product line (SPL) engineering ranks among the most advanced software practices based on these results [2]. One of the important and specific activities of SPL is domain engineering. Here, products in a product line are assembled from the organization’s core assets. Each core asset has an attached process for analysis and comparison of reuse scenarios or approaches that include without reuse, with white-box reuse, and with black-box reuse. A design of domain implementation involves the inclusion of descriptions of how the attached processes cooperate to yield products, and how the organization builds products for SPL. The next step after implementation is verification, which validates and verifies reusability for each core asset’s specifications. After successful testing of core assets in different use cases and scenarios, the domain engineering phase is complete and core assets are ready for reuse. One of the major benefits of software product line development (SPL) is its ability to curb software-intensive systems development cost. To achieve this goal, previous studies have examined cost optimization of domain engineering in the implementation [3] and verification processes [4,5]. However, verification at all times accounts for between 30 to 50% of a project’s effort [6]. Separate consideration of implementation and verification

1735 1736 Z. WU AND J. TANG cannot yield optimum development. Hence, more effort has been placed on increasing efficiency of implementation cost estimation [7], as well as testability technology for improving the efficiency of verification cost estimation [8,9]. Particularly, in recent studies with the advanced methodology of test cost estimate, models for cost optimization have tended to focus on coordinating joint decisions on the whole life cycle extending the system implementation decision to the quality verification management [10]. Afterwards, domain engineering decisions should be made in an integrated way so as to lead substantial savings in the main expenditures of SPL development. However, due to the complex and nonlinear relationship between the implementation and verification processes, research on models or algorithms optimizing development cost while simultaneously considering implementation and verification have received little attention. This paper attempts to tackle these still unsolved problems where domain implementation and verification built by multiple reuse scenarios and multiple optional numbers of testing considered jointly in order to achieve cost savings. In this paper, an integrated decision model (IDM) is provided by introducing 0-1 variables that represented alternative industrial reuse scenarios. Integer variables are employed to represent the number of tests on alternative scenarios regarding cost objective and reliability constraint simultaneously. IDM not only selects the most cost-effective reuse scenarios but also indicates the proper optimal testing to detect faults of each scenario, with consideration of the entire SPL reliability and system requirements. An examination of non-linear model indicates that integrated decision procedures are a two-layer decision. Hence, a Lagrange relaxation decomposition method – based on a relaxation technique and decomposition method – is developed and proposed in this work to solve the problem effectively. Following the introduction, Section 2 shows the objective function formulation and constraints presentation. Then, in Section 3 gives integrated decision process. A Lagrange relaxation decomposition method to solve the problem is provided in Section 4. And finally, concluding remarks are given in Section 5.

2. Cost Analysis and Objective Function. To formulate the problem, the following notations are used throughout the paper: n Number of modules within a target SPL system; mj Number of reuse scenarios available for module j; xij Decision variable, which is equal to 1 when module j is implemented using scenario i, and 0 if otherwise; zij An integer decision variable model that represents total number of tests performed on module j when implemented using scenario i. Implementation cost formulation: Wu and Tang [7] summarized the alternative reuse scenario in a product line. They also discussed that the implementation cost analysis method which enabled product line developers to automatically evaluate and compare all possible alternative reuse scenarios implementation cost Cij. The objective function of implementation cost can be formulation as Cij × Xij. Verification cost formulation: The cost of testing is largely a function of the number of tests performed z on each component’s reuse scenario; assuming a linear function this would be τ × z where τ is the cost per test [11]. Objective function F is formulated to represent the combined cost of implementation and verification to be minimized. ∑n ∑mj ∑n ∑mj F (xij, zij) = Implementation cost + Verification cost = cijxij + τijzij (1) j=1 i=1 j=1 i=1 Objective functions to be considered in the reuse scenario selection problem are designed to minimize cost of implementation; they are likewise geared towards minimizing the number of test assignment problems to minimize cost of verification phase. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1737 Formulation of reliability constraints. Based on the Testability and Bayes’ theorem, Wu and Tang [7] presents a testability function, ρ(z) (equal to (1 − η) − η(1 − η)2 ln(1 − η)z), which is the probability that an instance is failure-free during a single run given that z test cases have been performed. The following constraint can be obtained for each module: ρij(zij) ≥ (1 − εj)xij ∀i, j (2)

Parameter εj is accepted level of failure rate for module j in the SPL system and ηij is testability of reuse scenarios i for module j. However, estimated reliability may not improve in proportion to the number of successful tests. Growing reliability will end once the test has covered all necessary operations, i.e. obtained test cover test Γij. The following formulation can be obtained: ∑n ∑mj ∑n ∑mj ∗ zij ≤ Γijxij (3 ) j i j i Following Oded’s work [12], the eﬀect of module failures can be expressed as an exponential function with Sojourn time (sj) of each module. Constraining the reliability of a SPL is to constrain the probability of at least one failure occurrence in a system during the execution of a run. It can be expressed as follows: ∑n ∑mj ∑n ∑mj ∑n ∑mj sij(1 − ρij(zij))xij ≤ εJ or sijρij(zij)xij ≥ sijxij − εJ (4) j=1 i=1 j=1 i=1 j=1 i=1

Parameter εJ is accepted level of failure rate for the whole SPL system. Formulation of goal satisfaction constraints. In view of the user satisfaction evaluation [13] and goal-oriented requirement engineering approach [14], the performance of module j with scenario i; it can be evaluated in terms of a weighted satisfaction of∑ each goals Satij(k) based on operational distribution χijk formulated as Satij = χijk × Satij(k). k Thus, regardless of which scenario in a module is reused, the targeted software system should fulﬁll an accepted overall satisfaction level of at least R. It is given as follows: ∑n ∑mj ωjSatijxij ≥R (5) j=1 i=1

Parameter ωj is the weight of module j which expresses access reuse frequencies.

Figure 1. Hierarchical scheme of software system 1738 Z. WU AND J. TANG 3. Integrated Decisions Model for Domain Implementation and Verification. Without loss of generality, it is assumed that an SPL will be developed containing n modules. Each can be built using an optional alternative reuse scenario. Each module must satisfy one or several functional requirements with required levels. The goal-oriented requirement engineering approach [14] matches the goals of a system and the features of reuse scenarios through modules. Afterwards, selected components for each module are tested several times to verify their reliability (Figure 1). With this hierarchical scheme, the decision problem involves the manner of selecting reuse scenario for building each module. It involves assigning the number of times tests must be done to verify each module of a targeted system based on minimum implementation and verification cost under the constraints of functional goal satisfaction and reliability requirements. Based on the above, it can be concluded that an integrated decision model (IDM) for minimizing both implementation and verification costs is as follows:

∑n ∑mj ∑n ∑mj min F (xij, zij) = cijxij + τijzij j=1 i=1 j=1 i=1 (6) s.t. (2), (3∗), (4) and (5)

∑mj xij = 1 ∀j (7) i However, the TCP or WTCP are NP-hard in general. Therefore, majority of developed algorithms will merely provide the low bound of the least testing when SPL has a significant number of operations K. It is thus necessary to introduce a relaxation technique involving the conversion of hard constraint (3∗) into an objective to add a penalty to the latter if unsatisﬁed. On the other hand, the IDM is characterized by nonlinear programming. It can be solved using traditional nonlinear programming techniques. However, only the local optimal solution may be found. Therefore, a more eﬀective decomposition method is required to solve the IDM model.

4. Lagrange Relaxation Decomposition (LRD) Method. The IDM may be viewed as a two-layer decision. The first layer involves the decision on reuse scenario selection at the implementation stage, and the second involves the decision on the number of test assignment at the verification stage. By combining Lagrange multipliers into a two-layer decomposition, an LRD method with heuristics is developed to solve the mixed integrated decision problem. Formulation (3∗) is a hard fixed constraint, as discussed in the previous section. It provides a bridge between decisions in implementation and verification. By ∗ introducing Lagrange multipliers δij to Constraint (3 ), IDM can be decomposed into two integrated decision sub-problems corresponding to the two layers. The first pertains to reuse scenario selection sub-problem (RSS), and the second refers to the number of tests assignment sub-problem (NTA). These are presented below. For the sub-problem RSS:

∑n ∑mj ∑n ∑mj cos t min F1(xij) = cijxij + δijΓij xij j=1 i=1 j i (8) s.t. (5) and (7) For the sub-problem NTA: ∑n ∑n min F2(zij) = τjzj − δjzj j=1 j=1 (9) s.t. (2), (3∗) and (4) ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1739 The last term in the objective function (8) of sub-problem RSS represents verification- related costs, while Lagrange multiplier δij is interpreted as the verification cost for delivering unit cost required to perform a test case on module j with reuse scenarios i. For example, it can be determined in terms of a coefficient of verification cost as δij = τijλ. Coefficient λ of Lagrange multiplier δij satisfies 0 ≤ λ ≤ 1. It can be interpreted as the degree of the role of verification costs during implementation when formulating integrated decisions. For example, if the decision of the domain engineer depends entirely on implementation costs, then λ = 0. For a specified instance of the IDM, optimal λ∗ reflects the actual impact of verification planning on decisions of implementation assignment. A key point in LRD is the manner of traversal of all values of λ to obtain the global optimal solution. Conventionally, an initial value is set (e.g., λ = 0), which increases by a fixed step length (e.g., ∆λ = 0) until the stop value is obtained (e.g., λ = 1). However, it can be observed that both RSS and NTA are similar to the integer knapsack problem. Dantzig [15] demonstrated that an optimal solution for the continuous 0-1 knapsack problem may be obtained by sorting items according to their non-increasing profit-to-weight ratios (called efficiencies), and adding them to the knapsack until capacity is reached. Thus, the results indicate that LRD is more effective than previous methods in determining global optimal solutions for integrated decision problems.

5. Conclusions and Further Work. One of the major problems of domain engineering involves the effective coordination of domain implementation and verification. More specifically, it is about the integration of selecting reuse scenarios at the implementation phase and determining the number of tests to be performed for each scenario at the verification phase. Research described in this paper considers the joint decisions in selecting reuse scenarios and determining optimal number of tests when developing an SPL towards minimizing cost, while satisfying system and reliability requirements to a certain degree. An LRD method with heuristics is proposed to solve the integrated decision problem. Based on the LRD, integrated decision problem is solved by decomposing it into two subproblems in two different layers. The contributions of this paper lie in two aspects. First, an integrated decision problem was formulated by combining decisions on domain implementation and verification. A stop-test rule mandating an extension of the testability definition was proposed for effectively developing integrated decision problem. Second, a framework and an overall procedure of LRD combined with LMDH approach were developed to solve the integrated decision problem.

Acknowledgment. This work was ﬁnancially supported by the National Natural Sci- ence Foundation of China (NSFC) (70721001, 70625001), the Fundamental Research Funds for the Central Universities (N090604004), the National 973 Basic Research Project (2009CB320601).

REFERENCES

[1] T. Kishi and N. Noda, Formal veriﬁcation and software product lines – Using formal veriﬁcation techniques to verify designs within a product line, Communications of the ACM, vol.49, no.12, pp.73-77, 2006. [2] P. Clements and L. Northrop, Software Product Lines: Practices and Patterns, Addison-Wesley, Boston, 2002. [3] Y. J. Li and H. Gao, A domain optimization problem with boundary penalty cost functional, Journal of Mathematical Analysis and Applications, vol.301, no.1, pp.170-186, 2005. [4] R. M. Hierons, Verdict functions in testing with a fault domain or test hypotheses, ACM Transactions on Software Engineering and Methodology, vol.18, no.4, pp.1-19, 2009. [5] Y. Liu, C. Wei and S. Gao, Research on software reliability modeling based on stochastic petri nets and module level software rejuvenation, ICIC Express Letters, vol.3, no.3(B), pp.607-613, 2009. [6] M. Ellims, J. Bridges and D. C. Ince, The economics of unit testing, Empirical Software Engineering, vol.11, no.1, pp.5-31, 2006. 1740 Z. WU AND J. TANG

[7] Z. Q. Wu, J. F. Tang and L. Y. Wang, An optimization framework for reuse scenarios selection in software product line, Proc. of the Chinese Control and Decision Conference, Guilin, China, pp.1880-1884, 2009. [8] J. M. Voas and K. W. Miller, Software testability – The new veriﬁcation, IEEE Computer Society, vol.12, no.3, pp.17-28, 1995. [9] V. Cortellessa, F. Marinelli and P. Potena, Automated selection of software components based on cost/reliability tradeoﬀ, Lecture Notes in Computer Science, pp.66-81, 2006. [10] A. Kleyner and P. Sandborn, Minimizing life cycle cost by managing product reliability via validation plan and warranty return cost, International Journal of Production Economics, vol.112, no.2, pp.796- 807, 2008. [11] D. B. Brown, S. Maghsoodloo and W. H. Deason, A cost model for determining the optimal number of software test cases, IEEE Transactions on Software Engineering, vol.15, no.2, pp.218-221, 1989. [12] O. Berman and M. Cutler, Optimal software implementation considering reliability and cost, Com- puters and Operations Research, vol.25, no.10, pp.857-868, 1997. [13] L. Lin and H.-M. Lee, A new algorithm of software quality evaluation for user satisfaction, Inter- national Journal of Innovative Computing, Information and Control, vol.4, no.10, pp.2639-2648, 2008. [14] A. V. Lamsweerde and E. Letier, Handling obstacles in goal-oriented requirements engineering, IEEE Transactions on Software Engineering, vol.26, no.10, pp.978-1005, 2000. [15] G. B. Dantzig, Discrete-variable extremum problems, Operations Research, vol.5, no.2, pp.226-288, 1957. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1741-1746

A FIRST APPROACH TO ARTIFICIAL COGNITIVE CONTROL SYSTEM IMPLEMENTATION BASED ON THE SHARED CIRCUITS MODEL OF SOCIOCOGNITIVE CAPACITIES

Alfonso Sanchez´ Boza1 and Rodolfo Haber Guerra1,2

1Centro de Automáticay Robótica Consejo Superior de Investigaciones Cient´ıficas- Universidad Politécnicade Madrid CP 28500, Arganda del Rey, Madrid, Spain [email protected] 2Escuela PolitécnicaSuperior Universidad Autónomade Madrid CP 28049, Madrid, Spain [email protected] Received February 2010; accepted April 2010

Abstract. A first approach for designing and implementing an artificial cognitive control system based on the shared circuits models is presented in this work. The shared circuits model approach of sociocognitive capacities recently proposed by Hurley [1] is enriched and improved in this work. A five-layer computational architecture for designing artificial cognitive control systems is proposed on the basis of a modified shared circuits model for emulating sociocognitive experiences such as imitation, deliberation, and mindreading. An artificial cognitive control system is applied for controlling force in a manufacturing process that demonstrates the suitability of the suggested approach. Keywords: Artificial cognitive control, Embodied cognition, Imitation, Internal model control, Mirroring, Shared circuits model

1. Introduction. There are many definitions of intelligence, one of them is the ability of human beings to perform new, highly complex, unknown or arbitrary cognitive tasks efficiently and then explain those tasks with brief instructions. It has spurred many researchers in areas of knowledge such as control theory, computer science, and artificial intelligence (AI) to explore new paradigms to achieve a qualitative change and then to move from intelligent control systems to artificial cognitive control strategies [2]. A natural cognitive system displays effective behaviour through perception, action, deliberation, communication, and both individual interaction and interaction with the environment. During cognitive or executive control, the human brain and some animal brains process a wide variety of stimuli in parallel and choose an appropriate action (task context), even in the presence of a conflict of objectives and goals [3, 4, 5]. There is a wide variety of strategies and initiatives related with the partial or full emulation of cognitive capacities in computational architectures. Each one is based on a different conception of the nature of cognitive capacity, what makes a cognitive system, and how to analyze and synthesize such a system [6, 7]. The novelty of this work is that it is based on an neuroscientific and psychological approach, the shared circuits model (SCM) [1]. SCM approach serves as the foundation for designing an artificial cognitive control system where imitation, deliberation, and mindreading processes are emulated through computational efficient algorithms in a computational architecture. Hurleys approach suggests that these capacities can be achieved just by having control mechanisms, other- action mirroring and simulation. An artificial cognitive control system should incorporate these capacities and therefore it would be capable of responding efficiently and robustly

1741 1742 A. SANCHEZ´ BOZA AND R. HABER GUERRA to nonlinearities, disturbances and uncertainties. The modifications introduced to the SCM approach make that this preliminary version can be applied to design a control architecture for a case study: a high-performance drilling process. In order to improve efficiency of a high-performance drilling process, the current study focuses on the design and implementation of a control system for drilling force. This article is organized into four sections. The modified shared circuits model (MSCM) incorporated to an architecture in which is implemented an artificial cognitive control system is explained in Section 2. Section 3 shows the experimental results of applying an implementation of the MSCM to a case study represented by a high-performance drilling process. Finally, the conclusions are presented in Section 4.

2. An Architecture for Artificial Cognitive Control. Modified Shared Circuits Model. SCM approach is supported on a layered structure to describe how certain human capacities (i.e., imitation, deliberation, and mindreading) can be deployed thanks to subpersonal mechanisms of control, mirroring, and simulation (Figure 1). Basically, SCM is based on the observation of the human brain. It may be envisaged as making use of not only inverse models that estimate the necessary motor plan for accomplishing an objective in a given context, but also a forward model that enables the brain to anticipate the perceivable effects of its motor plan, with the object of improving response efficiency.

Figure 1. Depiction of SCM. Layer 5 monitors simulation of input acts or evoking objects. Using SCM layers 2 and 3, SCM can perform simulation at both ends and, with layer 5, enables strategic deliberation.

A computational architecture for an artificial cognitive control system is proposed for high-performance manufacturing processes, underpinned by the modified shared circuits model (MSCM, Figure 2). Therefore, it is necessary to enrich SCM approach from a computational science viewpoint. To develop a complex cognitive agent, it is necessary to make a global structure that would be a collection of information processing elements, linked by information forwarding elements layered a top physical/information interfaces [8]. Modifications to SCM are introduced to enrich and improve its capacities, taking into account the suggestions reported in the state-of-the-art and the main constraints of the SCM approach. Since a layer-based model is incorporated in a computational architecture, five modules are constructed made up of one or more processes performed by the above- described layers. At MSCM, module 1 is represented by a controller and an optimization/adjustment process for this controller to adapt it to new environmental conditions. Module 3 supports a set of inverse models that obtain an imitative output action and module 2 generates future output prediction to deliberate about module 1 actions or this module 3 imitative actions. Module 4 is in charge of inhibiting either module to distinguish between information from the agent himself and information from others, and MSCM module 5 gathers associations between dictated action and the possible, or counterfactual, inputs (i.e. the reaction of others). In this way, a functional parallelism between layers in SCM ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1743 and modules are established. The rest of modules 0 and a are introduced to take part in the decision of when modules act observing the control process success. Module 1 and 2 manage set of inverse and forward models respectively, and they optimize them in function of environmental changes. Several solutions could be used, like [9] or [10] if the model’s parameters are extensive. This is a modular approach that manages models, so each module can be developed separately. From the best of authors knowledge, the main novelties of this work are twofold. Firstly, the SCM is enriched and improved on the basis of the state of the art. For example, SCM does not cover the description of an executive level to manage functioning of layers, so modules in charge of this task are also introduced. Secondly, the implementation of an artificial cognitive control system has been developed using the enriched SCM, and the application to a high-performance manufacturing process corroborates on the basis of experimental results the suitability of the suggested approach.

Figure 2. Simpliﬁed block diagram of the MSCM proposed system.

In MSCM as in SCM, the relationships and interactions among modules make possible to artiﬁcially emulate the cognitive capacities of deliberation, imitation, and mindreading. So, in order to develop a computational framework aiming at control system design, it is necessary to address module interactions. Layers interactions is one of the main weaknesses of the SCM approach. This temporal pattern is essential to clarify how and when the system acts, and therefore it is necessary to set a method or strategy to establish a sequence of actions for each module. MSCM explores possible operating sequences of the diﬀerent modules (Figure 3) attending the results already reported in the literature [1, p.8,14,15][11, 12, 13].

1. Deliberate the possible actions to carry out, by means of interaction of modules 1, 2, and 5. 2. If any of the actions leads to success, execute it. (a) If there is noise in excess, module 2 learns the new eﬀects that have been produced. 3. If not, (a) If noise surpasses a threshold, go to (3.iii.A). (b) If not, (i) Deliberate about the possible actions of others (imitative actions), through the interaction of modules 2, 3, and 5. (ii) If any of the imitative actions leads to success, execute it. (A) Learn this action by incorporating the corresponding instrumental association into module 1’s private set of forward models. (iii) If not, (A) Through an optimization process, acquire a new action using the process model handled by module 2, whose results are handled by said optimization process in module 1. (B) Execute a new action by means of the operation of this module.

Figure 3. Algorithm of the systems action, imitation, and learning cycle. 1744 A. SANCHEZ´ BOZA AND R. HABER GUERRA 3. MSCM as the Basement to Control a Complex Process. An Application to the Case Study of High-Performance Drilling Process. In order to demonstrate the viability of an artificial cognitive control system based on MSCM foundations, the authors have selected the drilling process. Drilling is one of the most intensely used processes in the manufacturing of aircraft parts, automobile parts, and molds and dies in general. And the modified SCM (MSCM) proposed in this work offers the necessary theoretical framework to design an artificial cognitive control system. Here a neurofuzzy system like ANFIS [15] is exploited to combine the semantic transparency and intrinsic robustness of fuzzy systems [16] with the learning ability of artificial neural networks. The most adequate paradigms can be selected from among the extensive choice provided by Control Theory, Artificial Intelligence and its techniques, Computer Science, System Theory and Information Theory. The study and selection of the most viable method from among the many offered by the myriad topics mentioned above is not straightforward. One way is to exploit the advantages of neurofuzzy systems, as mentioned before. Their capacities for incorporating experience, for learning, and for adaptation and self-adjustment [17] are aligned with the capacities available in the MSCM for emulating sociocognitive experiences such as imitation, deliberation, and mindreading. The role of the internal models in the MSCM approach opens the possibility of using the design method provided by Internal Model Control paradigm [18], that theoretically guarantees control system robustness and stability in the presence of external disturbances. The role of modules 2 and 3 and their interaction can be effectively represented by neurofuzzy systems (e.g., ANFIS) and the IMC scheme. The IMC paradigm and the ANFIS neurofuzzy system are used in this work to provide functioning capabilities to the modules 2 and 3. The main rationale of using both methods was previously explained. ANFIS is used to generate direct models (the model used in module 2) and inverse models (the model used in module 3) which shape the knowledge on which the system is initially based.

Figure 4. A preliminary MSCM control architecture implemented in a real-world process.

A networked control is performed through a distributed implementation enriching the solution designed and implemented by Gajate et al. [19]. In our case two machines are used: one receives the user’s goals and the values measured by the sensors and it does executive functions, while the other emulates cognitive processes (Figure 4). And ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1745 MSCM uses several modules to perform an artiﬁcial cognitive control instead of one unique controller, as the Gajate’s solution. Communication between machines is achieved through the intermediary communications system Ice. So that communications are transparent to the network features and the machines that perform these processes (Figure 5).

interface Cognetcon { bool handshake(); idempotent bool sendNumVars(short numVars);

idempotent double sendValuesRecvAction(FloatList values); }; interface Mod1Server { idempotent void init(string controllerParamFile, double a,double b,double c) throws Error;

idempotent double control (double error, double reference, int responseIndex); }; interface Mod2Server { idempotent double response(double controlOutput, int responseIndex); };

Figure 5. Passage from the deﬁnition of the operations that support the executive and cognitive servers.

The main goal is to obtain a good transient response without overshoot using the cutting parameters given by the tool manufacturer for this tool and workpiece material combination. Experimental trials are conducted using a machining center equipped with an open computer numerical controller (Figure 6).

Figure 6. Resultant force y of the control exercised by the action of the modules 2 and 3 of MSCM.

4. Conclusion. This paper presents a first approach to design an artificial cognitive control system from the conceptual framework that is given by the shared circuit models approach to emulate sociocognitive capacities. The shared circuit model (SCM) approach is enriched and improved using the state-of-the-art on this field. Moreover, relevant reports 1746 A. SANCHEZ´ BOZA AND R. HABER GUERRA on this issue as well as the contributions of the authors are also outlined. The modified SCM (MSCM) is postulated from the viewpoint of System Theory and Computer Science. Therefore, a sequence of operating MSCM is proposed in this paper. The suggested procedure enables the activity of combined modules or a module alone. In general, MSCM goes beyond the SCM approach with the aim of a deriving a computational solution to a complex control problem. From a theoretical point of view, MSCM provides an alternative conceptual framework to perform control tasks in an efficient, robust fashion that characterizes human cognitive processes. Acknowledgment. This work was supported by DPI2008-01978 Networked cognitive control system for high-performance machining processes (COGNETCON) of the Spanish Ministry of Science and Innovation.

REFERENCES [1] S. Hurley, The shared circuits model (SCM): How control, mirroring, and simulation can enable imitation, deliberation, and mindreading, Behavioural and Brain Science, vol.31, no.1, pp.1-22+52- 58, 2008. [2] J. Albus, Toward a computational theory of mind, Journal of Mind Theory, vol.0, no.1, pp.1-38, 2008. [3] R. Huerta and T. Nowotny, Fast and robust learning by reinforcement signals: Explorations in the insect brain, Neural Computation, vol.21, no.8, pp.2123-2151, 2009. [4] M. Ito, Control of mental activities by internal models in the cerebellum, Nature Reviews Neuro- science, vol.9, no.4, pp.304-313, 2008. [5] M. I. Rabinovich, P. Varona, A. I. Selverston and H. D. I. Abarbanel, Dynamical principles in neuroscience, Reviews of Modern Physics, vol.78, no.4, 2006. [6] Z. Pylyshyn, Computation and Cognition: Toward a Foundation for Cognitive Science, MIT Press, 1984. [7] L. B. Thelen and E. Smith, A Dynamic System Approach to the Development of Cognition and Action, MIT Press, Cambridge, 1994. [8] R. Sanz, C. Hernández,A. Hernando, J. Gómezand J. Bermejo, Grounding robot autonomy in emotion and self-awareness, Lecture Notes in Computer Science, vol.5744, pp.23-43, 2009. [9] D. Martin, R. M. del Toro, R. E. Haber and J. Dorronsoro, Optimal tuning of a networked linear controller using a multi-objective genetic algorithm and its application to one complex electrome- chanical process, International Journal of Innovative Computing, Information and Control, vol.5, no.10(B), pp.3405-3414, 2009. [10] J. Li, X. Hu, Z. Pang and K. Qian, A parallel ant colony optimization algorithm based on fine- grained model with GPU-acceleration, International Journal of Innovative Computing, Information and Control, vol.5, no.11(A), pp.3707-3716, 2009. [11] M. Nielsen, The social motivation for social learning, Behavioral and Brain Sciences, vol.31, no.1, pp.33, 2008. [12] T. Makino, Failure, instead of inhibition, should be monitored for the distinction of self/other and actual/possible actions, Behavioral and Brain Sciences, vol.31, no.1, pp.32-33, 2008. [13] A. Meltzoff, Imitation and other minds: The “like me” hypothesis, in Perspectives on Imitation: From Neuroscience to Social Science – Two Volume Set, S. Hurley and N. Chater (eds.), The MIT Press, 2005. [14] M. Tomasello, The Cultural Origins of Human Cognition, Harvard University Press, 1999. [15] J.-S. R. Jang, Anfis: Adaptive-network-based fuzzy inference system, IEEE Transactions on Systems, Man and Cybernetics, vol.23, no.3, pp.665-685, 1993. [16] R. E. Precup, S. Preitl, J. K. Tar, M. L. Tomescu, M. Takacs, P. Korondi and P. Baranyi, Fuzzy control system performance enhancement by iterative learning control, IEEE Transactions on Industrial Electronics, vol.55, no.9, pp.3461-3475, 2008. [17] T. Fukuda and N. Kubota, An intelligent robotic system based on a fuzzy approach, Proc. of the IEEE, vol.87, no.9, pp.1448-1470, 1999. [18] M. Morari and E. Zafiriou, Robust Process Control, Prentice Hall, 1989. [19] A. Gajate, R. E. Haber and R. M. del Toro, Neurofuzzy drilling force-based control in an ethernet- based application, International Journal of Innovative Computing, Information and Control, vol.6, no.4, pp.373-386, 2010. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1747-1752

STUDY OF SHORE-BASED AIS NETWORK LINK CAPACITY

Chang Liu1 and Xinyu Wang2 1School of Information and Science Technology Dalian Maritime University No. 1 LingShui Road, High-Tech Zone, Dalian, P. R. China [email protected] 2Industry Technology Supervision and Research Center for Building Materials Beijing, P. R. China [email protected] Received February 2010; accepted April 2010

Abstract. This paper put forward a method of the capacity estimation of the shore- based AIS (Automatic Identification System) network, which is available to ensure the vessel data link more stable and reliable. Based on the analysis of the technical characteristics and transmission parameters of the shore-based AIS, we discussed the problem of communication conflict caused by the slot reuse which affects the capacity of shore-based AIS network. By experiment we proposed the demarcation method of shore-based AIS coverage and the design of the data link capacity which will help the vessel traffic service (VTS) management more efficient. Keywords: Automatic identification system (AIS), Vessel data link (VDL), Capacity, Net throughput, Slot reuse

1. Introduction. Automatic Identiﬁcation System (AIS) is a VHF digital mobile communication system based on self-organized TDMA (SOTDMA) technique. Some research about the capacity of ship borne AIS in a certain water area was carried out. But with the construction of the AIS network and shore-based facilities, the number of AIS land users is constantly increasing, which will have more information that transmitted through the AIS vessel data link (VDL) [1-3]. As the AIS services are security-related information transfer services, to ensure the VDL stable and reliable is essential for the vessel traﬃc management. How many users can the accommodate to shore-based network and whether can its capacity meet the growth requirements of the communication and also the surveillance and security information transmission in the future is an important issue. Based on the analysis and experiment of AIS data link characteristics, we discussed the capacity of the shore-based AIS network. 2. AIS Data Link Characteristics. As a mobile data communication system, the outstanding characteristic of AIS is that the mobile station can communicate with each other using self-organization protocol without the control of the base station [2]. Each AIS station has its own communication cell. The cell is a circle with the station as the center, and the radius D usually depends on the transmitting and receiving antenna height estimated by (1). (√ √ ) D = 3.6 h1 + h2 km (1)

Inside (1) h1 and h2 are the height of receiving and transmitting antennas. As a cellular mobile communication system, AIS uses SOTDMA protocol to communicate and realize the share of frequency and slots. The slot reuse will occur in these two conditions [4]. (1) Intentional slot reuse: a ship closer to the shore station may occupy the slot schedule of a distant ship when the link capacity is overload.

1747 1748 C. LIU AND X. WANG (2) Automatic slot reuse: two or more ships that are non-visible to each other, that is, they are not in the same communication cell, may send data packets using the same slot. Slot reuse may aﬀect the shore station correctly receiving the reports from the ship AIS, which will result in two conditions below [5]. (1) Confusion: AIS shore station can not correctly receive data packets from all AIS ships at the same slot. (2) Discrimination: AIS shore station can correctly receive data packets only from one of all ships in the same slot. Confusion and discrimination contribute to reduce the rate of AIS report from ship AIS to shore station. The report rate of ship AIS stations is usually evaluated by the two parameters as follows.

(1) Nominal report rate (Rr): the desired report rate received by AIS stations according to the standard [2]. The maximum rate is 30 per minute for the dynamic information. (2) Net report rate (Rn): the actual report rate received by AIS stations which may be less than the nominal report rate because of the slot reuse or interference. As we have known AIS is not a connection-oriented system but a broadcast system. And also the AIS information is real time, so the miss data will not be retransmitted. In order to obtain the processing capacity of AIS and the transmission quality of the data link we proposed two parameters as follows. (1) Required capacity (C): the maximum number of AIS ship stations that the shore-base station can accommodate within its communication cell. (2) Net throughput (Nt): the ratio of actual report rate and the nominal report rate from the same sender [3]. Net throughput of link is deﬁned as

Nt = Rn/Rr (2)

Because of slot reusing and interference, Nt will less than 1. These two parameters are very important for the design of AIS shore station. In the density traﬃc area the load of AIS data link is tend to be full, the receive data confusion and discrimination will occur which will result in the reduced net throughput. By experiment, the relationship curve of slot reuse and the required capacity is shown as in Figure 1. When the required capacity is 150%, the time slot reuse is nearly 80%, the net throughput of the AIS system may be less than 20%, and the system’s normal data transmission will be diﬃcult to be assured.

Figure 1. Curve between slot reuse and the required capacity ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1749 3. Calculation of Link Capacity and Net Throughput. From the analysis above, the capacity increases, the net throughput will decrease. In order to analyze the relationship about the capacity and the net throughput we suppose that the transmit power, the antenna gain and the receiver level of each AIS ship station are all equal. Suppose the distances of Ship 1 and Ship 2 away from the shore are respectively d1 and d2, shown in Figure 2. Generally, when

0.5 < d2/d1 < 2 or 0.5 < d1/d2 < 2 (3) Confusion occurs. The discrimination occurs when

d2/d1 > 2 or d1/d2 > 2 (4)

Figure 2. Relationship of d1 and d2

The shore station AIS can correctly receive data from Ship 1 or Ship 2, in other words, the shore station can correctly receive data from ship AIS which is closer.

Figure 3. Region partition of shore-base AIS station

Assume the communication cell radius of the shore station AIS is R, as in Figure 3, the distance from the shore station to the ship AIS is d. When R > d > R/2 and another ship in the region is not visible, automatic slot reuse may occur in the case of full link. Because the distance from ship to shore station does not meet (4), conﬂict ship data packet will be confusion. For the shore station, the AIS ships in the region selected time slot randomly, 1750 C. LIU AND X. WANG similar to the slot ALOHA system, so the region is deﬁned as the ALOHA region. In time slot ALOHA system, the maximum transmission success probability [6,7] is: 1 ρ = (5) e When the required capacity reaches 100%, in ALOHA region the net throughput is

Nt ≈ 37% (6) When R/2 > d > R/3 and another ship in the region is visible, ship communication maybe conflict with that in the ALOHA region. Suppose the distance from the ship T to the shore station is d = 0.4R, then the ship may be discriminated to the ship that the distance is bigger than 0.8R. But it does not affect the net reporting rate of ship T. But for the ships that the distance is less than 0.8R in ALOHA region, slot confusion maybe happen when communication conflict, resulting in the reduced net report rate of ship T. So the region R/2 > d > R/3 is called discrimination region. In the region R/3 > d, the ship will only conflict with ships of the distance d > 2R/3 (in the ALOHA region). At this point, if two ships conflict according to (4) the discrimination will happen, but does not affect the net reporting rate of ships at close range. So the net throughput in the region is 100%, and the region is called protected region. Table 1. Simulation result of net throughput and required capacity in different regions

Required capacity (C) d/R Net throughput (Nt) 10% 50% 100% 150% 200% 0 .00 1 .00 1 .00 1 .00 1 .00 1 .00 0 .05 1 .00 1 .00 1 .00 1 .00 1 .00 0 .10 1 .00 1 .00 1 .00 1 .00 1 .00 0 .15 1 .00 1 .00 1 .00 1 .00 1 .00 0 .20 1 .00 1 .00 1 .00 1 .00 1 .00 0 .25 1 .00 1 .00 1 .00 1 .00 1 .00 0 .30 1 .00 1 .00 1 .00 1 .00 1 .00 0 .35 0 .94 0 .75 0 .60 0 .50 0 .45 0 .40 0 .92 0 .68 0 .48 0 .36 0 .29 0 .45 0 .90 0 .63 0 .40 0 .26 0 .18 0 .50 0 .90 0 .61 0 .37 0 .22 0 .14 0 .55 0 .90 0 .61 0 .37 0 .22 0 .14 0 .60 0 .90 0 .61 0 .37 0 .22 0 .14 0 .65 0 .90 0 .61 0 .37 0 .22 0 .14 0 .70 0 .90 0 .61 0 .37 0 .22 0 .14 0 .75 0 .90 0 .61 0 .37 0 .22 0 .14 0 .80 0 .90 0 .61 0 .37 0 .22 0 .14 0 .85 0 .90 0 .61 0 .37 0 .22 0 .14 0 .90 0 .90 0 .61 0 .37 0 .22 0 .14 0 .95 0 .90 0 .61 0 .37 0 .22 0 .14 1 .00 0 .90 0 .61 0 .37 0 .22 0 .14

From the analysis above, when the required capacity is 100%, the net throughput of AIS shore stations for the ship in different regions is different. The region can be divided into three parts, respectively named as ALOHA region, discrimination region and protected region. Through the theoretical calculations and simulation analysis, we got the results of the relationship of the net throughput (Nt) and the required link capacity (C) in different ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1751 regions (d/R), as shown in Table 1. Within the coverage of the AIS shore station, the net throughput in ALOHA region is lowest, and reduced with the required capacity increased.

4. Design of AIS Shore-based Station Link Capacity. The purpose of designing link capacity of AIS shore station is to obtain the lowest net throughput and the maximum capacity in the monitoring coverage of AIS shore stations, according to the required reporting rate of ships. The key problem about the link capacity analysis of AIS shore station is to make statistics and forecast of the traffic distribution in its coverage and determine the dense traffic areas [8]. Table 2 shows the vessel traffic distribution of a certain water area, in which the shore station coverage is 72 km (about 40 nautical miles). From Table 2, within the coverage of the shore station, communication of AIS ship dynamic information is 3415 slots per minute.

Table 2. Distribution of traﬃc statistics in a certain water area

Ship Type Ship Capacity Report Period (s) Report Times /min Anchor, <3kn 270 180 90 Anchor, >3kn 30 10 180 0-14kn 100 10 600 0-14kn and change course 15 3 1 /3 270 14-23kn 110 6 1100 14-23kn and change course 23 2 690 > 23kn 10 2 300 > 23kn and change course 2 2 60 Others 50 24 125 Total 610 3415

Because there are 4500 slots in AIS link [2], the dynamic information listed in Table 2 occupies 76% of the entire link capacity of AIS shore station. Consider that there is some other information to occupy the time slots, AIS shore station for the dynamic information of the link capacity will be less than 4500 slots. If the AIS dynamic information occupies 80% of the available capacity, there will be 232 slots for some other information. In this case, the net throughput is 45% in the ALOHA region (36km to 72km). For the ship whose nominal report rate is 30/min, the net reporting rate is calculated as 13.5/min according to (2), less than the required report rate for VTS surveillance [1]. In order to achieve the required rate of shore-based monitoring, according to Table 1, the required capacity of AIS shore-based station should be less than 50% in order to ensure the eﬀective dynamic information of the vessels to be received.

5. Conclusions. In the SOTDMA communication mode, the coverage of shore-based AIS network can be divided into three regions according to the link characteristic, named as ALOHA, discrimination and protected region. In ALOHA region when the link capacity overloads, the net throughput will decrease evidently. By analyzing the relationship of the required capacity, the net throughput and the distance from the vessel to shore station, we design the capacity of shore-based AIS network. As a monitoring system, the capacity of the AIS stations is inﬁnite [9]. But for the shore-based AIS, the network capacity is limited in the case of the required net throughput. By theoretical analysis and computer simulation, this paper discussed a single link capacity and its related characteristics parameters. For the network constructed by a number of AIS shore stations, the capacity analysis remains to be further studied. 1752 C. LIU AND X. WANG Acknowledgment. This work is partially supported by the Application Basic Research Project of Ministry of Traﬃc, China, under Grant No. 2005329225060. We also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

REFERENCES [1] IALA, Recommendation on Automatic Identification System (AIS) Shore Station and Networking Aspects Relating to the AIS Service, 2002. [2] ITU-R M.1371, Technical Characteristics for a Universal Shipborne Automatic Identification System (AIS) Using Time Division Multiple Access in the VHF Maritime Mobile Band, 2001. [3] IEC 61193-2, Maritime Navigation and Radio-communication Equipment and Systems – Automatic Identification System (AIS), 2002. [4] Y. Hu, Data link capacitance and congestion resolution for AIS, Computer Measurement & Control, pp.1631-1634, 2007. [5] R. Kjellberg, Capacity and Throughput Using a Self-Organized Time Division Multiple Access VHF Data Link in Surveillance Applications, http://www.gpcsweden.com, 2008. [6] X. Xie, Computer Network, Dalian University of Technology Publishing House, 2001. [7] G. Sun and M. Liaog, Upper bound for transport capacity of sensor networks, ICIC Express Letters, vol.3, no.1, pp.93-98, 2009. [8] S. J. Chang, Development and analysis of AIS applications as an efficient tool for vessel traffic service, MTS/IEEE OCEANS 2004, vol.4, pp.2249-2253, 2004. [9] Z. Yang and H. Imazu, Algorithm for cooperative collision avoidance through communication with automatic identification system, IEEE Computation Intelligence for Modeling, Control and Automa- tion, pp.1084-1088, 2005. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1753-1759

ONTOLOGY AND RULE COMBINED REASONING FRAMEWORK DESIGN

Guanyu Li, Yi Liu and Buwei Chen Information Science and Technology College Dalian Maritime University Dalian 116026, P. R. China { rabitlee; sepc }@163.com; [email protected] Received February 2010; accepted April 2010

Abstract. It is known that ontology description language OWL DL has defects in regard to the expression and reasoning ability as its being restricted in description logic. Experience has proved that the combination of ontology and rule is an effective way to solve this problem. And by using SWRL, a novel framework of ontology and rule combined reasoning is proposed, which is named as SWRL Based Reasoning Mechanism Framework. In this framework, rule representation is introduced into OWL ontology, so the reasoning ability of OWL DL is significantly improved. Generally, SWRL based reasoning framework uses the descriptive logic based reasoning machine and Jess Tab to realize the transformation from OWL ontology to Jess fact base, and uses XSLT to realize the transformation from SWRL rule to Jess rule base, which results in the in- convenient operation. The proposed framework uses SWRL Bridge to combine Jess Rule Engine with Protégé-OWL, which can perform the two transformations mentioned above conveniently. The new OWL ontology obtained in such a manner includes the semantic relationships between the concepts which show the implicit knowledge in the former ontology, so the former ontology is substantially improved semantically. The experimental result shows that the availability factor of ontology knowledge in semantic web domain can be improved to a large extent by use of this framework. Keywords: Domain ontology, Semantic web, OWL, Reasoning, SWRL, Jess

1. Introduction. Being increasingly popular, the Internet greatly changes our lives [1]. The development of ontology has been one of the motivations of semantic web since it was envisioned [2]. However, some important knowledge is given implicitly in the ontology, which causes low availability factor of ontology knowledge. Firstly, the limitation of the ontology description language OWL DL is analyzed. Sec- ondly, the SWRL-based Reasoning Framework is proposed, which is considered as a kind of ontology and rule combined reasoning framework. Lastly, based on ontology and rule, the implicit information in the ontology can be deduced by using the reasoning machine Jess. 2. Related Work. The sublanguage OWL DL of Web Ontology Language OWL defined by the W3C has the limitation to Description Logic. Being compared with OWL DL, the rule has more powerful ability to describe the logic. For example, the concept Uncle can be defined by the first-order logic as: P arent(?x, ?y) ∧ Brother(?y, ?z) → Uncle(?x, ?z). But OWL DL can not define such relationship. Therefore, the rule description should play an important role in Semantic Web, so the Semantic Web Rule Language was proposed. The organization DARPA proposed the Semantic Web Rule Language-SWRL on No- vember 2003, which mainly consists of four parts – Imp, Atom, Variable and Built-in [3]. Imp contains SWRL rules. In Imp, head describes the result of reasoning, and body describes the basic form of the reasoning premise. In Imp, the basic ingredient of head and body is Atom. For example, all the clauses of Horn are used in its framework. Variable is

1753 1754 G. LI, Y. LIU AND B. CHEN to record the variable part in Atom. Built-in is the ingredient of the SWRL modulization which is utilized to record logic comparison relationship that the SWRL offers. Some specifications should be followed when editing SWRL rules. As an example, the specification of SWRL rules is as antecedent→consequent. antecedent and consequent are the extractions of the Atoms in the ontology, such as a1 ∧ ... ∧ an. Since SWRL rules consist of the head and body, it is supposed that S is SWRL knowledge base, OC is the set of the classes in OWL, OP is the attribute set of OWL, ST is the set of the constants of OWL and variables of SWRL, the specification of antecedent→consequent can be written as h1 ∧ ... ∧ hn ← b1 ∧ ... ∧ bm. Where hi, bj (1 ≤ i ≤ n, 1 ≤ j ≤ m) is Atom within C(i) (C ∈ OC , i ∈ ST ) and P (i, j)(P ∈ OP , i, j ∈ ST ). When the language SWRL is used to edit rules, the two points below should be followed. (1) All elements used in rules come from the classes or the attributes of the ontology; (2) The variables in the head of the rule must appear in the body of the rules, and it is impossible to introduce the new variables in the head of the rules, which is the safe restricted condition. In addition, when SWRL is used to edit rules, the rationality of rule descriptions is not checked, which may result in the following situation: the man-made rules and the OWL restriction contradict with each other. In brief, the prominent advantage of SWRL is the usage of ontology based rule language. The ontology language OWL supported by SWRL is the specification of W3C, and has more powerful ability to describe relationships. Meanwhile, SWRL also separates the ontology from the rule [4], and the rules described by the SWRL can be conveniently transformed to the rules in the present rule system.

3. The Rule Based Reasoning. Here, the reasoning machine of Jess is used to deal with reasoning part. Firstly, it transforms OWL ontology into the fact base, and transforms SWRL rules into the rule base. Then, it imports the facts and the rules into the working area of Jess reasoning engine to match the real facts and the rules. The rules are activated when the part antecedent of rule is satisﬁed. After matching, the activated rules are added to the pending area in order. Finally, the new facts will be gotten after the rules are run item by item. The new facts deduced are added into the fact base to serve the reasoning of the deeper level until the completion of the reasoning work.

4. SWRL-Based Reasoning Framework Design. Because the files in the format of OWL and in the format of SWRL can not be directly parsed by Jess reasoning engine, the ontology in the format of OWL and the rules in the format of SWRL should be transformed to the compatible format with Jess. To implement this mechanism, a sort of ontology and rule combined reasoning framework named as SWRL-based reasoning framework is given in Figure 1. The framework as shown in Figure 1 involves two transformations. The first is from OWL ontology to Jess fact base, and the other is from SWRL rule to Jess rule base. Protégé-OWL supplies a SWRL Bridge API. SWRL Bridge can be used to combine Jess Rule Engine with Protégé-OWL. Therefore, the framework can be used to realize the two transformations mentioned above. As to the two transformations, new reasoning fact base can be gotten by Jess reasoning, and then be transformed to the new OWL ontology. A. Transformation from OWL Ontology to Jess Factbase Because the reasoning engine Jess can not directly parse the ontology in the form of OWL, it must be transformed to the compatible form. During the transforming, two important attributes must be showed: (1) the attribute of instance’s class; (2) the attribute of the instance. Besides, the information same-as and different-form in the instance must be changed. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1755

Figure 1. SWRL based reasoning framewor

Proverbially, ontology includes five basic elements, so the transformed object from OWL ontology to the Jess fact base is naturally the very five basic elements. (1) The OWL formula for class is: howl:Class rdf:ID =“Ship”/i The corresponding formula for Jess is: (deftemplate Ship (slot name)) (2) The OWL formula for relation (take the subclassof for example) is: howl:Class rdf:ID=“Ship”i hrdfs:subClassOf rdf:resource=“#WaterTransportationTool”/i h/owl:Classi The corresponding formula for Jess is: (deftemplate Ship extends WaterTransportationTool) (3) The OWL formula for instance is: hShip rdf:ID=“Swallow”/i The corresponding formula for Jess is: (assert (Ship (name Swallow))) (assert (WaterTransportationTool (name Swallow))) Here, Swallow is the instance of class Ship. During the instance transformation, the information about class Ship to which instance Swallow belongs has to be gotten firstly, and the relevant information of father class Ship has to be gotten. In addition, if class Ship also has parent class, then the information about its parent class should be gotten. Hence, the instance transformation is an iterative process. Because the semantemes which the instance implies in OWL contain both the instance of the subclass and the one of its parent class, the instance transformation is not only the problem of the format transformation to be dealt with but also the axiom it implies needs to be transformed. (4) The OWL formula for function is: hShipMan rdf:ID=“M 01”i hhas Manager rdf:resource=“#M 02”/i h/ShipMani The corresponding formula for Jess is: (assert (hasManager M01 M02)) 1756 G. LI, Y. LIU AND B. CHEN (5) The axiom in OWL ontology is the most important, so the axiom transformation is obviously vital. A simple introduction to the transformation of the axiom subclass is also the parent class is given in the front OWL Formula (3). Relatively, the axiom transformation is more complicated. Firstly it must be decided which type the axiom belongs to and secondly it is transformed correspondingly. In detail, the related algorithm of axiom conversion is given in Table 1.

Table 1. Algorithm of axiom conversion

Algorithm 1 AxiomConvertor() 18: hT 0i=OWLObjectPropertyAssertionAxiom 1: begin 19: else if a ∈OWLClassPropertyAssertionAxiom 2: for each element e∈Ontology do 20: hT 0i=OWLClassPropertyAssertionAxiom 3: if e ∈OWLClass 21: else if a ∈OWLPropertyPropertyAssertionAxiom 4: hT i=Class 22: hT 0i=OWLPropertyPropertyAssertionAxiom 5: else if e ∈OWLIndividual 23: else if a ∈OWLSameIndividualsAxiom 6: hT i=Individual 24: hT 0i=OWLSameIndividualsAxiom 7: else if e ∈OWLDatatypeValue 25: else if a ∈OWLDiﬀerentIndividualsAxiom 8: hT i=DatatypeValue 26: hT 0i=OWLDiﬀerentIndividualsAxiom 9: representation=getOWLhT iRepresentation(e) 27: else if a ∈OWLClassAssertionAxiom 10: add(ArryList, representation) 28: hT 0i=OWLClassAssertionAxiom 11: else end 29: A = (hT 0i)a 12: end if 30: representation=gethT 0iRepresentation(A) 13: end for 31: add(ArryList, representation) 14: for each axiom a∈Ontology do 32: else end 15: if a ∈OWLDatatypePropertyAssertionAxiom 33: end if 16: hT 0i=OWLDatatypePropertyAssertionAxiom 34: end for 17: else if a ∈OWLObjectPropertyAssertionAxiom 35: end

B. Transformation from SWRL Rule to Jess Rulebase Firstly the edited SWRL rule as the source of Jess rule base should be transformed. The rule conversion algorithm is detailedly given in Table 2.

Table 2. Algorithm of rule conversion

Algorithm 2 RuleConvertor() 13: else if atom∈SameIndividualAtom atom=(atom b, atom h) 14: hT i=SameIndividualAtom 1: begin 15: else if atom∈DiﬀerentIndividualsAtom 2: rule=Rule(i) 16: hT i=DiﬀerentIndividualsAtom 3: if rule∈SWRLRule then 17: else if atom∈BuiltInAtom 4: atom b= getBodyAtoms() 18: hT i=BuiltInAtom 5: atom h= getHeadAtoms() 19: representation=gethT iRepresentation() 6: for all atom do 20: add(ArryList, representation) 7: if atom∈ClassAtom 21: else end 8: hT i=ClassAtom 22: end if 9: else if atom∈DatavaluedPropertyAtom 23: end for 10: hT i=DatavaluedPropertyAtom 24: end if 11: else if atom∈IndividualPropertyAtom 25: end 12: hT i=IndividualPropertyAtom

The SWRL rule consists of Imp whose components are both head and body. Since the basic ingredient allowed to appear in the head and body is Atom, the transformation of SWRL rule is the one of Atom. (1) When Atom serves as ClassAtom, its formula in the SWRL rule is: ClassA(?x). The corresponding formula of Jess is: (ClassA(name ?x) or (assert(ClassA(name ?x)). (2) When Atom serves as DatavaluedPropertyAtom, its formula in the SWRL rule is: DatavaluedPropertyB(?x, 20). ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1757 The corresponding formula of Jess is: (DatavaluedPropertyB(?x, 20) or (assert(DatavaluedPropertyB ?x, 20)). (3) When Atom serves as IndividualPropertyAtom, its formula in the SWRL rule is: IndividualPropertyC (?x,?y). The corresponding formula of Jess is: (IndividualPropertyC ?x?y) or (assert(IndividualPropertyC ?x ?y)). (4) When Atom serves as SameIndividualAtom, its formula in the SWRL rule is: sameAs(?x,?y). The corresponding formula of Jess is: (sameAs ?x ?y) or (assert(sameAs?x ?y)). (5) When Atom serves as DifferentIndividualsAtom, its formula in the SWRL rule is: differentFrom(?x,?y). The corresponding formula of Jess is: (differentFrom ?x ?y) or (assert(differentFrom?x ?y)). (6) When Atom serves as ClassAtom, taking greater Than for example, its formula in the SWRL rule is: greaterThan(age1,age2). The corresponding formula of Jess is: test(> age1 age2). After the transformation from OWL ontology and SWRL rules to the fact base and rule base of Jess, the method RunRuleEngine can be employed to start the Jess engine to reason. During the reasoning, the converted facts will be matched with the condition of the rules to get the activated rules, and the rules are added into the working agenda of Jess. These rules are run item-by-item to get the result of the reasoning. Finally, the new fact deduced is added into the Jess fact base which can be used for deeper level reasoning. When reasoning is accomplished, the method of writeAssertedIndividualsAnd- Properties2OWL() supplied by the class SWRLRule-EngineBridge can be used to write the deduced Jess facts into the original OWL ontology, so that the original ontology is updated, and a new ontology that is more sophisticated is gotten. 5. Demonstration and Verifying. In order to verify the proposed framework in this paper, a detailed instance is given in Table 3. Table 3. The segment of the ‘ShipMan’ ontology code

...... rdf :ID=“has colleague”i howl:Class rdf :ID=“Captain”i howl:inverseOf hrdfs:subClassOf i rdf :resource=“#has colleague”/i howl:Class rdf :ID=“Person”/i hrdfs:domain rdf :resource=“#Sailor”/i h/rdfs:subClassOf i hrdfs:range rdf :resource=“#Sailor”/i howl:disjointWithi h/owl:SymmetricPropertyi howl:Class rdf :ID=“Sailor”/i ...... h/owl:disjointWithi hCaptain rdf :ID=“Tom”i h/owl:Classi hmanager sailor rdf :resource=“#Gin”/i howl:Class rdf:about=“#Sailor”i hmanager sailor rdf :resource=“#Nat”/i hrdfs:subClassOf hmanager sailor rdf :resource=“#Jer”/i rdf :resource=“#Person”/i h/Captaini ...... howl:ObjectProperty hCaptain rdf :ID=“Jerry”i rdf :ID=“has manager”i hmanager sailor rdf :resource=“#Ell”/i hrdfs:range rdf:resource=“#Captian”/i hmanager sailor rdf :resource=“#Cas”/i hrdfs:domain rdf :resource=“#Sailor”/i h/Captaini howl:inverseOf hCaptain rdf :ID=“Jim”i rdf :resource=“#manager sailor”/i hmanager sailor rdf :resource=“#Zach”/i h/owl:ObjectPropertyi h/Captaini howl:SymmetricProperty 1758 G. LI, Y. LIU AND B. CHEN In Table 3, there are not any direct relations between Gin, Nat and Jer as well as between Cas and Ell. If someone directly inquires the ontology for the instance of Sailor that has the colleague relation to Gin, then the result will be empty. However, Gin, Nat and Jer have the common ruler Tom, and both Cas and Ell have the common ruler Jerry, so there is the colleague relation between Gin, Nat and Jer as well as between Cas and Ell. The knowledge is implied in the ontology. In order to reason the ontology by making use of the proposed framework, a SWRL rule needs to be defined as below: Sailor(?x) ∧ Sailor(?z) ∧ Captain(?y) ∧ hasManager(?x, ?y)∧ hasManager(?z, ?y) ∧ differentFrom(?x, ?y) → hasColleague(?x, ?y) After the reasoning, the instance Sailor that has the colleague relation will be deduced, and the detailed process is shown as follows. The transformed Jess fact: (assert (has manager Ell Jerry)); (assert (has manager Cas Jerry)); (assert (has manager Gin To m)); (assert (has manager Zach Jim)); (assert (has manager Jer Tom)); (assert (has manager Nat Tom)); differentFrom(A, B). The differentFrom(A, B) mentioned above indicates that there is a relation different- From between all the instances of Sailor and all the instances of Captain. Due to the space limit of this paper, we do not show all the relations. The transformed Jess rule is: (defrule def-has colleague (has manager ?x ?z)(has manager ?y ?z) (differentFrom ?x ?y)(Sailor (name ?x)) (Sailor (name ?y)) ⇒(assert(has colleague?x ?y))(assert(OWLProperty has colleague ?x?y)) The new fact after Jess reasoning is: (assert (has colleague Jer Gin)); (assert (has colleague Gin Jer)); (assert (has colleague Nat Jer)); (assert (has colleague Jer Nat)); (assert (has colleague Nat Gin)); (assert (has colleague Gin Nat)); (assert (has colleague Cas Ell)); (assert (has colleague Ell Cas)). The deduced new fact is written into the original ontology, and the original ontology is updated to get a new ontology. Therefore, if someone inquires the ontology for the instance of the Sailor that has the colleague relation to Gin, he will get the results including both Jer and Nat.

6. Conclusions. Since OWL DL cannot adequately describe some complicated rules in reasoning level, a ontology and rule combined reasoning framework (SWRL based reasoning framework) is proposed to get new ontology which has richer semantic relationships between concepts, so the knowledge of ontology is improved. Simply building the relevant SWRL rules in accordance with requirements, the reasoning service can be accomplished. So, not only the ontology knowledge availability factor is raised, but also the recall ratio and the precision ratio are raised in the information retrieve application. The framework can be improved to serve the uncertain ontology reasoning by referring to the advanced methods with respect to the reasoning algorithms, such as the extended neuro-fuzzy learning algorithm for tuning fuzzy rules [5].

Acknowledgment. This work is sponsored by National Natural Science Fund of China (Grant No. 60972090) and by Liaoning Province Natural Fund (Grant No. 20072142).

REFERENCES [1] L. Yu, X. Liu and F. Ren, Learnig to classify semantic orientation on-line document, International Journal of Innovative Computing, Information and Control, vol.5, no.12(A), pp.4637-4645, 2009. [2] X.-Q. Yang, N. Sun and T.-L. Sun, The application of latent semantic indexing and ontology in text classiﬁcation, International Journal of Innovative Computing, Information and Control, vol.5, no.12(A), pp.4491-4499, 2009. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1759

[3] L. Qian, A Inquiry System Design and Realization on the Base of the Reasoning of the Ontology and the Rule, Ph.D. Thesis, Southeast China University, 2007. [4] R. E. McGraph and J. Futrelle, Reasoning about provenance with OWL and SWRL rules, Lecture Notes in Computer Science, 2008. [5] Y. Shi, Fuzzy inference modeling based on fuzzy singleton-type reasoning, International Journal of Innovative Computing, Information and Control, vol.3, no.1, pp.13-20, 2007.

ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1761-1766

VULNERABILITY ASSESSMENT OF DISTRIBUTION NETWORKS BASED ON MULTI-AGENT SYSTEM AND QUANTUM COMPUTING

Xiangping Meng1, Kaige Yan2, Jingweijia Tan2 and Zhaoyu Pian1

1School of Electrical Engineering and Information Technology Changchun Institute of Technology Changchun 130012, P. R. China mxp [email protected] 2College of Computer Science and Technology Jilin University Changchun 130012, P. R. China Received February 2010; accepted April 2010

Abstract. To overcome the defects of information architecture of distribution networks, a coordination of distributed control structure is presented based on multi-agent system for vulnerability assessment. The new architecture makes use of multi-agent system’s advantages of handling of complex, dynamic, and distributed problems. Meanwhile, since the classical reinforcement learning of multi-agent system would be failed, when the number of agents is too large, a quantum reinforcement learning algorithm is proposed by combining quantum computing to perfect the assessment. Finally, the numerical simulations for both the classical Nash Q-learning and quantum reinforcement learning, and vulnerability assessment experiments based on an actual distribution network, have been investigated respectively. The results of simulation demonstrate that the improved model is more precise and highly eﬃcient for the vulnerability assessment. Keywords: Vulnerability assessment, Multi-agent system, Reinforcement learning, Quan- tum computing

1. Introduction. For the past years, many countries have suffered from serious black- outs, and the aftermath of the events poignantly illustrates the vast social disruption and economic loss [1,2]. Although the distribution network has been proven to be surprisingly robust and reliable, there does exist the potential disturbances, even small ones, to trigger an unfortunate cascade of events that cause large portions of the grid to blackout. Accordingly, the research of power system vulnerability assessment should be focused on. Chen et al. proposed a complex power system vulnerability assessment based on the risk theory [3]. In [4], the artificial neural network was used in network vulnerability assessment. And Wu et al. studied the onset and spreading of cascading failure on weighted heterogeneous networks by adopting a local weighted flow redistribution rule [5]. How- ever, those researchers’ works neglected the concrete engineering features. The existing information architecture of distribution networks is to use only one central controller to monitor the activities of all other devices, and all the decisions are made by the central controller. But with the development of society, the operations of power devices may not be centralized control anymore. Therefore, an intelligent, distributed control system is in more urgent need to achieve accurate control in a large-scale and complex distribution network. Recently, multi-agent system (MAS) has been more focused in distributed artificial intelligence, which is a coordinate operation to achieve the global goal [6]. In this paper, we implement the MAS to propose an improved model representing a coordination of distributed and centralized control structure for overcoming the defects of classical architecture. Meanwhile, a novel reinforcement learning algorithm is presented

1761 1762 X. MENG, K. YAN, J. TAN AND Z. PIAN by combining quantum computing (QC). Moreover, the comparison between the traditional Nash Q-learning and quantum reinforcement learning, and vulnerability assessment experiments with regard to actual oilﬁeld’s distribution network, has been investigated through numerical simulations respectively, and the results also verify the superiority of the proposed model both in precision and eﬃciency.

Figure 1. Framework of distribution networks control

2. Classical Information Architecture of Distribution Networks. Figure 1 shows the traditional information framework of distribution networks control. As illustrations of the literature, there are two categories of control methods, decentralized control and centralized control. The signals and information (i.e., control and vulnerability information) of all load devices and substations are sent to control center (the red ellipse part) in a one-way passing mode, and all the information is dealt in the top controller. This hierarchy involves long-distance transmission of vulnerability information and hence is diﬃcult to apply to fast control even though it can be technically implemented, moreover, large amounts of information can also cause blockage. In order to enhance the supervised eﬀectiveness of distribution networks, more decentralized controllers should be advocated. However, all the schemes of coordination proposed so far are based on the framework of decentralized control shown in Figure 1. There is no exchange of related information among local controllers. With the rapid development of technology, the evolution of distribution networks operation is more complex. Therefore, a more intelligent coordination of decentralized local controllers needs to be developed, which enables local controllers to exchange information together. Multi-agent theory has been widely applied in power systems recently. In this work, the MAS will be implemented to propose a new assessment architecture, which could guarantee fast and accurate vulnerability assessment of distribution networks.

3. Improved Architecture for Vulnerability Assessment Based on MAS. 3.1. Improved architecture. The most prominent property of classical assessment architecture is to only one controller directing all the actions of others. Once the central controller is at fault, it will aﬀect all other agents, and the entire system will be collapse. To avoid these problems, we use the hybrid and hierarchical architecture of MAS for the theme concerned in this paper, which consists in using several supervisors in multiple hierarchical levels (see Figure 2). ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1763

Figure 2. Improved framework of distribution networks control

According to the importance and hierarchy of the devices in distribution networks, three control layers can be defined, which constitute a vertical supervised mechanism. They are the reactive layer, coordination layer, and deliberative layer [6]. The reactive layer, attached to the lowest layer, is located in every load devices and is used to collect information of the environment. Load devices could be buses, large-scale power facilities, etc; The higher level is coordination layer. It takes the role of exchanging the information. It can trigger alarms received from the reactive layer, and can also pass the instructions of deliberative layer. Otherwise, the coordination layer is also a local controller. If a trig- gering event is under control (In the pre-set range), the control agents of the coordination layer issue instructions for the agents in reactive layer; The most top layer is the deliberative layer, which is the global supervisor and responsible for coordinating the whole system. All the information is sent to deliberative layer, in which the plans, decisions, and commands are made according to the principle of coordination and real states. To make full use of the architecture, the similar multi-agent modules are set up on each control nodes. Every multi-agent module consists of several functional agents, which play different roles in a vulnerability assessing process. As the module has completed technical functions, every control node becomes an autonomous local controller. Otherwise, with the communication agent, different modules could exchange their information to keep coordination and accuracy of assessment. Accordingly, a new vulnerability assessment mechanism is established based on the architecture and the multi-agent modules.

3.2. The learning rate drawbacks of MAS for vulnerability assessment. As we all know, there are a large number of load devices in a distribution network, and every load device is assigned a multi-agent module. In the proposed assessment mechanism, multi-agent learning deals with the problem domains involving multiple agents, and the agent not only learns what effects its actions have, but also how to coordinate or align its action choices with those of other agents. Accordingly, the search space involved can be unusually large, and classical searching algorithm turns to be inefficient. As in reinforcement learning algorithm, when the number of agents or/and agent’s action is too large, all of the action selection methods will be failed: the speed of learning is decreased sharply. Consequently, to implement assessment mechanism described above, the problem of low learning rate must be solved firstly.

4. A New Quantum Reinforcement Learning for Correcting Learning Rate Drawbacks of MAS. To solve the problem of learning rate deficiency, we try to introduce quantum mechanism to cooperate multi-agent reinforcement learning. 1764 X. MENG, K. YAN, J. TAN AND Z. PIAN 4.1. Multi-agent Q-learning (QLA). Learning behaviors in a multi-agent environment are crucial for developing and adapting multi-agent systems. The Q-learning is a standard reinforcement learning technique [7]. In multi-agent Q-learning, the Q-function of agent i is defined over states and joint-action vectors ~a = (a1, a2, ··· , an), rather than state-action pairs. The agents start with arbitrary Q-values, and the updating of Q value proceeds as following: [ ] i − i i · i Qt+1(s,~a) = (1 α)Qt(s,~a) + α rt + β V (st+1) (1) i where, V (st+1) is state value functions, and i i i V (st+1) = max f (Qt(st+1,~a)). (2) ai∈Ai 4.2. Quantum algorithm. 1. Quantum Bits: The unit of quantum information is the quantum bit (qubit). The qubit is a vector in a two-dimensional complex vector space with inner product, represented with quantum state. It is an arbitrary superposition state of two-state quantum system: |ψi = α |0i + β |1i , |α|2 + |β|2 = 1, (3) where α and β are complex coefficients. |0i and |1i correspond to classical bit 0 and 1. |α|2 and |β|2 represent the occurrence probabilities of |0i and |1i respectively when the project |ψi is measured, the outcome of the measurement is not deterministic. 2. Grover’s operator: Grover’s idea was to represent all numbers in {0, 1} via a superposition φ of n qubits, and shift their amplitudes so that the probability to find an element out of L in a measurement is near 1. To achieve this, a superposition of n qubits in which all elements have the same amplitude is created. Then the following operations are applied alternately: • Amplitudes of all elements ∈ L are reflected at zero. • Amplitudes of all elements are reflected at the average of all amplitudes. The two operators together are called the Grover-operator. The other fundamental operation required is the conditional phase shift operation which is an important element to carry out Grover iteration [8]. 4.3. Action probing based on quantum computing. At first, we initialize the action z }|n { E 11∑··· 1 E (n) 1 (n) f(s) = as = √ |ai, then f(s) can be re-expressed as f(s) = as = n √ 2 a=00···0 √ 1 2n − 1 1 ∑ √ |aki + |φi, where |φi = |ai. Define the angle θ satisfying n 2n 2n − 1 2 E a=ak 1 (n) sin θ = √ , thus f(s) = as = sin θ |aki + cos θ |φi, then from, we know that applying 2n E (n) Grover operator UGroverL times on as can be represented as:

L (n) | i | i UGrover as = sin((2L + 1)θ) ak + cos((2L + 1)θ) φ (4) Through repeating Grover operator, we can reinforce the probability amplitude of corresponding action according to the reward value. Classically, the classical search scale O(N) is dependent√ upon structuring within the database [8]. Grover operator oﬀers an improvement to O( N) and works just as well in a structured database as a disordered one. As Grover operator, the complexity of reinforcement learning reduces sharply. Con- sequently, we proposed a new quantum reinforcement learning.

5. Simulated Experiments and Results. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1765 5.1. The simulation of quantum reinforcement learning. We used the pursuit games in the grid world to verify the validity of learning algorithm presented above. There are ﬁve agents: four hunt agents and one target agent. At each episode, when the target agent is rounded by hunt agents, the game is over. When the hunt agents round the target agent at the same time, the hunt agents gain the maximal reward simultane- ity. We played this pursuit game both on the Nash Q-learning algorithm and quantum reinforcement learning, the experiment results are shown in Figure 3.

Figure 3. The performances of Nash Q-learning and quantum reinforcement learning As the Figure 3 shown, in multi-agent quantum reinforcement learning, the action selection method is obviously different from traditional multi-agent reinforcement learning algorithms, since Grover operator is used to explore multi-agent’s learning policies, multi- agent’s action selection method makes a good tradeoff between exploration and exploita- tion, and the updating process is carried out through parallel computation. Hence, the new quantum reinforcement learning lays a basic foundation for vulnerability assessment based on MAS. 5.2. The simulation of vulnerability assessment. According to improved assessment architecture and quantum reinforcement learning algorithm, we developed the software for vulnerability assessment of distribution networks. To verify the validity of the proposed algorithms and software, we implemented the software to assess vulnerability of one civil oilfield’s distribution network. In the experiment, the 110 KV, 35KV, and 10KV lines were selected to compute. Figure 4 shows the vulnerability ranks of 35KV lines, and Figure 5 illustrates the vulnerability value that is got by quantitative computes. Simulations show that the new assessment architecture and proposed quantum reinforcement learning make the vulnerability assessment more accurate and rapid. And the software developed with the proposed algorithms, will also be applied widely in distribution networks. 1766 X. MENG, K. YAN, J. TAN AND Z. PIAN

Figure 4. Vulnerability ranks of Figure 5. Assessment results 35KV lines

6. Conclusion. In certain time and places, the distribution network is very vulnerable, and even small ones could trigger an unfortunate cascade of events. Consequently, the vulnerability of distribution network should be researched. In this paper, a vulnerability assessment model was proposed for vulnerability analysis of distribution network, in which the MAS’s superiorities were fully utilized. Otherwise, to keep the rapid running of MAS in the new assessing process, a quantum reinforcement learning algorithm was proposed based on quantum theory, which uses Grover searching algorithm to reduce computing complexity that leads the learning operation of MAS to be failed. The ﬁnal tests on actual distribution network display that the proposed model is more precise and eﬃcient. And the proposed model and software can be used to make an accurate vulnerability assessment for the distribution networks. Acknowledgment. This work was supported by the National Natural Science Founda- tion of China under Grant No. 60974055 and the Changchun Science and Technology Plan Projects under Grant No. 08k218.

REFERENCES [1] H.-Y. Wu, C.-Y. Hsu, T.-F. Lee and F.-M. Fang, Improved SVM and ANN in incipient fault diagnosis of power transformers using clonal selection algorithms, International Journal of Innovative Computing, Information and Control, vol.5, no.7, pp.1959-1974, 2009. [2] H. Yoshikawa, K. Akama and H. Mabuchi, ET-based distributed cooperative system, International Journal of Innovative Computing, Information and Control, vol.5, no.12(A), pp.4655-4666, 2009. [3] W. Chen, Q. Jiang, Y. Cao and Z. Han, Risk-based vulnerability assessmnet in complex power system, Power System Techonolygy, vol.2, pp.12-19, 2005. [4] Q. Zhou, J. Davidson and A. A. Fouad, Application of artiﬁcial neural networks in power system security and vulnerability assessment, IEEE Trans. on Power Systems, vol.9, pp.525-532, 2002. [5] Z. X. Wu, G. Peng, W. X. Wang, S. Chan and E. E. M. Wong, Cascading failure spreading on weighted heterogeneous networks, Journal of Statistical Mechanics: Theory and Experiment, vol.2008, 2008. [6] C.-C. Liu, J. Jung, G. T. Heydt, V. Vittal and A. G. Phadke, The strategic power infrastructure defense (SPID) system: A conceptual design, IEEE Trans. on Control Systems Magazine, vol.20, no.4, pp.40-52, 2000. [7] J. Hu and M. P. Wellman, Nash Q-learning for general-sum stochastic games, Journal of Machine Learning Research, vol.4, pp.1039-1069, 2003. [8] L. Grover, A fast quantum mechanical algorithm for database search, Proc. of the 28th Annual ACM Symposium on Theory of Computation, pp.212-219, 1996. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1767-1772

A NEW MULTIPLE KERNEL LEARNING BASED LEAST SQUARE SUPPORT VECTOR REGRESSION AND ITS APPLICATION IN ON-LINE GAS HOLDER LEVEL PREDICTION OF STEEL INDUSTRY

Xiaoping Zhang, Jun Zhao∗ and Wei Wang Research Center of Information and Control Dalian University of Technology Dalian 116024, P. R. China zhang [email protected]; [email protected] ∗Corresponding author: [email protected] Received February 2010; accepted April 2010

Abstract. The key of gas scheduling in modern steel enterprises is to accurately predict gasholder level on-line. Because of the frequent and great ﬂuctuation of level, it is diﬃcult to be precisely predicted by the manual experience or the mechanism model based method. In this study, a class of MKL based on reduced gradient algorithm is extended using LSSVR, and the MKLLSSVR is developed. The MKLLSSVR overcomes the poor generalization of single kernel based LSSVR and the long training process of traditional MKL based SVR, and can rapidly give the optimal linear combination of kernels to base the resulting regressor for better interpretation. The simulation results with the real gasholder level data show the MKLLSSVR can achieve better prediction performance compared to the traditional MKL and single kernel based LSSVR. Keywords: Gasholder level prediction, Multiple kernel learning, Reduced gradient method, Least square support vector regression

1. Introduction. With the shortage of fossil energy (such as coal and oil) and the av- ocation of green manufacturing, making full use of by-product coal gas generated during steel production can greatly improve the energy saving level [1]. In byproduct energy scheduling for gas utilization and the safety operation of gasholder simultaneously, the real-time prediction for holder level is one of the most significant tasks. Heretofore, some scholars have paid attention on the online prediction for the holder level in steel industry. Iwao et al. in Kawasaki steel plant argued that the gasholder level exhibited a high self-correlation [1]. In their study, the previous level was employed using a time series model to predict the subsequent trend. However, the effect was limited because of the neglect of some influence factors, such as the generation and consumption of gas users. Then Kim et al. established a mechanism model that regarded the current level as the difference of all the generation and consumption of previous time [2]. Likewise, such method ignores the different impact of gas unit on the holder level. As the description by Iwao and Kim, the gasholder level is strongly affected by the previous level and the generation-consumption in the gas system. Therefore, the relationship among them is complex and with high nonlinearity. Although some effective applications had been carried out, such as finance [3], electrical industry [4], image coding [5], the LSSVR is generally based on a single kernel, and depends on the choices of a good kernel and the corresponding feature space [6]. However, the optimized single kernel cannot fully describe the complicated regression problem. Recent studies have shown that multiple kernel learning (MKL) is able to identify the appropriate combination of kernel functions to enrich the interpretation of regressor. Lanchriet et al. proposed the MKL framework as a semi-definite programming, and encoded it for a yeast protein functional classification [7]. For applying to the larger-scale problems, Bach

1767 1768 X. ZHANG, J. ZHAO AND W. WANG et al. introduced a dual formulation of the semi-definite programming as a second-order cone programming [8]. Subsequently, Sonnenburg et al. simplified the learning process by expressing the second-order cone programming as a semi-infinite linear programming, and put forward a wrapper algorithm with cutting planes method [9]. Rakotomamonjy et al. solved the MKL by a simple reduced gradient method (RGM) [10]. Note that the described fast approaches divided the MKL into two cycles [9,10], in which the inner cycle employed a standard SVR with linear combination of base kernels for the objective function update, and the outer cycle optimized the objective function to obtain the kernel weight vector. So the overall efficiency of MKL was tied to the single kernel based SVR. When dealing with the practical problem with the requirements of real-time and high precision, the effect will be restrained in spite of the contribution of RGM on saving the computation time. This paper combines the LSSVR with MKL to construct a MKLLSSVR for predicting the frequent non-flat variation of gasholder level. Firstly, instead of the single kernel, a series of kernels including various forms or scales are employed to enrich the features space, which make the regression function well interpret the complex problem. Secondly, the replacement of SVR by LSSVR in inner cycle greatly reduces the computation time of MKL, and simultaneously obtains the better objective function to further improve the RGM’s global optimization. The real data experiments demonstrate the high efficiency of MKLLSSVR in predicting the gasholder level over compared to the traditional MKL, single kernel LSSVR or the common used mechanism method.

2. Problem Statement. In Baosteel, blast furnace gas (BFG) is generated from the four blast furnaces. By the gas pipeline, it is supplied to many gas users as the secondary fuel for maintaining the production, for example, coke furnace (CF), hot blast furnace (HBF), continuous casting, heat treatment in rolling process, power plants, low pressure boilers (LPB), chemical plants, etc. And the rest are transported into the gasholder that works as a buffer to temporarily store the BFG. In general, the patterns of the generation and consumption for most of BFG units are largely different [2]. The various fluctuation of generation and consumption of gas units will influence the gasholder level change via gas pipeline. To sustain a stable running for the BFG supply and avoid the severe fluctuation of the holder level, its level has to be predicted in advance for guiding the gas scheduling.

3. Multiple Kernel Learning Least Square Support Vector Regression. Given a { }N { }m ∈ p set of training data xi, yi i=1 and positive deﬁnite function kernel kk k=1, where xi R is the input data; yi ∈ R is the target value; m is the initial amount of kernels; and N is the size of training data set. Under the functional framework [10], we propose the MKLLSSVR for regression problem is to solve the following convex optimization:

1 ∑m 1 ∑N min J{f , b, e, d} = kf k2 + C e2 k k Hk i 2 dk k=1 i=1 (1) ∑m ∑m s.t. yi = fk(xi) + b + ei ∀i; dk = 1, dk ≥ 0 ∀k k=1 k=1 ∑m Here f(x) = fk + b is the regression function learned by the MKLLSSVR. Each fk k=1 is trained in a diﬀerent reproduce hilbert kernel space Hk; Hk is associated with a basis kernel kk; b is the coeﬃcient of the regressor; dk with l1-norm sparse constraint is the kernel weight which controls the squared norm of fk in the objective function; ei is the training error on the ith training data point; C is the penalty factor which balances the empirical risk and the complexity of the regression function. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1769

Introduce the Lagrange multipliers αi, β and ηk, the Lagrangian of problem (1) is: ( ) 1 ∑m 1 ∑N ∑N ∑m L({f }, b, e, d, α, β, η) = kf k2 + C e2 − α f (x ) + b + e − y k k Hk i i k i i i 2 dk k=1( ) i=1 i=1 k=1 ∑m ∑m −β 1 − dk − ηkdk (2) k=1 k=1 We have the dual problem: ∑N max J(α, λ) = αiyi−λ i=1 ( ) ∑N 1 1 s.t. α = 0; λ ≥ αT k + I α ∀k, (3) i 2 k 2C i=1 1 ∑n where β + α2 = λ 4C i i=1 According to the minimization of the primal problem and its diﬀerentiability, we prefer to consider problem shown in Equation (1) as the following constrained optimization: ∑m min J(d), s.t. dk = 1, dk ≥ 0 k=1 1 ∑m 1 ∑N J(d) = min J{f , b, e, d} = kf k2 + C e2 (4) k k Hk i 2 dk k=1 i=1 ∑m s.t. yi = fk(xi) + b + ei k=1 By the optimality conditions, we derive the associated dual problem of (4): ( ) 1 ∑m 1 ∑N ∑N max J(a) = − α d k + I αT + α y s.t. α = 0 (5) 2 k k 2C i i i k=1 i=1 i=1

Then the gradient of J(d) with respect to dk is easily computed:

∂J 1 ∗ ∗T = − α kkα ∀k (6) ∂dk 2 According to the convex property and diﬀerentiability with Lipschitz gradient for J(·) [12], we have the reduced gradient r of J(d) in Equation (4): { ( ) ∂J ∂J ∑ ∂J ∂J rk = − ∀k =6 u; ru = − , u = arg max(dk) (7) ∂dk ∂du ∂dk ∂du { | 6 } k=6 u k dk=0 The feasible descent direction and update scheme for d with the step size s are given as:

Dk = {for ∀k =6 u, if rk > 0, −dkrk; for ∀k =6 u, if rk ≤ 0, −rk; for k = u, ru (8) d ← d + sD (9) The duality gap to monitor the convergence of the MKLLSSVR is formulated as: ( ) ( ( ) ) 1 ∑m 1 1 1 − ∗ ∗ ∗T ∗ ∗T DualGap = α dkkk + I α + max α kk + I α (10) 2 2C 2 k 2C k=1 1770 X. ZHANG, J. ZHAO AND W. WANG On the basis of the above reduced gradient, kernel weight updating and duality gap expression, the solving steps of the MKLLSSVR solved by RGM (MKLLSSVR(RGM)) is given as follows.

Step 1: Initialize the number of kernels and set the original weight dk = 1/m for k = 1, . . ., m; Step 2: Obtain α∗ by using LSSVR to solve the problem (4) with hybrid kernel K; Step 3: Renew the objective function J(d) of the equivalent problem (4); Step 4: Compute ∂J/∂dk, r and Dk; { } dv dk Step 5: Set the maximal step size smax = − v = arg min − ; Dv {k|Dk<0} Dk Step 6: Update the weight d and the hybrid kernel K; Step 7: With K, repeat Step2∼Step3 and obtain the new objective function Jnew (dnew); Step 8: Set d = dnew, Du = Du − Dv, Dv =0 and repeat Step 6∼Step 8 until Jnew (dnew) stops decrease; Step 9: Determine the optimal step size s∗ using the Armijo line search (s∗ = arg min J(d+ sD){s ∈ [0, smax]}), and update the weight d at the same time; Step 10: If the duality gap formulated by Equation (10) is less than the setting value, the MKLLSSVR ﬁnishes, otherwise goes back to Step 2. During the whole learning process of MKLLSSVR (RGM), the line search process involving the computation of the objective function is greatly speeded up by using LSSVR in inner cycle. Consequently, a substantial amount of computation time is further saved. Besides the advantage of time saving, LSSVR with hybrid kernel is easier to be precisely solved than the QP problems of SVR. This replacement ensures MKLLSSVR obtain a better objective function. Beneﬁting from the better objective value and feasible descent direction, the weight d can rapidly converge to KKT point, in which only several dk have the large values, and others are very small or even zero. Then, some base kernels with larger weight constitute the optimal linear combination of kernel to well extract the relevant knowledge about the problem for basing the regressor with good interpretation.

4. Experiments. In this section we evaluate the performance of MKLLSSVR (RGM) on the gasholder level prediction through comparing it with MKL based SVR (MKLSVR (RGM)), which is also solved by RGM, single kernel LSSVR optimized by 10 fold cross- validation (SKLLSSVR (10FCV)) and the holder level mechanism method (HLM) in [2]. We randomly choose 30 example sets with size of N = 2000 (98.5% as training data and 1.5% for testing) from Baosteel. The gas production-consumption flow of each unit and gas holder level is served as input and target value. For the MKL algorithms in comparison, 25 RBF-kernel sampling from the domain [0.01, 1000] and 5 Poly-kennel from [1, 5] are selected as the initial kernels. And RBF-kernel is adopted in SKLLSSVR (10FCV). The two MKL are trained for different values of hyperparameter C, where ε is set to 0.01 in MKLSVR (RGM). We choose C = 100 for MKLSVR (RGM), C = 55 for MKLLSSVR (RGM). MKLLSSVR (RGM) is implemented combined an LSSVR solver and SimpleMKL toolbox written in Matlab [9]. For a fair comparison, the same terminating criterion for all MKL algorithms are adopted, and the algorithm stops when the duality gap is lower than 0.01, or the number of iterations exceeds 1000. And the experiments are conducted on a PC with 3.6GHZ CPU and 1GB memory, all the algorithms are run 20 times. Here, we give some prediction results of 2# BFG holder level in Baosteel. Table 1 lists the prediction measures of the four algorithms in comparison. We also randomly select three groups of the results to picture on Figure 1. Regarding the prediction performance, it can be seen that HLM results in the largest mean absolute error (MAE) although it consumes the least time. As for the other three methods, the results are greatly improved. Whereas, the MAE obtained by SKLLSSVR (10FCV) is larger than ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1771 that by MKLSVR (RGM) and our MKLLSSVR (RGM), as the regressor through only one kernel is difficult to recover different trend of level information. Simultaneously, the training time is rather long due to the time-consuming validation. In contrast, MKLSVR (RGM) and the developed MKLLSSVR (RGM) select the most relevant combination of different kernel to construct the rich kernel space, in which the regressor with better interpretation is based. Moreover, by LSSVR instead of SVR, our approach can finish the 30 minutes prediction in less than one minute and generate far less MAE that meets the real time requirement of the practical prediction.

Table 1. Average performance measures of the four prediction methods

Method Trend MAE Time(s) Method Trend MAE Time(s) ascending 8.0965 ascending 2.2234 MKLSVR HLM stable 2.7112 0.005 stable 1.4818 756.90 (RGM) descending 6.0125 descending 2.0506 ascending 3.7617 ascending 1.0243 SKLLSSVR MKLLSSVR stable 1.7956 410.12 stable 0.9215 53.55 (10FCV) (RGM) descending 2.5947 descending 1.1938

(a) ascending trend (b) stable trend (c) descending trend

Figure 1. The trend prediction result of 2#BFG holder level

From Figure 1, the four algorithms in comparison can all predict the ascending, stable and descending trend of level in the future half an hour, but the deviation for HLM begins to become increasingly great as the prediction time goes on. Although, the great deviation is reduced obviously in SKLLSSVR and MKLSVR (RGM), it can also exist when the prediction time exceeds ten minutes. In contrast, the prediction result of the MKLLSSVR (RGM) proposed in this paper is the best and satisﬁes the precision requirement well.

5. Conclusions. The contribution of this paper is that a new MKLLSSVR has been proposed and applied to the gasholder level on-line prediction. In particular, the MK- LLSSVR overcomes the drawbacks of single kernel based LSSVR and MKLSVR. Our experimental results have shown that the developed MKLLSSVR is able to greatly improve the prediction precision over SKLLSSVR and reduces the prediction time over MKLSVR. Furthermore, the prediction performance prefers to the mechanism method 1772 X. ZHANG, J. ZHAO AND W. WANG used at present. So it can be generalized to other similar steel plant’s gasholder level prediction for oﬀering eﬀective guidance of gas real time balance scheduling. Acknowledgment. This work has been supported by the National High-Tech R&D Pro- gram of China (2007AA04Z1A9).

REFERENCES [1] I. Higashi, Energy balance of steel mills and utilization of byproduct gases, Transactions of the Iron and Steel Institute of Japan, vol.22, no.1, pp.57-65, 1982. [2] J. H. Kim, H. S. Yi and C. Han, A novel MILP model for plantwide multiperiod optimization of byproduct gas supply system in the iron and steel making process, Chemical Engineering Research Design, vol.81, no.8, pp.1015-1025, 2003. [3] J. A. K. Suykens, T. V. Gestel, J. D. Brabanter et al., Least Squares Support Vector Machines, World Scientific, Singapore, 2002. [4] G. F. Duan, Y. W. Chen and T. Sukekawa, Automatic optical inspection of micro drill bit in printed circuit board manufacturing using support vector machines, ICIC Express Letters, vol.5, no.11(B), pp.4347-4355, 2009. [5] Q. S. She, H. Y. Su, L. D. Dong and J. Chu, Support vector machine with adaptive parameters in image coding, ICIC Express Letters, vol.4, no.2, pp.359-367, 2008. [6] O. Chapelle, V. Vapnik, O. Bousquet and S. Mukherjee, Choosing multiple parameters for support vector machines, Machine Learning, vol.46, no.1, pp.131-159, 2002. [7] G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui and M. I. Jordan, Learning the kernel matrix with semidefinite programming, Journal of Machine Learning Research, vol.1, no.5, pp.27-72, 2004. [8] F. Bach, G. R. G. Lanckriet and M. I. Jordan, Multiple kernel learning, conic duality, and the SMO algorithm, Proc. of the 21st International Conference on Machine Learning, Banff, Alberta, Canada, 2004. [9] S. Sonnenburg, G. Ratsch, C. Schafer and B. Scholkopf, Large scale multiple kernel learning, Journal of Machine Learning Research, vol.7, no.7, pp.1531-1565, 2006. [10] A. Rakotomamonjy, F. R. Bach, S. Canu and Y. Grandvalet, SimpleMKL, Journal of Machine Learning Research, vol.9, no.11, pp.2491-2521, 2008. [11] J. F. Bonnans and A. Shapiro, Optimization problems with pertubation: A guided tour, SIAM Review, vol.40, no.2, pp.202-227, 1998. [12] D. Luenberger, Linear and Nonlinear Programming, Addison-Wesley, 1984. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1773-1778

THE PARAMETERIZATION OF ALL STABILIZING SIMPLE REPETITIVE CONTROLLERS WITH THE SPECIFIED INPUT-OUTPUT CHARACTERISTIC

Iwanori Murakami, Tatsuya Sakanushi, Kou Yamada, Yoshinori Ando Takaaki Hagiwara and Shun Matsuura Department of Mechanical System Engineering Gunma University 1-5-1 Tenjincho, Kiryu, Japan { murakami; t09801226; yamada; ando; t08801218; t10801252 }@gunma-u.ac.jp Received February 2010; accepted April 2010

Abstract. The simple repetitive control system proposed by Yamada et al. is a type of servomechanism for the periodic reference input. That is, the simple repetitive control system follows the periodic reference input with small steady state error, even if a periodic disturbance or uncertainty exists in the plant. In addition, simple repetitive control systems make transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. Yamada et al. clarified the parameterization of all stabilizing simple repetitive controllers. However, using the method by Yamada et al., it is complex to specify the low-pass filter in the internal model for the periodic reference input of which the role is to specify the input-output characteristic. The purpose of this paper is to propose the parameterization of all stabilizing simple repetitive controllers with the specified input-output characteristic such that the input-output characteristic can be specified beforehand. Keywords: Repetitive control, Finite numbers of poles, Parameterization

1. Introduction. A repetitive control system is a type of servomechanism for the periodic reference input. That is, the repetitive control system follows the periodic reference input without steady state error, even if a periodic disturbance or uncertainty exists in the plant [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. It is difficult to design stabilizing controllers for the strictly proper plant, because the repetitive control system that follows any periodic reference input without steady state error is a neutral type of time-delay control system [11]. To design a repetitive control system that follows any periodic reference input without steady state error, the plant needs to be biproper [3, 4, 5, 6, 7, 8, 9, 10, 11]. In practice, the plant is strictly proper. Many design methods for repetitive control systems for strictly proper plants have been given [3, 4, 5, 6, 7, 8, 9, 10, 11]. These studies are divided into two types. One uses a low-pass filter [3, 4, 5, 6, 7, 8, 9, 10] and the other uses an attenuator [11]. The latter is difficult to design because it uses a state variable time-delay in the repetitive controller [11]. The former has a simple structure and is easily designed. Therefore, the former type of repetitive control system is called the modified repetitive control system [3, 4, 5, 6, 7, 8, 9, 10]. Using modified repetitive controllers in [3, 4, 5, 6, 7, 8, 9, 10], even if the plant does not include time-delays, transfer functions from the periodic reference input to the output and from the disturbance to the output have infinite numbers of poles. This makes it difficult to specify the input-output characteristic and the disturbance attenuation characteristic. From the practical point of view, it is desirable that these characteristics should be easy to specify. Therefore, these transfer functions should have finite numbers of poles. To overcome this problem, Yamada et al. proposed simple repetitive control systems such that the controller works as a modified repetitive controller and transfer functions from the

1773 1774 I. MURAKAMI, T. SAKANUSHI, K. YAMADA ET AL. periodic reference input to the output and from the disturbance to the output have finite numbers of poles [14]. In addition, Yamada et al. clarified the parameterization of all stabilizing simple repetitive controllers. According to Yamada et al., the parameterization of all stabilizing simple repetitive controllers includes two free-parameters. One has the role to specify the disturbance attenuation characteristic. The other has the role to specify the low-pass filter in the internal model for the periodic reference input of which the role is to specify the input-output characteristic. However, using the method by Yamada et al., it is complex to specify the low-pass filter in the internal model for the periodic reference input. When we design a simple repetitive controller, if the low-pass filter in the internal model for the periodic reference input is settled beforehand, we can specify the input-output characteristic more easily than the method in [14]. This problem is solved by obtaining the parameterization of all stabilizing simple repetitive controllers with the specified input-output characteristic, which is the parameterization when the low-pass filter is settled beforehand. However, no paper has considered the problem to obtain the parameterization of all stabilizing simple repetitive controllers with the specified input- output characteristic. In addition, the parameterization is useful to design stabilizing controllers [15, 16, 17, 18]. In this paper, we propose the parameterization of all stabilizing simple repetitive controllers with the specified input-output characteristic such that the low-pass filter in the internal model for the periodic reference input is settled beforehand.

2. Simple Repetitive Controller with the Speciﬁed Input-output Character- istic and Problem Formulation. Consider the unity feedback control system given by { y(s) = G(s)u(s) + d(s) , (1) u(s) = C(s)(r(s) − y(s)) where G(s) ∈ R(s) is the strictly proper plant, C(s) is the controller, u(s) ∈ R is the control input, y(s) ∈ R is the output, d(s) ∈ R is the disturbance and r(s) ∈ R is the periodic reference input with period T > 0 satisfying r(t + T ) = r(t)(∀t ≥ 0). (2) According to [3, 4, 5, 6, 7, 8, 9, 10], the modiﬁed repetitive controller C(s) is written by the form in

C(s) = C1(s) + C2(s)Cr(s), (3) where C1(s) ∈ R(s) and C2(s) =6 0 ∈ R(s). Cr(s) is an internal model for the periodic reference input r(s) with period T and written by e−sT Cr(s) = , (4) 1 − q(s)e−sT where q(s) ∈ R(s) is a proper low-pass filter satisfying q(0) = 1. Using the modified repetitive controller C(s) in (3), transfer functions from the periodic reference input r(s) to the output y(s) and from the disturbance d(s) to the output y(s) in (1) are written as y(s) C(s)G(s) = r(s) 1 + C(s){G(s) } −sT C1(s) − (C1(s)q(s) − C2(s))e G(s) = −sT (5) 1 + C1(s)G(s) − {(1 + C1(s)G(s))q(s) − C2(s)G(s)} e ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1775 and y(s) 1 = d(s) 1 + C(s)G(s) 1 − q(s)e−sT = −sT , (6) 1 + C1(s)G(s) − {(1 + C1(s)G(s))q(s) − C2(s)G(s)} e respectively. Generally, transfer functions from the periodic reference input r(s) to the output y(s) in (5) and from the disturbance d(s) to the output y(s) in (6) have infinite numbers of poles. In order to specify the input-output characteristic and the disturbance attenuation characteristic easily, Yamada et al. proposed simple repetitive control systems such that the controller works as a modified repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles [14]. In addition, Yamada et al. clarified the parameterization of all stabilizing simple repetitive controllers. On the other hand, according to [3, 4, 5, 6, 7, 8, 9, 10], it is note that if the low-pass filter q(s) satisfy

1 − q(jωi) ' 0 (∀i = 0,...,Nmax) , (7)

where ωi(i = 1,...,Nmax) are frequency components of the periodic reference input r(s) written by 2π ω = i (i = 0,...,N ) (8) i T max

and ωNmax is the maximum frequency component of the periodic reference input r(s), then the output y(s) in (1) follows the periodic reference input r(s) with small steady state error. Using the result in [14], in order for q(s) to satisfy (7) in wide frequency range, we must design q(s) to be stable and of minimum phase. If we obtain the parameterization of all stabilizing simple repetitive controllers such that q(s) in (4) is settled beforehand, we can design the simple repetitive controller satisfying (7) more easily than the method in [14]. From above practical requirement, we propose the concept of the simple repetitive controller with the specified input-output characteristic as follows: Definition 2.1. (simple repetitive controller with the specified input-output characteristic) We call the controller C(s) a “simple repetitive controller with the specified input-output characteristic”, if following expressions hold true: 1. The low-pass filter q(s) ∈ RH∞ in (4) is settled beforehand. That is, the input-output characteristic is settled beforehand. 2. The controller C(s) works as a modified repetitive controller. That is, the controller C(s) is written by (3), where C1(s) ∈ R(s), C2(s) =6 0 ∈ R(s) and Cr(s) is written by (4). 3. The controller C(s) makes transfer functions from the periodic reference input r(s) to the output y(s) in (1) and from the disturbance d(s) to the output y(s) in (1) have finite numbers of poles. The problem considered in this paper is to propose the parameterization of all stabilizing simple repetitive controllers with the specified input-output characteristic.

3. The Parameterization of all Stabilizing Simple Repetitive Controllers with the Specified Input-output Characteristic. In this section, we clarify the parameterization of all stabilizing simple repetitive controllers with the specified input-output characteristic defined in Definition 2.1. In order to obtain the parameterization of all stabilizing simple repetitive controllers with the specified input-output characteristic, q(s) ∈ RH∞ is assumed to be settled 1776 I. MURAKAMI, T. SAKANUSHI, K. YAMADA ET AL. beforehand. The parameterization of all stabilizing simple repetitive controllers with the specified input-output characteristic is summarized in the following theorem. Theorem 3.1. There exists a stabilizing simple repetitive controller with the specified input-output characteristic if and only if the low-pass filter q(s) ∈ RH∞ in (4) takes the form: q(s) = N(s)¯q(s). (9)

Here, N(s) ∈ RH∞ and D(s) ∈ RH∞ are coprime factors of G(s) on RH∞ satisfying N(s) G(s) = (10) D(s) and q¯(s) =6 0 ∈ RH∞ is any function. When the low-pass filter q(s) ∈ RH∞ in (4) satisfies (9), the parameterization of all stabilizing simple repetitive controllers with the specified input-output characteristic is given by X(s) + D(s)Q(s) + D(s)(Y (s) − N(s)Q(s))q ¯(s)e−sT C(s) = . (11) Y (s) − N(s)Q(s) − N(s)(Y (s) − N(s)Q(s))q ¯(s)e−sT

Here, X(s) ∈ RH∞ and Y (s) ∈ RH∞ are functions satisfying X(s)N(s) + Y (s)D(s) = 1 (12) and Q(s) ∈ RH∞ is any function. Proof of this theorem requires following lemma. Lemma 3.1. Unity feedback control system in (1) is internally stable if and only if C(s) is written by X(s) + D(s)Q(s) C(s) = , (13) Y (s) − N(s)Q(s) where N(s) ∈ RH∞ and D(s) ∈ RH∞ are coprime factors of G(s) on RH∞ satisfying (10), X(s) ∈ RH∞ and Y (s) ∈ RH∞ are functions satisfying (12) and Q(s) ∈ RH∞ is any function [18]. Using Lemma 3.1, we shall show the proof of Theorem 3.1. Proof: First, the necessity is shown. That is, we show that if the controller C(s) in (3) makes the control system in (1) stable and makes the transfer function from the periodic reference input r(s) to the output y(s) of the control system in (1) have finite numbers of poles, then the low-pass filter q(s) must take the form (9). From the assumption that the controller C(s) in (3) makes the transfer function from the periodic reference input r(s) to the output y(s) of the control system in (1) have finite numbers of poles, { } −sT G(s)C(s) C1(s) − (C1(s)q(s) − C2(s))e G(s) = −sT (14) 1 + G(s)C(s) 1 + G(s)C1(s) − {(1 + G(s)C1(s))q(s) − C2(s)G(s)} e has finite numbers of poles. This implies that (1 + G(s)C (s))q(s) C (s) = 1 (15) 2 G(s) is satisfied, that is, C(s) is necessarily G(s)C (s) + q(s)e−sT C(s) = (1 ) . (16) G(s) 1 − q(s)e−sT ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1777 From the assumption that C(s) in (3) makes the control system in (1) stable, G(s)C(s) /(1 + G(s)C(s)), C(s)/(1 + G(s)C(s)), G(s)/(1 + G(s)C(s)) and 1/(1 + G(s)C(s)) are stable. From simple manipulation and (16), we have G(s)C(s) G(s)C (s) + q(s)e−sT = 1 , (17) 1 + G(s)C(s) 1 + G(s)C1(s) C(s) G(s)C (s) + q(s)e−sT = 1 , (18) 1 + G(s)C(s) (1 + G(s)C1(s))G(s) G(s) (1 − q(s)e−sT )G(s) = (19) 1 + G(s)C(s) 1 + G(s)C1(s) and 1 1 − q(s)e−sT = . (20) 1 + G(s)C(s) 1 + G(s)C1(s) From the assumption that all transfer functions in (17), (18), (19) and (20) are stable, G(s)C1(s)/(1 + G(s)C1(s)), C1(s)/(1 + G(s)C1(s)), G(s)/(1 + G(s)C1(s)) and 1/(1 + G(s)C1(s)) are stable. This means that C1(s) is an internally stabilizing controller for G(s). From Lemma 3.1, C1(s) must take the form: X(s) + D(s)Q(s) C (s) = , (21) 1 Y (s) − N(s)Q(s)

where Q(s) ∈ RH∞. From the assumption that the transfer function in (18) is stable, q(s) (Y (s) − N(s)Q(s)) D2(s)q(s) = (22) G(s) (1 + G(s)C1(s)) N(s) is stable. This implies that q(s) must take the form q(s) = N(s)¯q(s), (23)

whereq ¯(s) =6 0 ∈ RH∞ is any function. In this way, it is shown that if there exists a stabilizing simple repetitive controller with the specified input-output characteristic, then the low-pass filter q(s) must take the form (9). Next, we show that if (9) holds true, then C(s) is written by (11). Substituting (15), (21) and (23) into (3), we have (11). Thus, the necessity has been shown. Next, the sufficiency is shown. That is, it is shown that if q(s) and C(s) take the form (9) and (11), respectively, then the controller C(s) makes the control system in (1) stable, makes the transfer functions from r(s) and d(s) to y(s) of the control system in (1) have finite numbers of poles and works as a stabilizing modified repetitive controller. After simple manipulation, we have G(s)C(s) { } = X(s) + D(s)Q(s) + D(s)(Y (s) − N(s)Q(s))q ¯(s)e−sT N(s), (24) 1 + G(s)C(s) C(s) { } = X(s) + D(s)Q(s) + D(s)(Y (s) − N(s)Q(s))q ¯(s)e−sT D(s), (25) 1 + G(s)C(s) G(s) { ) = Y (s) − N(s)Q(s) − N(s)(Y (s) − N(s)Q(s))q ¯(s)e−sT N(s) (26) 1 + G(s)C(s) and 1 { } = Y (s) − N(s)Q(s) − N(s)(Y (s) − N(s)Q(s))q ¯(s)e−sT D(s). (27) 1 + G(s)C(s)

Since X(s) ∈ RH∞, Y (s) ∈ RH∞, N(s) ∈ RH∞, D(s) ∈ RH∞, Q(s) ∈ RH∞ and q¯(s) ∈ RH∞, the transfer functions in (24), (25), (26) and (27) are stable. In addition, 1778 I. MURAKAMI, T. SAKANUSHI, K. YAMADA ET AL. from the same reason, transfer functions from r(s) and d(s) to y(s) of the control system in (1) have ﬁnite numbers of poles. Next, we show that the controller in (11) works as a modiﬁed repetitive controller. The controller in (11) is rewritten by the form in (3), where X(s) + D(s)Q(s) C (s) = (28) 1 Y (s) − N(s)Q(s) and q¯(s) C (s) = . (29) 2 (Y (s) − N(s)Q(s))

From the assumption ofq ¯(s) =6 0, C2(s) =6 0 holds true. These expressions imply that the controller C(s) in (11) works as a modified repetitive controller. Thus, the sufficiency has been shown. We have thus proved Theorem 3.1. 4. Conclusions. In this paper, we proposed the parameterization of all stabilizing simple repetitive controllers with the specified input-output characteristic. This work was supported by JSPS Grant-in-Aid for Scientific Research (A20560210).

REFERENCES [1] T. Inoue, et al., High accuracy control magnet power supply of proton synchrotron in recurrent operation, Trans. Institute of Electrical Engineers of Japan, vol.C100, no.7, pp.234-240, 1980. [2] T. Inoue, S. Iwai and M. Nakano, High accuracy control of play-back servo system, Trans. Institute of Electrical Engineers of Japan, vol.C101, no.4, pp.89-96, 1981. [3] S. Hara, T. Omata and M. Nakano, Stability condition and synthesis methods for repetitive control system, Trans. Society of Instrument and Control Engineers, vol.22, no.1, pp.36-42, 1986. [4] S. Hara and Y. Yamamoto, Stability of multivariable repetitive control systems – Stability condition and class of stabilizing controllers, Trans. Society of Instrument and Control Engineers, vol.22, no.12, pp.1256-1261, 1986. [5] Y. Yamamoto and S. Hara, The internal model principle and stabilizability of repetitive control system, Trans. Society of Instrument and Control Engineers, vol.22, no.8, pp.830-834, 1987. [6] S. Hara, Y. Yamamoto, T. Omata and M. Nakano, Repetitive control system: A new type of servo system for periodic exogenous signals, IEEE Trans. Automatic Control, vol.AC-33, no.7, pp.659-668, 1988. [7] T. Nakano, T. Inoue, Y. Yamamoto and S. Hara, Repetitive Control, SICE Publications, 1989. [8] S. Hara, P. Trannitad and Y. Chen, Robust stabilization for repetitive control systems, Proc. of the 1st Asian Control Conference, pp.541-544, 1994. [9] G. Weiss, Repetitive control systems: Old and new ideas, Systems and Control in the Twenty-First Century, pp.389-404, 1997. [10] T. Omata, S. Hara and M. Nakano, Nonlinear repetitive control with application to trajectory control of manipulators, J. Robotic Systems, vol.4, no.5, pp.631-652, 1987. [11] K. Watanabe and M. Yamatari, Stabilization of repetitive control system – Spectral decomposition approach, Trans. Society of Instrument and Control Engineers, vol.22, no.5, pp.535-541, 1986. [12] M. Ikeda and M. Takano, Repetitive control for systems with nonzero relative degree, Proc. of the 29th CDC, pp.1667-1672, 1990. [13] H. Katoh and Y. Funahashi, A design method for repetitive controllers, Trans. Society of Instrument and Control Engineers, vol.32, no.12, pp.1601-1605, 1996. [14] K. Yamada, H. Takenaga, Y. Saitou and K. Satoh, Proposal for simple repetitive controllers, ECTI Transactions on Electrical Eng., Electronics, and Communications, vol.6, no.1, pp.64-72, 2008. [15] D. C. Youla, H. Jabr and J. J. Bongiorno, Modern Wiener-Hopf design of optimal controllers. Part I, IEEE Trans. on Automatic Control, vol.AC-21, pp.3-13, 1976. [16] V. Kucera, Discrete Linear System, The Polynomial Eqnarray Approach, Wiley, 1979. [17] J. J. Glaria and G. C. Goodwin, A parameterization for the class of all stabilizing controllers for linear minimum phase system, IEEE Trans. on Automatic Control, vol.AC-39, no.2, pp.433-434, 1994. [18] M. Vidyasagar, Control System Synthesis: A Factorization Approach, MIT Press, 1985.

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A NOVEL EPIDEMIC MODEL WITH TRANSMISSION MEDIUM ON COMPLEX NETWORKS

Chengyi Xia1,2, Junhai Ma1 and Zengqiang Chen3 1School of Management Tianjin University Tianjin 300072, P. R. China [email protected]; [email protected] 2Tianjin Key Laboratory of Intelligent Computing and Novel Software Technology Tianjin University of Technology Tianjin 300191, P. R. China 3Department of Automation Nankai University Tianjin 300071, P. R. China [email protected] Received February 2010; accepted April 2010

Abstract. Based on the susceptible-infective-removed-susceptible (SIRS) compartmen- tal model, a novel epidemic model with transmission medium is proposed to investigate the role of infective media in epidemic spreading on complex networks. The mean-ﬁeld analysis and numerical simulation both indicate that the infective media can greatly reduce the infection threshold on heterogeneous and homogeneous networks. These results are helpful for us to prevent the epidemic outbreaks and design some feasible containment strategies. Keywords: SIRS model, Transmission medium, Complex networks

1. Introduction. Over the past few years, some emerging infectious diseases have brought forward the large damage and posed a great threat to the global world, such as severe acute respiratory syndrome (SARS), avian influenza, swine influenza (H1N1) and son on. Thus, understanding the disease spreading behavior has become an active topic and attracted a lot of attention within medical practice and the scientific community [1]. Based on the framework of complex networks, some new progresses have been made in the field of the epidemic modeling. The susceptible-infected-susceptible (SIS) [2], susceptible- infected- removed (SIR) [3] and susceptible-infected (SI) [4] models on complex networks have been extensively investigated, the results have shown that there is an epidemic threshold (λc) for homogeneous networks but it is absent for heterogeneous networks under the thermodynamic limit [2-4]. These studies largely richen the knowledge of the epidemics on complex systems for the humankind, but they highly emphasize the role of network topology and ignore the effect of transmission mechanism on disease spreading. In reality, micro infection mechanism can also change the spreading behavior and exhibit the distinguishing conclusions [5-7]. In addition, many infectious human diseases, such as malaria, yellow fever and dengue fever, disease spreading is also carried out by other transmission pathways, e.g. the mosquitoes biting. That is to say, the epidemics proliferate by contacts between individuals and media as well as by contacts among individuals. Shi et al. [8] propose an improved SIS model to analyze the effect of infective medium on the spreading behavior on complex networks and find that the infective medium will reduce the epidemic threshold. However, the infected individuals can often be conferred to the immunity during a long time after

1785 1786 C. XIA, J. MA AND Z. CHEN being cured, and it is necessary to integrate the infective medium into SIRS epidemic model to further analyze the role of spreading medium in epidemic outbreaks. In this paper, we present a novel epidemic model with transmission medium, and it is shown that the transmission medium can largely reduce the critical threshold of epidemics on networks.

2. SIRS-Like Model with Transmission Medium. In this paper, the infective medium is added into the SIRS model and the system can be deﬁned as follows. The whole system is made up of two types of nodes, one is the host individual (e.g. people) and the other is infective medium node (e.g. mosquitoes). The host individuals are categorized into three classes: Susceptible (S), Infective (I) and Removed (R), and the medium individuals can only exist in one of two discrete states: Susceptible and Infective. Moreover, we neglect the details of infection mechanism within each individual in the model. The model can be described as Figure 1.

Figure 1. SIRS model with transmission medium

At each time step, a susceptible host is infected with the rate β if it is connected to one or more infective hosts, and the infective host is cured by the rate γ and enters into the removed state. Meanwhile, the removed host will keep the immunity for a certain period and then become susceptible again with the transition rate δ. In addition, each susceptible host is also infected with the probability β1 because of the bites by the infected mosquitoes. Each susceptible mosquito can be infected by the rate β2 as a result of biting on the infected hosts. Thus, all hosts in this system will run stochastically through the susceptible-infective-removed-susceptible cycle. It is also assumed that there exists no infection transmission among the mosquitoes, and the mosquitoes run stochastically through cycle susceptible-infective. Furthermore, we can suppose that the density of newly infective mosquitoes is proportional to the infected hosts as they are often biting persons without any selectivity. Based on the mean-ﬁeld theory [2-4], we will derive the critical threshold of infection spreading under the heterogeneous topology of complex networks. And the main result is easily extended into the cases in the homogeneous topology.

2.1. Heterogeneous topology. Recently it is found that many real complex networks display high heterogeneity with respect to the connectivity distribution [9]. Therefore, it is necessary to consider the epidemic model∑ defined on a network with general distribution P (k) and finite average degree hki = kP (k). k Let sk(t), ρk(t) and rk(t) be the relative density of susceptible, infective and removed nodes of connectivity k at time step t, respectively. They are related by the normalization condition sk(t) + ρk(t) + rk(t) = 1. Some global quantities such as the∑ infection density are therefore expressed as an average over various degree k, i.e. ρ(t) = P (k)ρk(t). At k the same time, the density of infective media is also set to be ϕk(t) = β2ρk(t), and hence ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1787 the system can be described as    dsk(t) − −  = βksk(t)Θk(t) β1β2sk(t)ρk(t) + δrk(t)  dt dρ (t) k = βks (t)Θ (t) + β β s (t)ρ (t) − γρ (t) (1)  dt k k 1 2 k k k   dr (t)  k = γρ (t) − δr (t) dt k k where Θk(t) indicates the probability that any link points to an infective node. We will discuss two different cases for uncorrelated and correlated networks, respectively. Firstly, we consider the heterogeneous networks without any degree correlations in which the probability Θk(t) is independent of the emanating node’s degree and proportional to the degree of the targeted node. Thus, the probability that a randomly chosen link points to an infected site is given by ∑ kP (k)ρ (t) Θ (t) = Θ(t) = k k (2) k hki

→ ∞ dsk(t) dρk(t) When t , the system arrives at the steady state and we set dt = 0, dt = 0, drk(t) dt = 0. There exists,  γ  r (∞) = ρ (∞) k δ k ∞ (3)  βkδΘ( ) ρk(∞) = γδ − β1β2δ + βk(γ + δ)Θ(∞) According to Equation (8), ∑ kP (k)ρ (∞) 1 ∑ βkδΘ(∞) Θ(∞) = k k = kP (k) hki hki k γδ − β β + βk(γ + δ)Θ(∞) 1 2 (4) 1 ∑ βδΘ(∞) = k2P (k) = f(Θ(∞)) hki k γδ − β1β2 + βk(γ + δ)Θ(∞) It is apparent that Θ(∞) = 0 is a trivial solution of Equation (4). To ensure a non-trivial solution 0 < Θ(∞) < 1, the following condition must be satisﬁed,

df(Θ(∞)) ∞ > 1 (5) dΘ( ) Θ(∞)=0 Inserting Equation (3) into Equation (4),

∞ ∑ − ∑ df(Θ( )) 1 2 βδ(γδ β1β2δ) 1 2 β = k P (k) = k P (k) > 1 ∞ h i k − 2 h i k − dΘ( ) Θ(∞)=0 k (γδ β1β2δ) k γ β1β2 (6) Let the effective spreading rate λ = β/γ, the condition can be rewritten as ( ) β hki β β λ = > 1 − 1 2 (7) γ hk2i γ That is, the infection threshold of the system is hki λ = (1 − β β ) (8) c hk2i 1 2 when we set the cure rate γ = 1 without lack of generality. Particularly, the threshold hki is reduced to λc = hk2i which is identical with the standard SIRS model on uncorrelated heterogeneous networks when there is no infective medium (i.e. β1 = β2 = 0). Secondly, we analyze the influence of degree correlation on the system behavior. The degree correlation is often present in many real complex systems, and social networks 1788 C. XIA, J. MA AND Z. CHEN (e.g. scientific collaboration networks) are assortative while technological networks (e.g. Internet) are disassortative [10]. We can take the conditional probability P (k0|k) to characterize this kind of correlation, and P (k0|k) indicates the probability which a node with given connectivity k is connected to a node with connectivity k0. Inserting the correlation into Θ(t), and Θ(t) can be rewritten as ∑ 0 Θ(t) = P (k |k)ρk0 (t) (9) k0 Under the stationary condition, we can have ∑ 0 ∞ ∞ 0| βk δΘ( ) Θ( ) = 0 P (k k) 0 (10) k γδ − β1β2 + βk (γ + δ)Θ(∞) Taking the similar method as before, the critical condition of infection transmission on correlated networks is ( ) β β 1 λ > 1 − 1 2 ∑ (11) 0 0| γ k0 k P (k k) − ∑(1 β1β2) Generally we assume γ = 1 and the critical threshold is λc = 0 0| . If the degree k0 k P (k k) correlation isn’t present in complex networks, the conditional probability can be described as P (k0|k) = k0P (k0)/hki. Equation (16) can be rewritten as ( ) ( ) ( ) β β 1 β β 1 β β hki λ > 1 − 1 2 ∑ = 1 − 1 2 ∑ = 1 − 1 2 0 0| 0 0 0 h i h 2i γ k0 k P (k k) γ k0 k k P (k )/ k γ k (12) Obviously, Equation (12) is totally equivalent to Equation (7) and the threshold is also hki − λc = hk2i (1 β1β2). 2.2. Homogeneous topology. For a homogeneous network (e.g. small-world one) [11], each node has roughly the same degree, i.e. k ≈ hki. And the whole system can obey the following differential equations,    ds(t) − h i −  = βs(t) k ρ(t) β1s(t)ϕ(t) + δr(t)  dt dρ(t) = βs(t)hkiρ(t) + β s(t)ϕ(t) − γρ(t) (13)  dt 1   dr(t)  = γρ(t) − δr(t) dt where 0 ≤ β, β1, β2, γ, δ ≤ 1, and we assume that s(t), ρ(t), r(t) denote the fraction of susceptible, infective and removed individuals over the total population respectively, which are coupled by the normalization condition s(t) + ρ(t) + r(t) = 1. As stated above, the density of infective medium can be written as ϕ(t) = β2ρ(t). We take the same method to perform the mean-field analysis for the system (13), the critical threshold for the homogeneous networks is 1 λ = (1 − β β ) (14) c hki 1 2 3. Numerical Simulation. To verify the above-mentioned theoretic predictions, large- scale simulations are performed on scale-free [8] and small-world [10] networks. In the simulation, we keep the network size N = 10000, hki ≈ 6, and the cure rate is also fixed to be γ = 1. Meanwhile, we assume β1 = β2 and the relationship between the steady- state infection density (ρ(∞)) and the effective spreading rate (λ) is plotted in Figure 2. All results are averaged over 20 independent implementations. Figure 2(a) describes the relation between the static infection density and effective spreading rate on scale- free networks. Similarly, from bottom to top, four curves indicate the different cases with β1 = β2 = 0, 0.5, 0.8 and 1.0. Again, the numerical results is ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1789

(a) (b)

Figure 2. Relationship between ρ(∞) and λ on (a) Scale-free; (b) Small world networks qualitatively consistent with the theoretical analysis of Equation (8). It is also shown that the critical threshold on scale-free networks is smaller that that of small-world networks because the heterogeneity is greatly increased in scale-free networks. In Figure 2(b), the simulation on small world networks is carried out. And β1 = β2 is also ﬁxed to be 0, 0.5, 0.8 and 1.0 respectively from bottom to top, and the phase transition is taken place at about 0.16, 0.12, 0.08 and 0. The simulation results agrees well with the analytical form of Equation (14). It’s clearly seen that the infection threshold is largely reduced with the increase of β1 = β2, that is, the infection medium will promote the outbreaks of disease spreading. In addition, the propagation threshold in scale-free networks is much smaller than that for small-world ones, and the result also indicates that the disease is prone to spreading in heterogeneous scale-free networks.

4. Conclusions. In this paper, we present a novel epidemic model with infective medium based on the standard SIRS model. The mean-ﬁeld theory is used to analyze the inﬂuence of infective media on epidemic outbreaks, and the theoretical and numerical simulation results indicate that the media can largely reduce the critical threshold of epidemic spreading. Current results can help us to realize the role of infective media when combating some infectious diseases such as malaria, yellow fever, dengue fever and so on. It is also instructive for us to prevent and control the transmission of other emerging infectious diseases.

Acknowledgment. This work is partially supported by the National Natural Science Foundation of China under Grant Nos. 60904063 and 60774088, China Postdoctoral Sci- ence Foundation under Grant No. 20090460694, the Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20090032110031 and the Devel- opment Fund of Science and Technology for the Higher Education in Tianjin under Grant No. 20090813.

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[3] Y. Moreno, R. Pastor-Satorras and A. Vespignani, Epidemic outbreaks in complex heterogeneous networks, European Physical Journal B, vol.26, pp.521-529, 2002. [4] M. Barthélemy, A. Barrat, R. Pastor-Satorras and A. Vespigani, Dynamical patterns of epidemic outbreaks in complex heterogeneous, Journal of Theoretical Biology, vol.235, pp.275-288, 2005. [5] R. Olinky and L. Stone, Unexpected epidemic thresholds in heterogeneous networks: The role of disease transmission, Physical Review E, vol.70, no.3, pp.030902:1-5, 2004. [6] C. Y. Xia, S. W. Sun, Z. X. Liu, et al., Epidemics of SIRS model with non-uniform transmission on scale-free networks, International Journal of Modern Physics B, vol.23, no.9, pp.2303-2313, 2009. [7] M. Ishikawa, On the spatio-temporal structure in the stochastic diffusive SI model, International Journal of Innovative Computing, Information and Control, vol.6, no.1, pp.63-73, 2010. [8] H. J. Shi, Z. S. Duan and G. R. Chen, An SIS model with infective medium on complex networks, Physica A, vol.387, pp.2133-2144, 2008. [9] A. L. Barabásiand R. Albert, Emergence of scaling in random networks, Science, vol.286, pp.509-512, 1999. [10] M. E. J. Newman, Assortative mixing in networks, Physical Review Letters, vol.89, no.20, pp.208701:1-4, 2002. [11] D. J. Watts and S. H. Strogatz, Collective dynamics of small world networks, Nature, vol.393, pp.440-442, 1998. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1791-1797

OUTPUT FEEDBACK SWITCHING CONTROLLER DESIGN FOR STATE-DELAYED LINEAR SYSTEMS WITH INPUT QUANTIZATION AND DISTURBANCES

Zhaobing Liu1,2, Huaguang Zhang1,2, Qiuye Sun2 and Dongsheng Yang2

1Key Laboratory of Integrated Automation for the Process Industry, Ministry of Education 2School of Information Science and Engineering Northeastern University No. 3-11 Wenhua Road, Heping District, Shenyang 110819, P. R. China [email protected]; [email protected]; { sunqiuye; yangdongsheng }@mail.neu.edu.cn Received February 2010; accepted April 2010

Abstract. In this paper, a dynamic output feedback switching controller for state- delayed linear systems with input quantization and matched disturbances is proposed. The developed controller consists of linear and nonlinear parts, of which the former is constructed with full dynamics to determine the fundamental characteristics of the output feedback, and the latter eliminates the inﬂuence of input quantization and matched disturbances. This means that each component of the latter part is designed as an integer multiple of the quantization level, which maintains the decreasing property of a Lyapunov function and achieves the global asymptotic stability rather than the practical stability, despite the impact of input quantization and matched disturbances. Keywords: Output feedback, Switching controller, Input quantization, Asymptotic stability, Matched disturbances

1. Introduction. Recent years have witnessed a growing interest in investigating effects of signal quantization on feedback control systems, see [1, 2, 3, 4, 5, 6, 7, 8, 9]. This is mainly because of the widespread use in control systems of digital computers that use finite-precision arithmetic. In the field of quantized feedback control, the handling of quantization errors caused by analog-to digital and digital-to analog converters in sensors and actuators or by encoders and decoders in networks-based control systems is a key issue. It is well known that a feedback law which globally asymptotically stabilizes a given system in the absence of quantization will in general fail to provide global asymptotic stability of the closed-loop system that arises in the presence of a quantizer with a finite number of values. As discussed in [2], there are two reasons to account for these changes in the systems behavior. One reason is saturation and another reason is deteri- oration of performance near the equilibrium. So in the presence of quantization errors, asymptotic convergence is impossible. In the existing literature on stabilization problems for quantization feedback systems, there are mainly two approaches. The first approach deals with the dynamic quantizers, which scales the quantization levels dynamically in order to improve the steady-state performance, see [2, 3]. The second approach considers static quantizers such as uniform and logarithmic, see [4, 5, 6, 7, 8, 9]. In this framework, a standard assumption is that parameters of the quantizer are fixed in advance and cannot be changed by the control designer and thus the structures of static quantizers are relatively simple in comparison with dynamic quantizers. We note that in the framework of uniform quantizers, the output feedback control [10, 11, 12] of state-delayed linear systems with input quantization and matched disturbances have not been researched yet. The objective of the present paper is to develop a dynamic

1791 1792 Z. LIU, H. ZHANG, Q. SUN AND D. YANG output feedback switching controller for state-delayed linear systems with input quantization and matched disturbances. The developed controller comprises linear and nonlinear parts. The former part which is designed with full dynamics plays a role in handling the fundamental characteristics of the output feedback. The latter part eliminates the eﬀect of input quantization and matched disturbances. In other words, each component of the latter part is designed as an integer multiple of the quantization level, which maintains the decreasing property of a Lyapunov function. In addition, the states aﬀected by the designed controller achieve the global asymptotic stability rather than the practical stability, despite the impact of input quantization and matched disturbances.

2. Problem Statement. Throughout this paper, kxkp denotes the p-norm, i.e., kxkp , p p 1 n (|x1| + ··· + |xn| ) p , p ≥ 1. When p = ∞, kxk∞ , max1≤i≤n |xi|. R denotes the n-dimensional Euclidean space. Consider a state-delayed linear system with input quantization and matched disturbances:

x˙(t) = Ax(t) + Aτ x(t − τ(t)) + B(Q(u(t)) + d(t)), y(t) = Cx(t), (1) where x(t) ∈ Rn, u(t) ∈ Rm and d(t) ∈ Rm are the state, control input, and the disturbance, respectively. Q(·) is the quantization operator. y(t) ∈ Rl is the measurement output. τ(t) is the time-varying delay with the assumption 0 ≤ τ(t) < ∞,τ ˙(t) ≤ m < 1. For d(t) and Q(·), it is assumed that the following assumptions are valid: Assumption 1: Each component of the disturbance d(t) at time t is bounded by εd(> 0), i.e.,

kd(t)k∞ ≤ εd. (2) Assumption 2: The operator Q(·) is deﬁned by a function round (·) that rounds toward the nearest integer, i.e.,

Q(u(t)) , εuround(u(t)/εu), (3) where εu(> 0) is called a quantizing level and Q(·) is the uniform quantizer with the fixed εu. We note that the quantization error Ou(t) is defined as Ou(t) , Q(u(t))−u(t). Based on the condition (3) and the definition of Ou(t), each component of Ou(t) at time t is bounded by the half of the quantizing level εu,i.e.,

kOu(t)k∞ ≤ εu/2, (4) and the saturation level of the quantization is suﬃcient large. Assumption 3: Rank(CB)=m and the invariant zeros of (A, B, C) ⊂ C −, where C − denotes the left half space of the complex plane. Lemma 2.1. (Ho¨lder’s Inequality). For α, β ∈ Rn, P ≥ 1, and q ≥ 1, the following inequality holds: T −1 −1 |α β| ≤ kαkpkβkq, p + q = 1. (5) For state-delayed linear systems with input quantization and matched disturbances, we design the following controller, which is the goal of this paper:

x˙ c(t) = Acxc(t) + Bcy(t),

uc(t) = Ccxc(t) + Dcy(t),

u(t) = uc(t) +u ¯(xc, y, t), (6) n where xc(t) ∈ R is the controller state, Ac,Bc,Cc, and Dc, are constant controller gain matrices with appropriate dimensions. And uc(t) denotes the linear part of controller and ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1793

m u¯(xc, y, t) ∈ R the nonlinear part, which is related to the switching control component to handle input quantization and disturbances.

3. Main Results. The system (1) can be represented via the auxiliary input-output connections:

x˙(t) = Ax(t) + Aτ x(t − τ(t)) + B(uc(t) +u ¯(xc, y, t) + Ou(t) + d(t)), y(t) = Cx(t). (7) Consequently, the resulting closed-loop system has the form ˙ ξ(t) = Ac1ξ(t) + Ac1τ ξ(t − τ(t)) + Bc1(¯u(xc, y, t) + Ou(t) + d(t)), (8) [ ] [ ] [ ] [ ] x(t) A + BDcCBCc Aτ 0 B where ξ(t) = , Ac1 = , Ac1τ = , Bc1 = . xc(t) BcCAc 0 0 0 We shall now consider quadratic Lyapunov stability with a candidate Lyapunov functional V (ξ(t)), mapping from R2n to R ∫ t V (ξ(t)) = ξT (t)P ξ(t) + ξT (r)ET QEξ(r)dr, (9) t−τ(t) [ ] where P = P T ∈ R2n and Q are positive constant matrices and E = I 0 . In order to facilitate the following analysis, we partition P and P −1 as [ ] [ ] YN − XM P = ,P 1 = , (10) N T ∗ M T ∗ where X,Y ∈ Rn×n, M, N ∈ Rn×n, and ∗ means irrelevant. To guarantee the Lyapunov stability, the derivative of the above functional should satisfy the following inequality condition: V˙ (ξ(t)) = 2ξT (t)P ξ˙(t) + ξT (t)ET QEξ(t) − (1 − τ˙(t))ξT (t − τ(t))ET QEξ(t − τ(t)) < 0. (11)

It is worth noting that in the developed controller (6), the linear part uc(t) determines the fundamental characteristics of the output feedback and the nonlinear partu ¯(xc, y, t) will be chosen to compensate the eﬀect of the quantization error and disturbances, where each component of the nonlinear is designed as an integer multiple of the quantizing level, T ξ (t)Bc1(¯u(xc, y, t) + Ou(t) + d(t)), which makes us choose a new switching function as follows: , T ≡ T T σ(xc, y, t) Bc1P ξ(t) B Y x(t) + B Nxc(t). (12) However, the “output feedback” feature does not allow us to use x(t) to construct the switching function. Therefore, we shall impose the following equality (hard) condition: BT Y ≡ GC, (13) where G is a constant matrix with an appropriate dimension. In this case, the switching function becomes T σ(xc, y, t) , Gy(t) + B Nxc(t), (14) In the following theorem, based on the output feedback switching controller (6), we shall present a new stabilizable criterion for the closed-loop system (8). Theorem 3.1. Based on Assumptions 1, 2, and 3, let us choose the nonlinear part of the , T ≡ T T controller via a switching function σ(xc, y, t) Bc1P ξ(t) B Y x(t) + B Nxc(t) as

u¯i(xc, y, t) , −εuNsgn(σi(xc, y, t)), (15) 1794 Z. LIU, H. ZHANG, Q. SUN AND D. YANG where u¯i(xc, y, t) and σi(xc, y, t) are the ith component of u¯(xc, y, t) and σ(xc, y, t), respectively, sgn(%) is the sign of a scalar %, N = d εu+2εd e, and the operator d%e denotes the 2εu nearest integer greater than or equal to a scalar %. If the following constrained inequalities   2(AX + BCˆ) AˆT + (A + BDCˆ ) A X  h   ∗ 2(YA + BCˆ ) YA I   h  < 0, (16) ∗ ∗ −(1 − m)Q 0 ∗ ∗ ∗ −Q−1

BT Y ≡ GC, (17) ˆ T T ˆ where A = Y (A + BDcC)X + NBcCX + YBCcM + NAcM , B = YBDc + NBc, ˆ T ˆ C = DcCX + CcM , D = Dc, are satisﬁed, then the state x(t) converges to the origin asymptotically. Proof: Considering conditions (8) and (11), we can attain ˙ T V (ξ(t)) = 2ξ (t)P {Ac1ξ(t) + Ac1τ ξ(t − τ(t)) + Bc1(¯u(xc, y, t) + Ou(t) + d(t))} + ξT (t)ET QEξ(t) − (1 − τ˙(t))ξT (t − τ(t))ET QEξ(t − τ(t)) T = 2ξ (t)P {Ac1ξ(t) + Ac1τ ξ(t − h(t))} + 2σ(xc, y, t){u¯(xc, y, t) + Ou(t) + d(t))} + ξT (t)ET QEξ(t) − (1 − τ˙(t))ξT (t − τ(t))ET QEξ(t − τ(t)). (18)

T By utilizing the conditions (2) and (4) and the relations |α β| ≤ kαk1kβk∞ from ˙ Lemma 2.1, it is shown thatu ¯(xc, y, t) in (15) ensures that the second term of V (ξ(t)) is negative,

2σ(xc, y, t){u¯(xc, y, t) + Ou(t) + d(t))}

≤ 2σ(xc, y, t)¯u(xc, y, t) + 2kσ(xc, y, t)k1{kOu(t)k∞ + kd(t)k∞} ≤ −2Nε kσ(x , y, t)k + 2ε kσ(x , y, t)k + ε kσ(x , y, t)k { u( c )1 d }c 1 u c 1 εu + 2εd ≤ −2εu + 2εd + εu kσ(xc, y, t)k1 = 0, (19) 2εu where, by choosing N in (15) as d εu+2εd e and using the relation −d%e ≤ −% for a scalar 2εu % ≥ 0, we can make the second term of V˙ (ξ(t)) negative, Then, V˙ (ξ(t)) can be rewritten as ˙ T T T V (ξ(t)) = 2ξ (t)P (Ac1ξ(t) + Ac1τ ξ(t − τ(t))) − (1 − m)ξ (t − τ(t))E QEξ(t − τ(t)) T T − −1 T −1 T + ξ (t)E QEξ(t) + (1 m) ξ (t)PA1Q A1 P ξ(t) − − −1 T −1 T (1 m) ξ (t)PA1Q A1 P ξ(t) T T − −1 −1 T T = ξ (t)(PAc1 + Ac1P + (1 m) PA1Q A1 P + E QE)ξ(t) − { − −1/2 T − − 1/2 − }T (1 m) A1 P ξ(t) (1 m) QEξ(t τ(t)) × −1{ − −1/2 T − − 1/2 − } Q (1 m) A1 P ξ(t) (1 m) QEξ(t τ(t)) T T − −1 −1 T T = ξ (t)(PAc1 + Ac1P + (1 m) PA1Q A1 P + E QE)ξ(t) < 0, (20) which is equivalent to the following matrix inequality T −1 −1 T T PAc1 + A P + (1 − m) PA1Q A P + E QE < 0, (21) [ ] c1 1 A where A = τ . It is obvious that the condition (21) is a nonlinear matrix inequality 1 0 and is diﬃcult to be solved. So, the following approach will be adopted to transform it ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1795 [ ] [ ] −1 X I into a linear matrix inequality. From (10), PP = I, we can obtain P T = , [ ] [ ] M 0 XI IY further, P = . M T 0 0 N T Deﬁne [ ] [ ] XI IY F = ,F = , 1 M T 0 2 0 N T

then PF1 = F2. By further matrix calculation, the following equations can be obtained F T PA F = F T A F 1 [ c1 1 2 c1 1 ] AX + B (D C X + C M T ) A + B D C = 2 c 2 c 2 c 2 , Y (A + B D C X) + NB C X + YB C M T + NA M T YA + (YB D + NB )C 2 c [2 ] c 2 2 c [ c ] [ 2 c] c 2 T T XI T T Aτ T T X F1 PF1 = F2 F1 = ,F1 PA1 = F2 A1 = ,F1 E = . (22) IY YAτ I

Combining the above equations, the following equations can be deﬁned: ˆ T T ˆ A = Y (A + BDcC)X + NBcCX + YBCcM + NAcM , B = YBDc + NBc, ˆ T ˆ C = DcCX + CcM , D = Dc, (23) where MN T = I − XY . On the other hand, utilizing the tranformation (23), pre and post-multiplying the left- { T } { } hand side inequality (21) by matrices diag F1 ,I and diag F1,I , respectively, the matrix inequality (21) is equivalent to the following linear matrix inequality   2(AX + BCˆ) AˆT + (A + BDCˆ ) A X  τ   ∗ 2(YA + BCˆ ) YA I   τ  < 0, (24) ∗ ∗ −(1 − m)Q 0 ∗ ∗ ∗ −Q−1 otherwise, the parameters of output-feedback controller can be calculated as following −1 ˆ T −1 T −1 −1 Ac = N (A − Y (A + BDcC)X)(M ) − BcCX(M ) − N YBCc, (25) −1 ˆ ˆ T −1 ˆ Bc = N (B − YBDc),Cc = (C − DcCX)(M ) ,Dc = D.

Remark 3.1. There is a diﬃculty in condition (17) in Theorem 3.1. First, equality (17) contains a hard constraint. However, this condition, in fact, can be handled with a simple relaxation technique into the following LMI condition: [ ] γI BT Y − GC 0 < , (26) YB − CT GT γI where γ will be set to an extremely small number related to the computational precision. Remark 3.2. Note that Theorem 3.1 does not present the computation of the controller, but the existence conditions of the controller. To compute the controller, ﬁrst compute some solutions (X,Y ) satisfying LMIs (16) and (26); second compute two full-column- rank matrices M,N through singular value decomposition such that MN T = I − XY.

4. Simulation Studies. In this section, we shall demonstrate the performance of the proposed controller Q(u(t)) = Q(uc(t)+¯u(xc, y, t)) in comparison with the linear controller 1796 Z. LIU, H. ZHANG, Q. SUN AND D. YANG

0.5 Proposed controller Linear controller 0.4

0.3 0.05 (t)

3 0 x 0.2 −0.05 −0.05 0 5 −3 0.05 −5 0 x 10 0.1

0 0.5 1 0 0.5 −0.5 0 −0.5 −1 −1 x (t) x (t) 2 1

Figure 1. Trajectories of the states for the linear controller and the proposed switching controller

Q(u(t)) = Q(uc(t)) that does not compensate for the quantization errors and disturbances. The system parameters are as follows: for x(0) = [ 1 −1 0.5 ]T ,       −3 0 1 0.2 0.1 0.1 0 ( ) 0 1 0 A =  1 2 0  ,A =  0.1 0.15 0.1  ,B =  1  ,C = , τ 1 1 0 0 1 −2 0.1 0.1 0.18 0

τ(t) = 1 + 0.5 sin(t), d(t) = 0.2r(t), r(t) = sin(2πt), εu = 2. (27)

For the data given in (27), we obtain the following additional information:

m = 0.5, εd = 0.2,N = 1. In Theorem 3.1, the solutions calculated by using the Matlab LMI toolbox are as follows:     −83.7289 −68.1414 −788.8867 −5.2082 −8.9493   4   Ac = 13.2228 −71.0508 78.2698 ,Bc = 10 ∗ 1.1439 −2.5247 , −4.9124 20.6408 −26.8743 −0.1838 0.6915 ( ) ( ) Cc = −0.0555 −0.0749 −0.7474 ,Dc = −89.8445 −73.7145 . Figure 1 presents the trajectories of the states for the proposed controller and linear controller. As shown in the ﬁgure, the states in the linear output-feedback controller that does not compensate for the quantization errors and disturbances cannot converge to the origin and remains around a relatively big bound, whereas the states in the proposed controller asymptotically converge to the origin despite quantization errors and matched disturbances.

5. Conclusion. This paper has developed a dynamic output feedback switching controller, based on a uniform quantizer, for delayed-state linear systems with input quantization and matched disturbances. The proposed controller consisted of two control parts: a linear part to determines the fundamental characteristics of the output feedback, while a nonlinear part diminishes the impact of input quantization and matched disturbances. Noticeably, in the case of the proposed controller, the nonlinear part successfully made the states asymptotically converge to the origin despite input quantization and matched disturbances. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1797 Acknowledgment. This work was supported by the 111 Project (B08015), the Na- tional Natural Science Foundation of China (50977008, 60774048, 60904101) and the Special Fund for Basic Scientiﬁc Research of Central Colleges, Northeastern University (N090604005, N090404009). The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

REFERENCES [1] L. Zhou and G. P. Lu, Quantized feedback stabilization for networked control systems with nonlinear perturbation, International Journal of Innovative Computing, Information and Control, vol.6, no.6, pp.2485-2496, 2010. [2] D. Liberzon, Hybrid feedback stabilization of systems with quantized signals, Automatica, vol.39, no.9, pp.1543-1554, 2003. [3] R. W. Brockett and D. Liberzon, Quantized feedback stabilization of linear systems, IEEE Trans- actions on Automatic Control, vol.45, no.7, pp.1279-1289, 2000. [4] D. F. Delchamps, Stabilizing a linear system with quantized state feedback, IEEE Transactions on Automatic Control, vol.35, no.8, pp.916-924, 1990. [5] N. Elia and S. K. Mitter, Stabilization of linear systems with limited information, IEEE Transactions on Automatic Control, vol.46, no.9, pp.1384-1400, 2001. [6] M. Fu and L. Xie, The sector bound approach to quantized feedback control, IEEE Transactions on Automatic Control, vol.50, no.11, pp.1698-1711, 2005. [7] M. L. Corradini and G. Orlando, Robust quantized feedback stabilization of linear systems, Auto- matica, vol.44, no.9, pp.2458-2462, 2008. [8] E. Fridman and M. Dambrine, Control under quantization, saturation and delay: An LMI approach, Automatica, vol.45, no.10, pp.2258-2264, 2009. [9] S. W. Yun, Y. J. Choi and P. Park, H2 control of continuous-time uncertain linear systems with input quantization and matched disturbances, Automatica, vol.45, no.10, pp.2435-2439, 2009. [10] T. E. Jeung, H. J. Kim and B. H. Park, H∞ output feedback controller design for linear systems with time-varying delayed state, IEEE Transactions on Automatic Control, vol.43, no.7, pp.971-974, 1998. [11] P. Park, D. J. Choi and S. G. Kong, Output feedback variable structure control for linear systems with uncertainties and disturbances, Automatica, vol.43, no.1, pp.72-79, 2007. [12] F. Long, C. L. Li and C. Z. Cui, Dynamic output feedback H∞ control for a class of switched linear systems with exponential uncertainty, International Journal of Innovative Computing, Information and Control, vol.6, no.4, pp.1727-1736, 2010.

ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1799-1804

FUZZY VARIABLE OF ECONOMETRICS BASED ON FUZZY MEMBERSHIP FUNCTION

Xiaoyue Zhou1,2, Kaiqi Zou2 and Yanfang Wang2

1Management College China University of Mining and Technology Beijing 100083, P. R. China [email protected] 2College of Information Engineering Dalian University Dalian 116622, P. R. China [email protected] Received February 2010; accepted April 2010

Abstract. Econometrics is the ﬁeld of economics that concerns itself with the application of mathematical statistics and the tools of statistical inference to the empirical measurement of relationships postulated by economic theory. In econometrics, the variable represented by fuzzy set is neglected by the researchers, such as ‘educational level’, ‘a rapid economic development’ and so on. In this paper, a new kind of variable named fuzzy variable is proposed to deﬁne this kind of variable. The gap between fuzzy mathematics and econometrics is connected by the concept of fuzzy variable. At the same time, aiming at the time series with fuzziness, the author presents the fuzzy variable time series and two examples are given to show the forms and usage of them. Keywords: Fuzzy variable, Fuzzy variable time series, Membership function

1. Introduction. Since econometrics was proposed in 1930s it has occupied signiﬁcant status in the research of economic theory. Econometrics should not be taken as synonym with the application of mathematics to economics. It is the uniﬁcation of statistics, economics theory and mathematics that is powerful. Applied econometric methods will be used for estimation of important quantities analysis of economic outcomes, markets or individual behavior, testing theories, and for forecasting. The econometric model is the mathematic expression which describes the relationship among the variables based on the economic theory and the sample. The variables are the dependent or explained variable and the independent or explanatory variables. The dependent variable is the regress and the independent variables are the regressors in [1,2]. In the classical econometrics, the independent variables include exogenous variable, lagged dependent variable and dummy variable. But a kind of variable is always neglected which is the variable with fuzziness. For example, we would expect, on average, higher levels of education to be associated with higher incomes. That will lead a higher consumption. We can get the regression model of consumption, income and educational level which can be expressed by the equation of C = β1Y + β2EDU + ε. Here, C is people’s consumption, Y is income, EDU is the educational level and β1 and β2 are the marginal propensity to consume and the elasticity of educational level. The level of education should be expressed with fuzzy language such as ‘high’, ‘not high’, ‘low’, and so on or the grade of membership. That means it should be a variable represented by fuzzy sets. But some researchers take the ratio of the graduates to the population representing the educational level in [3]. If we take this variable into this function, the elasticity of

1799 1800 X. ZHOU, K. ZOU AND Y. WANG educational level is low. The importance of educational level is not shown enough. But if we take the fuzzy variable of the educational level, the elasticity is higher and the equation gets more close to the real world. In the work of [4-6], Song and Chissom presented the theory of fuzzy time series to overcome the drawback of the classical time series methods. They defined the universe of discourse and proposed the fuzzy set and fuzzy relationship. In [7-10], the authors deal with the forecasting problems under a fuzzy environment and they get some fuzzy inferential rules. This method is different from any stochastic methods. But these fuzzy time series are difficult to be used in econometrics. In order to find the variables with fuzziness for econometrics we have to seek after new ways. In this paper the author presents the fuzzy variable time series to solve this problem. This paper is divided into four parts: the first part introduces the data of econometrics and the definition of fuzzy variable is proposed. Then two examples are given to show how to get fuzzy variable time series and apply them into econometrics.

2. The Data of Econometrics. There are several data in econometrics that are very important to the empirical models. (1) The common data i. Time series data ii. Panel data iii. 0-1 variable data (2) Fuzzy variable data Fuzzy variable data are the variable data that possess fuzziness. In econometrics, some time series data are fuzzy such as the ‘educational level’, and so on. But most fuzzy time series are defined by a ratio and it is not objective enough. Since these data have characteristics, nothing but fuzzy logic can be applied. Fuzzy mathematics was proposed by Professor Zadeh in 1960s. It aims at the fuzzy phenomenon and solves the problem with precise mathematic method. It has been used in many fields such as cybernetics, data mining, and so on (see [11,12]). In this paper the author proposes the fuzzy variables to define the variable with fuzziness and the data expression of the fuzzy variables are the grade of membership. In practice, some concepts are fuzzy such as ‘young person’. We can’t arbitrarily say a 30-year-old man is ‘young’ or ‘not young’. In fact a grade is usually defined to assess how much he belongs to the set of ‘young person’. The grade that he belongs to the fuzzy set ‘young person’ is called the grade of membership. The data of fuzzy time series should be fuzzy grades of membership and it is related with fuzzy membership function. We define the fuzzy time series as fuzzy variable time series. We need define the fuzzy membership function according to the research purpose. The membership function is a function from universe of discourse U to [0, 1]. In practice, there are some methods to get the fuzzy membership functions in [13,14]. i. If the fuzzy set reflects the normal consciousness such as ‘young person’, ‘economy increases fast’ and so on, the fuzzy statistics method is suited to get the membership function. ii. We can use the DELPHI method to get the membership function of a fuzzy set such as an expert values a feasibility of a project. iii. If a fuzzy concept is combined with some fuzzy factors we can solve the membership function of these factors and then colligate the membership function of the fuzzy concept. This method is called factor weighted method. Let the universe of discourse be a Descartes product of n factor sets, that is

U = U1 × U2 × ... × Un ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1801

Let Ai ∈ F(Ui)(i = 1, 2, . . . , n), Ai ∈ F(Ui) here A is composited by A1, A2, ..., An.

Let ∑n µA(u) = δi · µA (ui) i=1 i ∈ u =∑ (u1, u2, . . ., un) U;(δ1, δ2, . . ., δn) is the weighted vector and they satisfy the equation n of i=1 δi = 1. δi represents the significance of factor i. In this paper we define fuzzy variable time series by weighted-average method. Definition 2.1. Let u ∈ U. µA : U → [0, 1] is a mapping from U to the interval [0,1] and A is called a fuzzy subset in U. µ is called the membership function of A and written by µA. The value of µA(u) represents the fuzzy grade of membership u in A and it shows the grade that u belongs to A in [15].

Deﬁnition 2.2. Let auij be the time series of a variable of period j in a model.

µA : U → [0, 1]

µ is the membership function of A. The value of µA(ui) is the grade of membership of ui to A. Let ∑ n a · µ (u ) z = i=1∑ uij A i j n a ∑ i=1 uij n Here u = 1, 2, . . ., n, i=1 auij is the sum of auij of period j. zj is called the fuzzy variable time series of period j. 3. Two Examples. (1) The membership function of A is discrete. The regression model of the consumption, income and educational can be expressed by the equation of C = β1Y + β2EDU + ε. Here C is people’s consumption, Y is income, EDU is the educational level and β1 and β2 are the marginal propensity to consume and the elasticity of educational level. The level of education should be expressed with fuzzy language such as ‘high’, ‘not high’, ‘low’, and so on or the grade of membership. That means it should be a variable represented by fuzzy sets. Based on the weighed-average method we take the fuzzy variable time series to deﬁne the fuzzy variables.

Let au1j, au2j, au3j, au4j, au5j, au6j, be the number of graduates of the graduates, universities or colleges, senior high schools, vocational schools, junior high schools and elementary schools of year j. A is a fuzzy set of ‘educational level is high’ and we can deﬁne µA(u1) = 1, µA(u2) = 0.9, µA(u3) = µA(u4) = 0.7, µA(u5) = 0.4, µA(u6) = 0.1. Here the membership function of A is discrete. We can get the fuzzy variable time series by ∑ 6 a · µ (u ) i=1∑ uij A i zj = 6 i=1 auij The fuzzy variable time series of ‘educational level’ are shown:

z1990 = 0.2722, z1991 = 0.2689, z1992 = 0.2711, z1993 = 0.2748, z1994 = 0.2716, z1995 = 0.2753, z1996 = 0.2813, z1997 = 0.2881, z1998 = 0.2889, z1999 = 0.2826, z2000 = 0.2846, z2001 = 0.2917, z2002 = 0.3031, z2003 = 0.3205, z2004 = 0.3407, z2005 = 0.3637, z2006 = 0.3807, z2007 = 0.3957. ∑ 6 i=1 auij is the total number of auij of graduates in period j. 1802 X. ZHOU, K. ZOU AND Y. WANG

Figure 1. Fuzzy variable time series of educational level from year 1990 to 2007

The graph of educational level is shown as Figure 1. The educational level of China has been mounting up from 1990s. Especially after 2000, the whole educational level raised up quickly because the government pays much attention to the edbiz. More and more people wake up to the importance of education of the whole nation. The consumption function that generated with software eviews is shown as:

LNCONSUME = 0.6627 ∗ LNINCOME + 2.4949 ∗ EDUCATION + 13.2241

The marginal propensity to consume is 0.6627 and the elasticity of educational level is 2.4949. That means if the educational level increases 1%, the consumption of our country increases 2.49%. The educational level of our country is very signiﬁcant to people’s consuming. But if we take the ratio of the graduates to the population representing the educational level we will get the equation shown as:

LNCONSUME = 0.6681 ∗ LNINCOME + 0.01153 ∗ EDUCATION + 13.8755

The elasticity of educational level is 0.01153 which shows that the educational level is not important to the consumption. The root of this problem is that the analyst neglects the people whose educational level is not university. But the consumption is the whole nation’s consumption. (2) The membership function of A is continuous. Today the percentage of old population in China becomes larger and larger with the development of economy and medical undertaking. In a general way, the larger the percentage of old population in a country, the more demand for life insurance. Not only old people but also young people need life insurance products, so it is necessary to consider the demand of whole population when we study the demand for life insurance. The author take the fuzzy set A ‘not young’ to express the ageing of population.

Let auij be the population of age ui and year j. A is deﬁned as the fuzzy set ‘not young’ and µA(ui) is the grade of membership of ui to A. Consider Zadeh’s membership function ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1803 of ‘aged’, the membership function of age u to fuzzy set A ‘not young’ is deﬁned as  [ ( ) ]−  2 1  26 − 25  1 − 1 + if ui ≤ 26  5 [ ] ( ) −1 µA(ui) =  u − 25 2  1 − 1 + i if 27 ≤ u ≤ 79  i  5 1 if ui ≥ 80 Here the membership function of A is continuous. We put ∑ n a · µ (u ) i=1∑ uij A i zj = n i=1 auij here zj is called the fuzzy∑ variable time series of year j and it represents the ageing of n population of our country. i=1 auij is the whole population of year j and n is the upper of age. The fuzzy variable time series zj from year 1995–2007 are shown as

z1995 = 0.4409, z1996 = 0.5181, z1997 = 0.4715, z1998 = 0.4837, z1999 = 0.4946, z2000 = 0.5064, z2001 = 0.5131, z2002 = 0.5267, z2003 = 0.5464, z2004 = 0.5487, z2005 = 0.5022, z2006 = 0.5227, z2007 = 0.5162.

4. Conclusions. The techniques used in econometrics have been employed in a widen- ing variety of ﬁelds, including political methodology health economics, medical research, transportation engineering and numerous others. But the variables with fuzziness are always neglected. The author proposed a new kind of variable named fuzzy variables with weighted-average method. The gap between the econometrics and fuzzy mathematics is bridged by the concept of fuzzy variable. It will lead a more objective method for econometrics.

Acknowledgment. This work is supported by the Natural Science Funds of China (60873042).

REFERENCES

[1] F. Hayashi, Econometrics, Shanghai University of Finance and Economics Press, Shanghai, 2005. [2] W. H. Greene, Econometric Analysis, China Renmin University Press, Beijing, 2004. [3] L. J. Fu, Panel data analysis in econometrics of china insurance demand, Journal of Harbin Senior Finance College, no.4, pp.33-35, 2004. [4] Q. Song and B. S. Chissom, New models for forecasting enrollments: Fuzzy time series and neural network approaches, Annual Meeting of the American Educational Research Association, pp.12-16, 1993. [5] Q. Song and B. S. Chissom, Fuzzy time series and its models, Fuzzy Sets and Systems, vol.54, pp.269-277, 1993. [6] Q. Song and B. S. Chissom, Forecasting enrollments with fuzzy time series-part 2, Fuzzy Sets and Systems, vol.62, pp.1-9, 1994. [7] S. Chen, Forecasting enrollments based on fuzzy time series, Fuzzy Sets and Systems, vol.81, pp.311- 319, 1996. [8] T. A. Jilani, S. M. A. Burney and C. Ardil, Fuzzy metric approach for fuzzy time series forecasting based on frequency density based partitioning, Proc. of World Academy of Science, Engineering and Technology, vol.23, pp.333-338, 2007. [9] M. F. Wu and X. Jiang, Forecasting model based on fuzzy time series with an example to Shanghai stock index, Value Engineering, no.11, pp.165-168, 2008. [10] B. Wu and Y. C. Lin, Fuzzy time series analysis and forecasting: With an example to Taiwan weighted stock index, ACTA Mathematical Appliatae Sinaca, vol.25, pp.67-76, 2002. [11] C.-C. Chou, Application of a fuzzy MCDM model to the evaluation of plant location, International Journal of Innovative Computing, Information and Control, vol.6, no.6, pp.2581-2594, 2010. 1804 X. ZHOU, K. ZOU AND Y. WANG

[12] F.-T. Lin and T.-R. Tsai, A two-stage genetic algorithm for solving the transportation problem with fuzzy demands and fuzzy supplies, International Journal of Innovative Computing, Information and Control, vol.5, no.12, pp.4775-4785, 2010. [13] A. G. Li, Z. H. Zhang, Y. Meng and C. Gu, Fuzzy Mathematics and its Applications, Metallurgical Industry Press, Beijing, 2005. [14] L. Y. Han and P. Z. Wang, Applied Fuzzy Mathematics, Capital University of Economic and Trade, 1989. [15] L. A. Zadeh, Fuzzy sets, Information and Control, no.8, pp.338-353, 1965. [16] X. T. Zhang, A Guide to Using Eviews, China Machine Press, Beijing, 2007. [17] http://www.stats.gov.cn/. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1805-1810

APPLYING IMAGE PROCESSING TECHNIQUE TO RADAR TARGET TRACKING PROBLEMS

Kuen-Cheng Wang1, Yi-Nung Chung1, Chao-Hsing Hsu2 and Tsair-Rong Chen1 1Department of Electrical Engineering National Changhua University of Education No. 2, Shi-Da Road, Changhua City 500, Taiwan [email protected] 2Department of Electronic Engineering Chienkuo Technology University Changhua 500, Taiwan [email protected] Received February 2010; accepted April 2010

Abstract. Data association plays an important role in a radar multiple-target tracking (MTT) system. An approach for data association using image information is investigated in this paper. An algorithm applying the Competitive Hopﬁeld Neural Network (CHNN) is developed to match between radar measurements and existing target tracks. If target maneuvering situations are occurred, an adaptive maneuvering estimator denoted dynamic multiple-model estimator is applied to solve the estimation problems. According to the simulation results, this algorithm can solve the multiple-target tracking problems successfully. Keywords: Data association, Image information, Competitive Hopﬁeld neural network

1. Introduction. Data association is the key technique for a radar tracking system. Many authors presented the data association algorithms, for example, the Joint Proba- bilistic Data Association method suited for a high false target density environment was investigated in [1]. Another approach using traditional Hopfield Neural Network, which took weighted objective cost and constraints into an overall energy function was presented in [2]. This approach had one problem that the weighting values between the objective cost and constraints in the overall energy function were very difficult to be properly determined. An improved algorithm denoted Competitive Hopfield Neural Network-based was developed in [3]. In this algorithm, it was found that the approach could reduce the burden of determining the proper weighting factors as in [2]. The data association algorithms addressed above only use the quantity data to determine the correlation between the measurements and the existing targets. However, in a dense target environment, some targets can be very close to each other. The measurements produced by these close targets can confuse data association computation algorithms and result in inaccurate target association. If there is more information offered for radar systems, the tracking results should be more accurate. In this paper, an approach using both quantity data and image information is developed. In order to combine these two different attributes, a fusion algorithm based on the Competitive Hopfield Neural Net- work [4] is applied to match between radar measurements and existing targets. Moreover, target maneuvering situations usually cause severe tracking error, if the tracking system does not apply maneuvering estimation algorithms. In this paper, an adaptive maneuvering compensator denoted dynamic multiple-model estimator [5] is applied to modify the parameters of the tracking filter and the maneuvering problems will be solved also.

1805 1806 K.-C. WANG, Y.-N. CHUNG, C.-H. HSU AND T.-R. CHEN 2. The Image Processing. In this tracking algorithm, the image processing is adopted to identify the contour of the targets. The process of main works for conducting image processing is shown in Figure 1. In order to eﬀectively determine the attribute of targets, the preprocessing step is used with image processing methods to determine the features of targets.

Figure 1. Image identiﬁcation process

(1) Gray transformation and spatial filtering: In order to enhance the computation efficiency, when the sensor obtains the target images, the gray level can be obtained by using Equation (1). Y = 0.299FR + 0.587FG + 0.114FB (1) where Y is the image gray level, FR is the red color level, FG is the green color level, and FB is the blue color level, respectively. After the gray level of image is obtained, the spatial filtering or the neighborhood processing [6] is conducted to reduce the noise and enhance the edge of target image. Usually, the low pass filter is used at first. However, if the filtering result is not quite well, then the noise can be reduced more effectively by using the median filter. (2) Segmentation: This process is used to abstract the figures of the targets from the background of the image. The thresholding method is adopted here to get rid of the noise and the hole from the figure of the target in order to get a complete binary image. After the contour is obtained in Cartesian coordinates, the invariant moment of the contour can be found by using Equation (2). Contour = image − (image SE) (2) After obtaining the binary images which are eroded by the structuring elements, the contour skin of the image of the target can be removed. After the contour is obtained, the features of each kind of target can be determined by calculating the invariant moment of the contours of the targets. Different kinds of targets have different moments. (3) Coordinate transformation: The image of target may have different feature, therefore we need operate the coordinate transformation to match the relation of images. The operations include shift, enlarge, shrink, and rotation. The operations can be conducted ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1807 by multiply the following matrices. Assume the original coordinate system is x-y plane and the changed coordinate is (x’, y’).  1 0 0 (i) Shift transformation matrix:  0 1 0  ∆x ∆y 1   sx 0 0   (ii) Enlarge and shrink transformation matrix: 0 sy 0  0 0 1 cos θ sin θ 0 (iii) Rotation transformation matrix:  − sin θ cos θ 0  0 0 1 (4) Template matching After operating the segmentation and coordinate transformation, the cross correlation coefficient between the image of measurement and image of existing target can be obtained by using the template matching. The cross correlation coefficient can be calculated by Equation (2). K∑−1 (Ti − mT )(Si − ms) i=0 RTS = √ √ (3) K∑−1 K∑−1 2 2 (Ti − mT ) (Si − ms) i=0 i=0 where RTS: Cross correlation coefficient Ti: The i-th pixel of template image Si: The i-th pixel of measurement image mT : The average value of pixel of template image mS: The average value of pixel of measurement image In the simulation, we apply the proposed image processing to match the F-16 airplane. The template image of F-16 is shown in Figure 2.

Figure 2. F-16 template image

3. Fusion Algorithm Based on Competitive Hopfield Neural Network. After the image processing, one fusion algorithm denoted Competitive Hopfield Neural Network is applied to perform the data association computation to match the radar measurements and existing targets. Assume that the Vx,i denotes the binary state of the (x, i)th neuron 1808 K.-C. WANG, Y.-N. CHUNG, C.-H. HSU AND T.-R. CHEN and Tx,i;y,j denotes the interconnection strength between neuron (x, i) and neuron (y, j). A neuron (x, i) in this network receives weighted inputs Tx,i;y,jVy,j from each neuron (y, j) and a bias input Ix,i from outside. Thus, the total input to neuron (x, i) is computed as ∑n ∑m Ux,i = Tx,i;y,jVy,j + Ix,i (4) y=1 j=1 The Lyapunov function of the Hopfield network given by ∑n ∑n ∑m ∑m ∑n ∑m E = − Tx,i;y,jVx,iVy,j − 2 Ix,iVx,i (5) x=1 y=1 i=1 j=1 x=1 i=1

By applying the network to data association, let the state of Vx,i denote an association status between the x-th radar measurement and the i-th target, with “1” and “0” indicating associated and not associated, respectively. Then the objective function used for obtaining measurements and radar targets association with the best decision is given by ∑n ∑m ∑n ∑n ∑m ∑m E = A dx,iVx,i + B Vx,iVy,jδx,i x=1 i=1 x=1 y=1 i=1 j=1 ( ) (6) ∑m ∑n ∑n ∑m + C Vx,i − 1 + D Fx,iVx,i i=1 x=1 x=1 i=1

The distance dx,i is then defined as  [ ]  τ T (k)s(k)−1τ(k) 1/2 if x =6 i and x > m ∞ 6 ≤ ≤ dx,i =  if x = i and 1 x m (7) r if x = i where τ(k) is innovation, S(k) is the covariance matrix of the innovation, and r is the radius of gate. Fx,i is the cross correlation coefficient between measurement image and true target image. The second term in Equation (6) attempts to ensure that each measurement can be associated with only one target. The third term forces the condition that each target has one and only one associated measurement. The parameters A, B, C and D specify the important factors in the objective function. In order to reduce the burden of determining the values of the weighting factors, a competitive winner-take-all updating is proposed as follows: { 1, if U = max {U ······ U } V = x,i 1,i n,i (8) x,i 0, otherwise With this modified updating rule, the hard constraint that each target should be associated with one and only one measurement will be automatically embedded inside the network evolution results. As such, the third term can be subsequently removed from the objective function. Thus, the objective function can be further simplified as follows: ∑n ∑m ∑n ∑n ∑m ∑m E = (Adx,i + DFx,i) Vx,i + B Vx,iVy,jδx,y (9) x=1 i=1 x=1 y=1 i=1 j=1 It is also worth noting that once the competitive winner-take-all updating is applied, with A and D set to be 1, B can be easily set to be the radius of gate, r which is a relatively constant. Therefore, the network would be avoided from trapping into irrational solutions. Comparing the resultant objective function in Equation (9) with the Lyapunov function of the Hopfield network in Equation (5), it can be obtained that Ad + DF I = x,i x,i (10) x,i −2

Tx,i;y,j = −Bδx,y (11) ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1809 4. Dynamic Multiple-Model Estimator. In this paper, we apply a maneuvering estimation algorithm together with an adaptive procedure denoted dynamic multiple-model estimator [5] which can modify the tracking filter to allow the maneuvers to be tracked without diverging or severely distorting the estimate. In this approach [5], the possible maneuver hypotheses are assumed for each of the tracking targets. Then, we apply Kalman filtering technique to make the state estimation based on the corresponding likelihood function shown as Equation (12). { } k−1 k−1 1 1 −1 p(Z(k) β ,Z ) = exp − /2τ(k)S (k)τ(k) (12) (2π)M/2 |S(k)|1/2 The proposed algorithm consists of an equivalent bank of Kalman filters which will estimate the target’s acceleration if the situation of maneuvering is occurred. Based on this approach, the most approximate target’s acceleration will be estimated. After the acceleration has been estimated, it is applied to modify the parameters of the tracking filter. With this approach, the radar system will obtain more accurate estimations for the multiple maneuvering target tracking.

5. Simulations. In the simulations, two kinds of information are offered. The quantity data is computed by using Kalman filters to estimate the state vector Xˆ(k |k) recursively. The image information is conducted by proposed image processing. The results of tracking multiple targets in the planar case are simulated by using two different methods. In the simulation, two targets is chosen with the initial conditions as listed in Table 1. The maneuvering situations for the target are shown in Table 2. We assume all the noise to be uncorrelated. In the simulation, we apply two different data association techniques namely, the one-step conditional maximum likelihood and the proposed algorithm in this paper for comparison. For tacking targets with maneuvering situations, we employ the adaptive compensation procedure. The simulation result is shown in Figure 3. The tracking RMS errors of positions and velocities are shown in Table 3. From Table 3, we can see that the proposed algorithm demonstrates better performance, with smaller averaged position errors and velocity errors, than other method.

Figure 3. Typical simulation results of tracking two target 1810 K.-C. WANG, Y.-N. CHUNG, C.-H. HSU AND T.-R. CHEN Table 1. Initial conditions of tracking two targets

x(m) x˙ (m/s) y(m) y˙(m/s) Target 1 2000 550 15000 0 Target 2 2000 550 25000 0

Table 2. Maneuvering status of tracking two targets

Step 25∼45 step 60∼80 step other step a(x) a(y) a(x) a(y) a(x) a(y) Acceleration (m/s2) (m/s2) (m/s2) (m/s2) (m/s2) (m/s2) Target 1 0 20 35 –45 0 0 Target 2 0 –20 35 45 0 0

Table 3. RMS error of tracking two targets

Position error (m) Velocity error (m/s) Target 1 133.8 32.1 Method 1 Target 2 135.3 31.8 Target 1 113.1 26.3 Method 2 Target 2 108.6 27.6

6. Conclusions. In this paper, a data association algorithm using the image information is developed. A fusion algorithm denoted the Competitive Hopﬁeld Neural Network algorithm is applied to combine the quantity data and image information. The advantage of this approach is that if there is more information oﬀered for radar systems, the tracking results will be more accurate. Based on the simulation results, the proposed approach has more accurate tracking results when tracking maneuvering targets. Acknowledgement. The work was supported by the National Science Council under Grant NSC 96-2622-E-018-006-CC3.

REFERENCES [1] K. C. Chang, C. Y. Chong and Y. Bar-Shalom, Joint probabilistic data and association distributed sensor networks, IEEE Trans. Automa. Contr., vol.AC-31, pp.889-897, 1986. [2] D. Sengupta and R. A. Iltis, Neural solution to the multitarget tracking data association problem, IEEE Trans. Aerosp. Electron. Syst., vol.25, pp.86-108, 1989. [3] Y. N. Chung, P. H. Chou, M. R. Yang and H. T. Chen, Multiple-target tracking with competitive hopﬁeld neural network-based data association, IEEE Trans. Aerosp. Electron. Syst., vol.43, no.3, pp.1180-1188, 2007. [4] P. C. Chung, C. T. Tsai, E. L. Chen and Y. N. Sun, Polygonal approximation using a competitive hopﬁeld neural network, Pattern Recognition, vol.27, no.11, pp.1505-1512, 1994. [5] Y.-N. Chung, T.-C. Hsu, M.-L. Li, T.-S. Pan and C.-H. Hsu, A dynamic multiple-model estimator and neural algorithm for radar system, International Journal of Innovative Computing, Information and Control, vol.5, no.12(B), pp.4809-4817, 2009. [6] R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd Edition, Prentice Hall, 2002. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1811-1816

FAULT DETECTION AND DIAGNOSIS FOR PROCESS CONTROL RIG USING ARTIFICIAL INTELLIGENT

Rubiyah Yusof1, Ribhan Zafira Abdul Rahman2 and Marzuki Khalid1

1Center for Artiﬁcial Intelligence and Robotics (CAIRO) Universiti Teknologi Malaysia Jalan Semarak, Kuala Lumpur 54100, Malaysia [email protected]; [email protected]

2Department of Electrical and Electronics, Faculty of Engineering Universiti Putra Malaysia Serdang, Selangor 43400, Malaysia [email protected] Received February 2010; accepted April 2010

Abstract. This paper focuses on the application of artiﬁcial intelligent techniques in fault detection and diagnosis. The objective of this paper is to detect and diagnose the faults to a process control rig. Fuzzy logic with genetic algorithm method is used to develop fault model and to detect the fault where this task is performed by using the error signals, where when error signal is zero or nearly zero, the system is in normal condition, and when the fault occurs, error signals should distinctively diverge from zero. Meanwhile, neural network is used for fault classiﬁcation where this task is performed by identifying the fault in the system. Keywords: Fault detection and diagnosis, Fuzzy logic, Genetic algorithms, Neural network, Process control

1. Introduction. With the proliferation of computers and their integration into activities of daily existence, one formidable problem is to build a computer that can monitor process control system components, diagnose faults detected and provide solutions without human intervention. Associated with an increasing demand for high performance as well as for more safety and reliability of dynamic systems, and a natural trend toward system automation, fault detection and diagnosis is becoming a strategic necessity as a result of increasing economic and environmental demands. Classical methods such as dynamic models of the process are used for the fault detection. They are often monitored using estimation techniques [1,2] or parity equations [3,4] because faults are supposed to appear as state changes caused by malfunctions. The residual signals will generate by comparing the behaviours of the model and real system, which, in the presence of faults, take non-zero values. Some of researchers investigated very intensively the rule-based expert systems have also been investigated for fault detection and diagnosis problems [5,6]. However, these systems need an extensive database of rules and the accuracy of diagnosis depends on the rules. In recent years, a neural networks (NN) has been widely applied in the field chemical engineering, in process control, and as a powerful tool of function approximation and pattern recognition [7]. NN also were studied and applied to fault detection and diagnosis problem. NN have been used either as predictor or dynamic models for the fault diagnosis and pattern classifiers for fault identification. Other researchers have been found which related to the elements in this research. Fekih et el. [8] describe about system identification techniques for nonlinear system by using

1811 1812 R. YUSOF, R. Z. ABDUL RAHMAN AND M. KHALID neural networks for fault detection with the speciﬁc goal of residual generation. Mean- while, Wang et el. [9] investigates the problem of robust fault detection for discrete-time switched systems with state delays where the system will guarantees both sensitivity to faults and robustness to disturbances. In this paper, we develop model based fault detection and diagnosis. Fuzzy modeling, genetic algorithm and recursive least square was combined to represent the fault models. Meanwhile, a neural network is used for fault diagnosis system.

2. Methodology. In this research, model based fault diagnosis is used for fault detection and diagnosis. Figure 1 shows the general structure of diagnosis system [10]. The diagnosis consists of two sequential steps: residual generation and residual evaluation. In ﬁrst step, a number of residual signals are generated in order to determine the state of the process. In this step, the fault models need to be developed in order to generate the residuals. On developing fault model, this paper will used Takagi Sugeno Fuzzy Model with genetic algorithm and recursive least square same as technique from Rubiyah et al. where the proposed technique is used to estimated the fault model from the real system [11-13]. After the fault model was developed, the residual will generated as Subsection 2.1. The next step, neural network is used for residual evaluation to isolate the faults. The objective of fault isolation is to determine if a fault has occurred and also the location of the fault, by analyzing the residual vector.

Figure 1. The general structure of diagnosis system

2.1. Residual generation. This block is used to compute residuals by using the available measurements from the monitored system to generate residual signals. This residual (fault symptom) should indicate any fault occurrence. If the fault symptom is always zero or near to zero, that means there is no fault condition. However if fault symptom is not zero, that means the fault occurs. The diagram for generating residuals is shown in Figure 2. Table 1 shows the fault type and fault injection method for twelve faults applied to the system.

Figure 2. Residual generation ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1813

e = f(X) − g(X) where X = set of inputs f(X) = output of actual system g(X) = output of system model e = residual signal

Table 1. Fault type and fault injection method for twelve faults

Fault Fault Type Fault Injection Method 1 Fault Free None 2 Heater Fault Disconnect wire at DAQ to heater Low inlet flowrate of the water 3 Decrease primary valve opening to 5-20% from the heating element High outlet flowrate of the water 4 Increase primary valve opening to 40-50% from the heating element 5 Level sensor faulty Disconnect wire at DAQ from level sensor 6 Secondary flow sensor faulty Disconnect wire at DAQ from flow sensor 7 Primary flow sensor faulty Disconnect wire at DAQ from flow sensor Disconnect wire at DAQ from temperature 8 Temperature sensor T faulty c sensor Disconnect wire at DAQ from temperature 9 Temperature sensor T faulty h sensor Disconnect wire at DAQ from temperature 10 Temperature sensor T faulty he sensor Low inlet flowrate of the water 11 Decrease valve opening to 20-25% in the compartment tank Open solenoid valve 3 at the bottom of the 12 Compartment tank leaking tank

2.1.1. The TS fuzzy model. The structure of the TS fuzzy model consists of three main components: the antecedent part, the rule base and the consequent part. Input variables are represented by membership functions as in the standard fuzzy system. In the consequent part, mathematical functions are used instead of membership functions. The structure can be seen as a combination of linguistic and mathematical regression modeling. In this paper, GA is used for the optimization of the parameters of the Gaussian membership function at the antecedent part of the fuzzy model. Meanwhile, the RLS approach is used to obtain the parameters of the membership functions in the antecedent part. It is one member of a family of prediction error identiﬁcation that is based on the minimization of prediction error functions.

2.2. Residual evaluation. This block examines residuals for the likelihood of faults and decision rule is then applied to determine if any faults have occurred. So, the aim of residual evaluation step is the reliable identification and classification of the different process states and phase. The difficulty in this step is the assignment of the relevant residual to the corresponding process phases. There are several methods for implementing residue evaluation, e.g. statistical methods, Fuzzy Logic (FL) systems, neural networks and expert systems [14]. In this paper, neural network is used to classify the fault in the system. 1814 R. YUSOF, R. Z. ABDUL RAHMAN AND M. KHALID 2.2.1. The artificial neural network. Artificial Neural Network (ANN) is the term used to describe a computer model to simulate human brain. It is a system loosely modeled on the human brain. It consists of a set of interconnected simple processing unit which combine to output a signal to solve a certain problem based on the input signal it received. The interconnected simple processing unit has adjustable gains that are slowly adjusted through iterations influenced by the input-output patterns given to the ANN. In this paper, back propogation neural network with multilayer perceptron (MLP) is used. A multilayer perceptron is shown in Figure 3. It is a net with one or more layers of node (also called hidden units) between the input units and output units. There are four input residuals from the fuzzy model have been entered to the input layer, and then will be forwarded to fifteen hidden layers and at last will go to twelve output layer. The twelve output layer is chosen because of there are twelve fault need to classify in this paper.

Figure 3. A multilayer neural network

3. The Process Control Rig. The components involved in this research under study are sump tank, compartment tank, heating element, heat exchanger, cooling radiator, centrifugal pump and pump from heat exchanger to heating element. The instruments involved in the process control rig that connected to the computer are five temperature sensors, two flow sensors, level sensor, two servo valves, solenoid valve, heater, and data acquisition card. Figure 4 shows the schematic of process control rig. The inputs of the systems consist of 3 manipulated variables: heat supply (Q), heating element flowrate (qh), sump tank flowrate (qc), and 4 controlled variables: temperature of heating element (The), temperature of hot water from heat exchanger (Th), temperature of cold water from heat exchanger (Tc), level of compartment tank (h). The selection of the input variables is based on a physical knowledge of the process.

4. Result and Discussion. Figure 5 shows the residuals graph of every fault in the systems. These residuals are obtained from the four models from the system for twelve faults occurred in the system as Table 1. For example, the first 388 data from the graph is fault 1 where the system is in normal condition. The residuals show that all are nearest zero values. The next example is for fault 2, the data from 399 to 786, where there are faulty on heater, will affect the temperature value as shown in the graph. The residuals for The,Th and Tc all are distinctively diverging from zero. The next stage of this paper is residual evaluation. In this stage, the faults are classified according to their symptoms and faults. The supervised learning, by using back- propagation method is used. The target pattern is same as the number of faults. For example, if fault equal to 1, the target is equal to 1, if fault 2 and so on until fault 12. The result for the fault classification is shown in Table 2. The result shows that the overall accuracy is increase when the number of epoch increases. The choice of learning rate and ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1815

Figure 4. Process control rig

Figure 5. Residual generation for every fault momentum rate is important. Trying and error method is used to get the best learning rate and momentum rate. If the learning rate is too high, maybe there are a missing data in learning process because the learning is too fast.

Table 2. Fault classiﬁcation using neural networks

Epoch 1000 3000 3000 3000 3000 Learning Rate 0.2 0.2 0.7 0.1 0.1 Momentum Rate 0.5 0.5 0.007 0.007 0.5 Training MSE 0.1334 0.1049 0.1321 0.0850 0.0903 Overall Accuracy (%) 90.01 92.22 86.19 92.92 92.72

5. Conclusion. This paper has shown successful fault detection and diagnosis of a process control rig based on TS type of fuzzy model with GA and RLS approach and neural networks. TS with GA and RLS are used to model the fault and to generate the residuals data and neural networks is used to classify the faults. 1816 R. YUSOF, R. Z. ABDUL RAHMAN AND M. KHALID

REFERENCES [1] A. S. Willsky, A survey of design methods for failure detection in dynamic systems, Automatica, vol.12, 1976. [2] R. Isermann, Process fault detection based on modeling and estimation methods: A survey, Auto- matica, vol.20, 1984. [3] J. Gertler, Generating directional residuals with dynamic parity equations, Proc. of the IFCA/IMACS Symp., Baden, 1991. [4] R. J. Patton and J. Chen, Parity space approach to model based fault diagnosis: A tutorial survey and some new results, Proc. of the IFAC/IMACS Symp., Baden, 1991. [5] M. A. Kramer, Malfunction diagnosis using quantitative models with non-boolean reasoning in expert systems, AIChE, vol.33, no.1, pp.130-140, 1987. [6] S. H. Rich and V. Venkatasubramanian, Model-based reasoning in diagnostic expert system for chemical process plant, Computers and Chemical Engineering, vol.11, no.2, pp.111-122, 1987. [7] T. Fujiwara, Process Modeling for Fault Detection Using Neural Networks, System and Control Engineering, Nara Institute of Science and Technology, Japan. [8] A. Fekih, H. Xu and F. N. Chowdhury, Neural networks based system identiﬁcation techniques for model besed fault detection of nonlinear systems, International Journal of Innovative Computing, Information and Control, vol.3, no.5, pp.1073-1085, 2007. [9] Y. Wang, W. Wang and D. Wang, LMI approach to design fault detection ﬁlter for discrete-time switched systems with state delays, International Journal of Innovative Computing, Information and Control, vol.6, no.1, pp.387-397, 2010. [10] V. Pallade, R. J. Patton, F. J. Uppal, J. Quevedo and S. Daley, Fault diagnosis of an industrial gas turbine using neuro-fuzzy methods, IFAC, 2002. [11] R. Yusof, M. Khalid and M. F. Ibrahim, Fuzzy modeling for reboiler system, IEEE TENCON 2004, Chiang Mai, Thailand, 2004. [12] R. Z. Abdul Rahman, R. Yusof, M. Khalid and M. F. Ibrahim, Fuzzy modelling using genetic algorithm and recursive least square for process control application, International Journal of Simulation Systems, Science and Technology, pp.34-46, 2009. [13] R. Yusof, R. Z. Abdul Rahman and M. Khalid, Fuzzy modeling with genetic algorithm for process control rig, Proc. of the International Conference on Modeling, Simulation and Applied Optimisation, Sharjah, 2009. [14] C. W. Frey, M. Sajidman and H.-B. Kuntze, A Neuro-Fuzzy Supervisory Control System for Industrial Batch Processes. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1817-1822

SYNTACTIC FEATURE BASED WORD SENSE DISAMBIGUATION OF ENGLISH MODAL VERBS BY NA¨IVE BAYESIAN MODEL

Jianping Yu∗, Jilin Fu and Jianli Duan

College of Foreign Studies Yanshan University Qinhuangdao 066004, P. R. China ∗Corresponding author: [email protected] Received February 2010; accepted April 2010

Abstract. Ambiguity is a common phenomenon in the natural language. A high accuracy of word sense disambiguation (WSD) is very important for machine translation, information indexing and text sorting. This paper studies the WSD of English modal verbs by na¨ıveBayesian model. Special attention is paid to feature selection. Six syntactic features are selected and used for modeling and testing the na¨ıveBayesian model. The test to the model shows that the correct disambiguation reaches 94%. Some further experiments are conducted and the ranking of inﬂuence of the features on the result of WSD is given from great to little. Keywords: Word sense disambiguation, Syntactic feature, Modal verb, Na¨ıve Bayesian model

1. Introduction. Word sense disambiguation (WSD) is acknowledged to be one of the most difficult problems in the field of natural language processing and plays an important role in text processing. In the process of WSD, one essential part is to design a WSD model on the basis of a classifying principle and algorithm. However, whatever the model is, the linguistic information is inevitable because the researchers have to find proper linguistic features to design and experiment the model. Therefore, feature selection is an important task, and to know which linguistic feature has a greater influence on the sense of target word and which has less have become a key problem for the WSD model designers. Yu et al. [1,2] have made pioneer studies to investigate the contributions of different linguistic features to the WSD of English modal verb may and must by BP neural network and have got good experimental results. This paper will extend the study of WSD of must by a different method – Na¨ıve Bayesian model. Na¨ıve Bayes (NB) has accumulated a considerable record of success in the field of WSD. Hristea [3] applied a na¨ıve Bayes model in unsupervised WSD, and found that the feature selection using a knowledge source of type WordNet is more effective in disambiguation than the local type features (like part-of-speech tags). He [4] also studied the WSD of adjectives with the method lying at the border between unsupervised and knowledge-based techniques. Yu et al. [5] used the method of information gain to calculate the weight of different position context of the ambiguous words to improve the Bayesian Model, and the method is proven effective. Fan et al. [6] proposed a feature selection method based on information gain to improve the Bayesian model. Tan et al. [7] proposed a method based on the Bayes and machine readable dictionary, and the method showed a high accuracy of WSD when the scale of the tagged corpus is limited. Pan et al. [8] built a multiple classifier system composed of three Bayesian classifiers for WSD of English nouns and achieved better results of WSD than the individual classifiers. Lu et al. [9] made a comparison of WSD of Chinese regular words by neural network and by Bayesian model and found that Bayesian model worked better in Chinese WSD than neural network.

1817 1818 J. YU, J. FU AND J. DUAN In a word, na¨ıve Bayesian classifiers have been extensively used in WSD and are proven to be one of the best methods for WSD whether they work by themselves or are combined with other methods. They have been used to disambiguate verbs, nouns, adjectives of both Chinese and English words, to name a few, but its application in the WSD of English modals verbs has not been found. Since English modal verbs are a much more complex system and the senses of them are much more ambiguous than those of the regular verbs and nouns, the WSD of modal verbs would be challenging and significant for both semantic study and the study of natural language processing. This paper disambiguates the root meaning from the epistemic meaning of English modal verb must by na¨ıve Bayesian classifier with the objectives of: 1) to extend the application of na¨ıve Bayesian model from the WSD of regular verbs, nouns and adjectives to that of modal verbs, which is a more complex semantic level; 2) to see from the experiments the influence of different linguistic features on the WSD of English modal verb must and to provide some useful references and implications for the feature selection in the design of the Bayesian models for WSD of other modal verbs and for the study of natural language processing.

2. Bayesian Classifier. Bayesian decision theory is one of the basic theories of the classic statistic model. It claims that given the total probability of each class of the samples or the probability distribution and the numbers of classes to be classified, the class of the samples can be decided by the influence of the samples in the feature space on the probability of the class [10]. Bayesian classifier for WSD is proposed by Gale, et al. [11], and its basic ideas are: the senses of a polysemant depend on the co-text it occurs. If a polysemant w has 2 or more senses (si ≥ 2), its actual sense in a context can be determined by arg maxs P (si|c). According to Bayesian formula: P (c| s )P (s ) P (s | c) = i i (1) i P (c) When calculating the maximum of the conditional probability, the denominator can be neglected. Based on the independency hypothesis: ∏ P (c| si) = p(vk|si) (2) w∈c The actual sense of a polysemant in a context is obtained by: [ ] ∏ | sî = argsi max P (si) P (vk si) (3) vk∈c here, P (si) is the prior probability, and P (vk|si) is the feature probability. They are estimated by maximum likelihood methods:

N(vk, si) N(si) P (vk| si) = ,P (si) = (4) N(si) N(w) here, N(vk, si) refers to the number of co-occurrence of vk and si in the training corpus. N(si) is the occurrence of si in the training corpus, and N(w) refers to the number of occurrence of word w in the training corpus.

3. Design of the Na¨ıve Bayesian Model. In order to build a na¨ıve Bayesian model for WSD of English modal verb must, two corpora are established. Each of the corpora contains about a half million words and is composed of written and spoken data, including research articles, novels, movie lines and news reports. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1819 The meanings of must are tagged according to the categorization of Coates’ [12]:  {  strong obligation (core) root meaning must  weak obligation or necessity (periphery) epistemic meaning – confident inference (periphery) For example: (a) “You RTmust play this ten times over”, Miss Jarrova would say, pointing with re- lentless fingers to a jumble of crotchets and quavers. (RT stands for root meaning) (b) That place EPmust make quite a profit for it was packed out and has been all week. (EP stands for epistemic meaning) The model to be established will distinguish the root meaning of must from the epistemic meaning of must. By using the Concordance Tool of Wordsmith 4.0, the statistical results of occurrence of must in the two corpora are shown in Table 1.

Table 1. The occurrence of must in the two corpora

PP PP Sort PP Root must Percentage Epistemic must Percentage Corpora PPP Training 287 69% 131 31% Testing 154 63% 92 37%

Fifty samples are taken from the training corpus, 25 samples for the sense of root must and 25 for the epistemic must. Coates [12] studied the semantics of English modal auxiliaries and summarized some syntactic co-occurrence features for English modal verbs. These features can be used as the co-text information for WSD. As far as must is concerned, eight features, such as negation, voice, must + agentive verb, animate subject, must + perfective aspect, must + stative verbs, must + progressive aspect and existential subject + must are put into consideration. Since the last two features didn’t occur in the testing set, they are neglected. Now, the following 6 syntactic features (vk, k = 1, . . ., 6) are extracted: 1. negation; 4. animate subject; 2. voice; 5. must + perfective aspect; 3. must + agentive verb; 6. must + stative verb These features are all bi-valued variables. The two values are complementary with each other with one value supporting epistemic must and the other supporting root must. Now, train the na¨ıve Bayesian model. Firstly, count up the occurrences of the relevant variables and features. Secondly, calculate the prior probability P (si) and the feature probability P (vk|si) of each of the 50 samples in the training set by formulae (4). The Bayesian model is designed. In order to test the na¨ıve Bayesian model, another 50 samples are randomly collected from the testing corpus with 25 for epistemic must and 25 for root must. Repeat the steps of counting and calculation in the process of training of the model. The disambiguation is a process of calculation and comparison, and the right sense is derived from Equation (3). The tested results are shown in Table 2 and Figure 1. From Table 2 and Figure 1, it can be seen that of the 50 tested samples, 47 are correctly disambiguated; the correct disambiguation reached 94%, which is an ideal result. Some further experiments are carried out in order to see the influence of different syntactic features on the result of WSD of must. The experiments are conducted by deleting one linguistic feature a time from the testing data set, and then calculate thes î by Equation (3). The experimental results are listed in Table 3. 1820 J. YU, J. FU AND J. DUAN Table 2. The tested results of WSD of must by the na¨ıve Bayesian model

Tested results Tested results No. Target No. Target Root Epi si Root Epi si 1 ROOT 0.021 4E-05 ROOT 26 EPI 0 0.009 EPI 2 ROOT 0.053 7E-05 ROOT 27 EPI 0.021 0.087 EPI 3 ROOT 0.199 0.009 ROOT 28 EPI 0.021 0.087 EPI 4 ROOT 0.002 0 ROOT 29 EPI 0.021 0.087 EPI 5 ROOT 0.085 0.034 ROOT 30 EPI 0.08 0.006 ROOT 6 ROOT 0.199 0.009 ROOT 31 EPI 0 0.001 EPI 7 ROOT 0.199 0.009 ROOT 32 EPI 0 0.014 EPI 8 ROOT 0.016 0 ROOT 33 EPI 0.199 0.009 ROOT 9 ROOT 0.199 0.009 ROOT 34 EPI 0 0.014 EPI 10 ROOT 0.199 0.009 ROOT 35 EPI 0.199 0.009 ROOT 11 ROOT 0.08 0.006 ROOT 36 EPI 0 0.001 EPI 12 ROOT 0.085 0.034 ROOT 37 EPI 0 0.001 EPI 13 ROOT 0.085 0.034 ROOT 38 EPI 0 0.014 EPI 14 ROOT 0.199 0.009 ROOT 39 EPI 0.021 0.087 EPI 15 ROOT 0.034 0.023 ROOT 40 EPI 0.021 0.087 EPI 16 ROOT 0.199 0.009 ROOT 41 EPI 0.021 0.087 EPI 17 ROOT 0.199 0.009 ROOT 42 EPI 0 0.0009 EPI 18 ROOT 0.199 0.009 ROOT 43 EPI 0.009 0.059 EPI 19 ROOT 0.002 0 ROOT 44 EPI 0 0.001 EPI 20 ROOT 0.006 0.0007 ROOT 45 EPI 0 0.014 EPI 21 ROOT 0.199 0.009 ROOT 46 EPI 0 0.001 EPI 22 ROOT 0.199 0.009 ROOT 47 EPI 0 0.014 EPI 23 ROOT 0.199 0.009 ROOT 48 EPI 0 0.0009 EPI 24 ROOT 0.034 0.023 ROOT 49 EPI 0 0.001 EPI 25 ROOT 0.08 0.006 ROOT 50 EPI 0 0.005 EPI

Figure 1. Tested results of WSD of must by the na¨ıve Bayesian model

From the results in Table 3 we can see that in the WSD of must by na¨ıve Bayesian model, the deletion of the syntactic feature 5 causes the maximum decrease in the correct disambiguation, which implying that this syntactic feature might bring the greatest influence on the result of WSD of must among the 6 features. Feature 6 also shows a relatively great influence on the result of WSD of must. The feature 1 and 2 bring less ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1821 Table 3. Tested results of WSD of must by neglecting different syntactic features hh hhhh hhhh Results hhh Correct disambiguation (%) Deleted features hhhh 0 none 94 1 negation 92 2 voice 92 3 must + agentive 94 4 animacy of subject 94 5 must + perfective 76 6 must + stative 84

influence than features 5 and 6. The deletion of features 3 and 4 cause no change in correct disambiguation. This might imply that the two features are not quite independent from the other features. Through the comparison of the tested results, the influence of different syntactic features on the word sense disambiguation of must can be roughly ranked from great to little successively as follows: 1) must + perfective aspect 3) negation; voice 2) must + stative verb 4) must + agentive verb; animate subject

4. Conclusions. A na¨ıve Bayesian model is built for the word sense disambiguation (WSD) of English modal verb must based on 6 syntactic co-occurrence features, and the test to the model shows an accuracy of disambiguation of 94% which is an ideal result. The further experiments with the model find that for the na¨ıve Bayesian model, the ‘must + perfective aspect’ feature has the greatest influence on the result of WSD of must, and the ‘must + stative verb’ feature has the second greatest influence. The features of negation and voice have a little influence and the ‘animate subject’ and ‘must + agentive verb’ features seem to have no influence on the results of WSD of must. The findings provide some references for the WSD of other modal verbs by naive Bayesian models and the study of natural language processing.

REFERENCES [1] J. Yu, H. Dong, J. Fu and T. Bai, An investigation of contributions of diﬀerent linguistic features to the WSD of English modal verb MAY by BP neural network, ICIC Express Letters, vol.3, no.3(A), pp.391-396, 2009. [2] J. Yu, L. An and J. Fu, Word sense disambiguation of English modal verb must by neural network, ICIC Express Letters, vol.4, no.1, pp.83-88, 2010. [3] F. T. Hristea, Recent advances concerning the usage of the na¨ıve bayes model in unsupervised word sense disambiguation, International Review on Computers and Software, vol.4, no.1, pp.54-67, 2009. [4] F. T. Hristea, Adjective sense disambiguation at the border between unsupervised and knowledge- based techniques, Fundamenta Informaticae, vol.91, no.3-4, pp.547-562, 2009. [5] T. Zheng, B. Deng, B. Hou, L. Han and J. Guo, Word sense disambiguation based on Bayes model and information gain, Proc. of the 2nd International Conference on Future Generation Communication and Networking, vol.2, pp.153-157, 2008. [6] D. Fan, Z. Lu, R. Zhang and S. Pan, Chinese word sense disambiguation based on Bayesian model improved by information gain, Journal of Electronics and Information Technology, vol.30, no.12, pp.2926-2929, 2008. [7] W. Tan, H. Fu, L. Liu and X. Yang, Method of word sense disambiguation based on bayes and machine readable dictionary, Computer Applications, vol.26, no.6, pp.1389-1395, 2006. [8] Z. Pan, Y. Hong and J. Yao, A multiple Bayes classiﬁcation solution to word sense disambiguation, ACM International Conference Proceeding Series, vol.403, pp.97-99, 2009. [9] Z. Lu, T. Liu, J. Lang and S. Li, Chinese word sense disambiguation: Neural network vs. Bayesian network, High Technology Communication, vol.8, pp.15-19, 2004. [10] X. Wen, Pattern Recognition and Condition Monitoring, Science Press, Beijing, 2007. 1822 J. YU, J. FU AND J. DUAN

[11] W. A. Gale, K. W. Church and D. Yarosky, A method for disambiguating word senses in a large corpus, Computer and Humanities, vol.26, pp.415-439, 1992. [12] J. Coates, The Semantics of the Modal Auxiliaries, Routledge Press, London, 1983. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1823-1830

A ROBUST ADAPTIVE BEAMFORMING OPTIMIZATION CONTROL METHOD VIA SECOND-ORDER CONE PROGRAMMING FOR BISTATIC MIMO RADAR SYSTEMS

Fulai Liu1,2,∗, Changyin Sun1, Jinkuan Wang2 and Ruiyan Du2 1School of Automation Southeast University Nanjing, P. R. China ∗Corresponding author: [email protected] 2Engineer Optimization and Smart Antenna Institute Northeastern University at Qinhuangdao Qinhuangdao, P. R. China Received February 2010; accepted April 2010

Abstract. This paper presents an eﬀective robust supergain beamforming method with sidelobe control for bistatic MIMO radar systems. In this proposed approach, the beamforming optimization problem is formulated as a second-order cone programming (SOCP) problem. The advantage of the proposed method is that it can not only guarantee that the sidelobes are strictly below some given (prescribed) threshold value but also improve the robustness of the supergain beamformer against random errors such as amplitude and phase errors of sensors, and imprecise positioning of sensors, etc. Simulation results are presented to verify the eﬃciency of the proposed method. Keywords: Bistatic MIMO radar, Second-order cone programming (SOCP), Robust beamforming, Sidelobe control, Supergain

1. Introduction. A MIMO (multiple-input multiple-output) radar uses multiple antennas to simultaneously transmit several (possibly linearly independent) waveforms and it also uses multiple antennas to receive the reflected signals. As compared to phased array radars, the use of MIMO radars with colocated antennas can improve angular resolution, increase the upper limit on the number of detectable targets, improve parameter iden- tifiability, extend the array aperture by virtual sensors, and enhance the flexibility for transmit/receive beampattern design [1-3]. According to their antenna configurations, two classes of MIMO radar technologies have been discussed in the literatures. The first one is statistical MIMO radar [4, 5]. All of its antennas are far from each other so that they obtain echoes from different angles of target to combat target fades. The second category is bistatic MIMO radar [6, 7], which uses closely spaced antennas to achieve coherent processing gain. In this paper, we are concerned with the received beamforming optimization for bistatic MIMO radar systems. One of the most popular approaches to adaptive beamforming is the so-called minimum variance distortionless response (MVDR) processor, which minimizes the array output power while maintains a distortionless mainlobe response toward the desired signal. Un- fortunately, the MVDR beamformer may have unacceptably high sidelobes, which may lead to significant performance degradation in the case of unexpected interfering signals. The issue of sidelobes control is especially important for both deterministic and adaptive arrays. Indeed, after the appearance of any new interferer, the MVDR beamformer requires a certain transition time to suppress it, and therefore, during this time interval its performance may break down. Many approaches to sidelobe control have been proposed (see [8-11] and references therein). For example, the artificial interferences impinge

1823 1824 F. LIU, C. SUN, J. WANG AND R. DU on the array from directions outside the main beam [8]. The interference powers are then adjusted iteratively until the desired sidelobe behavior is achieved or until the best attainable beampattern has been found. The method in [9], unlike that in [8], has a user- predefined controlled mainlobe beamwidth, and the peaks of the sidelobe are minimized. More recently, several beamforming using convex optimization with strictly controlled sidelobes have been presented in [10, 11]. These adaptive beamforming methods based on convex optimization can minimize the power of interferences and noise, while maintain distortionless response in the direction of signal and provide the lower beampattern sidelobes than some given threshold value. However, several important errors such as amplitude and phase errors in sensor channels and imprecise positioning, must exist in realistic antenna array. These errors are nearly uncorrelated from sensor to sensor and affect the beamformer in a similar manner to spatially white noise. The array gain against uncorrelated or spatially white noise is a good measure of the array processor’s robustness to errors. Cox et al. [12] proposed to use the so-called white noise gain constraint (WNC) to obtain reasonable values of diagonal loading factor. Unfortunately, the relationship between the diagonal loading factor and the parameters of the WNC is not simple, and to satisfy this constraint, a multistep iterative procedure is required to adjust the diagonal loading factor [12, 13]. A supergain beamforming method via second-order cone programming (SOCP) is proposed in [14]. This method makes use of constrained approach based on SOCP to guarantee that the white noise array gain of the achieved beamformer is strictly above the threshold. In this paper, we present an effective robust supergain beamforming method with sidelobe control for bistatic MIMO radar systems. In this proposed approach, the beamforming optimization problem is formulated as a SOCP problem. The advantage of the proposed method is that it can guarantee that the sidelobes are strictly below the prescribed threshold and the white noise array gain of the achieved beamformer is strictly above the prescribed threshold. This paper is organized as follows. Section 2 presents the bistatic MIMO radar scheme and the associated data model. The robust adaptive beamforming method based on SOCP is addressed in Section 3. In Section 4, simulation results are presented to verify the performance of the proposed approach. Section 5 concludes the paper.

2. Background. Consider a narrowband MIMO radar system, with M arbitrarily located transmitting antennas and N arbitrarily located receiving antennas. The sys- L×1 tem simultaneously transmits M linearly independent waveforms, denoted by sn ∈ C (n = 1, ··· ,M) with L being the data sample number. Let θs be the location parameter of a desired target, for example, the direction-of-arrival (DOA) when the targets are in the far field of the arrays. Let b(φs) be the corresponding steering vector for the transmitting antenna array. At time t, the waveform vector of the reflected signal from the target at T T θs is b(φs)ss(t) with (·) standing for the transpose and ss(t) = [s1(t), s2(t), ··· , sM (t)] in which sk(t) denoting the transmitting data of the kth antenna. Note that b(φs)ss(t) is a function of the location parameter θs. Hence, the signals reflected from targets at different locations are linearly independent of each other. The N × 1 complex vector of the received antenna array observation∑ at time t can be T J modelled as x(t) = xs(t) + xi(t) + n(t) = a(θs)β(θs)b (φs)ss(t) + j=1 a(θj)sj(t) + n(t) T N×1 where the column vector x(t) = [x1(t), ··· , xN (t)] ∈ C with xk(t) presenting the output of the kth received antenna. xs(t), xi(t), and n(t) are the statistically independent components of the desired signal, interference, and antenna noise, respectively. The de- T N×1 sired signal vector xs(t) = a(θs)β(θs)b (φs)ss(t). a(θs) ∈ C is the steering vector of the receiving antenna array for the desired signal which comes from θs. β(θs) ∈ C denotes the complex amplitude of the reflected signal from θs, which is proportional to∑ the dadar cross × J sections (RCS) of the focal point θs. The N 1 interference vector xi(t) = j=1 a(θj)sj(t) ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1825

with a(θj) denoting the steering vector of the receiving array for the jth interference signal T N×1 sj(t) which comes from θj. The column vector n(t) = [n1(t), ··· , nN (t)] ∈ C with nk(t) denoting the additive noise of the k received antenna. The beamformer output is given by y(t) = wH x(t) (1) where w is the N × 1 weight vector, and (·)H denotes the Hermitian transpose. The MVDR beamformer minimizes the array output power while keeping the unit gain in the direction of the desired signal H H min w Rw subject to w a(θs) = 1 (2) w where R = E{x(t)xH (t)} is the N × N array covariance matrix. Here, E{·} denotes the statistical expectation. a(θs) is the N × 1 steering vector of the desired signal. A closed-form solution to (2) is given by

1 −1 wMVDR = H −1 R a(θs) (3) a(θs) R a(θs) In practice, the sample covariance matrix 1 ∑K Rˆ = x(k)xH (k) (4) K k=1 is used in (3) to replace the true array covariance matrix R. Here, K denotes the number of snapshots.

3. Robust Adaptive Beamforming Optimization Control. 3.1. Array gain control. From (1), it is easy to know{ that the} mean{ square power} output of the beamformer can be expressed as P = E |y(k)|2 = E |wH x(k)|2 = H H H T w Rsw+w Riw+w Rnw where the desired signal covariance matrix Rs = a(θs)β(θs)b { H } ∗ ∗ H · ∗ (φs)E ss(t)ss (t) b (φs)β (θs)a (θs). The superscript ( ) stands for Hermitian opera- { H } tion{ without} transpose. Ri = E xixi is the interference covariance matrix. Rn = E n(k)nH (k) is the N × N noise covariance matrix which is an identical matrix for the 2 case of spatial white noise and identical noise spectra at each received antenna. σn is the noise power. ∗ 6 ∗ For the orthogonal-transmitted waveforms such that sksl = 0 (k = l) and sksk = | |2 2 { H } { H } 2 2 sk = σs ,E ss(t)ss (t) can be rewritten as E ss(t)ss (t) = σs IM×M . Here, σs denotes the transmitted signal power at each transmitting antenna. IM×M presents the M × M identical matrix. M is the number of antennas in the transmitting array. There- | |2 2 H fore, the desired signal covariance matrix Rs can be reduced as M β(θs) σs a(θs)a (θs). H Here, β(θs) can be estimated by the least squares (LS) method [1]. That is, w Rsw = | |2 2| H |2 M β(θs) σs w a(θs) . Then, the mean square power output of the beamformer can be | |2 2| H |2 H 2 H reexpressed as P = M β(θs) σs w a(θs) + w Riw + σnw w. The received array gain is deﬁned as the output signal-to-noise ratio (SNR) divided by | |2 2| H |2 2 H | |2| H |2 M β(θs) σs w a(θs) /(σnw w) M β(θs) w a(θs) the input SNR and is given by G = 2 2 = H . σs /σn w w H Invoking the distortionless constraint w a(θs) = 1, the received array gain for MVDR | |2 M β(θs) | |2k k−2 k · k beamformer is given by G = wH w = M β(θs) w where stands for the Euclidean norm. To improve the beamformer robustness against random errors such as channel errors, array location perturbations, etc., a received array gain constraint [14] can be imposed on the array weights such that 2 −2 2 2 2 2 2 G = M|β(θs)| kwk ≥ δ ⇐⇒ kwk ≤ ε = M|β(θ)| /δ (5) 1826 F. LIU, C. SUN, J. WANG AND R. DU where δ2 can be speciﬁed according to the variance of array sensor gain, phase and the array location perturbations for a desired robustness level.

3.2. Sidelobe control. It is well known that the MVDR beamformer can have unacceptably high sidelobes in the case of low sample support. In adaptive array systems, this may lead to a substantial performance degradation in the presence of unexpected (i.e., suddenly appearing) interferers. Indeed, after the appearance of any new interferer, the MVDR beamformer requires a certain transition time to suppress it, and therefore, during this time interval its performance may break down. Let θj ∈ Θ(j = 1, ··· ,J) be a chosen grid that approximates the sidelobe beampattern areas Θ using a ﬁnite number of angles. To control the sidelobe level, we use the following multiple quadratic inequality constraints outside the mainlobe beampattern area

H 2 2 |w a(θj)| ≤ ξ , j = 1, ··· ,J (6) where ξ2 is the prescribed sidelobe level.

3.3. Second-order cone formulation. Adding the received array gain constraint (5) and side level constraints (6) to the MVDR beamforming problem (2) and using the sample covariance matrix (4), we obtain the following modiﬁed MVDR problem

H ˆ H 2 2 H 2 2 min w Rw subject to w a(θs) = 1, kwk ≤ ε , |w a(θj)| ≤ ξ (j = 1, ··· ,J) (7) w

This problem has quadratic objective function (note that Rˆ is positive semidefinite). There is a single linear equality constraint and multiple quadratic inequality constraints. Therefore, the optimization problem (7) is convex. Recent advances in convex optimization can motivate a class of algorithms for the above optimization problem. An efficient SOCP-based approach for MVDR beamforming is developed as follows. T The dual standard form of convex conic optimization problem is defined as maxy b y subject to c − AT y ∈ K where y is a vector containing the designed variables. A is an arbitrary matrix. b and c are arbitrary vectors. K is a symmetric cone consisting of Cartesian products of elementary cones (each corresponding to a constraint). Note that A, b, and c can be complex-valued and must have matching dimensions. For our problem, the elementary cones are either SOCs (for inequality constraints) or 4 zero-cones{ {0}(for equality constraints).} The q-dimensional SOC is defined as SOCq+1 =

(x , x ) ∈ R × Cq x ≥ kx k where x is a real scalar. x is a complex q-dimensional 1 2 1 2 1 2 { } 4 vector. k·k denotes the Euclidean norm. The zero cone is defined as {0} = x ∈ C x = 0 . For example, with K as {0}f × SOCq+1, the condition c − AT y ∈ K indicates that the first f elements of vector c−AT y are constrained to be equal to zero, while the remaining q + 1 elements must lie in a SOC. In what follows we formulate the convex optimization problem (7) in the dual standard form of SOC program, which can be solved efficiently using the well-established interior point method [15]. First of all, we convert the quadratic objective function of (7) to a linear one. Notice that wH Rwˆ = kLwk2 where L is the Cholesky factor of Rˆ , i.e., LH L = Rˆ . Clearly, minimizing wH Rwˆ is equivalent to minimizing kLwk2. Introducing a new scalar nonnegative variable τ and a new constraint kLwk ≤ τ, we can convert (7) into the following form minτ,w τ H 2 2 H 2 2 subject to kLwk ≤ τ, w a(θs) = 1, kwk ≤ ε , |w a(θj)| ≤ ξ (j = 1, ··· ,J). Since 2 2 H 2 2 kwk ≤ ε and |a (θj)w| ≤ ξ (j = 1, ··· ,J), the quadratic inequality constraints can H written as SOC constraints kwk ≤ ε and |a (θj)w| ≤ ξ (j = 1, ··· ,J). Introducing new T T variables y1 = τ, y2 = ε, y3 = ξ, y4 = w and y = [y1, y2, y3, y4 ] , we obtain the following ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1827 problem H min y1 subject to y2 = ε, y3 = ξ, a (θs)y4 = 1, y k k ≤ k k ≤ | H | ≤ ··· Ly4 y1, y4 y2, a (θj)y4 y3 (j = 1, 2, ,J)(8) 4 T T Define b = [−1, 0, ··· , 0] so that −y1 = b y. Among the constraints of (8) the first H three equalities y2 = ε, y3 = ξ, a (θs)y4 = 1 can be represented as three zero-cone constraints      ε − y ε 0 1 0 0T 2 4  −    −  T  − T ∈ { }3 ξ y3 = ξ 0 0 1 0 y = c1 A1 y 0 . H H 1 − a (θs)y4 1 0 0 0 a (θs) k k ≤ k k ≤ | H | ≤ ··· The SOC constraints Ly4 y1, y4 y2, a (θj)y4 y3 (j = 1, ,J) take the following form ( ) ( ) ( ) − T 4 y1 0 − 1 0 0 0 − T ∈ N+1 = − y = c2 A2 y SOC Ly4 0 0 0 0 L ( ) ( ) ( ) − T 4 y2 0 − 0 1 0 0 − T ∈ N+1 = y = c3 A3 y SOC y4 0 0 0 0 −I ( ) ( ) ( ) − T 4 y3 0 − 0 0 1 0 − T ∈ 2 ··· H = H y = cj+3 Aj+3y SOC j = 1, , J. a (θj)y4 0 0 0 0 −a (θj) 4 4 ··· T T T ··· T Let c = [c1, c2, , cJ+3] and A = [A1 , A2 , , AJ+3], where cj and Aj (j = 1, ··· ,J + 3) are defined according to the equations above. Then, the constraints of (8) become c − AT y ∈ K where K is the symmetric cone corresponding to the constraints 3 N+1 N+1 2 2 K = {0} × SOC × SOC |SOC × ·{z · · × SOC} . Thus, with the above definitions of J y, L, A, b, c and K, we have rewritten the convex optimization problem (7) in the standard form of dual SOC program. Notice that we have complex data and variables in the formulation, but this can be accommodated by the existing interior point codes [15]. If the above convex optimization problem is feasible, the proposed adaptive beamformer can be obtained from the optimal solution for y. However, the problem may be infeasible, depending on the chosen received array gain parameter δ2, sidelobe control parameter ξ2 and the mainlobe width. The advantage of the SOC-programming-based approach is that the infeasibility can be easily detected by the convex optimization software [15].

4. Simulation Results. In this section, we conduct some simulations to validate the proposed algorithm. Consider a MIMO radar system where a ULA with M = N = 10 antenna elements and half-wavelength spacing between adjacent elements is used for both ◦ transmitting and receiving. The direction∪ of the desired signal is θs = 0 . The sidelobe beampattern areas Θ = [−90◦, −12◦] [12◦, 90◦] are chosen and a uniform grid is used to obtain the angles θj (j = 1, ··· ,J). The SNR is equal to -10dB. Two interferer signals are assumed to have the direction of −20◦ and 20◦, respectively. Sensor noises are modelled as spatially and temporally white Gaussian processes. It is assumed that ξ2 = 10−2.6, i.e., we require the beampattern sidelobe level below −26dB. The convex optimization software [15] is used to compute the weight vector of our proposed method that employs the constant white noise array gain constrain Gw = 3dB (i.e., δ = 2.2387) and the sidelobes control level constrain ξ2 = 10−2.6. In the first simulation, we use 512 snapshots to estimate the sample covariance matrix and compute the directional patterns of the proposed method and MVDR. These directional patterns are plotted in Figure 1. As shown in this figure, the proposed method can guarantee that the sidelobe constraints are exactly satisfied. 1828 F. LIU, C. SUN, J. WANG AND R. DU In the second simulation, a scenario with the signal steering vector mismatch and the array location perturbations is considered. Assume that the array location perturbations are statistically independent zero-mean Gaussian random variables with standard devi- ◦ ation σp = 0.01. Assume that the signal steering vector mismatch is euqal to 3 , i.e., 4θ = 3◦ mismatch in signal look direction. Figure 2 gives the performance of methods tested versus the snapshots DOA for SNR = −5dB. In the final simulation, the array gain is considered. Assume that an desired target locate at (φ, θ) = (10◦, 0◦) where (φ, θ) shown in Figure 1. The SNR is −10dB. The array weights of the proposed method and MVDR beamformer point at the DOA θ are computed for a nominal array. The corresponding array gains can also be computed by Equation (11). In this case, the deviation of channel gain and phase are σg = 0.1 and ◦ σθ = 3 , respectively. Figure 3 gives the two aforementioned beamformers in terms of the array gain versus the frequency. It is easy to know that the proposed method can provide a good robustness against the channel gain and phase errors.

0 MVDR Proposed method

−10

−20

−30

−40

−50 Directional Pattern (dB)

−60

−70

−80 −100 −80 −60 −40 −20 0 20 40 60 80 100 Fidld of View (Degree)

Figure 1. Direction patterns of the proposed method and MVDR

0 MVDR Proposed method

−10

−20

−30

−40

−50 Directional Pattern (dB)

−60

−70

−80 −100 −80 −60 −40 −20 0 20 40 60 80 100 Fidld of View (Degree)

◦ Figure 2. Comparison of the beampatterns with 4θ = 3 and σp = 0.01 versus DOA ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1829

proposed method 18 MVDR

12 Array Gain (dB)

6 400 800 1200 1600 2000 2400 Frequency(Hz)

Figure 3. Array gains versus frequency

5. Conclusions. This paper presents an eﬀective robust supergain beamforming method with sidelobe control for bistatic MIMO radar systems. In this proposed approach, the beamforming optimization problem is formulated as a SOCP problem. The advantage of the proposed method is that it can not only guarantee that the sidelobes are strictly below some given (prescribed) threshold value but also improve the robustness of the supergain beamformer agianst random errors such as amplitude and phase errors in sensor chanels and imprecise positioning of sensors, etc. Simulation results are presented to verify the eﬃciency of the proposed method.

Acknowledgment. This work has been supported by the National Natural Science Foun- dation of China under Grant No. 60874108 and 60904035, and by Directive Plan of Sci- ence Research from the Bureau of Education of Hebei Province, China, under Grant No. Z2009105.

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[1] J. Z. Xu, J. Li and P. Stoica, Target detection and parameter estimation for MIMO radar systems, IEEE Transactions on Aerospace and Electronic Systems, vol.44, no.3, pp.927-939, 2008. [2] Q. Jiang, J. Xiao, D. H. He and H. P. Hu, Application of the genetic algorithm in design polyphase orthogonal code, ICIC Express Letters, vol.2, no.4, pp.359-364, 2008. [3] C. Y. Chen and P. Vaidyanathan, MIMO radar space-time adaptive processing using prolate spher- oidal wave functions, IEEE Transactions on Signal Processing, vol.56, no.2, pp.623-635, 2008. [4] E. Fisher, A. Haimovich, R. Blum, L. Cimini, D. Chizhik and R. Valenzuela, Spatial diversity in radarsmodels and detection performance, IEEE Transactions on Signal Processing, vol.54, no.3, pp.823-838, 2006. [5] A. M. Haimovich, R. Blum and L. Cimini, MIMO radar with widely separated antennas, IEEE Signal Processing Magazine, vol.25, no.1, pp.116-129, 2008. [6] J. Li, P. Stoica, L. Z. Xu and W. Roberts, On parameter identiﬁability of MIMO radars, IEEE Signal Processing Letters, vol.14, no.12, pp.968-971, 2007. [7] H. Yan, J. Li and G. Liao, Multitarget identiﬁcation and localization using bistatic MIMO radar systems, EURASIP Journal on Advances in Signal Processing, vol.2008, no.8, pp.1-8, 2008. [8] C. A. Olen and R. T. Compton, A numerical pattern synthesis algorithm for arrays, IEEE Transac- tions on Antennas and Propagation, vol.38, no.10, pp.1666-1676, 1990. [9] I. D. Dotlic and A. J. Zejak, Arbitrary antenna array pattern synthesis using minimax algorithm, Electron. Lett., vol.37, no.4, pp.206-208, 2001. [10] J. Liu, A. B. Gershman, Z. Q. Luo and K. M. Wong, Adaptive beamforming with sidelobe control: A second-order cone programming approach, IEEE Signal Process. Lett., vol.10, no.11, pp.331-334, 2003. 1830 F. LIU, C. SUN, J. WANG AND R. DU

[11] S. F. Yan and J. M. Hovem, Array pattern synthesis with robustness against manifold vectors uncertainty, IEEE Journal of Oceanic Engineering, vol.33, no.4, pp.405-413, 2008. [12] H. Cox, R. M. Zeskind and M. H. Owen, Robust adaptive beamforming, IEEE Trans. Acoust, Speech, Signal Processing, vol.5, no.10, pp.365-376, 1985. [13] H. Song, W. A. Kuperman, W. S. Hodgkiss, P. Gerstoft and J. S. Kim, Null broadening with snapshot-deﬁcient covariance matrices in passive sonar, IEEE Journal of Oceanic Engineering, vol.28, no.2, pp.250-261, 2003. [14] S. F. Yan and Y. L. Ma, Robust supergain beamforming for circular array via second-order cone programming, Applied Acoustics, vol.66, no.9, pp.1018-1032, 2003. [15] M. Grant and S. Boyd, CVX: Matlab Software for Disciplined Convex Programming, http://stanford. edu/ boyd/cvx/download.html, 2009. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1831-1837

STUDY OF PARAMETERS SELECTION IN FINITE ELEMENT MODEL UPDATING BASED ON PARAMETER CORRECTION

Linren Zhou and Jinping Ou School of Civil Engineering Dalian University of Technology Dalian 116024, P. R. China [email protected] Received February 2010; accepted April 2010

Abstract. The sensitivity and significance levels of design parameters to modal eigenvalues have been performed to investigate the reasonability of parameters selection for model updating based on finite element (FE) model simulation of a cable-stayed bridge laboratorial model. The analysis indicates that sensitivity analysis has clear conception and easily to be applied to practical engineering, but the results show partly and qualitatively the sensitivity of design parameters. Variance analysis, based on testing samples generated by full factorial design, orthogonal design, Taguchi design, uniform design and central composite design of design of experiment (DOE) in the global design space, were discussed and contrasted for significance analysis, the results could quantitatively show the significance levels of design parameters to modal eigenvalues, and the optimal method of DOE discussed above is central composite design. Keywords: Parameter selection, FE model updating, Sensitivity analysis, Design of experiment, Variance analysis

1. Introduction. An accurate and effective numerical model is significantly important to parameter identification, damage detection and safety assessment in structural healthy monitoring (SHM) of engineering structures [1,2]. The state of structure is always difficult to be estimated because so many errors have been brought in structural design, construction, numerical modeling, as well as the uncertainty of loads and environmental factors. FE model updating based on the field measured data and optimization theory is an effective way to obtain a precise state model of structures in different phases of the service life. Model updating is a research focus and has made considerable progress in the past two decades, especially with the development and application of optimization theory [3]. A literature review on model updating based on structural dynamics can be found in Mottershead and Friswell [4]. According to the modified objects, the method of FE model updating could be classified into two types: matrices updating and parameters correction. It is well known that design parameters are the main error source in numerical analysis model of structures [5]. The method of modifying structural design parameters is always adopted to achieve a reliable updated numerical model which is more close to the practical situations of structure. The design parameters include all input variables in numerical simulation, such as the material properties, geometric properties, boundary conditions, loads, etc. The key point of parameters correction is which parameters to be selected for model updating, which will significantly impact the calculation convergence and the credibility of updated results. Logically, all possible parameters should be considered for correction in model updating. However, if too many parameters are included in the updating procedure, the possibility of obtaining a reliable model may decrease [6]. On the other hand, if the number of parameters is not enough or missing some important parameters, the updated model may also be unreasonable or unreliable. Therefore, reasonability and availability of

1831 1832 L. ZHOU AND J. OU parameters selection is an important issue and need more comprehensive study. Generally, these parameters which have obvious effect on the targeted Eigenvaules will be selected on the adjustment list. There are many strategies to estimate the effects of design parameters on the selected Eigenvaules, method of sensitivity analysis based on engineering experience is widely used, and variance analysis based on DOE for the parameters selection can be found in the work of [7]. DOE based on mathematical statistics theory, directly address how to efficiently and reasonably choose testing samples in global design space and make plan for experiments [8]. Common artificial experiments have to test repeatedly at one certain testing point and statistic analysis should be employed for result processing. Different from traditional experiment design, the input and output are determinate in deterministic numerical simulation, namely, each testing point just need one calculation. Therefore, whether those methods of DOE serving for traditional experiments could be applied to deterministic numerical simulation need some further research. In this paper, based on the FE model of the laboratorial physical model of Shandong Binzhou Yellow River Highway Bridge, some global and local design parameters, such as material properties, fabrication errors and boundary condition, are selected to be corrected by sensitivity analysis and variance analysis in FE model simulation. Some commonly used methods of DOE are discussed and contrasted to investigate the reasonability of parameters selection for FE model updating.

2. Sensitivity Analysis. 2.1. Method of sensitivity analysis. Sensitivity could be simply understood as the differential coefficient of function in mathematics. In FE model updating based on the parameters correction, the relationship between design parameter P and characteristic equation f is so complicated that can not be expressed by mathematical formulas, here designated as f(P ), do Taylor expansion at the point of design parameter p and ignore the high-order terms ∑n ∂f f(p + ∆p) = f(p) + ∆p (1) p i=1 i The Equation (1) is equivalent to S∆p = R (2) where R is residual error vector, R = f(p + ∆p) − f(p), ∆p is the modified vector of design parameters, ∆p = (∆p , ∆p ,..., ∆p )T , S is sensitivity matrix: 1 2 N  ∂f1 ∂f1 ∂f1  ···   ∂p1 ∂p2 ∂pn   . . . .  S =  . . .. .  (3)   ∂fm ∂fm ··· ∂fm ∂p1 ∂p2 ∂pn where n and m is the number of variables to be corrected and characteristic quantities selected respectively. Output of function f could be modal frequency, modal shapes, modal assurance criterion (MAC) and the combinations of above parameters. Residual vectors and sensitivity matrices depend on what characteristic quantities are selected. 2.2. The engineering background and FE model. In this paper, a three-dimensional FE model of a long-span cable-stayed bridge laboratorial physical model is established to investigate the parameters selection for FE model updating. The physical model with 1/40 of scale factor was designed and manufactured according to similarity theory based on the prototype of Shandong Bin Zhou Yellow River Highway Bridge. The material of bridge deck and towers is aluminum alloy, and steel wires with different section area are ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1833 used as cables. The physical model is total 15.2m in length with bridge deck of 0.82m in width, the height of middle pylon and side pylon are 3.1m and 1.9m, respectively. The total weight of aluminum alloy is about 1ton. A three-dimensional FE model of the laboratorial model was built by program of ANSYS software with ANSYS Parametric Design Language (APDL). SHELL63 element was adopted to simulate the bridge deck, LINK10 element is utilized to generate the cable, and the other components were built with BEAM188 element. The laboratorial physical model and its FE model are shown in Figure 1.

Figure 1. Bridge laboratorial physical model and its FE model

2.3. Selection of design parameters. There are some diﬀerences between the prototype and physical model. The major errors of laboratorial model come from materials, fabrication and boundary condition. Therefore, a total of seven parameters are selected as the objectives for investigation in FE model updating, they are summarized in Table 1. The inﬂuence scope of these parameters is sort descending as E1, D1, E4, D2, E2, E5 and E3. The parameter level for sample generating is changing around the base value with 10% step amplitude. The levels are determined by the amount of samples and method of DOE. Table 1. Design parameters for model updating

Parameters Notation Parameters Notation Model of aluminum alloy E1 Model of boundary cables E5 Model of deck connection E2 Density of aluminum alloy D1 Model of middle tower cross E3 Density of additional mass D2 Model of deck cables E4

2.4. Output variables of FE model analysis. Structural modal characteristics are widely used in FE model updating. In this study, the first 20 order frequencies and MAC are used to analysis the sensitivity of modal characteristic quantities to design parameters. Modal shapes show the spatial vibration mode of structures, field testing model shapes and calculated model shapes are always different because uncertain factors and errors are possibly brought in design, modeling, testing and calculation. MAC is adopted to estimate the difference between them. The ith MAC of modal shape is T 2 (φaiφei) MACi = T T (4) (φaiφai)(φeiφei)

where φai, φei is the ith simulated modal shape and testing modal shape respectively. 0 ≤ MACi ≤ 1, both modal shapes are the same when MACi = 1. 1834 L. ZHOU AND J. OU

Figure 2. Sensitivity of modal frequencies to parameters

2.5. Sensitivity analysis of design parameters to output. ANSYS software is used for numerical simulation, sensitivity of the lowest 20 modal frequencies, residual error and MAC of mode shapes with respect to the seven design parameters were obtained by using the forward difference method based on the calculation of 35 testing samples with 5 levels. The results are shown in Figures 2 and 3. Figure 2 illustrates the sensitivity of frequencies with respect to the seven design parameters, it indicates that frequencies have bigger sensitivity to the global parameters than the local ones, and the sensitivity decreases with localize of parameters. To one certain parameter, different order frequencies have different sensitivity. Figure 3 shows the sensitivity of MAC to design parameters. Similar to the frequencies, the global parameters have bigger sensitivity than the local parameters. Comparing Figure 2 with Figure 3, It is obvious that the frequencies more sensitive to design parameters than MAC.

Figure 3. Sensitivity of MAC to parameters

3. Significance Analysis Based on DOE. 3.1. Methods of DOE. With today’s ever-increasing complexity of models, DOE has become an essential part of the modeling process. In this study, several methods of ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1835 DOE are utilized to select samples for FE model simulation; they are full factorial design (FFD), orthogonal design (OD), uniform design (UD), Taguchi method (TD) and Central Composite Design (CCD). And variance analysis and regression analysis are adopted to study the influence between response output and design parameters. 3.2. Statistical analysis for data processing. Variance analysis studies the correlation between independent variable and dependent variable based on limited testing samples from DEO. Whether the independent variable has significant effect on the dependent variable is determined through F-test of Statistical Hypothesis Testing. Assumed that the factor A has r levels and the gross capacity of sample is n, the F-statistics could be calculated by SS /(r − 1) F = f (5) SSe/(n − r)

F obeys F-distribution with a general form as F (r−1, n−r) and P (F > Fa(r−1, n−r)) = a with a given significance level a, If F > Fa(r − 1, n − r), the null hypothesis will be rejected. Where SSf and SSe are the square sum of factors and errors, respectively, r − 1 and n − r are the degree of freedom (DOF) of factors and errors, respectively. Uniform design is a commonly used method of DOF. Compared with orthogonal design, the character of “balance and dispersion” is strengthened and the “regularity and com- parability” is weakened, so multiple linear regression analysis is used for data processing of uniform design samples. In this study, multiply liner regression analysis is employed by the module of multivariable analysis in Statistical Analysis System (SAS). SAS is one of most famous data analysis software recognized as the global standard for statistical analysis in terms of both breadth and depth, it has powerful functions in data processing, management and presentation, and has been extensively applied to data processing in the field of agriculture, biology, finance, medicine and so on [9,10]. Different functions of SAS can be implemented by corresponding programs, and the STAT module of SAS is applied to data statistical analysis. 3.3. Simulation and statistic analysis. In this paper, adopting the results of full factorial analysis as the reference values, the performances of other four methods of DOE are compared with it based on the significance analysis of modal eigenvalues. The process mainly includes following three steps. 1. Generate experimental samples. The selection of parameters is the same as sensitivity analysis. Experimental design of seven factors with three levels is employed, the ratio of three levels to the base value is 0.9, 1.0 and 1.1, respectively. The least samples are generated by corresponding methods of DOE for FE Simulation. 2. Simulation. All sets of experimental points are analyzed as input by FE simulation, and modal eigenvalues are extracted as output for the subsequent data processing. 3. Testing of significance. Variance analysis with a significance level of 0.05 (a = 0.05) is used for the significance test of FFD, OD, TD and CCD. Multiply liner regression by using SAS is adopted to process the results of UD with a significance level of 0.1 (t = 0.1). The selection of design parameters and modal eigenvalues are the same as sensitivity analysis. Studying the influence of parameters to the first 20 order frequencies and MAC with given significance level a = 0.05 and t = 0.1, when P (F ) < a (or P (T ) < t), it is believed that the parameters have significance influence on the eigenvalues. Tables 2 and 3 indicate the significance levels of parameters to modal eigenvalues, thr values indicate the number of parameters that have significant influence on the first 20 order modal eigenvalues. Table 2 shows the significance levels of frequencies. It indicates that all the five methods of DOE could reflect the trend of significance level of design parameters to frequencies, and it is obvious that the significance levels depend on the influence range of parameters, 1836 L. ZHOU AND J. OU Table 2. Significance level of Table 3. Significance level of parameters to frequencies parameters to MAC

Par. OD TD UD CCD FFD Par. OD TD UD CCD FFD E1 20 20 20 20 20 E1 3 12 5 18 20 E2 9 13 10 11 17 E2 0 13 3 4 5 E3 4 4 0 0 2 E3 4 12 0 0 0 E4 9 20 12 19 20 E4 3 14 5 18 18 E5 6 20 3 7 13 E5 0 5 0 6 9 D1 15 20 20 20 20 D1 6 14 8 13 14 D2 15 20 20 20 20 D2 2 13 9 15 15 that is, global parameters, such as the modulus and density of overall bridge and cables, significantly impact on frequencies, local parameters such as changes of bridge connections have little effect on frequencies. Assume the result of full factorial analysis as reference value is reliable, other four methods of DEO compared with it one by one with the same factors and levels, the smaller the difference between them, the better the method of DOE is. The results show that the availability of these methods in descending order is CCD, TD, UD and OD. The TD has better performance with fewer samples and CCD is better with little more samples. For local parameters, the significance test has big difference between each method, which may be due to different of methods and sample number used, that means more samples are necessary for significance test of local parameters. The significance levels of design parameters to MAC are summarized in Table 3. The main situation is similar to the frequencies; the global parameters are more significantly effect on MAC than local ones. It could be observed that the influence of parameters to MAC is different in each method of DOE. Compared with FFD, the result of CCD is more satisfied. On the other hand, OD, TD and UD are nearly invalidity to indicate the significance of each parameter.

4. Conclusions. In this paper, parameters selection for model updating is investigated by sensitivity analysis and statistic analysis based on the FE model simulation of laboratorial physical model of Shandong Binzhou Yellow River Highway Bridge. Sensitivity analysis which based on engineering experience has advantages of under- standability and little amount of calculation. It is feasible for simple models with few design parameters; however, it could only qualitatively analysis the influence of design parameters on output response. The significance analysis with reasonable samples generated by DOE has the ability to quantitatively analyze the significance levels of design parameters to characteristic quantities in deterministic simulation of FE model updating. It was observed by contrastive analysis that significance analysis is valid for frequencies by using the five methods of DOE mentioned above, but to model shapes, only CCD is successful.

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[1] J. P. Ou, Advances on vibration control and health monitoring of civil infrastructures in mainland China, International Symposium on Network and Center – Based Research for Smart Structures Technologies and Earthquake Engineering, pp.6-10, 2004. [2] A review of structural health monitoring literature: 1996-2001, Los Alamos National Laboratory Report, LA-13976-MS, 2003. [3] C. Liu and Y. P. Wang, A new evolutionary algorithm for multi-objective optimization problems, ICIC Express Letters, vol.1, no.1, pp.93-98, 2007. [4] J. Mottershed and M. I. Friswell, Model updating in structural dynamics: A survey, Journal of Sound and Vibration, vol.167, no.2, pp.347-375, 2003. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1837

[5] H. Li and H. Ding, Progress in model updating for structural dynamics, Advance in Mechanics, vol.35, no.2, pp.170-180, 2005. [6] K. D. Hjelmstad and M. R. Bana, On building ﬁnite element models of structures form modal response, Earthquake Engineering & Structural Dynamics, vol.24, no.1, pp.53-67, 1995. [7] Q. G. Fei, L. M. Zhang, A. Q. Li and Q. T. Guo, Finite element model updating using statistics analysis, Journal of Vibration and Shock, vol.24, no.3, pp.23-26, 2005. [8] T. B. Barker, Quality by Experimental Design, Marcel Dekker, New York, 1994. [9] D. Wu, J. F. Sun and L. Y. Feng, Expression of test power in hypothesis testing with SAS, Journal of Zhengzhou University (Medical Sciences), vol.42, no.6, pp.9-11, 2007. [10] P. Chen, C. Z. Wang, J. Zhou and P. Liu, Prediction and analysis for the index of Shanghai stock exchange by SAS system on monthly data, Journal of Systems Engineerin – Theory & Practice, no.6, pp.72-78, 2003.

ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1839-1844

DYNAMIC MODELING OF 3D FACIAL EXPRESSION

Jing Chi1,2 1School of Computer Science and Technology Shandong University Ji’nan, P. R. China peace world [email protected] 2Department of Computer Science and Technology Shandong Economic University Ji’nan, P. R. China Received February 2010; accepted April 2010

Abstract. We propose a novel dynamic modeling method for 3D facial geometry and motion captured at video rate. A new criterion for optimally matching two meshes is introduced in our method. Based on the new criterion, our method can automatically construct a deformable dynamic mesh that closely approximate the captured face mesh sequence without manually appointing corresponding points to guide each mesh matching. Experiments demonstrate the accuracy and eﬃciency of our proposed method. Keywords: Dynamic modeling, Facial expression, Mesh matching

1. Introduction. In computer graphics, dynamic modeling of 3D facial expression has been an important and challenging problem, not only for its wide application in expression recognition, synthetic character animation, etc. but also for its inherent difficulties in accurately capturing the likeness and performance of a human face. Due to the complex physical structure of human face, even the most detailed changes in expression can reveal rich moods and emotions, whereas humans are especially good at detecting and recognizing subtle expressions. So, accurate simulation of expression is very difficult. Although these difficulties may be overcome with the aid of highly skilled animators, it will spend tremendous amount of artistry, skill and time. Our goal is to capture the dynamics of a human face and create a model that accurately reflects his shape and dynamic expression without animator’s intervention in the whole modeling process as soon as possible. Generally, the face data are obtained by two ways. In the first way, a face mesh sequence is acquired at video rate with 3D scanner. Each mesh reflects the facial expression at a certain time. In the second way, two or more synchronized image sequences are taken from different viewpoints, from which the 3D surface meshes are reconstructed with spacetime stereo matching technique [1]. These two ways both yield spatially and temporally continuous meshes, but such a mesh sequence is inherently unstructured, uncompressed and incomplete since each mesh has different topology, and the intra-frame corresponding points mapping to the same point on the human face can not be found. These limitations make it difficult to accurately capture the dynamic expression and reanimate the captured expression. We resolve the problem by creating a single deformable mesh, named as a dynamic model, to integratedly represent the captured mesh sequence. The dynamic model is deformed to closely approximate each captured mesh to generate new meshes with the same topology. The integrated dynamic model will support further processing such as hole filling, expression editing, etc. Here, the approximation accuracy affects the modeling realism, and the manual intervention affects the modeling efficiency. So, research of more realistic and automatic methods for dynamic modeling is meaningful and urgent.

1839 1840 J. CHI 2. Background. Recent research on dynamic modeling with face data obtained at video rate has introduced many methods. [2,3] utilize a dynamic model to match the captured image sequence. [4,5] compute the dynamic model and the motion directly from the image sequence. These techniques in [2-5] all produce low-resolution results. [6,7] introduce high-resolution dynamic models to capture the fine-grain expression variation. [8-10] introduce non-rigid matching techniques to create a dynamic model. [8] extends the Iterative Closest Point (ICP) algorithm to non-rigid ICP framework by introducing new mesh matching constraints. Minimizing these constraints can deform the dynamic model towards the captured mesh. [9] segments the dynamic model into two-scale resolutions to match the global rigid and local non-rigid deformation respectively. The non-rigid matching integrates the implicit shape representation and Free Form Deformation (FFD). The implicit representation increases computational complexity while FFD is indirect to control deformation. The techniques in [8-10] all need users to designate facial feature correspondences to constraint the matching of dynamic model and each captured mesh, which spends large amount of skill and time, and not achieve automatic matching. Simi- larly, the techniques in [2-7] are also not automatic. [11-13] utilize optical flow as constraints to build the dynamic model. [11] uses optical flow to constraint intra-frame vertex motion, so as to automatically match a dynamic model to the depth map sequence recovered from images. The optical flow is estimated from the image sequence which is not always acquired. Moreover, the optical flow computation is complex and not robust, so the matching accuracy is unwanted in many cases.

3. Method. According to the above disadvantages, we propose a new automatic dynamic modeling method in this paper. A new criterion consisting of nearest-point constraint, normal-consistency constraint and regularization constraint is constructed in our method, which can automatically constraint the mesh matching in dynamic modeling process and generate suggested results.

Figure 1. Illustration of basic idea

3.1. Basic idea. Our method is based on the premise that arbitrary two adjacent meshes in the captured sequence are very close spatially and temporally. The captured mesh sequence is obtained with video rate, e.g., 25f/sec, so the premise can be ensured. The deformation between adjacent meshes is very small since they are very close. Assuming the captured mesh sequence consists of H frames, we now deform the hth frame to optimally match the h + 1th frame. For convenience, we call the hth frame source mesh and the h + 1th frame target mesh. In ideal case, each source vertex after being displaced should map to a point on the target mesh, and has the same normal with the target point. As shown in Figure 1, the mesh is target mesh, and the source vertices after being displaced are marked by dots. For example, the hollow dot maps onto the target vertex and has the same normal with the target vertex; the solid dot maps into the target triangle and has the same normal with the triangle. Obviously, the new mesh constructed by these displaced source vertices well reflects the shape of the target mesh since they are on the target mesh. It means that, to get ideal matching results, the distance between the source mesh after ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1841 being deformed and the target mesh should be small, and the normal difference between the source vertex after being deformed and its corresponding target point should also be small. We will give the matching criterion based on the distance and normal-consistency constraints in Section 3.2. Based on the matching criterion, we can use the first frame of the captured mesh sequence as a deformable dynamic model, and match it through the th whole sequence. Specifically, deform the first frame S1 to match the 2 frame and denote th the deformed mesh as S2, then S2 and the 3 frame satisfy the adjacent frame properties; th th deform S2 to match the 3 frame and denoted as S3; . . . ; deform SH−1 to match the H frame. After the matching process, all the meshes {Si|i = 1, 2,...,H} have the same topology and reflect the captured dynamic expression.

3.2. The matching criterion. Based on the above basic idea, we will discuss the new criterion for matching two adjacent meshes in this section. Let the captured mesh sequence be {Gh|h = 1, 2,...,H}. Where, each frame Gh = {Ph,Eh} with vertex set Ph = {phj} th th and edge set Eh = {(jh1, jh2)}. Take the matching between the h frame and the h + 1 th frame for example, we aim to solve for a displacement dhj for each vertex phj of the h frame such that the deformed mesh with vertex set {phj + dhj} optimally approximate the h + 1th frame. We give the new criterion as follows. As discussed above, to get ideal matching result, the distance between the hth frame th Gh after being deformed and the h + 1 frame Gh+1 should be small. The distance can be expressed as ∑ 2 E1 ({dhj}) = uhj kphj + dhj − chjk (1)

phj ∈Ph 0 0 where, the new mesh got by deforming Gh is denoted as Gh, phj + dhj is the vertex on Gh, and its nearest compatible point on the mesh Gh+1 is denoted as chj. k·k is the Euclidean distance. uhj is a weight factor to control the influence of the mesh Gh+1 on the mesh Gh. We call Equation (1) the nearest-point constraint. 0 A point p on Gh and a point c on Gh+1 is considered to be compatible if the difference in normal orientations between them is less than 90◦ and the distance between them is within 0 a threshold. For each point phj, we first search its nearest compatible vertex chj on Gh+1, 0 0 then find the nearest compatible point chj from chj and the triangles surrounding chj. If no compatible point could be found, uhj is set to zero. Here, the triangles surrounding 0 chj is computed and stored only once, and normal compatible is judged beforehand to remove unnecessary distance computation, all these accelerate the nearest-point search. Similarly, to get ideal matching result, the normal difference between the vertex on Gh after being displaced and its corresponding point on Gh+1 should also be small. The normal difference can be expressed as ∑ { } − 2 E2( dhj ) = vhj Nphj +dhj Nchj (2)

phj ∈Ph k·k where, phj + dhj, chj and is deﬁned as Equation (1). Nphj +dhj and Nchj are the unit normals at point phj + dhj and chj, respectively. vhj is a weight factor which will be set to zero when no corresponding chj is found. We call Equation (2) the normal-consistency constraint. In general, matching meshes only with the constraints (1) and (2) will not result in a very attractive mesh, because the neighboring vertices on the mesh Gh may displace to disparate parts of the mesh Gh+1. So, we add a new constraint to enforce the similar displacements on the neighboring vertices on Gh. Speciﬁcally, ∑ { } k − k2 k − k2 E3( dhj ) = djh1 djh2 / pjh1 pjh2 (3)

(jh1,jh2)∈Eh 1842 J. CHI where, pjh1 and pjh2 are the neighboring vertices on Gh. We call Equation (3) the regularization constraint. From Equations (1) – (3), we can get the new matching criterion as follows

E({dhj}) = a1E1 + a2E2 + a3E3 (4) where a1, a2 and a3 are the term weights. We can compute the optimal deformation of Gh to match the mesh Gh+1 by iteratively optimizing Equation (4). 3.3. Analysis. The new criterion does not contain feature correspondences constraint usually used in many existing mesh matching technique, so it does not need user to select feature points on the meshes, and consequently, it can achieve automatic matching between adjacent meshes. Moreover, the new criterion does not contain optical ﬂow constraint, so it can avoid unstable and complex computation. The nearest-point constraint and the regularization constraint are usually used in some existing techniques, but the normal-consistency constraint is the new proposed constraint in this paper. The normal- consistency constraint can well ensure the rationality and correctness of the intra-frame vertex motion.

(a) (b) (c) (d)

Figure 2. The computed deformation with diﬀerent constraints. (a) The hth frame; (b) The h + 1th frame; (c) Deformation with constraints (1) and (3); (d) Deformation with the new criterion

As show in Figure 2, (a) and (b) is two adjacent frames in a captured mesh sequence. The computed deformation of (a) to match (b) only with nearest-point and regularization constraints is (c). It can be seen from (c) that the vertices on the lower lip of (a) are wrongly displaced to the upper lip of (b). The computed deformation of (a) with new criterion is (d). Obviously, the vertices on the lower lip of (a) are displaced to correct locations. The normal at each new vertex is approximately consistent with the one at its corresponding point while the distance between two meshes is very small. As discussed as in Section 3.1, we can use the first frame to automatically match through the whole sequence. Firstly, we match G1 to G2 and denote the new deformed mesh as 0 0 0 G2; then, recursively get Gh+1 given Gh that has match the mesh Gh. All the new meshes { 0 | 0 } Gi i = 1, 2,...,H,G1 = G1 compose a mesh sequence with the same topology which reflects the dynamic expression and can be represented as the deformation of the dynamic mesh G1. If the first frame has holes, we can firstly use a user defined dynamic model to 0 0 match the first frame G1 [11] and denote the deformed mesh as G1, then use G1 to match through the whole captured sequence. 4. Experiments. The new dynamic modeling method is conducted on several different mesh sequences captured at video rate. Our system is implemented using C++ under the windows environment. Figure 3 shows one of the experiments. Figures 3(a) and (b) are the first and the second frames in the captured mesh sequence respectively. The deformation of (a) computed with the new criterion result in the new mesh (c) which optimally matches (b). (d) – (f) shows some selected matching results obtained in the whole matching process which well reflect the subtle expressions. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1843

(a) The ﬁrst frame (b) The second frame (c) The result to match (b)

(d) (e) (f)

Figure 3. The automatic matching results with the new method

5. Conclusions. Base on the properties between the adjacent frames in the captured mesh sequence acquired with video rate, we propose a new automatic method for dynamic modeling of 3D facial expression. The new proposed matching criterion not only ensures optimal intra-frame vertex motion without manual intervention, but also well simulates the subtle expressions. The new method may result in unwanted results when the adjacent frames are not close, e.g., the mesh sequence is not acquired with video rate. In the future work, we will look into improvement of the method by incorporating other new constraints.

Acknowledgment. This work is partially supported by the State 863 Project under grant 2009AA01Z304, the National Nature Science Foundation under grants 60970046, 60773166, the Project of Shandong Province Higher Educational Science and Technology Program under grant J08LJ72, 2007gg10001004, ZR2009GQ004. The authors gratefully acknowledge Prof. Li Zhang at University of Washington for his supply of 3D face data. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

REFERENCES

[1] J. Davis, R. Ramamoorthi and S. Rusinkiewicz, Spacetime stereo: A unifying framework for depth from triangulation, Proc. of the IEEE Conf. on Computer Vision and Pattern Recognition, pp.359- 366, 2003. [2] F. Pighin, D. H. Salesin and R. Szeliski, Resynthesizing facial animation through 3D model-based tracking, Proc. of the Int. Conf. on Computer Vision, pp.143-150, 1999. [3] V. Blanz, C. Basso, T. Poggio and T. Vetter, Reanimating faces in images and video, Proc. of the EUROGRAPHICS, vol.22, pp.641-650, 2003. [4] L. Torresani, D. B. Yang, E. J. Alexander and C. Bregler, Tracking and modeling non-rigid objects with rank constraints, Proc. of the IEEE Conf. on Computer Vision and Pattern Recognition, pp.493- 500, 2001. [5] S. D. Lin, J.-H. Lin and C.-C. Chiang, Combining scale invariant feature transform with principal component analysis in face recognition, ICIC Express Letters, vol.3, no.4(A), pp.927-932, 2009. [6] Y. Wang, X. Huang, C.-S. Lee, S. Zhang, Z. Li, D. Samaras, D. Metaxas, A. Elgammal and P. Huang, High resolution acquisition, learning and transfer of dynamic 3-D facial expressions, Com- puter Graphics Forum, vol.23, no.3, pp.677-686, 2004. 1844 J. CHI

[7] M. Wand, B. Adams, M. Ovsjanikov, A. Berner, M. Bokeloh, P. Jenke, L. Guibas, H.-P. Seidel and A. Schilling, Efficient reconstruction of nonrigid shape and motion from real-time 3D data, ACM Transactions on Graphics, vol.28, no.2, 2009. [8] B. Amberg, S. Romdhani and T. Vetter, Optimal step nonrigid ICP algorithms for surface registration, Proc. of the IEEE Conf. on Computer Vision and Pattern Recognition, pp.1-8, 2007. [9] X. Huang, S. Zhang, Y. Wang, D. Metaxas and D. Samaras, A hierarchical framework for high resolution facial expression tracking, Proc. of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshop, pp.22-29, 2004. [10] H. Li, R. W. Sumner and M. Pauly, Global correspondence optimization for non-rigid registration of depth scans, Eurographics Symposium on Geometry Processing, vol.27, no.5, pp.1421-1430, 2008. [11] L. Zhang, N. Snavely, B. Curless and S. M. Seitz, Spacetime faces: High resolution capture for modeling and animation, ACM Transaction on Graphics, vol.23, no.3, pp.548-558, 2004. [12] D. Decarlo and D. Metaxas, Optical flow constraints on deformable models with applications to face tracking, International Journal of Computer Vision, vol.38, no.2, pp.99-127, 2000. [13] D. Decarlo and D. Metaxas, Adjusting shape parameters using model based optical flow residuals, IEEE Trans. on Pattern Analysis and Machine Intelligence, vol.24, no.6, pp.814-823, 2002. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1845-1850

CHAOS IN SMALL-WORLD CELLULAR NEURAL NETWORK

Qiaolun Gu1 and Tiegang Gao2 1School of Information Technology and Engineering Tianjin University of Technology and Education Liulin Dong, Hexi District, Tianjin, P. R. China [email protected] 2College of Software Nankai University No. 94, Nankai District, Tianjin, P. R. China [email protected] Received February 2010; accepted April 2010

Abstract. This paper investigates complex dynamics of a class of small-world cellular neural network (SWCNN), which is constructed by introducing some random couplings between cells to adding to the original Chua-Yang CNN. The simulations show that SWCNN with 3-neurons displays complex characteristics from chaos to various periodic orbits for diﬀerent random coupling weight, and this phenomenon exists whether the random coupling direction is bidirectional or unilateral. The Lyapunov exponents spectrum and the bifurcation are also given to verify the results. Keywords: Small-world model, Cellular neural network, Chaos, Bifurcation

1. Introduction. It is well known that cellular neural networks (CNN’s) are arrays of nonlinear locally connected cells, such local connection property makes them perfectly suitable for VLSI implementation and analog image processing, so CNN has been successfully used for various high-speed parallel signals processing applications such as image processing, pattern recognition as well as modeling of various phenomenon in nonlinear systems [1-4]. Cellular Neural Networks (CNN’s) were introduced by Chua and Yang in [5], since then, a number of authors have studied nonlinear dynamics in CNNs, which are typical completely local connectivity. Zou and Nossek have found bifurcation and chaos in small autonomous networks with only two or three cells [6]. Biey et al. investigated equilibrium bifurcation and other complex dynamic in a ﬁrst-order autonomous space-invariant CNN [7]. Yang presents a new class of low dimensional chaotic and hyper-chaotic cellular neural networks modeled by ordinary diﬀerent equations with some simple local connections [8,9]. All the above research are based on the CNN with only local connections, however, in many cases in real life, many network topologies such as biological, technological and social networks are known to be not completely random nor completely local but somewhere in between, so Nishio proposed a new form of networks called Small-World Cellular Neural Network (SWCNN) [10,11], which is constructed by introducing some random coupling between cells of the original Chua-Yang CNN, and gives some typical application in image processing and watermarking technique based on the connection topology of SWCNN[12]. Among the various dynamics of CNN, deterministic chaos if of much interest and has been studied for its potential application in information security and optimization algorithm. In this letter, we investigated the chaotic dynamics of a one-dimensional regular array SWCNN and gave some bifurcation analysis. Based on Lyapunov exponents and bifurcation diagram, SWCNN with 3-neurons undergoes changes from chaos to various periodic orbits with random coupling weight varying.

1845 1846 Q. GU AND T. GAO The rest of the paper is organized as follows, in Section 2, the topology connection and the dynamics of SWCNN with 3-neurons are presented, some concluding remarks and conclusions are given in Section 3.

2. Chaos in 3-Neuron SWCNN.

2.1. Network topology of SWCNN. The SWCNN is obtained by adding some random coupling between cells in the original Chua-Yang CNN [5], i.e. besides its local coupling, each cell in the array is only permitted a maximum of one random coupling to another cell. The state equation of each cell is formulated by Equation (1). ∑ x (t) = −x (t) + I + A(i, j; k, l)y (t) ij ij ∈ kl ∑ c(k,l) Nr(i,j) + B(i, j; k, l)ukl(t) + WcM(i, j, p, q)ypq(t) c(k,l)∈Nr(i,j) 1 y (t) = (|x (t) + 1| − |x (t) − 1|) i = 1, 2, . . . , M, j = 1, 2,...,N. (1) ij 2 ij ij where Nr(i, j) denotes the neighbor cells of radius r of a cell c(i, j), A, B and I are real constants called as feedback template, control template and bias current, respectively; x(i, j), y(i, j) and u(i, j) denotes the state, output and input of the cell, respectively; M(i, j, p, q) describes the small-world map that is randomly created by program with indicating the probability pc in advance, if there is a coupling between one cell c(i, j) and another cell c(p, q), then the M(i, j, p, q) is equal to 1, otherwise is zero; and Wc stands for the coupling weight between the randomly coupled cells. Some complex dynamics and application of the small-world cellular neural network can be found in references [11,12].

2.2. Chaos in 3-neuron SWCNN. Some chaos phenomenon has been found in low dimensional cellular neural networks with some simple connection matrices [8], here the chaotic cellular network proposed by X. Yang is described in the following form x˙ = −x + W · f(x), x ∈ R3 (2) [ ] T 1 | | − | − | where f(x) = f(x1) f(x2) f(x3) , fi(xi) = 2 ( xi(t) + 1 xi(t) 1 ), W is weight matrix. It has been shown that when W is properly selected; 3-neurons cell networks display the complex dynamics such as chaos, limit cycle under the condition Wij = 0 for |i − j| > 1. Obviously, the CNN (2) is only a special case of SWCNN, i.e. when pc = 0, r = 1 the SWCNN is completely the same with the ordinary CNN. Here, we will discuss the SWCNN with 3-neuron, which are in the following form ∑ xi(t) = −xi(t) + I + A(i; k)yk(t) + WcM(i; p)yp(t) c(k)∈Nr(i) 1 y (t) = (|x (t) + 1| − |x (t) − 1|) i = 1, 2, 3. (3) i 2 i i It can be seen SWCNN (3) is very simple, and only has the random coupling to another cell compared with CNN (2), we will discuss the dynamics of system (3) under the two kinds of random coupling, which will be given in the following, the local connection matrix is chosen as   1.2 1.6 0 W =  −1.6 1 0.9  (4) 0 2.2 1.5 ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1847 2.2.1. The dynamics of (3) with no random coupling except for local connections. When there is no local connection between them, i.e. Wc = 0, this is the same form as CNN (2), the CNN is described in the following form  x˙ 1 = −x1 + 1.2f(x1) + 1.6f(x2) − −  x˙ 2 = x2 1.6f(x1) + f(x2) + 0.9f(x3) (5) x˙ 3 = −x3 + 2.2f(x2) + 1.5f(x3) The connection topology of CNN is illustrated in Figure 1. It can be proved by Runge- Kutta iteration formula that the phase portraits of CNN is periodic orbit.

Figure 1. The connection topology of CNN with only local connections

2.2.2. The dynamics of (3) with unilateral random coupling. We assume that the random coupling is unilateral, and weight Wc between cell x1 and x3 is an adjustable parameter. When pc = 1, the random coupling weight between x1 and x3 is changeable, the SWCNN equation is deﬁned by Equation (6).   x˙ 1 = −x1 + 1.2f(x1) + 1.6f(x2) + kf(x3) − −  x˙ 2 = x2 1.6f(x1) + f(x2) + 0.9f(x3) (6) x˙ 3 = −x3 + 2.2f(x2) + 1.5f(x3) The connection topology can be illustrated in Figure 3.

Figure 2. The connection topology of 3-neuron SWCNN with bidirectional random coupling

In order to study the dynamics of the SWCNN (6) with bidirectional random coupling between x1 and x3, Lyapunov exponents is used to help us judge the complex behavior of the system. Some simulations results are described as follows 1) For k = −0.06, three Lyapunov exponents are λ1 = 0.3095, λ2 = 0, λ3 = −0.5887. Therefore, chaos occurs for such a parameter, the phase portraits are shown in Figure 3(a). 2) For k = −0.092, three Lyapunov exponents are λ1 = −0.0645, λ2 = 0, λ3 = −0.2365. At this time, system (3) enters into two-periodic limit cycles, which are shown in Figure 3(b). 3) For k = −0.11, three Lyapunov exponents are λ1 = −0.1871, λ2 = 0, λ3 = −0.2001 the system evolves into a periodic limit cycle, which are shown in Figure 3(c). The Lyapunov exponents of (3) with the varying kare depicted in Figure 4. While the corresponding bifurcation diagram of state x with respect k is given in Figure 5. 1848 Q. GU AND T. GAO

(a) (b) (c)

Figure 3. Phase portraits of the SWCNN (6) with diﬀerent k, (a) chaos (k = −0.06), (b) two-periodic orbits (k = −0.092), (c) periodic orbits (k = −0.11)

Figure 4. Lyapunov expo- Figure 5. Bifurcation dia- nents versus k gram for increasing k

2.2.3. The dynamics of (3) with bidirectional random coupling. In this section, we assume that, besides its local connections, each cell in the array has up to one random coupling to another cell; moreover, the coupling direction is bidirectional, the connection topology of unilateral random coupling SWCNN illustrated in Figure 6.

Figure 6. The connection topology of 3-neuron SWCNN with unilateral random coupling

The SWCNN with 3-Neuron of unilateral random coupling is formulated by Equation (7).   x˙ 1 = −x1 + 1.2f(x1) + 1.6f(x2) + kf(x3) − −  x˙ 2 = x2 1.6f(x1) + f(x2) + 0.9f(x3) (7) x˙ 3 = −x3 + uf(x1) + 2.2f(x2) + 1.5f(x3) ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1849

where k stands for the coupling weight from cell x3 to x1, u stands for the coupling weight from cell x1 to x3. It has been shown that SWCNN (7) enters into limit cycle with parameters of u = 0, k = −0.05 from Section 2.2.3, we will show that, when k = −0.05, and varying u, system (7) has complex dynamics such as chaos and periodic orbits, the corresponding bifurcation diagram of state x1 with respect u is given in Figure 7. The stability of SWCNN (5) are summarized as follows 1) When −0.004 ≤ u ≤ 0 is satisfied, SWCNN (5) enters into a periodic orbits. 2) When −0.018 ≤ u ≤ 0 < −0.004 is satisfied, SWCNN (5) displays a two-periodic orbits. 3) When −0.02 ≤ u ≤ 0 < −0.018 is satisfied, SWCNN (5) shows a four-periodic orbits. 4) When −0.16 ≤ u ≤ 0 < −0.02 is satisfied, SWCNN (5) displays chaotic attractors. 5) When −0.2 ≤ u ≤ 0 < −0.16 is satisfied, SWCNN (5) enters into a periodic orbits. Some typical Lyapunov exponents of SWCNN (7) are tabulated in Table 1, the four- periodic orbits with u = −0.019 and chaotic attractor with u = −0.04 are shown in Figure 8. Table 1. Some typical parameter values of u that lead to different system portraits

u λ1 λ2 λ3 State of System 0 –0.2391 0 –0.6602 Periodic orbits –0.008 –0.2372 0 –0.6568 Two-periodic orbits –0.05 0.2668 0 –0.5953 chaos –0.096 –0.0751 0 –0.6935 Periodic orbits

Figure 7. Bifurcation diagram for increasing u

3. Conclusions. In this paper, we investigated complex dynamics of a class of small- world cellular neural network (SWCNN), which is constructed by introducing some random couplings between cells to adding to the original Chua-Yang CNN. The simulations show that SWCNN with 3-neurons displays complex characteristics from chaos to various periodic orbits for diﬀerent random coupling weight, and this phenomenon exists whether the random coupling direction is bidirectional or unilateral, and therefore may possess the better capabilities of solving various problems, compared with the conventional CNN with only local connections.

Acknowledgment. This work is partially supported by Key Program of the Tianjin Natural Science Fund, China (Grant # 07JCZDJC06600), and NSFC (Grant # 60873117). 1850 Q. GU AND T. GAO

(a) (b)

Figure 8. Phase portraits of the SWCNN (7) with diﬀerent u, (a) four- periodic orbits (u = −0.019), (b) chaotic attractor (u = −0.04)

REFERENCES [1] E. Y. Chou, B. J. Sheu and R. C. Chang, VLSI design of optimization and image processing cellular neural networks, IEEE Trans. Circuits Syst. I, Fundamental Theory Appl., vol.44, pp.12-20, 1997. [2] M. E. Yalcin, J. Vandewalle, P. Arena, A. Basile and L. Fortuna, Watermarking on CNN-UM for image and video authentication sign, Inter. J. Circuit Theo. Appl., vol.32, pp.591-607, 2004. [3] S. Wang and M. Wang, A new detection algorithm based on fuzzy cellular neural networks for white blood cell detection, IEEE Trans. Inform. Techno. in Bipmedicine, vol.10, pp.5-10, 2006. [4] Y. Chen and W. Su, New robust stability of cellular neural networks with time-varying discrete and distribute delays, International Journal of Innovative Computing, Information and Control, vol.3, no.6(B), pp.1549-1556, 2007. [5] L. O. Chua and L. Yang, Cellular neural networks: Theory, IEEE Trans. Circuits Syst., vol.35, pp.1257-1272, 1988. [6] F. Zou and J. A. Nossek, Bifurcation and chaos in cellular neural networks, IEEE Trans. Circuits Syst. I, Fundamental Theory Appl., vol.40, pp.166-173, 1993. [7] M. Biey, M. Gilli and P. Checco, Complex dynamics phenomenon in space-invariant cellular neural networks, IEEE Trans. Circuits Syst. I, Fundamental Theory Appl., vol.49, pp.340-345, 2002. [8] X. S. Yang and Q. Li, Horseshoe chaos in cellular neural networks, Int. J. Bifurcation and Chaos, vol.16, pp.157-161, 2006. [9] L. Wang, W. Liu, H. Shi and J. M. Zurada, Cellular neural networks with transient chaos, IEEE Trans. Circuit Syst. II, Express Briefs, vol.54, pp.440-444, 2007. [10] K. Tsurutak, Z. Yang, Y. Nishio and A. Ushida, Diﬀusion analysis of direction-preserving small-world CNN, Proc. of IEEE International Workshop on Cellular Neural Networks and their Applications, pp.352-357, 2004. [11] K. Tsurutak, Z. Yang, Y. Nishio and A. Ushida, On two types of network topologies of small-world cellular neural networks, Proc. of RISP International Workshop on Nonlinear Circuits and Signal Processing, pp.113-116, 2004. [12] G. Timar and D. Balya, Regular small-world cellular neural networks: Key properties and experiments, Proc. of the 2004 International Symposium on Circuits and Systems, pp.69-72, 2004. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1851-1856

EVALUATING THE QUALITY OF EDUCATION VIA LINGUISTIC AGGREGATION OPERATOR

Ying Qiao1, Xin Liu2 and Li Zou2

1School of Politics Xihua University Chengdu 610039, P. R. China [email protected] 2Mathematics College Liaoning Normal University Dalian 116029, P. R. China [email protected] Received February 2010; accepted April 2010

Abstract. Evaluating the quality of higher education is multi-criteria and group decision making problem. In this paper, we evaluate the quality of education based on linguistic aggregation operator, in which, evaluation linguistic values are represented by 2-tuple linguistic model. Moreover, we consider weights of experts as well as criteria in linguistic aggregation operator. The advantages of our method are that it is qualitative evaluation, evaluation results are represented by linguistic values, on the other hand, there is no loss of information due to using 2-tuple linguistic representation model. Our method can be an alternative method to evaluate the quality of higher education. Keywords: The quality of higher education, 2-tuple linguistic model, Linguistic aggregation operator, Decision making

1. Introduction. Education has a great deal of inﬂuence on the development of a country. By improvement in the quality of education, education has contributed to international competitiveness of its country. To evaluate the quality of higher education, there are many criteria to be used, e.g., Teaching Method, Quality of Students, Curriculums Oﬀered, Learning Environment, Basic Ability of Students, and Adaptability of Students. Hence, evaluating the quality of higher education is multi-criteria decision making. On the other hand, it is no doubt that the quality of higher education is evaluated by actors (e.g., educational experts, students and employers) to insure rationality. Hence, the problem of evaluating the quality of higher education is group decision making. Moreover, evaluating results of criteria, e.g., Learning Environment and Adaptability of Students, cannot be assessed precisely in a quantitative form but may be in a qualitative one, hence, the problem of evaluating the quality of higher education is also linguistic decision making, and the use of a linguistic approach is necessary in evaluating the quality of higher education. In linguistic decision analysis, we pay attention to solve decision making problems under linguistic information. The problem is associated with [1]: (1) The choice of the linguistic value set with its semantic; (2) The choice of the aggregation operator of linguistic information; (3) The choice of the best alternatives. In the above mentioned three steps, the aim of (1) consists of establishing the linguistic variable [2] or linguistic expression domain with a view to provide the linguistic performance values. In practice, fuzzy numbers or an ordered structure of linguistic values can be used to explain their semantic [2, 3]; the aim of (2) is to carry out the aggregation of linguistic information, there are many numeric aggregation operators [4, 5] and linguistic aggregation operators [6, 7, 8, 9] to

1851 1852 Y. QIAO, X. LIU AND L. ZOU aggregate them; the aim of (3) consists of ﬁnding the best alternatives from the linguistic performance values by a linguistic choice function. The organization of this paper is as following: In Section 2, we discuss the framework of the quality of higher education. Linguistic aggregation operator is reviewed in Section 3. In Section 4, we discuss evaluating the quality of higher education based on the 2-tuple weighted aggregation operator. We conclude in Section 5.

2. The Framework of the Quality of Higher Education. The quality of higher education is evaluated in numerous ways due to different education programmes [10, 11]. In this paper, we select “Teaching Method”, “Quality of Students”, “Curriculums Offered”, “Learning Environment”, “Basic Ability of Students” and “Adaptability of Students” as criteria, according to the six criteria, actors give their evaluations of universities (or colleges). Formally, evaluating the quality of higher education can be finished by the following decision table (Table 1):

Table 1. Evaluation of the quality of higher education

Teaching Quality of Curriculums Learning Basic Ability Adaptability Method Students Oﬀered Environment of Students of Students u1 u2 . . un

In Table 1, alternatives {u1, u2, ··· , un} are universities (or colleges), which are evaluated by actors according to the above mentioned six criteria. Actors are educational experts, students, and employers. In these criteria, we notice that evaluating results cannot be assessed precisely in a quantitative form but may be in a qualitative one, from a practical point of view, qualitative evaluating the quality of higher education is more suitable than quantitative evaluating. In this paper, we select the following linguistic values as evaluating linguistic value set of the problem: EV = {very low, fairly low, pretty low, medium, almost high, more or less high, very high}. (1)

Their semantics are explained by an ordered structure of EV , i.e., very low(s1) < fairly low(s2) < pretty low(s3) < medium(s4) < almost high(s5) < more or less high(s6)

Table 2. Evaluating results of 10 educational experts for university u1

s1 s2 s3 s4 s5 s6 s7 Teaching Method 2 3 2 2 1 Quality of Students 3 2 3 2 Curriculums Oﬀered 2 3 4 1 Learning Environment 2 4 1 3 Basic Ability of Students 1 3 4 2 Adaptability of Students 3 3 2 1 1

Table 3. Evaluating results of 10 employers for university u1

s1 s2 s3 s4 s5 s6 s7 Teaching Method 1 4 3 2 Quality of Students 1 4 4 1 Curriculums Oﬀered 2 4 3 1 Learning Environment 5 2 3 Basic Ability of Students 5 2 2 1 Adaptability of Students 7 2 1

Table 4. Evaluating results of 30 students for university u1

s1 s2 s3 s4 s5 s6 s7 Teaching Method 3 12 6 6 3 Quality of Students 6 12 12 Curriculums Oﬀered 3 14 4 6 3 Learning Environment 7 10 8 5 Basic Ability of Students 10 6 8 6 Adaptability of Students 15 8 6 1

3. Linguistic Aggregation Operator. Linguistic aggregation operator is to carry out the aggregation of linguistic information, formally, it aggregates semantics of evaluating linguistic values. In this paper, we adopt the 2-tuple linguistic representation model to express semantics of evaluating linguistic values, i.e., let S = {s0, ··· , sg} be the initial ﬁnite linguistic value set. Formally, the 2-tuple linguistic representation model is formed by (si, α), in which, si ∈ S(i ∈ {0, 1, ··· , g}) and α ∈ [−0.5, 0.5), i.e., linguistic information is encoded in the space S × [−0.5, 0.5). Based on the representation (si, α), we can easily obtain the following symbolic translation of linguistic values from β ∈ [0, g] to S × [−0.5, 0.5): ∆ : [0, g] → S × [−0.5, 0.5),

β 7−→ (si, α), (2) 1854 Y. QIAO, X. LIU AND L. ZOU in which, i = round(β)(round(·) is the usual round operation), α = β − i ∈ [−0.5, 0.5). Intuitively, ∆(β) = (si, α) expresses that si is the closest linguistic value to β, and α is the value of the symbolic translation. In fact, this model deﬁnes a set of transformation functions between linguistic values and 2-tuples linguistic representations as well as numeric values and 2-tuples linguistic representations. This makes us easily to process linguistic information, e.g., we have the following linguistic aggregation operators: Let a set of 2-tuples linguistic representations { ··· } ··· ∈ be x∑= (s1, α1), , (sn, αn) and weight vector W = (w1, , wn) such that wi [0, 1] n and i=1 wi = 1. 1. The 2-tuple arithmetic mean xe: ( ) ( ( )) ∑n 1 1 ∑n xe = ∆ × ∆−1(s , α ) = ∆ × β . n i i n i i=1 i=1 2. The 2-tuple weighted aggregation F w¯: ( ) ( ) ∑n ∑n w¯ −1 F = ∆ wi × ∆ (si, αi) = ∆ wi × βi . i=1 i=1 3. The 2-tuple OWA operator F e: ( ) ∑n e ··· × ∗ F ((s1, α1), (s2, α2), , (sn, αn)) = ∆ wj βj , j=1 ∗ { −1 | ··· } in which, βj is the jth largest of βi = ∆ (si, αi) i = 1, 2, , n .

4. Evaluating the Quality of Higher Education based on F w¯. In this paper, we adopt the 2-tuple weighted aggregation F w¯ to aggregate evaluating results of the quality of higher education, and EV is rewritten by

EV = {(s1, 0), (s2, 0), (s3, 0), (s4, 0), (s5, 0), (s6, 0), (s7, 0)}. Because there are three kinds of information sources, i.e., group of educational experts, group of employers and group of students, it is no doubt that their weights are different due to their professional background, in which, weights of educational experts about Teaching Method, Quality of Students, Curriculums Offered, and Basic Ability of Students are more than others, however, weights of employers about Basic Ability of Students and Adaptability of Students are more than others. On the other hand, weights of six criteria are different in evaluating of the quality of higher education, e.g., weights of Teaching Method, Curriculums Offered and Learning Environment are more than others. Based on the above mentioned analysis, we set different weights of different actors and criteria, which are shown in Tables 5 and 6, respectively. Table 5. Weights of actors for criteria

educational experts employers students Teaching Method 0.618 0.191 0.191 Quality of Students 0.4 0.4 0.2 Curriculums Oﬀered 0.618 0.191 0.191 Learning Environment 0.5 0.1 0.4 Basic Ability of Students 0.4 0.4 0.2 Adaptability of Students 0.3 0.5 0.2

According to statistics of evaluating results of every group, we adopt the following three steps to obtain evaluating results of every alternative: ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1855 1. For every alternative, every criterion and every group, we adopt the 2-tuple arithmetic mean xe to obtain evaluating result of the group for the alternative and the criterion; 2. For every alternative and every criterion, we adopt the 2-tuple weighted aggregation F w¯ to obtain evaluating result of three groups for the alternative and the criterion, in which, weights of actors are decided in Table 5; 3. For every alternative, we adopt the 2-tuple weighted aggregation F w¯ to obtain evaluating result of six criteria for the alternative, in which, weights of criteria are decided in Table 6. Table 6. Weights of criteria for the quality of higher education

Teaching Method Quality of Students Curriculums Oﬀered 0.206 0.128 0.206 Learning Environment Basic Ability of Students Adaptability of Students 0.206 0.127 0.127

Example 4.1. Continues Example 2.1. Here, names of 10 universities are anonymous, and denoted by {u1, u2, ··· , u10}. Table 7 shows that statistics of evaluating results of 10 educational experts.

Table 7. Evaluating results of 10 educational experts for u1

e1 e2 e3 e4 e5 e6 e7 e8 e9 e10 Teaching Method s4 s4 s3 s4 s3 s5 s7 s6 s5 s6 Quality of Students s4 s6 s5 s4 s6 s7 s6 s7 s5 s4 Curriculums Oﬀered s6 s6 s4 s4 s6 s5 s6 s5 s5 s7 Learning Environment s4 s7 s5 s5 s7 s5 s4 s7 s5 s4 Basic Ability of Students s4 s7 s6 s5 s6 s5 s6 s6 s5 s7 Adaptability of Students s3 s4 s3 s4 s4 s5 s6 s7 s5 s3

According to Table 7, we can obtain evaluating results of 10 educational experts for university u1, e.g., for Teaching Method, evaluating result of 10 educational experts is e x (s4, s4, s3, s4, s3, s5, s7, s6, s5, s6)

= s 4+4+3+4+3+5+7+6+5+6 = s4.7 = (s5, −0.3). 10

Table 8 shows that evaluating results of three groups for university u1. According to w¯ Tables 5 and 8, we use F to obtain evaluating result of three groups for u1, e.g., for Teaching Method, we have w¯ F ((s5, −0.3), (s6, −0.4), (s4, −0.2))

= 0.618 × (s5, −0.3) + 0.191 × (s6, −0.4) + 0.191 × (s4, −0.2)

= s(0.618×4.7+0.191×(5.6+3.8)) = s4.7 = (s5, −0.3).

The last column of Table 8 shows evaluating result for every criterion of u1. According to Table 6 and the last column of Table 8, we use F w¯ to obtain the ﬁnal evaluating result of u1, i.e., w¯ F ((s5, −0.3), (s6, −0.4), (s5, −0.13), (s5, 0.49), (s5, 0.3), (s4, 0.48))

= 0.206 × (s5, −0.3) + 0.128 × (s6, −0.4) + 0.206 × (s5, −0.13) + 0.206 × (s5, 0.49)

+0.127 × (s5, 0.3) + 0.127 × (s4, 0.48)

= s(0.206×4.7+0.128×5.6+0.206×4.87+0.206×5.49+0.127×5.3+0.127×4.48)

= s5.05 = (s5, 0.05). 1856 Y. QIAO, X. LIU AND L. ZOU

Table 8. Evaluating results of three groups for university u1

educational experts employers students result Teaching Method (s5, −0.3) (s6, −0.4) (s4, −0.2) (s5, −0.3) Quality of Students (s5, 0.4) (s6, −0.5) (s6, 0.2) (s6, −0.4) Curriculums Oﬀered (s5, 0.4) (s4, 0.3) (s4, −0.3) (s5, −0.13) Learning Environment (s6, −0.5) (s6, −0.2) (s5, 0.4) (s5, 0.49) Basic Ability of Students (s6, −0.3) (s5, −0.1) (s5, 0.3) (s5, 0.3) Adaptability of Students (s4, 0.4) (s4, 0.4) (s5, −0.2) (s4, 0.48)

5. Conclusions. Evaluating the quality of higher education is multi-criteria and group decision making problem. In this paper, we identify weights of experts as well as criteria in linguistic aggregation operator, and use the 2-tuple weighted aggregation operator to evaluating the quality of higher education, example shows that our method is an qualitative evaluation and no loss of information. Acknowledgment. This work is partly supported by the research fund of key laboratory of the radio signals intelligent processing (XZD0818-09) and technique support project of sichuan province (2008GZ0118).

REFERENCES [1] F. Herrera, E. Herrera-Viedma and J. L. Verdegay, A sequential selection process in group decision making with linguistic assessment, Information Science, vol.85, pp.223-239, 1995. [2] L. A. Zadeh, The concept of linguistic variable and its application to approximate reasoning, Part 1, 2, 3, Information Sciences, vol.8-9, pp.199-249, 301-357, 43-80, 1975. [3] Z. Pei, D. Ruan, J. Liu and Y. Xu, Linguistic values based intelligent information processing: Theory, methods, and application, in Atlantis Computational Intelligence Systems – Vol. 1, D. Ruan (ed.), Atlantis press and World Scientiﬁc, 2009. [4] Z. S. Xu and Q. L. Da, An overview of operators for aggregating information, International Journal of Intelligent Systems, vol.18, pp.953-969, 2003. [5] Z. S. Xu, Dependent uncertain ordered weighted aggregation operators, Information Fusion, vol.9, pp.310-316, 2008. [6] F. Herrera and L. Martineez, A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems, vol.8, pp.746-752, 2000. [7] Z. S. Xu, An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations, Decision Support Systems, vol.41, pp.488-499, 2006. [8] Z. Pei, D. Ruan, Y. Xu and J. Liu, Gathering linguistic information in distributed intelligent agent on the internet, International Journal of Intelligent Systems, vol.22, pp.435-453, 2007. [9] Z. Pei, Fuzzy risk analysis based on linguistic information fusion, ICIC Express Letters, vol.3, no.3(A), pp.325-330, 2009. [10] Y. Wang, Y. Qiao and Z. Pei, Combining evidence and its application in synthesis decision, Proc. of the 2nd International Conference on Machine Learning and Cybernetics, pp.1769-1801, 2003. [11] S. H. Khan and M. Saeed, Evaluating the quality of BEd programme: Students’ views of their college experiences, Teaching and Teacher Education, vol.26, no.4, pp.760-766, 2010. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1857-1862

COLLABORATIVE FILTERING ALGORITHM BASED ON FEEDBACK CONTROL

Baoming Zhao and Guishi Deng Institute of Systems Engineering Dalian University of Technology Dalian 116023, P. R. China [email protected] Received February 2010; accepted April 2010

Abstract. By comparing the feedback on the recommendation results provided by the users and prediction results provided by the collaborative recommendation, we calculate the prediction errors between them. The prediction errors are used in the feedback control- based collaborative recommendation model, which is built according to the feedback control theory and the collaborative recommendation model, which makes the prediction errors as one of the parameters modifying process of the traditional collaborative recommendation model in order to control the future recommendation results. According to the feedback control-based collaborative recommendation model, the traditional collaborative filtering algorithm is modified by using the machine learning methods and feedback control theory to adjust the recommender system to the user’s changed preference. Finally, we test the feedback control-based collaborative filtering algorithm in the Digg dataset with three different feedback control methods, and the results prove the new algorithm is effective and superior to the traditional collaborative filtering algorithm. Keywords: Collaborative filtering, Feedback control, Machine learning

1. Introduction. Recommendation systems refer to the systems which aim at filtering out the predicting items automatically on be half of the users according to their personal preferences. Recommendation is a key method to solve the information overload problem and has been developed for recommending items such as books, Usenet articles [1], movies, music and so on. Most of the recommendation systems provide the recommendation list in order to make the users choose which one is better; however, these systems are unable to use the users’ feedback to improve the accuracy of the system. In order to learn the users’ preference and preference changes, we focus on the errors between the users’ feedback to the recommendation results and the system prediction results, and how to use the prediction errors to control the future recommendation by modifying the parameters in collaborative filtering algorithm. The main contribution of this paper is using the machine learning methods to learn the users’ feedback in order to control and influence the future recommendations. We attempt to improve the predictions based on two assumptions: (1) Given a user, he will change his preference with the time, and these changes can be reflected in his feedback, (2) Given a system, the feedback control can influence the output and the results can be used to influence the input. Based on the assumptions, we transform the feedback to prediction errors, which react on the recommendation system. The remainder of this paper is organized as follows. Section 2 provides a brief review of related work. We present the feedback control-based collaborative recommendation model in Section 3. Section 4 provides the detail algorithm for the new model. Empirical evaluations of our approaches and comparisons with traditional collaborative filtering approach are presented in the Section 5. Section 6 draws conclusions and discusses future researches.

1857 1858 B. ZHAO AND G. DENG 2. Background. 2.1. Collaborative filtering. Collaborative filtering (CF) refers to a process for predicting items based on the preferences of other users with similar behavior. As one of the most successful technologies for recommender system, it has been wildly developed and used [2]. The collaborative filtering can be divided into two types: memory-based [3,4] and model-based algorithm [5,6]. In the collaborative filtering algorithm, there are two important steps: calculating the similarity between the active user and the other users, and calculating the prediction of some item for the user. 2.1.1. Pearson similarity. The Pearson similarity is one common method to calculate the similarities in the collaborative recommendation systems, given as [7] ∑ (v −v¯a)(v −v¯ ) sim(a, i) = √∑ j a,j ∑i,j i (1) − 2 − 2 j (va,j v¯a) j (vi,j v¯i) where sim(a, i) is the similarity between the ath user and the ith user (e.g., other users in the system), va,j is the rating of the ath user for the jth item, vi,j is the rating of the ith user for the jth item,v ¯a is the average of the ath user’s ratings,v ¯i is the average of the ith user’s ratings.

2.1.2. Prediction rating. Let Pa,j denote the prediction rating of the ath user for the jth item. The Pa,j can be computed by ∑I Pa,j =v ¯a + wˆ(a, i)(vi,j − v¯i) (2) i=1 ∑l wherew ˆ(a, i) = sim(a, i)/ |sim(a, i)|. i=1 2.2. Prediction errors. The deﬁnition of the prediction errors is that the diﬀerence between the user’ feedback for the item and the system prediction rating for the same item, given as

ea,j = Pa,j − Ta,j (3) where ea,j is the prediction errors of the ath user for the jth item, the Ta,j is the true rating of the ath user for the jth item. Assuming the system knows the exact accuracy similarity, which isw ˆ(a, i), the collaborative recommendation system will calculate the accuracy user preference according to the formulation 2. However, the assumption is impossible to exist due to some inevitable problem, such as the sparse of the datasets and the cold start etc.. What the recommendation can do is to approach the accuracy similarity as near as possible, which causes the error occurs. Let the w(a, i) be the accuracy similarity between the ath user and the ith user. The system will get the accuracy result for the user which is Ta,jgiven as ∑I Ta,j =v ¯a + w(a, i)(vi,j − v¯i) (4) i=1 So the ath user’s prediction errors for the jth item can be described as ∑I ea,j = Pa,j − Ta,j = (w ˆ(a, i) − w(a, i))(vi,j − v¯i) (5) i=1 From the formulation 5, the prediction error occurs due to the diﬀerence between the true similarity and the predicted similarity. The way to improve the accuracy of the system is to reduce the similarity deviation, making the similarity reﬂects the true relationship between the user and the others. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1859

In other way, let ei,j be the prediction errors occurs from the deviation between true rating of the ith user for the jth item and feedback of the ath user for the ith item, which can be given as: ei,j = vi,j −Ta,j; lete ˆi,j be the prediction errors occurs from the deviation between true rating of the ith user for the jth item and rating predicted by the system of the ath user for the ith item, which can be given as:e ˆi,j = vi,j − Pa,j.

2.3. Related works. The study of the feedback in the recommendation concentrates on the three aspects: The first issue is how to capture feedback. This study focus on how to get the feedback, without any doubt, a trustworthy system can get more feedback, and the users like the recommendation system could provide the reason why recommends these to them and consider their education and culture background [8]. During the interactive process, the privacy is also a key problem, the privacy protected mechanism is important to capture the user’s feedback [9]. The second issue is how to recognize the feedback. Liu used the Bayesian feedback cloud model to recognize the illegibility concepts (e.g. relatively like or relatively used well) [10]. The third one is how to apply the feedback in the recommendation. On the one hand, they learn the user preference changes and the rating style by tracing users’ feedback time [11]; On the other hand, the conversational recommendation, which includes the content-based system and collaborative-based system, recommends by asking the users what they need for several times [12]. However, the related work is based on the fixed model, and the adding item is just as the new item to the item profile, neglecting the relationship between the changes of user’s preference and the model.

3. Feedback Control-based Collaborative Recommendation Model. The new model for the collaborative commendation based on feedback control as follows:

Figure 1. Feedback control-based collaborative recommendation model

In the traditional collaborative recommendation model, the recommender collects the user’s profile, other users’ profile and profile of the items, calculates the prediction for the user on some item, and provides the results to the user. In the new model, the feedback is used to be compared with the prediction calculated by the recommender. After the comparison, errors matrix can be computed and used to be the data for the recommender to ‘learn’. In most SNS networks, the user’s friends like to provide the opinions on some interesting items (e.g. movies, images and so on), and the feedback which they provide can be used in this model. 1860 B. ZHAO AND G. DENG 4. Algorithms. The algorithm can be described as follows: (1) Calculate the similarity by using the formulation 1; (2) Predict some item for the user by using the formulation 2; (3) Compare the prediction and the feedback to compute the prediction error matrix; (4) Modify the similarity matrix by using the prediction errors (ei,j,e î,j) according to the feedback control algorithm; (5) Predict future preference for the user on different item using the new similarity matrix.

4.1. Prediction error and feedback time-based feedback control algorithm. Pre- diction error and feedback time-based feedback control (ETFC) algorithm needs to consider two factors: prediction errors and feedback time. We have two principles: (1) if the ei,j is smaller, the similarity should be bigger; (2) if the feedback is more current, the feedback is more important. Because of the fact that the smaller |ei,j| will cause |eî,j| bigger, the evaluation criteria for principle (1) can be described as the comparison of |ei,j| and |eî,j|. According to these two principles, we choose exponentially forgetting function as penalty function to punish the similarity which causes the system make the big prediction errors. The exponentially forgetting function can be given as: w0 = λiw, where 0.9 < λ < 1. The exponentially forgetting function could modify the similarity according to prediction errors (the principle (1) by choosing different λ (called forgetting factor), and according to the feedback time (principle (2)) by choosing different i at the same time. We can sort the user’s similarity matrix on time, given as (w(t), w(t+i), w(t+l)), which owns different penalty factor, that is (λl, λi+1, λi, λi−1, λ0). Fixing λ, because of λi+1 < λi < λi−1, it shows that the similarity with earlier time do little effort to the form of current similarity matrix. In contrast, we choose w0 = λiw, (λ > 1) as activation function to encourage the similarity which causes the prediction near to the feedback. The sorted similarity matrix also owns different activation factor, that is (λ0, λi−1, vλi, λi+1, λl), which shows the near time do bigger effort to form the current similarity matrix. The detail step of the ETFC algorithm is as follows: (1) compute the activation or penalty function by the formulation below:  ×  0.1 ei,j t  (1.2 − ) , if |ei,j| ≤ |eî,j| Max(|ei,j|) λ(ei,j, t) = × ,  0.1 ei,j l−t (1.0 − ) , if |ei,j| > |eî,j| Max(|ei,j|) where the Max(|ei,j|) is the maximum of the ei,j which is different according to different datasets; 0 (2) compute new similarity matrix: w(a, i) = λ(ei,j, t)w(a, i).

4.2. Steepest descent-based feedback control algorithm. Steepest descent-based feedback control (SDFC) algorithm using the steepest descent method to modify the ∑N ∑M 1 2 similarity. Let the error function be E = (f(Ta.j) − f(Pa,j)) , where f(x) = 2 a=1 j=1 1 is the Sigmoid function. The optimal similarity can be computed by calculating (1 + e−x) ∗ w = arg minw E(w). According to the steepest descent method, the weights updating ∂E rule can be computed as ∆w(a, i) = −η , where the η is the study rate to control ∂w(a, i) the step size for searching w∗. In the machine learning theory, the η can be choose from 0.1 to 1. The detail algorithm is as follows: ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1861 (1) calculate the ∆w(a, i), ∂E ∆w(a, i) = −η = η(d − f(P ))f(P )(1 − f(P ))(v − v¯); ∂w(a, i) a,j a,j a,j i,j (2) update the new similarity matrix: w(a, i)0 = w(a, i) + ∆w(a, i). 4.3. Hybrid-based feedback control algorithm. The hybrid-based feedback control (HFC) algorithm is combined ETFC algorithm and SDFC algorithm. The SDFC algorithm needs to learn the data for hundreds of times, wasting of too much time on achieving the convergence, but the SDFC algorithm could be combined with the ETFC algorithm in order to shorten the study time greatly. The algorithm is as follows: (1) calculate the w(a, i)0 = w(a, i) + ∆w(a, i) by using SDFC; 00 0 (2) calculate the w(a, i) = λ(ei,j, t)w(a, i) by using ETFC.

5. Experiments. 5.1. Dataset. In the experiment, we collect the dataset from Digg (http://digg.com) from June 2009 to January 2010, which contains 6958 items and 973 users. The dataset includes the information of users and items and especially the feedback with time stamp. The digg feedback shows the user like the item recommended by the system; and the comment feedback shows the user is so interesting in the recommendation results that they are willing to write the comment in several minutes and share it with friends. 5.2. Evaluation criterion. We employ the Mean Absolute Error (MAE) for evaluating the prediction accuracy. The MAE is the average of the absolute diﬀerence between the actual and predicted ratings. The measure has widely been used in the study of recommenders. A smaller value of MAE indicates a better performance.

Table 1. Performance comparison using MAE

TP CF ETFC HFC TP CF ETFC HFC 0.5 0.6463 0.6284 0.6282 0.5 0.6465 0.6295 0.6293 0.6 0.6367 0.6176 0.6171 0.6 0.6377 0.6193 0.6188 0.7 0.6354 0.6166 0.6162 0.7 0.6358 0.6177 0.6174 0.8 0.6271 0.6069 0.6061 0.8 0.6275 0.6082 0.6074 0.9 0.6115 0.5879 0.5867 0.9 0.6118 0.5891 0.5879 (a) AP=0.2 (b) AP =0.3

5.3. Experimental results. We did ten experiments according to the five different Training set percent (TP), which ranges from 0.5 to 0.9 and two different Active user percent (AP), which ranges from 0.2 to 0.3 and the study rate η = 0.2. As the Table 1 has shown that the collaborative recommendation based on feedback control make the MAE improved under the TP equals 0.5, 0.6, 0.7, 0.8 and 0.9 in the experiments. Especially, the Hybrid-based feedback control algorithm performs better than the ETFC and the traditional CF algorithm, which improved 4% at most. Besides that, if the new algorithm learns more items, the accuracy will be improved much bigger.

6. Conclusion and Future Work. In this paper, we built feedback control-based collaborative recommendation model. Based on the model, we proposed to use the machine learning method and feedback control theory to design the feedback control algorithms in order to control the future recommendation and to obtain the optimal user similarity matrix. We have tried three different feedback algorithms to control the CF algorithm in order to compare which one is better. The experiment with Digg dataset shows that the 1862 B. ZHAO AND G. DENG collaborative filtering algorithm based on feedback control is superior to traditional CF algorithm. For the future work, we are interested in studying which machine learning algorithm and feedback control algorithm is more effective in the collaborative recommendation based on feedback control, besides that, we will try our feedback control ideas in some other improved CF algorithms in order to test the popularity of the feedback control algorithm. Acknowledgment. This work is partially supported by Major Program of National Nat- ural Science Foundation of China (No. 70890080, 70890083), Natural Science Foundation of China (No. 70972059). Thanks to the Digg dataset.

REFERENCES [1] J. Konstan, B. N. Miller, D. Maltz, J. L. Herlocker, L. Cordon and J. Riedl, Applying collaborative filtering to usenet news, Communications of the ACM, vol.40, no.3, pp.77-87, 1997. [2] J. L. Herlocker, J. A. Konstan, A. Borchers and J. Riedl, An algorithmic framework for performing collaborative filtering, SIGIR Conference on Research and Development in Information Retrieval, pp.230-237, 1999. [3] J. S. Breese, D. Heckerman and C. Kadie, Empirical analysis of predictive algorithms for collaborative filtering, Proc. of the 14th Conference on Uncertainty in Artificial Intelligence Madison, pp.43-52, 1998. [4] A. Nakamura and N. Abe, Collaborative filtering using weighted majority prediction algorithms, Proc. of the 15th Int. Conference on Machine Learning Madison, pp.395-403, 1998. [5] L. Getoor and M. Sahami, Using probabilistic relational models for collaborative filtering, Proc. of Workshop on Web Usage Analysis and User Profiling, San Diego, 1999. [6] T. Hofmann, Collaborative filtering via gaussian probabilistic latent semantic analysis, Proc. of the 26th Ann. Int. ACM SIGIR Conference, Toronto, pp.259-266, 2003. [7] U. Shardanand and P. Maes, Social information filtering: Algorithms for automating ‘Word of Mouth’, Proc. of the Conference on Human Factors in Computing Systems Denver, pp.210-217, 1995. [8] L. Chen and P. Pu, Trust building in recommender agents, Proc. of the 2nd Int. Conference on E-Business and Telecommunication Networks, pp.135-145, 2005. [9] J. Canny, Collaborative filtering with privacy via factor analysis, Proc. of the 25th Int. ACM SIGIR Conference on Research and Development in Information Retrieval, New York, pp.238-245, 2002. [10] J. Liu and G. Deng, Analysis and design of Bayesian feedback cloud model, Systems Engineering- Theory and Practice, vol.28, no.7, pp.138-143, 2008. [11] T. Q. Lee and Y. Park, A time-based approach to effective recommender systems using implicit feedback, Expert Systems with Applications: An International Journal, vol.34, no.4, pp.3055-3062, 2008. [12] R. Rafter and B. Smyth, Conversational collaborative recommendation – An experimental analysis, Artificial Intelligence Review, vol.24, no.3-4, pp.301-318, 2005.

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DESIGN OF NODE WITH SOPC IN THE WIRELESS SENSOR NETWORK

Jigang Tong, Zhenxin Zhang, Qinglin Sun and Zengqiang Chen Department of Automation Nankai University Tianjin 300071, P. R. China [email protected]; [email protected] Received March 2010; accepted May 2010

Abstract. A wireless sensor network has been widely used but its real-time data processing capability is still limited. This paper proposes a novel wireless sensor network node design based on SOPC (System on a Programmable Chip). In our design we adopt two schemes in FPGA development board: It can be either embedded a single processor, various necessary IP core and custom IP core with FSL (Fast Simplex Link) in it; or a dual processor and relative IP core according to our actual needs. If necessary, a µCLinux operating system can also be embedded on it. The design makes full use of the superiority of SOPC in real-time data processing and it completes a better node design. Keywords: Wireless sensor network, SOPC, FPGA, ZigBee, Microblaze, µCLinux

1. Introduction. With rapid development of technology in many disciplines, a wireless sensor network has attracted extensive attentions and has relative research [1-3]. Ac- cording to the application environment and requirements, it is classified into multiple categories [4] and combines with a static and dynamic node, which makes the whole network more flexible and convenient [5-7]. The microprocessor of the nodes is often an 8bit, 16bit MCU or different series of ARM according to different needs [8]. However, when faced with various application fields, there are some limitations in its data-processing capacity and flexibility. SOPC based on FPGA affords one or multiple processor and plenty of logic cells, which all works in instruction pipeline like common processor. Moreover, it has super parallel processing capacity and flexible configuration. Therefore, it can solve these problems effectively. This paper proposes a novel wireless sensor network node design method based on SOPC. In the FPGA development board, a variety of IP cores and single (32-bit Mi- croblaze processor) or dual processor (two Microblaze) are embedded, and the operation system is µCLinux system. The method combines the advantages of the SOPC with the flexibility of wireless sensor networks, which achieve a superior design of sensor network node.

2. The Structure of Node and Radio Frequency Transceiver Module. 2.1. The structure of the sensor node. The structure and material object of network node based on SOPC are shown in Figure 1 and Figure 2, respectively. The node consists of two parts: radio frequency transceiver module which concentrates on CC2430 chip and real-time data processing module based on FPGA development board (Xilinx Spartan-3E-1600E, contains 1600,000 system cells). The radio frequency transceiver module is composed of CC2430 chip and serial driver chip SP3223E, which perform wireless interconnection, data receiving and sending. After hardware conﬁguration and software development, the embedded operating system of FPGA will perform data transceiver through its RS232 serial port together with radio frequency transceiver module.

1869 1870 J. TONG, Z. ZHANG, Q. SUN AND Z. CHEN

Figure 1. Sensor node struc- Figure 2. Sensor node mate- ture diagram rial object

2.2. Radio frequency transceiver module. ZigBee protocol is widely applied in the wireless sensor networks, and is considered as the most important technologies in improving the network control [9]. The designed radio frequency module is shown in Figure 3. The CC2430 makes use of its own MCU (8051) based on Zigbee protocol and CSMA/CA technology to communicate with other network nodes. To complete the data transmission of CC2430 UART, we need to initialize serial interface: set the clock control register CLKCON, and let the clock crystal frequency 32MHz. The P0 port function of CC2430 is set as peripheral function, which is consistent with the used pin in the hardware circuit design. An internal baud rate generator is on CC2430 chip. After setting the BAUD E bit of baud rate control register and BAUD E bit of generic control register in USART0, the baud rate used for UART transfers can be obtained according to the following equation: (256 + BAUD M) × 2BAUD E Bandrate = × F 228 The receiving and sending of data is realized by interruptions of serial transceiver. The way of serial communication is determined by control and status register and control register in USART0. Program in this Function body assigns the serial data to be sended to buﬀer register U0BUF of USART0. Finally, the interruption of the system is allowed to occur.

Figure 3. Radio frequency transceiver module schematic diagram

The setting and usage of radio frequency transceiver module is the same as the routine application. After its program setting is finished, it will send data to and receive data from other network nodes. Then, the whole system will begin to work. At the same time, the module alone can act as a coordinator, router or simple application in wireless network. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1871 3. Data-processing module of FPGA development board. It is well known that FPGA is a semi-custom chip with flexible design and usage. The unique capability of processing data module based on SOPC is flexible to customize the processing systems according to the needs. By assigning specific function to specific processor, tailored solutions can be obtained for different requirements. The FPGA development board contains plentiful peripheral I/O ports and memory modules. It can satisfy the requirements in the field data processing, such as real-time manner. The design embedded µCLinux system based on single processor or two and combines with basic hardware circuit on the board. 3.1. The setting of development environment. Linux is installed so as to establish a crosscompiler environment of µCLinux, and the EDK 9.2 and ISE 9.2 of Windows version are also installed. As shown in Figure 4, the transplant of µCLinux includes the design of hardware and software. Hardware design is completed by EDK and ISE, and software design is completed under the Linux environment. The rectangulars and ovals in Figure 4 are work under Windows and Linux respectively. Linux kernel obtains hardware information through the BSP (Board Support Package). The final configuration files of the hardware and software will be downloaded to FLASH in U-Boot.

Figure 4. The transplant ﬂow chart of µCLinux

3.2. The hardware conﬁguration of FPGA. In the hardware design, one can embed µCLinux system based on Microblaze processor in the FPGA development board, and combine with various necessary IP cores. In our design we embed a single or dual processors, various necessary and custom IP cores according to practical needs.

Figure 5. Minimum single processor hardware system

3.2.1. Minimum system with single processor. As shown in Figure 5, the minimum single processor system is designed to transplant µCLinux system. In the system, Microblaze is central processing unit and connects a PLB bus. 10/100 Ethernet is necessary to the configuration of target board. MDM is the Microprocessor debug module, and offers a JTAG interface. UART is used to be a standard I/O port; PLB TIMER is a system 1872 J. TONG, Z. ZHANG, Q. SUN AND Z. CHEN clock. If necessary, a custom IP core is connected to the Microblaze as its co-processor to accelerate the time-critical algorithm in the system. The above design ultimately gets a system bit file (that contains allocation, placement in FPGA, etc.). It creates a BSP file, which contains the information of peripheral address and is the basis of µCLinux operating on peripherals.

3.2.2. The system with dual processor. A common situation in a system is the appearance of real-time and non real-time tasks simultaneously, but a solution based on a single processor may be bogged down. In order to avoid the situation, one processor as the slave is dedicated to perform the real-time control task, and other regular and non-special tasks are performed by the master processor. There are many advantages in this scheme based on dual processors obviously. The designed dual processor architecture is shown in Figure 6, where the two processors exchange information by shared component and co-ordinate to realize some functions. The shared components include external memory controller (MPMC), shared local memory (BRAM), XPS Mailbox and XPS Mutex. They allow two processors to communicate in various ways. Sharing memory is the fastest asynchronous mode of communication. The key shared peripheral and memory is external memory controller MPMC. Shared BRAM provides an extremely fast way to transmit kilobyte sized data. XPS Mailbox is suitable for small and medium messages. XPS Mutex is used for communication synchronization.

Figure 6. Dual processor architecture

3.3. Software development of FPGA. When the hardware conﬁguration of FPGA is completed, we start to design the software which mainly includes software development of dual processor system and transplant of µCLinux system.

3.3.1. Software design of dual processor. During the designing process of dual processor software, the main problems are the assignment of the memory maps and communication between the two processors. Memory map of dual processors. As shown in Figure 7, the two MicroBlaze processor realize peripherals interface by mapping memory to I/O. Either processor uses a separate system bus. All memory and peripheral elements are totally isolated with the shared elements. Each shared memory is used in a non-conﬂicting manner. The two separate executables ﬁles (ELF) are mapped into its own local memories in the system. It is able to share code between the two processors by using shared memory when both processors are executing the same software. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1873

Figure 7. Dual MicroBlaze processor memory map

Communication and Synchronization. Between the two MicroBlaze processors, the most common communication manner is by shared memory and Mailbox. (1) Shared memory communication. Sharing memory communication is the most common way. Shared global variable or data is in memory, and software on one processor can access or modify the variable and make it visible for another. Here XPS Mutex hardware synchronization module is provided to create mutual exclusion regions. The processor is free to acquire or release the region and serially access it. When one processor accesses the region, another processor’s access is forbidden at the same time.

Figure 8. Dual processor Figure 9. Dual processor XPS mutex XPS mailbox

(2) Message Passing. The mailbox has a channel through which messages are queued in a FIFO manner from one end by a sender, and received at the other by the receiver. Figure 9 shows the XPS mailbox communication mode. The message passing between processors is in the form of read ( ) and write ( ) calls, and mailbox is treated as a serially accessed file. The communication between the processors can be in a synchronous or asynchronous mode. Besides, we need to assign one processor as the main processor and install µCLinux system, the other is the slave and used to perform the dedicated task. It completes in EDK . 3.3.2. The transplant of µCLinux system. We install relative tools in Linux, add the BSP, select the appropriate types of CPU and its peripherals, configure the appropriate softeware applications. After the above setting is completed, we compile the kernel of µCLinux and get the file image.bin, FS-Boot source file and U-Boot configuration file. Because the size of BRAM is too small, the U-Boot method is adopted: After the system is powered up, the FS-Boot get running to copy U-Boot file to DDR and make it run, the 1874 J. TONG, Z. ZHANG, Q. SUN AND Z. CHEN U-Boot will copy linux kernel file to DDR and achieve the boot of µCLinux. Until now we complete the transplant of µCLinux. After the configuration of FPGA, the use rate of internal resources is shown on Table 1 and Table 2. When the system is operating, the usage of DDR is 5304KB in single processor system or 5918KB in dual processor and its total memory is 60312KB. So it will reserve adequate resource for the user to develop it latter in this way. Table 1. Resource statistics Table 2. Resource statistics in single processor in dual processor

Parameter Usage Total Usage rate Parameter Usage Total Usage rate BUFGMUX 6 24 25% BUFGMUX 6 24 25% MULT18X18SIO 3 36 8% MULT18X18SIO 6 36 16% DCM 2 8 25% DCM 2 8 25% RAMB16 17 36 47% RAMB16 34 36 94% SLICES 4597 14752 31% SLICES 10309 14752 69%

4. Conclusions. The µCLinux system and relative hardware IP core are embedded in the FPGA development board. It connects the radio frequency transceiver module with serial port and process the transported data of wireless network in advance. A single or dual processor is embedded into the development board according to the practical situation. The scheme is able to meet with complicated ﬁeld data processing and control requirements. It makes good use of the advantages in wireless network and SOPC, and combines them well. Acknowledgment. This work is supported by the National Science Foundation of China under grant 60774088, the Specialized Research Fund for the Doctoral Program of Higher Education of China Under Grant 20090031110029.

REFERENCES [1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam and E. Cayirci, Wireless sensor networks: A survey, Computer Networks, vol.38, no.4, pp.393-422, 2002. [2] C. T. Li, M. S. Hwang and Y. P. Chu, An eﬃcient sensor-to-sensor authenticated path-key es- tablishment scheme for secure communications in wireless sensor networks, International Journal Innovative Computing, Information and Control, vol.5, no.8, pp.2107-2124, 2009. [3] H. Nakano, A. Utani, A. Miyauchi and H. Yamamoto, An eﬃcient data gathering scheme using a chaotic PCNN in wireless sensor networks with multiple sink nodes, ICIC Express Letters, vol.3, no.3(B), pp.805-811, 2009. [4] R. M. Ruairi, M. T. Keane and G. Coleman, A wireless sensor network application requirements taxonomy, Proc. of 2nd IEEE Conference on Sensor Technologies and Applications, Cap Esterel, France, pp.209-216, 2008. [5] D. Culler, D. Estrin and M. Srivastava, Guest editors’ introduction: Overview of sensor networks, Computer, vol.37, no.8, pp.41-49, 2004. [6] R. C. Luo, L. C. Tu and O. Chen, Auto-deployment of mobile nodes in wireless sensor networks using grid method, Proc. of the 3rd IEEE Conference on Industrial Technology, Hong Kong, pp.359-364, 2005. [7] I. F. Akyildiz and I. H. Kasimoglu, Wireless sensor and actor networks: Research challenges, Ad Hoc Networks, vol.2, no.4. pp.351-367, 2004. [8] S. Liang, Y. Tang and Q. Zhu, Passive wake-up scheme for wireless sensor networks, ICIC Express Letters, vol.2, no.2, pp.149-154, 2008. [9] ZigBee Technical Documents, http://www.zigbee.org. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1875-1880

RESEARCH ON THE SENSORLESS CONTROL OF SPMSM BASED ON A REDUCED-ORDER VARIABLE STRUCTURE MRAS OBSERVER

Lipeng Wang, Huaguang Zhang, Zhaobing Liu, Limin Hou and Xiuchong Liu

School of Information Science and Technology Northeastern University No. 11, Lane 3, WenHua Road, HePing District, Shenyang 110819, P. R. China [email protected] Received February 2010; accepted April 2010

Abstract. Due to id = 0, based on the mathematical model of surface permanent magnet synchronous motor (SPMSM), a scheme of a reduced-order MRAS with variable structure controller as the adaptive mechanism is proposed in this paper. The new MRAS scheme is adopted to estimate the speed and position of the motor, acting as the feedback sensor like the speed/position shaft sensor. The method has simple structure and robustness to the variation of speed command and load torque. Theoretical analysis and matlab simulation results have veriﬁed the feasibility and eﬀectiveness of the proposed method. Keywords: SPMSM, Variable structure control, Reduced-order, MRAS, Sensorless

1. Introduction. Permanent magnet synchronous motors (PMSMs) have been widely used due to its rugged construction, easy maintenance, high eﬃciency, high torque to current ratio, and low inertia. In general, a sensor like optical encoder is necessary for the PMSM control system in order to obtain the rotor position and speed. However, sensors increase the complexity, weight and cost of the system. Nowadays, many researchers have paid attention to the sensorless of PMSM using model reference adaptive system (MRAS) [1-5]. Among them, the reference [1] applies full-order MRAS to estimate speed/position. The reference [2] adopts MRAS based on the theory of parameter optimization, but due to the application of the Quasi Gradient Decent Algorithm, the method is a bit complicated. In this paper, id = 0 of vector control is adopted, so reduced-order MRAS could be induced for the SPMSM. Sliding mode variable structure (SMC) is simple, and easy to combine with other intelligent methods, most of all it has robustness to external disturbances [6-10]. In order to reduce the complexity of the control algorithm and enhance the robustness of the system, a novel reduced-order MRAS control strategy with the variable structure controller as adaptive mechanism is proposed in this paper. The stability of the system is proved by Lyapunov theory and Matlab simulation results have veriﬁed the proposed method has great robustness.

2. Problem Statement and Preliminaries. For simplicity, several assumptions are made in the PMSM mathematical model. Magnetic saturation is neglected and motor is assumed to have a smooth rotor. No saliency eﬀect is considered. The induced EMF is sinusoidal and eddy current and hysteresis losses are assumed to be negligible. Thus the electrical equations of the PMSM can be described in the d-q rotating reference as follows:

1875 1876 L. WANG, H. ZHANG, Z. LIU, L. HOU AND X. LIU

  di R u  d − s d  = id + weiq +  dt Ld Ld   diq − Rs − − φr uq  = iq weid we +  dt Lq Lq Lq dw B 1 1 (1)  r = − w + T − T  r e L  dt J J J  3pφ  T = r i  e q  2 we = pwr where, ud, uq, id, iq are stator voltage and current in d-q axes; Ld, Lq are inductances in d-q axis, here Ld = Lq = L for the SPMSM; Rs is stator resistance; φr is rotor magnetomotive force; we is electronic angular velocity; wr is rotor angular velocity; B, J are friction coefficient and monent of inertia; p is the number of the poles of the motor. From (1), we can get [ ] [ ] [ ] i + φ /L i + φ /L u + R φ /L P d r d = A d r d + B d s r d (2) iq iq uq [ ] [ ] i + φ /L u + R φ /L We define i0= d r d , u0= d s r d , P is the differential operator (P = iq uq d/dt) then

P i0 = Ai0 + Bu0 (3) [ ] [ ] −R /L w 1/L 0 where A = s d r , B= d . −wr −Rs/Lq 0 1/Lq The equation of the adjustable model can be given as

piˆ0 = Aiˆ 0 + Bu0 (4) [ ] [ ] [ ] ˆ − ˆ0 id + φr/Ld ˆ0 ud + Rsφr/Ld ˆ Rs/Ld wˆr where i = , u = , A= − − . ˆiq uq wˆr Rs/Lq Deﬁne the generalized error e = i0 − iˆ0, and (5) is obtained by subtracting (4) from (3). [ ] [ ][ ] [ ] − ˆ0 ed Rs/Ld wr ed − − id P = − − J(wr wˆr) ˆ0 (5) eq wr Rs/Lq eq iq [ ] 0 −1 where e = i0 − iˆ0 , e = i0 − iˆ0 , J = . d d d q q q 1 0 From Equation (5), we can get

P e = Ae − Iw v = De (6)

− − ˆ0 ˆ0 where w = J(wr wr)i , select D = I, then v = Ie = e. According to the theorem of Popov hyperstability, if the following conditions: −1 1) the forward∫ path transfer matrix H(s) = D(SI − A) is strictly positive real. t0 T ≥ − 2 ≥ 2) η(0, t0) = 0 v wdt γ0 , where t0 0, γ0 is a positive constant, which is independent of t0 are satisfied, the system of the MRAS speed identification is asymptotically stable in the large scale and lim e(t) = 0. t→0 ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1877 3. Reduced-order Variable-structure MRAS Speed Identification. According to the theorem of Popov hyperstability, based on conventional full-order MRAS [1], replacing 0 0 id, iq with id, iq, the estimated speed could be described as follows: φ wˆ = 2w ˆ /p = 2{k [i î − i î − r (î − i )] r e p d q q d L q q ∫ q t φr + Ki[idîq − iqîd − (îq − iq)]dτ}/p (7) 0 Lq

where, id, îd are the real and observered current of d-axis current respectively; iq, îq are the real and observered current of q-axis current respectively. Due to id = 0 control strategy is applied, id, îd are nearly zero, so the reduced-order MRAS could be deduced as follows [3]: ∫ t φr φr wˆr = 2w ê/p = 2[kp(îq − iq) + Ki(îq − iq) dτ]/p (8) Lq 0 Lq In this paper, the sliding mode variable structure strategy is used instead of the conventional constant gain PI controller as the adaptive mechanism to fit with the speed- estimation problem. A new speed-estimation adaptation law for the sliding mode scheme is based on Lyapunov theory to ensure stability and fast error dynamics. Define the error of q-axis current as e1 = îq − iq, and choosing the sliding surface as ∫ t S = e1 + k e1(τ)dτ (9) 0 such that the error dynamics at the sliding surface S = 0 will be forced to exponentially decay to zero. When the system reaches the sliding surface, this gives ˙ S =e ˙1 + ke1 = 0 (10) so we could get

Rs φr (k − )eq + (we − wˆe) + weid = 0 (11) Lq Lq

Due to id = 0, if eq = 0, thenw ˆe = we. The estimated speed is designed as follows:

wˆr = 2w ˆe/p = 2kssat(S, ε)/p (12) { σ/ε (|σ| ≤ ε) sat(σ) = (13) sign(σ)(|σ| > ε)

Theorem 3.1. If the reaching condition (SS˙ < 0) is satisfied, with the designed speed identification law in (12), the estimated speed converges to the actual value quickly and accurately, and the designed speed identification system will be stabilized. Proof: In order to prove the stability of the designed reduced-order variable structure MRAS [6], define the lyapunov function V as V = ST S (14) The derivative of the Lyapunov function (14) can be derived as

˙ T φr Rs V = S [ (wr − kssat(S)) + (k − )e1] Lq Lq

T φr Rs ≤ |S |[ (wr − kssat(S)) + (k − )e1] (15) Lq Lq 1878 L. WANG, H. ZHANG, Z. LIU, L. HOU AND X. LIU If the inequality

Lq Rs ks > | (k − )e1 + wr| (16) φr Lq is satisfied, then ST S < 0, V˙ < 0. and the system state trajectories are forced toward the sliding surface and stay on it in the finite time. Theorem 3.2. The designed speed identification law in (12) is robust to the disturbance. Proof: Considering that the error existing in the speed identification system affect the designed sliding surface, such as measure error, load disturbance etc., the dynamics of the sliding surface is rewritten as ˙ ˙0 0 S = eq + eq + ζ (17) where ζ denotes the sum of various noise. The derivative of the Lyapunov function (14) is

˙ T φr Rs V = S [ (wr − kssat(S)) + (k − )e1 + ζ] Lq Lq

T φr Rs ≤ |S |[ (wr − kssat(S)) + (k − )e1 + ζ] (18) Lq Lq If the inequality is given by

Lq Rs ks > | (k − )e1 + wr + ζ| (19) φr Lq then V˙ < 0, and the system trajectories are still forced toward the sliding surface, which indicates the designed control system is stable in the situation of external disturbances. 4. Simulation Results. Based on the traditional magnetic orientation control, the reference d-axis current id = 0 and SVPWM method is used in the control of the two-level three-phase inverter. The reduced-order variable structure MRAS scheme acts as the feedback sensor like the speed/position shaft sensor. It can work out the rotor’s angular speed and produce the rotor’s angular position. The control block diagram of the whole system is shown in Figure 1. The parameters of a PMSM used in Figure 1 is shown in Table 1. Table 1.

Parameters Value Base speed wb 2000 rpm Armature resistance Rs 0.9585 Ω d-axis inductance Ld 0.00525 H q-axis inductance Lq 0.00525 H Magnet ﬂux linkage φr 0.1827 W b Number of poles p 8 Motor inertia J 0.0006329 Kg · m2 Friction coeﬃcient B 0.0003035 N · m · s

During the simulation, the parameters of the the reduced-order variable structure MRAS are chosen as: ks = 1000, ε = 2, k = 200. The system is started with no load. Then the proposed scheme is veriﬁed by the test of two operating conditions deﬁned by 1) The speed command (w∗) changes from 80rad/s to –80rad/s at t=0.09s. 2) The speed command changes from 0 to 160rad/s in 0.05s, The system is started with no load. The load torque (TL) is increased to 5Nm at t=0.08s, back to 0Nm at t=0.12s, and then decreased to –5Nm at t=0.16s, back to 0Nm at 0.2s. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1879

Figure 1. Block diagram of the sensorless control system

100 2

80 1.5 60 82 1 81 40 80 0.5 20 0.04 0.05 0.06

0 0

Speed (rad/s) −20 −0.5 Speed Error (rad/s) −40 −1 −60 −1.5 −80 w wˆ −100 −2 0 0.05 0.1 0.15 0.2 0.25 0 0.05 0.1 0.15 0.2 0.25 Time (s) Time (s) (a) The speed (b) The speed error

Figure 2. Dynamic response of the proposed system when the reference speed change

Figures 2 and 3 show the responses of the system under the conditions of the speed command and load torque variation. In Figure 2, the transient speed responses have a good dynamic performance and the maximum speed error is 0.5rad/s (accuracy is 0.625%) if the speed command is abruptly varied from the positive value to the negative value. In Figure 3, the estimated speed quickly approaches the actual value in case of two suddenly load variation, the speed error is always kept at nearly zero during the steady state and the maximum speed error is 1.2rad/s (accuracy is 0.75%).

1 1 1880 L. WANG, H. ZHANG, Z. LIU, L. HOU AND X. LIU

180 2

160 1.5 165 140 1

120 0.5 100 160 0 80

Speed (rad/s) −0.5 60 Speed Error (rad/s) 155 0.1 0.15 0.2 0.25 −1 40

20 −1.5 w wˆ 0 −2 0 0.05 0.1 0.15 0.2 0.25 0 0.05 0.1 0.15 0.2 0.25 Time (s) Time (s) (a) The speed (b) The speed error

Figure 3. Dynamic response of the proposed system when the load torque change

5. Conclusions. In this paper, a scheme of a reduced-order variable structure MRAS is proposed for SPMSM. The stability of the system is proved by Lyapunov theory. Under the conditions of the variation of speed command and load torque, simulation results have verified the proposed method has satisfactory performance for the speed identification. Acknowledgment. This work was supported by National Nature Science Foundation of China (50977008) and the Special Fund for Basic Scientific Research of Central Colleges, Northeastern University (N090604005).

REFERENCES [1] M. Zhang, Y. Li, T. Zhao, Z. Liu and L. Huang, A speed fluctuation reduction method for sensorless PMSM-compressor system, IEEE, pp.1633-1637, 2005. [2] F. Zhou, J. Yang and B. Li, A novel speed observer based on parameter-optimized MRAS for PMSMs, ICNSC, pp.1708-1713, 2008. [3] Z. Wang, Q. Teng and C. Zhang, Speed identification about PMSM with MRAS, Proc. of the 6th IEEE IPEMC, pp.1880-1884, 2009. [4] Y. Liu, J. Wan, G. Li, C. Yuan and H. Shen, MRAS speed identification for PMSM based on fuzzy PI control, Proc. of the 4th IEEE Conference on Industrial Electronics and Applications, pp.1995-1998,

2009. 1 [5] Y. Liang and Y. Li, Sensorless control of PM synchronous motors based on1 MRAS method and initial position estimation, Electrical Machines and Systems, vol.1, pp.96-99, 2003. [6] M. Zhang, Z. Yu, H. Huan and Y. Zhou, The sliding mode variable structure control based on composite reaching law of active magnetic bearing, International Journal of Innovative Computing, Information and Control, vol.2, no.1, pp.59-63, 2008. [7] X. Zhong, H. Xing and K. Fujimoto, Sliding mode variable structure control for uncertain stochastic systems, International Journal of Innovative Computing, Information and Control, vol.3, no.2, pp.397-406, 2007. [8] Y. Jiang, Q. Hu and G. Ma, Design of robust adaptive integral variable structure attitude controller with application to ﬂexible spacecraft, International Journal of Innovative Computing, Information and Control, vol.4, no.9, pp.2431-2440, 2008. [9] H.-M. Chen, Z.-Y. Chen and J.-P. Su, Design of a siding mode controller for a water tank liquid level control system, International Journal of Innovative Computing, Information and Control, vol.4, no.12, pp.3149-3159, 2008. [10] S. M. Gadoue, D. Giaouris and J. W. Finch, MRAS sensorless vector control of an induction motor using new sliding-mode and fuzzy-logic adaptation mechanisms, IEEE Transactions on Energy Conversion, pp.1-9, 2009. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1881-1886

PRODUCTION PLANNING BASED ON EVOLUTIONARY MIXED-INTEGER NONLINEAR PROGRAMMING

Yung-Chien Lin1, Yung-Chin Lin1,2 and Kuo-Lan Su2

1Department of Electrical Engineering WuFeng Institute of Technology Chiayi County 621, Taiwan { chien-lin; yclin }@mail.wfc.edu.tw

2Department of Electrical Engineering National Yunlin University of Science and Technology Yunlin County 640, Taiwan [email protected] Received February 2010; accepted April 2010

Abstract. Production planning is one of the most important decision-making problems in manufacturing processes. The problem is complex due to coupling with combinatorial property and conflict constraints. To describe production planning, a mixed-integer nonlinear programming (MINLP) model is developed to formulate this decision-making problem. On the other hand, in order to effectively make an optimal decision, a mixed- integer evolutionary algorithm is proposed to solve this MINLP problem. Finally, an experimental example is used to test the algorithm. The experimental results demonstrate the proposed algorithm can effectively handle the production planning problem. Keywords: Production planning, Mixed-integer nonlinear programming, Evolutionary algorithm

1. Introduction. In a batch manufacturing system, production planning is one of the most important decision-making problems [1]. In such a manufacturing system, several alternative production routes are available to perform the same operations, and the selection of production routes makes a vital impact on the benefit and performance of the manufacturing system. Hence, in order to take into account the investment cost, operating cost and production profit simultaneously, the optimal design of production planning is important in such a production decision-making problem. In order to describe this decision-making problem, we develop a mixed-integer nonlinear programming (MINLP) model to formulate this production planning problem. In the MINLP model, continuous variables are used to describe the interactive relationships (e.g. mass balances, energy balances, physical phenomena, etc.), and integer variables are used to represent the existence of processes and the operational status of the processing units. Due to the coupling with combinatorial property and conflict constraints, this decision-making problem is complex and difficult to solve. Evolutionary algorithms (EAs) [2-13] have been demonstrated a promising candidate for solving complex optimization problems, including the constrained optimization problems. For constrained optimization problems, Michalewicz and Schoenauer [13] surveyed and compared several constraint-handling techniques used in EAs. Of these techniques, the penalty function method is one of the most popularly used techniques to handle the constraints. However, the penalty function methods have a fatal drawback, that is, when the penalty parameters become large, the penalty function tends to be ill-conditioned near the boundary of feasible domain. Thus it may lead to a local solution or an infeasible

1881 1882 Y.-C. LIN, Y.-C. LIN AND K.-L. SU solution. In order to improve this drawback, we develop a mixed-integer evolutionary algorithm based on Lagrange method to solve the constrained MINLP problems. In this paper, we not only formulate an MINLP model to describe the production planning problem, but also propose a mixed-integer evolutionary algorithm to handle them. The proposed algorithm has been successfully applied to a number of mixed-integer optimization problems [14,15]. Finally, a production planning problem presented by Karimi [1] is employed to test the performance of the proposed method. The computational results demonstrate that the proposed method performs much better than the penalty method. 2. MINLP Formulation for Production Planning. Consider an N-product multipurpose process, and assume that the production occurs in the form of the long campaigns. To formulate all possible production plans, we must identify all possible sets of compatible products. The compatible products mean that two or more products can be produced simultaneously; i.e., no processing unit is used by more than one product at the same time. From these sets, we ﬁrst identify the maximal sets, which are not subsets of any other set. For example, consider a 2-product multipurpose process, and its scheme is shown in Figure 1. In Figure 1, the compatible product sets are:

{P1 (Route1)} , {P2 (Route1)} , {P1 (Route2)} , {P1 (Route1) , P2 (Route1)} and {P1 (Route1) , P1 (Route2)} .

Hence, the maximal sets are {P1 (Route1) , P2 (Route1)} and {P1 (Route1) , P1 (Route2)}.

Figure 1. Multipurpose batch process with multiple production routes In addition to using the aforementioned intuitive procedure to derive the maximal sets, a systematic procedure given by Vaselenak et al. [16] can be used to derive the same maximal sets. Let n denote the number of maximal sets for the given N products and let Gi, for i = 1, . . . , n, denotes the ith maximal set. Hence, we can construct n production campaigns with length ti for i = 1, . . . , n. To plan which campaign can be selected in the production horizon time, we deﬁne a set of integer or binary variables as follows: { 1, if campaign i is selected in the horizon time s = for i = 1, . . . , n (1) i 0, otherwise Since the total available production time (i.e. the horizon time H) is to be divided among the n campaigns, we must have:

s1t1 + s2t2 + ··· + sntn ≤ H (2)

From the above, we know that the campaign i produces only the products in Gi. However, for campaign i, it is not necessary to produce all the products in Gi, and not necessary to produce the products in full length ti. Thus, the campaign i may produce one or more products from Gi for diﬀerent amounts of time which cannot exceed ti. With this, we can deﬁne a set of integer or binary variables d as follows: { kri 1, if product P using Route r is in campaign i d = k (3) kri 0, otherwise ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1883

for k = 1,...,N; r = 1,...,Rk; i = 1, . . . , n

where Rk denotes the number of production routes for product Pk. Corresponding to dkri, let θkri be the processing time for product Pk using Route r in Gi. The length of campaign i is the maximum production time for the grouping products in Gi. Therefore, the campaign length ti can be stated by: t = max {d θ } (4) i kri kri k=1,...,N, r=1,...,Rk

On the other hand, a product may be produced in more than one campaign. Let Tkr, for k = 1,...,N; r = 1,...,Rk, denote the total production time for product Pk using Route r during the horizon time. For instance as shown in Figure 3, product P1 is produced in campaign 1 and campaign 2 by diﬀerent routes as below:

in campaign 1: {P1 (Route 1) , P2 (Route 1)}

in campaign 2: {P1 (Route 1) , P1 (Route 2)}

Therefore, the respective production time for product P1 using Route 1 and Route 2 are T11 and T12, and must satisfy the following horizon constraints: d111θ111 + d112θ112 = T11 and d122θ122 = T12. Hence, we can calculate Tkr in terms of the appropriate and relevant variables dkri and θkri. To further generalize the constraints, the binary variables si are used to derive a new set of constraints as follows:

s1dkr1θkr1 + s2dkr2θkr2 + ··· + sndkrnθkrn = Tkr, k = 1,...,N; r = 1,...,Rk (5)

Let qkr be the total amount of product k produced by the route r. Let Bkr denote its batch size (i.e. the amount of ﬁnal product produced in each batch) and Θkr denote its cycle time (i.e. the average time required to produce one batch). In the planning problem, Bkr and Θkr must be prespeciﬁed. From Tkr, Bkr and Θkr, we can obtain the amount of qkr: qkr = BkrTkr/Θkr (6)

Let Qk be the ﬁnal total amount of product k produced in the horizon time. Qk can be computed by the following equation:

∑Rk ∑Rk Qk = qkr = BkrTkr/Θkr (7) r=1 r=1 L On the other hand, the minimum demand amount Qk and the maximum demand U amount Qk give the lower and upper bounds on Qk respectively. That is L ≤ ≤ U Qk Qk Qk (8)

Finally, if we deﬁne Γk as the proﬁt in k$ per Mg of product k, then the complete planning problem can be formulated as follows: ∑N maximize ΓkQk si,dkri,θkri (9) k=1 subject to Equations. (2), (4), (5), (6), (7) and (8).

3. Evolutionary Mixed-Integer Nonlinear Programming. Let us consider a constrained MINLP problem as follows: min f(x, y) x,y

subject to hj(x, y) = 0, j = 1, . . . , me (10)

gj(x, y) ≤ 0, j = 1, . . . , mi

where x represents an nC -dimensional vector of continuous variables, y is a nI -dimensional vector of integer variables, and hj(x, y) and gj(x, y) stand for the equality and inequality 1884 Y.-C. LIN, Y.-C. LIN AND K.-L. SU constraints respectively. To abbreviate these expressions, a compact notation z = (x, y) is used in the following discussions, and the problem is referred to as primal problem. An augmented Lagrange function corresponding to the primal problem is deﬁned by:

∑me { } ∑mi { } 2 − 2 h i2 − 2 La(z, ν, υ) = f(z) + αk [hk(z) + νk] νk + βk gk(z) + υk + υk (11) k=1 k=1 where αk and βk are positive penalty parameters, the bracket operation is denoted as h i { } ≥ g + = max g, 0 , and ν = (ν1, . . . , νme ) and υ = (υ1, . . . , υmi ) 0 are the corresponding Lagrange multipliers. In nonlinear programming, the saddle point theorem [17] states that, if a point is a saddle point of the augmented Lagrange function associated with the primal problem, then the point is the solution of the primal problem. Accordingly, the saddle point theorem can be used to solve mixed-integer constrained optimization problems. According to the saddle point theorem, we can construct an evolutionary max-min algorithm to solve mixed-integer constrained optimization problems. The evolutionary min-max algorithm (MIHDE-AMM) includes two phases as stated in Table 1. In the first phase (step 2 in Table 1), a mixed-integer evolutionary algorithm, called Mixed- Integer Hybrid Differential Evolution (MIHDE) [15], is used to minimize the augmented Lagrange function with multipliers fixed. In the second phase (step 3 in Table 1), the Lagrange multipliers are updated to ascend the value of the dual function toward obtaining maximization of the dual problem. The update of the Lagrange multipliers is based on the exact or approximate minimum of the augmented Lagrange function with multipliers fixed. As stated by Arora et al. [18], an exact or approximate minimum is necessary in order to ensure proper shift of the Lagrange function towards the required solution.

Table 1. Evolutionary max-min algorithm (MIHDE-AMM)

Step 1. Set initial iteration index: l = 0. l l Set initial multipliers: νk = 0 for k = 1, . . . , me, υk = 0 for k = 1, . . . , mi. Set penalty parameters: αk > 0 for k = 1, . . . , me, βk > 0 for k = 1, . . . , mi. l l Step 2. Use MIHDE to minimize La(z, ν , υ ). l l l l l Let zb = (x , y )b be a minimum solution to the function La(z, ν , υ ). Step 3. Update the multipliers as follows: l+1 l l νk = h k(zb) + νk l+1 l l υk = gk(zb) + υk + Step 4. Update αk and βk, if necessary. Step 5. Stop if stopping criterion is satisﬁed. Otherwise, let l = l + 1 and repeat Steps 2 to 4.

4. Experimental Example. Consider a three-product planning problem proposed by Karimi [1]. The possible production routes are described by Figure 2. We can arrange them in 9 diﬀerent campaigns as shown in Figure 3. In Figure 3, the notation, A1, denotes route 1 for product A, B1 denotes route 1 for product B, C1 denotes route 1 for product C, A2 denotes route 2 for product A, etc. The batch data, demands and proﬁts for products are shown in Table 2. With possible production campaigns and Table 2, we can formulate this planning problem as a MINLP problem as shown in (9) including 27 continuous variables and 36 integer variables. For comparison, the MIHDE-AMM algorithm and the MIHDE based on penalty function method (MIHDE-PFM) are applied to solve this production planning problem. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1885

Figure 2. Possible produc- Figure 3. Possible production routes for product A, B tion campaig and C Table 2. Batch data, demands and proﬁts for products

Batch Data Demand Proﬁt Product Route Batch Size (kg) Cycle Time (h) QL (Mg) QU (Mg) Γ ($/kg) 1 2500 6.2 A 100 150 1.0 2 2000 5.4 1 1670 4.8 B 250 300 0.8 2 1330 4.0 1 500 3.2 C 2 1000 4.9 150 200 0.5 3 1500 6.4

Table 3 shows that the best objective function values and their corresponding constraints obtained by MIHDE-AMM and MIHDE-PFM with various penalty parameters. The optimal solutions for various penalty parameters are nearly identical and feasible. The feasible solutions are not obtained by MIHDE-PFM because some inequality constraints are violated. From this comparison, MIHDE-AMM outperforms MIHDE-PFM in terms of the solution quality. The result shows that the constraints of the production planning problem seem to be very sensitive to MIHDE-PFM.

Table 3. MIHDE-AMM and MIHDE-PFM for various penalty parameters βk, k = 1,..., 7

MIHDE-AMM MIHDE-PFM Item 3 6 3 6 βk = 1 βk = 10 βk = 10 βk = 1 βk = 10 βk = 10 maxf(z) 454.249×103 454.249×103 454.249×103 490.001×103† 454.516×103† 454.249×103† −3 −5 −5 1 −1 −4 g1(z) –1.507×10 –4.101×10 –3.492×10 9.608×10 ‡ 3.665×10 ‡ 3.244×10 ‡ 4 4 4 4 4 4 g2(z) –5.000×10 –5.000×10 –5.000×10 –5.000×10 –5.000×10 –5.000×10 4 4 4 4 4 4 g3(z) –3.656×10 –3.656×10 –3.656×10 –5.000×10 –3.690×10 –3.656×10 −3 −2 −1 4 −4 −3 g4(z) –1.708×10 –2.245×10 –1.102×10 –5.000×10 3.627×10 ‡ –2.445×10 −2 −1 −2 −1 −1 −3 g5(z) –1.645×10 –1.485×10 –8.191×10 4.712×10 ‡ –1.383×10 –1.110×10 4 4 4 −1 4 4 g6(z) –1.344×10 –1.344×10 –1.344×10 3.081×10 ‡ –1.310×10 –1.344×10 4 4 4 −2 4 4 g7(z) –5.000×10 –5.000×10 –5.000×10 7.614×10 ‡ –5.000×10 –5.000×10 †: The solution is infeasible. ‡: The constraint is violated.

The optimal production planning including campaign 2, 6 and 8 is obtained by MIHDE- AMM. From the computational result, product A is produced to its maximum demand level 150 Mg, product C is produced to its minimum demand level 150 Mg, and product B 1886 Y.-C. LIN, Y.-C. LIN AND K.-L. SU is produced at an intermediate demand level 286.561 Mg. A total profit of about 454.249 k$ is anticipated from the optimal production planning. 5. Conclusions. In this paper, a mixed-integer nonlinear programming (MINLP) model is developed to formulate the production planning problem. In order to effectively find the optimal solution, a mixed-integer evolutionary algorithm is proposed to solve this MINLP problem. From computational results, we can find that better results are obtained in comparison with the penalty function method. This demonstrates that the algorithm can effectively handle the production planning problem.

REFERENCES [1] I. A. Karimi, Production planning in multipurpose batch plants in CACHE, Chemical Engineering Optimization Models with GAMS, vol.6, 1991. [2] Z. Michalewicz, Genetic Algorithm + Data Structure = Evolution Programs, Springer-Verlag, 1994. [3] T. Back, D. Fogel and Z. Michalewicz, Handbook of Evolutionary Computation, Oxford Univ. Press, New York, 1997. [4] S. Z. Zhao and P. N. Suganthan, Multi-objective evolutionary algorithm with ensemble of external archives, International Journal of Innovative Computing, Information and Control, vol.6, no.4, pp.1713-1726, 2010. [5] F. T. Lin, Simulating fuzzy numbers for solving fuzzy equations with constraints using genetic algorithms, International Journal of Innovative Computing, Information and Control, vol.6, no.1, pp.239-254, 2010. [6] M. Rashid and A. R. Baig, PSOGP: A genetic programming based adaptable evolutionary hybrid particle swarm optimization, International Journal of Innovative Computing, Information and Con- trol, vol.6, no.1, pp.287-296, 2010. [7] F. T. Lin and T. R. Tsai, A two-stage genetic algorithm for solving the transportation problem with fuzzy demands and fuzzy supplies, International Journal of Innovative Computing, Information and Control, vol.5, no.12, pp.4775-4785, 2009. [8] J. F. Chang, A performance comparison between genetic algorithms and particle swarm optimization applied in constructing equity portfolios, International Journal of Innovative Computing, Informa- tion and Control, vol.5, no.12, pp.5069-5079, 2009. [9] P. W. Tsai, J. S. Pan, B. Y. Liao and S. C. Chu, Enhanced artiﬁcial bee colony optimization, International Journal of Innovative Computing, Information and Control, vol.5, no.12, pp.5081- 5092, 2009. [10] Y. Chen, Z. Fan and M. Xie, A hybrid grouping genetic algorithm approach for constructing diverse reviewer groups in group decision making, ICIC Express Letters, vol.4, no.2, pp.365-373, 2010. [11] Z. Wang and M. Li, A hybrid coevolutionary algorithm for learning classiﬁcation rules set, ICIC Express Letters, vol.4, no.2, pp.401-406, 2010. [12] R. J. Kuo, T. L. Hu and Z. Y. Chen, Evolutionary algorithm-based RBF neural network for oil price forecasting, ICIC Express Letters, vol.3, no.3, pp.701-705, 2009. [13] Z. Michalewicz and M. Schoenauer, Evolutionary algorithms for constrained parameter optimization problems, Evolutionary Computation, vol.4, no.1, pp.1-32, 1996. [14] Y. C. Lin, K. S. Hwang and F. S. Wang, An evolutionary lagrange method for mixed-integer constrained optimization problems, Engineering Optimization, vol.35, no.3, pp.267-284, 2003. [15] Y. C. Lin, K. S. Hwang and F. S. Wang, A mixed-coding scheme of evolutionary algorithms to solve mixed-integer nonlinear programming problems, Computers and Mathematics with Applications, vol.47, pp.1295-1307, 2004. [16] J. A. Vaselenak, I. E. Grossmann and A. W. Westerberg, An embedding formulation for the optimal scheduling and design of multipurpose batch plants, Industrial and Engineering Chemistry Research, vol.26, pp.139-148, 1987. [17] D. A. Wismer and R. Chattergy, Introduction to Nonlinear Optimization, Elsevier North-Holland, 1978. [18] J. S. Arora, A. I. Chahande and J. K. Paeng, Multiplier methods for engineering optimization, Int. J. Numerical Methods in Engineering, vol.32, pp.1485-1525, 1991. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1887-1892

HIDING SECRET INFORMATION IN MODIFIED LOCALLY ADAPTIVE DATA COMPRESSION CODE

Chin-Chen Chang1, Kuo-Nan Chen2 and Zhi-Hui Wang3

1Department of Information Engineering and Computer Science Feng Chia University 100 Wenhwa Rd., Seatwen, Taichung 40724, Taiwan [email protected] 2Department of Computer Science and Information Engineering National Chung Cheng University 160 San-Hsing, Ming-Hsiung, Chiayi 621, Taiwan [email protected] 3School of Software Dalian University of Technology No. 2, Linggong Road, Ganjingzi District, Dalian 116024, P. R. China [email protected] Received February 2010; accepted April 2010

Abstract. A data hiding scheme based on the locally adaptive data compression scheme (LADCS) is proposed in this paper. By analyzing and exploiting the features of the compression codes generated by LADCS, our proposed scheme can embed secret bits in the compression code without size expansion. The experimental results showed that our proposed scheme was successful in making the secret bits more secure by embedding them in the compression codes without losing the advantages of LADCS. Keywords: Compression code, Data hiding, Secret bits, Locally adaptive data compression scheme

1. Introduction. In this information explosion age, the most commonly used channel for communication is the Internet. Although networking technology has improved rapidly, the availability of adequate network bandwidth is a concern because of the significant increases in the sizes of files generated by current computer technologies. Therefore, many data compression technologies have been proposed to solve the networking bandwidth problem. Data compression technologies can be categorized into lossy [1,2] and lossless [3-5] from the integrity of reconstructed data. Although lossy data compression schemes have better compression ratios than lossless schemes, the original data cannot be reversed completely. Lossy data compression technologies have been used extensively for video files and images due to their file structure characteristics, i.e., they can be recognized with a certain degree of distortion. On the other hand, the application of lossy data compression schemes to reduce file size is not suitable for some data structures, such as text documents. Any changes or distortions can make a text document meaningless or unidentifiable, so only lossless compression schemes can be applied for them. Since the Internet is a public environment, malicious attackers can intercept any messages that are transmitted. Many researchers have proposed ways to solve this problem so that messages can be transmitted securely on the Internet. Encryption approaches, such as AES [6], DES [7] and RSA [8] make transmitted messages secure by encrypting the messages into ciphertext with keys. Then, the ciphertext can be decrypted only by authorized users who have the proper keys. Different from encryption approaches, data

1887 1888 C.-C. CHANG, K.-N. CHEN AND Z.-H. WANG hiding technologies [9-12] embed the secret message in some cover ﬁles, and the secret message can only be extracted with the proper ways. To solve the problems of networking bandwidth and transmission security, a data hiding scheme based on the locally adaptive data compression scheme is proposed in this paper. The secret message is embedded in the text documents during the compression process. Most importantly, a major contribution of the proposed data hiding scheme is that the ﬁnal compressed data are not expanded in size after the secret messages are embedded. This paper is organized as follows. In Section 2, a brief description of the locally adaptive data compression scheme is presented. Section 3 describes the proposed scheme, including the embedding and extracting procedures. Section 4 presents the experimental results to show the performance of our proposed scheme. Our conclusions are given in Section 5.

2. Related Work. In 1986, Bentley et al. proposed a data compression scheme that ex- ploits the locality of reference [5]. In [5], the authors proved that the locally adaptive data compression scheme never performs much worse than the well-known Huﬀman coding and can perform substantially better. The basic concepts of compression and decompression are described as follows. In the compression stage, the sender uses a word list WLs (treated as a template stack and initially empty) to record the position of the word that is to be compressed. The, it is assumed that there are n diﬀerent words in WLs, that they are positioned from 0 to n − 1, and that the word w that is to be compressed cannot be found in the WLs. First, the to-be-compressed word w is put into WLs with the position nand output (n||w) as the compression code. Then, WLs is adjusted by moving w to the front of the WLs and resorting the remaining words in order from 1 to n. Otherwise, if the to-be-compressed word w exists in WLs at position p, output p as the compression code, move w to the front of WLs (position 0), and resort the remainder of the words in WLs in order from 1 to n. The compression processes are shown in Figure 1, in which the message to be compressed is “THE DOG ON THE”.

Figure 1. Example encoding of the locally adaptive data compression scheme

At the receiving end, the receiver also has a word list called WLr initially empty. When the receiver gets the compressed codes “0 THE 1 DOG 2 ON 2”, a word is decompressed and restored to the original text format if it is preceded by a position number (i.e., position number, word). After the word has been decompressed, WLr is adjusted by moving this word to the front of WLr. Otherwise, if a position number is followed by another position number or if a position number is at the end of the compressed code, the scheme outputs the word in WLr that is indexed by this position number moves the indicated word to ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1889

the front of WLr, and sorts the remaining words in order. The decompression processes are shown in Figure 2 and this is followed by a compression example.

Figure 2. Example of decompression in the locally adaptive data compression scheme

3. The Proposed Scheme. In the proposed scheme, the binary secret messages are embedded in the “interval space” of the compression codes. The compression and decompression procedures are described as follows. 3.1. The compression procedure. Before introducing our proposed scheme, two characteristics of the compression result generated by the locally adaptive compression scheme are illustrated. The first characteristic is that the number of words in the word list decides the size of each position number in the compression code. For example, if there are five d e words in the word list, then log2 5 = 3 bits are needed to represent the position number of the next to-be-compressed word. The second characteristic is that, if the position number is increasing, it would increase continuously. Thus, we can have a continuous number sequence if we count the position number from small to large in the final compression code. With the information concerning these two background characteristics, the compression procedure is introduced as follows. Assume a to-be-compressed text is composed as T = {wi|i = 1 to n}, where wi indicates the ith word in the text. In our proposed scheme, the interval space for embedding secret > bits occurs only when i =5. If we assume that the first four words are w1 =6 w2 =6 w3 =6 w4, the compressed code would be “0 w1 1 w2 10 w3 11 w4”, where the position number is expressed in binary representation. If the fifth word w5 cannot be found in word list, application of the traditional locally adaptive compression scheme would provide a compression result of “0 w1 1 w2 10 w3 11 w4 100 w5”. However, if the position number “100” is kept from using to make an interrupt to be a hiding space. For instance, if position numbers “101” and “110” are used to stand for secret bit 0 and secret bit 1, respectively, and the secret bit to be embedded is “1”. The compression code for the first five words would be “0 w1 1 w2 10 w3 11 w4 110 w5”. 3.2. The decompression procedure. When the receiver gets the compression code, the decompression process is the same as that of the traditional locally adaptive data compression scheme, unless a gap is found when the position numbers are being counted. Followed the example given in Section 3.1, the compression code “0 w1 1 w2 10 w3 11 w4 110 w5” is received. A secret bit can be extracted when the receiver finds that an interval exists while counting the position numbers, i.e., the number 4 (100) is missing. By applying the same substitution method (101 → bit “0” and 110 → bit “1”), secret bit “1” can be extracted, and the original text w1w2w3w4w5 can be recovered. 1890 C.-C. CHANG, K.-N. CHEN AND Z.-H. WANG 4. The Experimental Results. To evaluate the performance of our proposed scheme, five news documents obtained from the Internet [13] were used. Figure 3 shows one segment of the documents. By observing Table 1, it is apparent that the final compression codes with secret bits embedded have no size expansion compared with the compression codes produced by LADCS (without secret bits embedded). Table 1. Performance of the proposed scheme compared to LADCS

Cover File Compressed Secret bit Compressed ﬁle size Final media size ﬁle size (Bytes) stream and secret bit compression (News) (Bytes) (LADC) size (Bits) stream size (Bytes) codes (Bytes) (1) 11054 10815 4096 14911 10815 (2) 12864 12717 3053 15770 12717 (3) 8876 8674 5432 14106 8674 (4) 9017 8225 1940 10165 8225 (5) 18167 18062 2305 20367 18062

To further evaluate the performance of our proposed scheme, we compared it with the scheme proposed by Chang et al. in 2009 [14]. The results, which are shown in Table 2, provide further evidence that our proposed scheme can hide secret bits in the compression codes without expanding their size. Table 2. Comparison of our proposed scheme with Chang et al.’s scheme

Cover File Compressed Secret bit stream Final compressed media size ﬁle size (Bytes) size (Bits) size (Bytes) (News) (Bytes) (LADC) Proposed scheme [14] Proposed scheme [14] (1) 11054 10815 4096 11054 10815 10715 (2) 12864 12717 3053 12864 12717 13174 (3) 8876 8674 5432 8876 8674 8945 (4) 9017 8225 1940 9017 8225 9099 (5) 18167 18062 2305 18167 18062 18535

5. Conclusions. We have proposed a data hiding scheme based on the locally adaptive data compression scheme (LADCS). By using the characteristics of the compression codes generated by LADCS, our proposed scheme can embed secret bits in the compression codes without size expansion. The experimental results showed that, in addition to providing the advantages of LADCS, our proposed scheme made secret messages more secure by embedding them in the compression code.

REFERENCES [1] S. Kavitha, S. M. M. Roomi and N. Ramaraj, Lossy compression through segmentation on low depth-of-ﬁeld images, Digital Signal Processing, vol.19, no.1, pp.59-65, 2009. [2] I. P. A. Bita, M. Barret and D. T. Pham, On optimal transforms in lossy compression of multicom- ponent images with JPEG 2000, Signal Processing, vol.90, no.3, pp.759-773, 2010. [3] J. L. Bentley, D. D. Sleator, R. E. Tarjan and V. K. Wei, A locally adaptive data compression scheme, Communications of the ACM, vol.29, no.4, pp.320-330, 1986. [4] T. Fang, On performance of lossless compression for HDR image quantized in color space, Signal Processing: Image Communication, vol.24, no.5, pp.397-404, 2009. [5] A. B. Hussein, A novel lossless data compression scheme based on the error correcting hamming codes, Computers and Mathematics with Applications, vol.56, no.1, pp.143-150, 2008. [6] National Institute of Standards and Technology, Announcing the Advanced Encryption Standard (AES), Federal Information Processing Standards Publication, vol.197, 2001. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1891

Figure 3. A segment of one news document 1892 C.-C. CHANG, K.-N. CHEN AND Z.-H. WANG

[7] National Institute of Standards and Technology, Data Encryption Standard (DES), Federal Infor- mation Processing Standards Publication, vol.46, 1977. [8] R. L. Rivest, A. Shamir and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, vol.21, pp.120-126, 1978. [9] C. C. Lin, W. L. Tai and C. C. Chang, Multilevel reversible data hiding based on histogram modi- ﬁcation of diﬀerence images, Pattern Recognition, vol.41, no.12, pp.3582-3591, 2008. [10] I. S. Lee and W. H. Tsai, Data hiding in grayscale images by dynamic programming based on a human visual model, Pattern Recognition, vol.42, no.7, pp.1604-1611, 2009. [11] Z. X. Yin, C. C. Chang and Y. P. Zhang, An information hiding scheme based on (7, 4) hamming code oriented wet paper codes, International Journal of Innovative Computing, Information and Control, vol.6, no.7, pp.3121-3130, 2010. [12] C. C. Lin, Y. H. Chen and C. C. Chang, LSB-based high-capacity data embedding scheme for digital images, International Journal of Innovative Computing, Information and Control, vol.5, no.11(B), pp.4283-4289, 2009. [13] http://www.cnn.com/, 2008. [14] C. C. Chang, C. F. Lee and L. Y. Chuang, Embedding secret binary message using locally adaptive data compression coding, International Journal of Computer Sciences and Engineering Systems, vol.3, no.1, pp.55-61, 2009. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1893-1898

GENETIC PROGRAMMING BASED PERCEPTUAL SHAPING OF A DIGITAL WATERMARK IN THE WAVELET DOMAIN

Asma Ahmad and Anwar M. Mirza

Department of Computer Science National University of Computer and Emerging Sciences FAST-NU, A. K. Brohi Road, H-11/4, Islamabad 44000, Pakistan { asma.ahmad; anwar.m.mirza }@nu.edu.pk Received February 2010; accepted April 2010

Abstract. This paper presents an intelligent perceptual shaping technique which creates a robust, yet imperceptible watermark for any digital image. This is achieved by exploiting the human visual system’s sensitivity to texture, as well as other local image characteristics obtained from the wavelet domain. The digital watermarking technique is intelligent as it perceptually shapes the watermark in line with the cover image using Ge- netic Programming (GP). Perceptual model generated by Noise Visibility Function (NVF) is considered as an optimization problem in GP. Advantages of the proposed technique include: i) Intelligent visual masking by utilizing the time-frequency localization property of wavelet transforms and ii) Improved resistance to attack on the watermark. The performance and accuracy of the proposed technique is successfully tested on standard images under compression, geometric transforms and noise attacks. Keywords: Digital watermarking, Genetic programming, Noise visibility function, Wavelets

1. Introduction. With the increasing use of the Internet as a platform for exchange of digital information, there are serious concerns about its unauthorized use and manipulation, which would be harmful to the interests of the owner of such information. This has highlighted the issues of data integrity, and its authenticity for the bonafide users. To deal with such matters of concern, we need techniques that can be used to protect and verify ownership, and correctness of the digital information. Digital watermarking is the one of such techniques. To solve the data security and ownership issues with digital watermarking, quite significant research work has been done in the recent past. Like in [1], authors proposed a watermarking scheme consisting of two phases, the feature point based watermark synchronization and the Discrete Wavelet Transform (DWT) based watermark embedding/extraction. There resultant watermark is empirically proved to be resistant against the verity of attacks. Recently, Machine Learning (ML) techniques are applied in the field of watermarking. In [2], proposes a novel robust image watermarking scheme based on singular value decomposition (SVD) and micro-genetic algorithm. However, in watermarking, most of the ML techniques are used for detection of a hidden message. In [3,4] have used Support Vector Machine (SVM) for detecting hidden messages in an image. Similarly, [5,6] have used neural networks in watermarking and capacity analysis respectively. Pereira et al. [7] has used Linear Programming to optimally embed a watermark in transform-domain. Evolutionary algorithms are used by several different authors in digital watermarking, but generally most of the work focuses on watermark analysis and its detection. In [8], proposes an evolutionary method for digital image watermarking using Genetic Algorithm (GA). In their work, authors provided a flexible and effective benchmarking tool, exploiting GA to test the robustness of watermarking techniques under a combination of given

1893 1894 A. AHMAD AND A. M. MIRZA attacks and to find the best possible un-watermarked image. The degradation evaluation is done taken into account both the classical PSNR metric and the perceptual metric Weighted Peak Signal to Noise Ratio (WPSNR). However, for optimization WPSNR is taken into account. For further reading one may refer to [9-11]. The focus of this research work is to exploit the characteristics of wavelets and Genetic Programming (GP) for intelligent optimization of the Perceptual Shaping Function (PSF) in watermarking. The result of our proposed methodology will be an image Adaptive Genetic Perceptual Shaping Function (AGPSF) which improves the PSF proposed by Khan et al. [12]. The major contribution of our research work is the optimal perceptual shaping of a watermark, according to the Human Visual System (HVS) properties in the wavelet domain. Use of the wavelet domain gives us a multi-resolution analysis capability for the perceptual shaping of the watermark. Additionally, we considered Noise Visibility Function (NVF) as an optimization problem [13]. Proposed technique employees GP search mechanism to achieve the optimal tradeoff between the two conflicting requirements i.e. imperceptibility and robustness, and thus finds out an optimal PSF. Our analysis showed that a high energy watermark with a better resistance against attacks, can be embedded in the wavelet domain than the one found by Khan et al. [12]. Experimentation proved that proposed methodology is robust and imperceptible against attacks of various categories. The paper is arranged as: Section 2 describes the overall system architecture. Sections 3 and 4 covers implementation details and experimental results respectively. While Section 5 covers testing of proposed scheme and Section 6 sum up the discussion with conclusions.

2. Proposed Approach. We present an algorithm that creates an watermark by identifying those regions where human eye is less insightful for added noise (watermark in our case) but also these regions are robust against the possible set of attacks (including compression). The outline of the proposed approach is shown in Figure 1. In the following sub sections, each of the phases will be discussed in detail:

Figure 1. Block diagram of proposed methodology

2.1. Image blocking and coefficient selection. Initially in the training phase, the cover image (in our case Lena) is divided into the 8×8 blocks and DWT (in our case db2) of each of the block is taken. Since watermarking has strong relationship with the local image characteristics, the perceptual model we selected for optimization is non-stationary Gaussian model based NVF [13]. Hence in addition, the corresponding coefficients of NVF are also selected. NVF is a function that characterizes the local image properties and identifies the texture and edge regions where a watermark can be embed with more strength [5,6]. A non-stationary Gaussian Model can be presented as: 1 NVF (i, j) = 2 (1) 1 + σx(i, j) ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1895

2 where σx is the local variance of the image in a window centered on the pixel with coordinates (i, j). Selected coefficients of the wavelet transform and corresponding NVF values are then input as the terminals in GP simulation. 2.2. Evolution of perceptual shaping function. Genetic programming was selected for the evolution of an intelligent image Adaptive Perceptual Shaping Function (APSF). Selected coefficients of the wavelet transform and corresponding NVF values of image blocks are taken input terminals in GP simulation. The GP function set comprised of simpler set of functions containing plus, minus, times, divide, sin, cos and log. While in addition to selected wavelet coefficients and corresponding NVF values, a random number within the range [−1, +1] is also used as constant terminal in the set. It must be noted for comparison purpose the parameter settings are identical to the one proposed by [12]. 2.3. Perceptual mask creation. The output of each GP simulation is an evolved AG- PSF, which in turn is input for the perceptual mask creation module. Each AGPSF operates on the host image in DWT-domain. For each of the selected DWT coefficient (COFF) of a block, the corresponding AGPSF returns a value, the magnitude of which represents the maximum alteration done on that selected coefficient. A perceptual mask is developed for the cover image by executing AGPSF on all of the DWT coefficients. To sum up the above process by using an equation we can write: Ω(i, j) = AGP SF (NVF (i, j),COFF (i, j)) (2) 2.4. Watermark generation. Once perceptual mask is created, in next phase a watermark is developed by multiplying a pseudo-random Gaussian distributed number with the perceptual mask produced by (2). Suppose PRN denotes to pseudo-random number we get: W = Ω ∗ PSN (3) 2.5. Watermark embedding. Once the watermark is developed, it is embedded to the host image in the wavelet domain. Every image block is first decomposed through DWT into levels: let us call the sub-band at resolution level and with orientation. The watermark, consisting of a pseudorandom binary sequence and AGPSF, is inserted by modifying the wavelet coefficients belonging to the detail bands. 2.6. Fitness evaluation. In fitness evaluation module we calculated the fitness of every member of a population generated by genetic programming and give it a rank or fitness value in terms of its imperceptibility and robustness. In our case, we evaluated each individual in terms of the SSIM [14] at a certain rank of predicted robustness (MSS) [12].

F itness = SSIMP.R (4) The results of fitness evaluation are then used as the fitness function or scoring criteria in GP simulation. The GP simulation is terminated when either the fitness score exceeds 0.98 with MSS ≥ 20.0, or the number of generations approaches a predefined limit, which in our simulation is set to 20. The foresaid process (Step 2.2 ∼ 2.6) continues until an AGPSF of desirable properties is found. The best fit individual AGPSF expression is saved and is then used for testing proposes, thus to empirically prove methodology superiority. 2.7. Best-evolved GPSF. Expression of the best GPSF in standard notation is:

π(k1, k2) = cos(NVF (counter1, counter2) + Log(I(counter1, counter2) + 0.85)) +(NVF (counter1, counter2) − 0.158)/ cos(NVF (counter1, counter2) ∗ 0.5894) +(I(counter1, counter2) + 0.4825) + (sin(I(counter1, counter2)) − 0.874) (5) 1896 A. AHMAD AND A. M. MIRZA 3. Implementation Details. For experimentation we have used MATLAB environment. While for GP, we have used GPLAB toolbox [15]. Most of the parameters used are left as in default setting. However, since the research work proposed in this paper is an eﬀort to improve the idea proposed by [12], therefore, we decided to keep the same parameter setting, which would be helpful in making comparisons easy and meaningful.

4. Results and Discussions. Table 1 gives a comparison of our proposed methodology and the one proposed by Khan et al. [12]. The two techniques are compared in terms of the marked image quality (SSIM), estimated robustness (MSS), and other image quality measures. In order to preserve the preferred value of SSIM, and thus to maintain desired level of imperceptibility, we multiplied both perceptual shaping functions with a scaling factor. In Table 1, columns 3 and 4 represent the watermark scaling factor and MSS respectively. While columns 5-8 show watermarked image quality in terms of different measures. We used different image quality measures because it will compare our findings with the one reported by A. Khan [12] in detail, thus empirically proving a superiority of our proposed technique. From experimentation, it was observed that in case of AGPSF, keeping same distortion of the resultant image as the one proposed by Khan et al. [12] case, the watermark is inserted with eminent power. Thus the watermark shaping ability of the evolved AGPSF is better than the former. But since both the optimal perceptual shaping techniques are in different transform domains, so authenticity of comparison is open to question.

Table 1. Perceptual shaping comparisons for diﬀerent images

Watermark Watermark Watermarked Image Test Perceptual Strength Power Quality Measures Images Model Scaling MSS MSE PSNR wPSNR SSIM Factor GPM [12] 0.3910 27.224 9.3570 38.419 42.7858 0.9810 Lena AGPSF 0.792 28.242 3.1793 43.107 48.423 0.9871 GPM [12] 0.357 68.618 23.563 34.408 44.023 0.9809 Baboon AGPSF 0.781 68.349 15.183 36.317 40.794 0.9865 GPM [12] 0.417 27.153 9.3220 38.435 41.421 0.9810 Airplane AGPSF 0.797 25.419 0.8457 48.858 53.571 0.9944 GPM [12] 0.335 46.064 15.770 36.150 41.849 0.9810 Couples AGPSF 0.738 52.1334 4.4417 41.655 46.854 0.9872 Chemical GPM [12] 0.358 39.538 13.588 36.799 42.0516 0.9809 plant AGPSF 0.791 43.481 3.4187 42.792 48.307 0.987

5. Testing of Watermark against Attacks. Through experimentation it is confirmed that the embedded watermark is robust against attacks since only one sharp peak in the cross-correlation coefficient is detected after testing 1000 sets of different random numbers. In experimentation, we tested our proposed technique using db2, bior and CDF wavelets, however, here only results for db2 are shown. Our proposed scheme is successfully tested for robustness when subjected to image attacks like filtering, geometric transformations, image compression, cascading attacks etc. However, for demonstration purpose only the detector’s response for geometric and cascading attacks are given.

5.1. Geometric attacks. In order to show the robustness against the geometric attacks, cropping and zero-boarder are used. The detector response is well above the threshold for cropping factor and is tested up to 75%. Figure 2 summarize the results. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1897

Figure 2. Cropping attack (Ratio = 75%) and detector response of watermarked images

5.2. Cascading attacks. The proposed watermarking scheme was also tested against cascading attacks. Firstly image was compressed with JPEG QF 50% and then subjected to the Lowpass ﬁltering. Afterwards, noise was added to the same corrupted image. And ﬁnally the image was cropped. The results summarized in Figure 3 prove robustness of our proposed scheme against cascading attacks.

Figure 3. Cascading attacks and detector response of watermarked images

6. Conclusions and Future Enhancements. This work focused on the intelligent concealment of a digital watermark. We proposed an image adaptive perceptual shaping function evolved by using genetic programming. We have successfully tested the performance of our technique against a variety of image attacks, and the results as obtained are very promising. There are many future directions for intelligent perceptual shaping. For instance, instead of optimization of the watermarking strength for pre-defined coefficients, the selection of DWT coefficients can also be performed intelligently. Moreover, a detailed study of the DWT coefficients in terms of malicious attacks can be carried out to find secure and promising regions.

REFERENCES [1] L. L. D. Li, B. L. Guo and J. S. Pan, Robust image watermarking using feature based local invariant regions, International Journal of Innovative Computing, Information and Control, vol.4, no.8, pp.1977-1986, 2008. [2] C. C. Lai, H. C. Huang and C. C. Tsai, A digital watermarking scheme based on singular value decomposition and micro-genetic algorithm, International Journal of Innovative Computing, Infor- mation and Control, vol.5, no.7, pp.1867-1873, 2009. [3] H.-H. Tsai and D.-W. Sun, Color image watermark extraction based on support vector machines, Information Sciences, vol.177, no.2, pp.550-569, 2007. 1898 A. AHMAD AND A. M. MIRZA

[4] Y. Fu, R. Shen and H. Lu, Optimal watermark detection based on support vector machines, Proc. of the International Symposium on Neural Networks, Dalian, China, pp.552-557, 2004. [5] X. Zhang and F. Zhang, A blind watermarking algorithm based on neural network, Proc. of the International Conference on Neural Networks and Brain, Beijing, China, 2005. [6] F. Zhang and H. Zhang, Image watermarking capacity analysis using hopﬁeld neural network, Proc. of the 5th Paciﬁc Rim Conference on Multimedia, Tokyo, Japan, pp.755-762, 2004. [7] S. Pereira, S. Voloshynoskiy and T. Pun, Optimal transform domain watermark embedding via linear programming, Signal Processing, vol.81, no.6, pp.1251-1260, 2001. [8] G. Boato, V. Conotter and F. G. B. D. Natale, GA-based robustness evaluation method for digital image watermarking, Proc. of the IWDW 2007, Guangzhou, 2007. [9] P. Kumsawat, K. Attakitmongcol and A. Srikaew, An optimal robust digital image watermarking based on genetic algorithms in multiwavelet domain, WSEAS Trans. on Signal Processing, vol.5, no.1, pp.42-51, 2009. [10] H. Jung and M. Jeon, Enhanced SVD based watermarking with genetic algorithm, Proc. of Interna- tional Conference FGCN/ACN 2009 Held as Part FGIT Conference, Jeju Island, Korea, pp.586-593, 2009. [11] H. C. Huang, S. Wang and J. S. Pan, Genetic watermarking based on transform domain technique, Pattern Recognition, vol.37, no.3, pp.555-565, 2004. [12] A. Khan, A. M. Mirza and A. Majid, Intelligent perceptual shaping of a digital watermark: Exploit- ing characteristics of human visual system, International Journal of Knowledge-Based Intelligent Engineering Systems, vol.10, no.3, pp.213-223, 2006. [13] S. Voloshynovskiy, A. Herrigel, N. Baumgaertner and T. Pun, A stochastic approach to content adaptive digital image watermarking, Proc. of the International Workshop on Information Hiding, Berlin, Germany, pp.212-236, 1999. [14] Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, Image quality assessment: From error visibility to structural similarity, Proc. of IEEE Trans. on Image Processing, vol.13, no.4, pp.600-612, 2004. [15] GPLAB Tool, http://gplab.sourceforge.net. [16] A. Khan, Intelligent Perceptual Shaping of a Digital Watermark, Ph.D. Thesis, Ghulam Ishaq Khan Institute of Engineering Sciences and Tectnology, Topi, Swabi, 2006.

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ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1913-1918

SPATIALLY ADAPTIVE BAYESSHRINK THRESHOLDING WITH ELLIPTIC DIRECTIONAL WINDOWS IN THE NONSUBSAMPLED CONTOURLET DOMAIN FOR IMAGE DENOISING

Xiaohong Shen1,2, Yulin Zhang1 and Caiming Zhang2 1School of Control Science and Engineering Shandong University Jinan 250061, P. R. China [email protected] 2School of Computer Science and Technology Shandong Economic University Jinan 250014, P. R. China Received February 2010; accepted April 2010

Abstract. According to anisotropic energy clusters of subbands in the nonsubsampled contourlet domain, elliptic directional windows are introduced to estimate the local signal level of each noisy coefficient in this paper. The proposed threshold for image denoising is the combination of the spatially adaptive BayesShrink threshold and the local signal estimation with elliptic directional windows. Considering the dependency of coefficients not only within and across scales but also in a certain directional neighborhood, the proposed threshold further fits the anisotropic and directional feature of the nonsubsampled contourlet transform. Compared with some current outstanding algorithms for image denoising, the experimental results show that the proposed algorithm obviously outperforms in both visual quality and PSNR value, and effectively preserves edges and texture information of original images. Keywords: Image denoising, Nonsubsampled contourlet transform, Directional window, BayesShrink threshold, Multiscale geometric analysis

1. Introduction. More recently, multiscale geometric analysis (MGA) has provided a powerful tool for image denoising. Up to now, many MGA methods have been proposed, such as ridgelet [1], curvelet [2], shearlet [3], contourlet [4], etc. Among them, the contourlet transform (CT) distinguishes itself by its efficiency and flexible structure which allows for different and flexible number of directions at each scale. When working with denoising, it is often preferable using a redundant representation of signals. By allowing redundancy, it is possible to enrich the set of basis functions so that the representation is more efficient in capturing specific signal features independently of their location (shift- invariance property). The nonsubsampled contourlet transform (NSCT), which is the redundant version of CT, has proven to outperform CT significantly in image denoising [5]. Thresholding method applied in the sparse or near-sparse transform domain where only a small subset of the coefficients represents all or most of the signal energy is especially effective for image denoising. Certainly, finding a suitable threshold is not an easy task, and there are many works focus on it. The spatially adaptive BayesShrink (BS-SA) threshold [5] is one of the excellent thresholds in the NSCT domain. In this threshold scheme, the signal standard deviation of a noisy coefficient is estimated from its neighboring coefficients contained in a square window. In fact, the square window is grounded on an assumption that the energy distribution of the image in each directional subband is isotropic. However, this is not true for most images. The energy clusters in each directional subband generally exhibit distinct directional features. Reasonably,

1913 1914 X. SHEN, Y. ZHANG AND C. ZHANG the anisotropic directional window, which matches the direction of the energy clusters’ distribution in each subband, should be more suitable than the square window for signal estimation in the NSCT domain. Therefore, in this paper, we adapt the elliptic directional windows scheme [6,7] to fit the BS-SA threshold modification for the NSCT domain, and propose the spatially adaptive BayesShrink threshold with the elliptic directional windows (BS-EWSA threshold). The proposed threshold which makes use of the anisotropic energy clusters in the subband can obtain good thresholding results within and around energy clusters. Experiments show that the proposed algorithm achieves the promising denoising performance both in the PSNR and in the visual appearance. The paper is organized as follows. In Section 2, we briefly introduce the NSCT. In Section 3, we provide details of designing the elliptic directional windows and present the proposed BS-EWSA threshold. In Section 4, we discuss the parameter selection of elliptic directional windows and give the experimental results. Finally, conclusions are drawn in Section 5.

2. Nonsubsampled Contourlet Transform and BayesShrink Thresholding. 2.1. Nonsubsampled contourlet transform. The NSCT is a flexible multiscale, mul- tidirection and shift-invariant transform that has a fast implementation. It is composed of a nonsubsampled pyramid structure and a nonsubsampled directional filter bank structure [5]. Different from CT, the NSCT eliminate the downsampler and upsampler in the decomposition and reconstruction stage, which leads to the shift-invariance property of the NSCT. Figure 1 shows the subbands of “Boat” image by one-scale and four-directional NSCT decomposition.

(a) lowpass subband (b) directional subbands

Figure 1. One-scale and four-directional NSCT decomposition of “Boat” image

2.2. Image denoising by spatially adaptive BayesShrink thresholding. Assume that an observed image that is corrupted by additive white Gaussian noise of zero mean 2 and variance σε is represented in the NSCT domain by

yj,k(m, n) = xj,k(m, n) + εj,k(m, n), (1) where yj,k(m, n), xj,k(m, n) and εj,k(m, n) are the NSCT coeﬃcients in the subband at jth scale and kth direction of the observed noisy image, noise-free image and noise, respectively. Given the signal in each NSCT subband being generalized Gaussian distributed, the BS-SA threshold, following [5], is σ2 εj,k Tj,k(m, n) = , (2) σxj,k(m,n) ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1915

where σxj,k(m,n) denotes the signal deviation of the coeﬃcient at the location (m, n) in the subband indexed by scale i and direction j, and σ2 is the noise variance in the εj,k corresponding subband. Obviously, the BS-SA threshold is adaptive to not only the scale and the direction, but also the space (or location).

3. Spatially Adaptive BayesShrink Thresholding with Elliptic Directional Win- dows. In [5], the signal deviation of each noisy coefficient is estimated locally using the neighboring coefficients contained in a square window. The square window imposes an assumption that the energy distribution in the square neighborhood is isotropic. However, in Figure 1(b), it is clear that the energy clusters in each directional subband are mainly distributed along its own distinct direction. By contrast, white Gaussian noise energy is uniformly distributed on all of the NSCT coefficients approximately. Therefore, using the traditional square window often results in the signal underestimation within and around energy clusters. To preserve the edges and texture in images, we introduce the signal estimation method based on elliptic directional windows into the BS-AS threshold and develop the BS-EWAS threshold.

3.1. Elliptic directional windows. An elliptic directional window along direction θ with parameter r and a [6,7] is deﬁned by { ( ) sin2 θ W (r, a, θ) = (m, n): + a2 cos2 θ m2 a2 ( ) } (3) a4 − 1 cos2 θ + sin 2θmn + + a2 sin2 θ n2 ≤ r2 , a2 a2 where r ≥ 1, a ≥ 1, and θ ∈ [−π, π], r, a and θ determine the size, shape and the principal axis direction of the window respectively. For example, W (r, a, 0) shows a horizontal elliptic window and W (r, a, π/2) represents a vertical window. To capture the signal energy eﬀectively, the direction of the elliptic window is set to be perpendicular to the selected frequency direction of its oriented subband. Let lj be the number of directional decomposition at jth scale, then the elliptic directional window for the subband at jth scale and kth direction is described as

Wj,k = W (r, a, θj,k), (4) ( ) 3 2k−1 where θj,k = − π, k = 1, 2, . . . , lj. Figure 2(a) gives the frequency partition by 4 2lj one-scale and four-directional NSCT decomposition. The four elliptic directional windows applied in the corresponding subbands are listed in Figure 2(b), where r = 12 and a = 1.5.

(a) (b)

Figure 2. Example of elliptic directional windows. (a) Frequency partition; (b) Elliptic directional windows for oriented subbands 1916 X. SHEN, Y. ZHANG AND C. ZHANG 3.2. The proposed threshold. Instead of the square window, the elliptic directional window is used to select the neighboring coeﬃcients with strong dependency. Utilizing the maximum likelihood estimator, the signal variance of each noisy NSCT coeﬃcient is estimated by the local average     1 ∑ σ2 = max 0, y2 (m + p, n + q) − σ2 , (5) xj,k(m,n)  j,k εj,k  NWj,k (p,q)∈Wj,k where Wj,k and NWj,k denote the elliptic directional window and its size, respectively. Further, the proposed BS-EWSA threshold is obtained by substituting Equation (5) into Equation (2). Compared to the BS-SA threshold, the proposed threshold takes full use of the captured directional information of images and extends to the anisotropic spatially adaptability.

4. Experimental Results. In this section, all of the NSCT decompositions are set to 4 scale levels with 4, 4, 8 and 8 directions at each scale level (from coarse to fine scale), respectively. The 9-7 filters and the CD filters [8] are used for the multiscale decomposition and the multidirectional decomposition.

4.1. Parameter selection of elliptic windows. The 512 × 512 noisy “Lena” image corrupted by additive Gaussian white noise with σε = 20 is used as tested image to study inﬂuences of the size and shape of elliptic windows to the proposed algorithm. As mentioned that NSCT eliminates the downsampler, the elliptic window applied in each subband is set to be the same size. Table 1 lists the PSNR values of the proposed algorithm using the diﬀerent windows. It can be seen that the PSNR values are almost invariant when r = 10, 11, 12, 13, 14, 15 and a = 1.2, 1.5. Similar results can obtained from other test images. This indicates that the proposed algorithm is robust against the window’s parameter change in a relatively large range, which is advantageous to practical applications.

Table 1. Comparison of diﬀerent windows when subbands use the same size windows r 3 6 9 10 11 12 13 14 15 a = 1 31.47 32.44 32.71 32.74 32.76 32.77 32.76 32.76 32.75 a = 1.2 31.47 32.45 32.72 32.75 32.77 32.77 32.77 32.77 32.76 a = 1.5 31.47 32.46 32.72 32.75 32.77 32.77 32.77 32.76 32.75 a = 1.8 31.52 32.47 32.71 32.74 32.75 32.76 32.76 32.75 32.74 a = 2 31.61 32.45 32.69 32.73 32.74 32.75 32.75 32.74 32.73

4.2. Performance comparison to other denoising algorithms. To verify the performance of the proposed algorithm, we compare the proposed thresholding algorithm with the BS-SA thresholding algorithm and the bivariate shrinkage algorithm (BivShrink) [9], which are the two best denoising methods at present in the literature. For the proposed algorithm, we use the elliptic directional windows with r = 12 and a = 1.2. Table 2 gives the PSNR values of the three algorithms for the “Lena” and “Barbara” noisy images with diﬀerent noise levels. As manifested, the proposed algorithm performs better, no matter what the noise level or image is. In the case of the “Lena” image, the proposed algorithm gains about 0.4 dB in PSNR compared to the BivShrink algorithm, and 0.2 ∼ 0.4dB compared to the BS-AS algorithm. For the “Barbara” image, the proposed algorithm gains about 0.9dB compared to the BivShrink algorithm, and 0.1 ∼ 0.3dB compared to the BS-EWSA algorithm. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1917 Table 2. Comparison of diﬀerent denoising algorithms

Image Lena Barbara Noise level σε 15 20 25 30 15 20 25 30 Noisy 24.65 22.13 20.17 18.63 24.65 22.13 20.17 18.63 BivShrink 33.67 32.40 31.40 30.54 31.31 29.80 28.61 27.65 PSNR BS-SA 33.67 32.50 31.45 30.70 31.94 30.60 29.40 28.56 BS-EWSA 34.08 32.77 31.74 30.89 32.25 30.71 29.52 28.67

(a) (b)

Figure 3. Image denoising with BS-AS thresholding and the proposed algorithm. The noisy intensity is 20. (a) Denoised with BS-AS thresholding on Lena (PSNR=32.50); (b) Denoised with the proposed algorithm on Lena (PSNR=32.77); (c) Denoised with BS-AS thresholding on Barbara (PSNR=30.60); (d) Denoised with the proposed algorithm on Barbara (PSNR=30.71)

As a further examination, the denoising results visually are explored. Figure 3 displays denoised images with both BS-SA thresholding and the proposed algorithms for noisy “Lena” and “Barbara” image with σε = 20, respectively. For “Barbara” image, both algorithms perform excellent and the improvement of the proposed algorithm is slight. For “Lena” image, the proposed algorithm reduces the artifacts that often occur in the BS-SA algorithm apparently. In terms of the PSNR value and the visual quality of the denoised image, the proposed algorithm is superior to the other denoising algorithms. The reason, we believe, lies in that (1) the NSCT provides the multiscale, multidirectional and shift-invariance properties and (2) the BS-EWSA threshold considers the dependency of coeﬃcients not only within and across scales but also in a certain directional neighborhood.

5. Conclusion. In this paper, we propose a new NSCT image denoising algorithm with the spatially adaptive BayesShrink threshold based on elliptic directional windows. The threshold which explores the anisotropic and directional features of NSCT deeply obtains 1918 X. SHEN, Y. ZHANG AND C. ZHANG the adaptability in anisotropic neighborhood as well as in scale and direction. The experiments results show the algorithm outperforms the relevant algorithms both in the visual quality and PSNR value. Acknowledgement. This work is partially supported by the National Nature Science Foundation of China (Grant No. 60773166), the Natural Scienece Foundation of Shan- dong Province (Grant No. ZR2009GQ015) and Project of Shandong Province Higher Educational Science and Technology Program (Grant No. J08LJ72). The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

REFERENCES [1] M. N. Do and M. Vetterli, The finite ridgelet transform for image representation, IEEE Trans. Image Processing, vol.12, pp.16-28, 2003. [2] J. L. Starck, E. J. Candes and D. L. Donoho, The curvelet transform for image denoising, IEEE Trans. Image Processing, vol.11, pp.670-684, 2002. [3] Q. Guo and S. N. Yu, Shearlet-based image denoising using a local multivariate prior model, ICIC Express Letters, vol.3, no.3(B), pp.751-756, 2009. [4] M. N. Do and M. Vetterli, The contourlet transform: An efficient directional multiresolution image representation, IEEE Trans. Image Processing, vol.14, pp.2091-2106, 2005. [5] A. L. Cunha, J. P. Zhou and M. N. Do, The nonsubsampled contourlet transform: Theory, design and application, IEEE Trans. Image Processing, vol.15, pp.3089-3101, 2006. [6] P. L. Shui, Image denoising algorithm via doubly local wiener filtering with directional windows in wavelet domain, IEEE Signal Process. Lett., vol.12, pp.681-684, 2005. [7] Z. F. Zhou and P. L. Shui, Contourlet-based image denoising algorithm using directional windows, Electronics Lett., vol.43, pp.92-93, 2007. [8] D. Y. Duncan and M. N. Do, Directional multiscale modeling of images using the contourlet transform, IEEE Trans. Image Processing, vol.15, pp.1610-1620, 2006. [9] L. Sendur and I. W. Selesnick, Bivariate shrinkage with local variance estimation, IEEE Signal Process. Lett., vol.9, pp.438-441, 2002. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1919-1924

APPLICATION OF TYPE-2 FUZZY LOGIC SYSTEM IN INDOOR TEMPERATURE CONTROL

Tao Wang, Long Li and Shaocheng Tong Department of Mathematics and Physics Liaoning University of Technology Jinzhou 121001, P. R. China Quwangtao [email protected] Received February 2010; accepted April 2010

Abstract. This paper first presents a type-2 fuzzy logic system, which includes fuzzifier, rule base, fuzzy inference engine, and output processor. The output processor includes type-reducer and defuzzifier, it generates type-1 fuzzy set output and the antecedent or consequent sets in IF-THEN are type-2 fuzzy sets. Based on type-2 fuzzy logic system, a fuzzy control algorithm is developed to control the indoor temperature regulation problem, and achieve a desired control effect. Keywords: Type-2 fuzzy logic system, Indoor temperature control, Fuzzy control algorithm

1. Introduction. Fuzzy logic controller (FLC) has been successfully applied to many application problems [1,2]. To date all these applications are focused on conventional type-1 fuzzy logic system. While designing a type-1 FLS, the skills and knowledge are needed to decide both the membership functions and fuzzy rules. The linguistic terms that are used in antecedents and consequents have different meanings for different experts. Specialists often provide different conclusions for the same rule base. Type-1 FLS whose membership functions are type-1 fuzzy sets, is unable to directly handle rule uncertainties. To deal with this problem, the concept of type-2 fuzzy sets was introduced by Zadeh [3] as an extension of type-1 fuzzy sets. Compared to type-1 fuzzy sets, type-2 fuzzy sets handle the vagueness inherent in linguistic words. The uncertainties are modelled using a fuzzy membership function. Therefore, type-2 fuzzy logic system is more suitable in circumstances where it is difficult to determine the exact membership function for a fuzzy set; which is very useful for incorporating uncertainties [4-10]. This paper first develops a type-2 FLC, which includes fuzzifier, rule base, fuzzy inference engine, and output processor. The output processor includes type-reducer and defuzzifier, it generates 1-type fuzzy set output. A type-2 FLC is again characterized by IF-THEN rules, but its antecent or consequent sets are type-2 fuzzy sets. Based on type-2 FLC, a fuzzy control algorithm is developed to control the indoor temperature regulation problem, and achieve a desired control effect. 2. Interval Type-2 Fuzzy Logic Systems. A type-2 FLS includes a fuzzifier, a rule base, fuzzy inference engine, and an output processor, as we can see in Figure 1. The output processor includes a type-reducer and defuzzifier, it generates a type-1 fuzzy set output (from the type-reducer) or a crisp number (from the defuzzifier). T 2.1. Fuzzifer. The fuzzifier maps a crisp point X = (x1, ··· , xp) ∈ X1 ×X2 ×· · ·×Xp ≡ ˜ X into a type-2 fuzzy set Ax in X, which is a type-2 fuzzy set in this case. We will use a type-2 singleton fuzzifier, in singleton fuzzification, the input fuzzy set has only a single point with nonzero membership [5]. A˜ is a type fuzzy singleton if µ (x) = 1/1 for x = x0 x A˜x and µ (x) = 1/0 for all other x =6 x0. A˜x

1919 1920 T. WANG, L. LI AND S. TONG 2.2. Rules. The structure of rules in a type-1 FLS and a type-2 FLS is the same, but in the latter the antecedents and the consequents x1 ∈ X1, ..., xp ∈ Xp and one out y ∈ Y , which is a multiple input single output (MISO) system, if we assume there are M rules, the lth rule in the type-2 FLS can be written as follows: l ˜l ˜l ˜l R : IF x1 is F1 and xp is Fp, THEN y is G , l = 1, 2,...,M (1) 2.3. Inference. In the type-2 FLS, the inference engine combines rules and provides a mapping from input type-2 fuzzy sets to output type-2 fuzzy sets. It is necessary to compute the unions ∪, and the meet ∩, as well as extended sup-star compositions of ˜l × · · · × ˜l ˜l type-2 relations [5]. If F1 Fp = A , Equation (1) can be re-written as l ˜l × · · · × ˜l → ˜l ˜l → ˜l R : F1 Fp G = A G , l = 1, 2,...,M (2) l R is described by the membership function µRl (x, y) = µRl (x1, . . . , xp, y), where

µRl (X, y) = µA¯ l→G¯ l (X, y) can be written as:

µRl (X, y) = µA˜l→G˜l (X, y)

= µ ˜l (x1) ∩ · · · ∩ µ ˜l (xp) ∩ µ ˜l (y) F1 Fp G (3) p = [∩ µ ˜l (xi)] ∩ µ ˜l (y) i=1 Fi G l ˜ In general, the p-dimensional input to R is given by the type-2 fuzzy set Ax whose membership function is µ (X) = µ (x ) ∩ · · · ∩ µ (x ) = ∩p µ (x ) (4) A˜x x˜1 1 x˜p p i=1 x˜i i ˜ where Xi (i = 1, 2, ··· , p) are the labels of the fuzzy sets describing the inputs. Each rule Rl determines a type-2 fuzzy set B˜l = A˜ ◦ Rl such that: [ x ] µ l (y) = ∪ ∈ µ (X) ∩ µ l (X, y) , y ∈ Y, l = 1, 2, ··· ,M (5) B˜ x X A˜X R In the FLS we used interval type-2 fuzzy sets and meet under product t-norm, so the result of the input and antecedent operations, which are contained in the ﬁring set ∩p 0 ≡ l 0 i=1µF˜ (xi) F (x ) is an interval type-1 set i [ ] [ ] F l(x0) = f l(x0), f¯l(x0) ≡ f l, f¯l (6)

l 0 0 0 l 0 0 0 where f (x ) = µ (x ) ∗ · · · ∗ µ (x ), f¯ (x ) =µ ¯ ¯l (x ) ∗ · · · ∗ µ¯ ¯l (x ), ∗ is the product ¯l 1 ¯l p F 1 Fp p F1 Fp 1 operation.

2.4. Type-reducer. The type-reducer generates a type-1 fuzzy set output which is then converted into a crisp output through the defuzziﬁer. This type-1 fuzzy set is also an interval set, for the case of our FLS we used center of sets (cos) type reduction, Y cos which is expressed as ∫ ∫ ∫ ∫ /∑ M y θ ··· ··· ··· ∑i=1 i i Ycos(x) = [yl, yr] = 1 M (7) ∈ 1 1 ∈ M M 1∈ 1 ¯1 M ∈ M ¯M i y [yl ,yr ] y [yl ,yr ] f [f ,f ] f [f ,f ] i=1 f

This interval set is determined by its two end points, yl and yr, which corresponds to the centroid of the type-2 interval consequent set G˜i ∫ ∫ /∑ N y θ ··· ∑i=1 i i i i CG˜i = 1 N = [yl , yr] (8) ∈ ∈ θ1 Jy1 θN JyN i=1 θi before the computation of Y cos (x), we must evaluate Equation (7), and its two end i points, yl and yr. If the values of fi and yi that are associated with yl are denoted fl and ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1921

i i yl , respectively, and the values of fi and yi that are associated with yr are denoted fr and yi , respectively, from Equation (8), we have r ∑ ∑ M i i M i i i=1 fl yl i=1 fryr yl = ∑ , yr = ∑ (9) M i M i i=1 fl i=1 fr 2.5. Defuzzifier. From the type-reducer we obtain an interval set Y cos, and then to defuzzify it, we use the average of yl and yr, so the defuzzified output of an interval singleton type-2 FLS is y + y y(X) = l r (10) 2 3. Indoor Temperature Fuzzy Control Design. 3.1. Indoor temperature fuzzy control principle. Indoor temperature fuzzy control is based on fuzzy rule base, fuzzy inference, fuzzification and defuzzification. Indoor temperature fuzzy control system usually has two inputs: indoor temperature and the changing rate of temperature. The system output is the amount of temperature adjustment, indoor temperature control problem is that using current measured indoor temperature T and the changing rate of temperature dT , the controller is designed by using given the regulation of temperature dU. The control objective is to keep the room temperature moderate constant. Indoor temperature fuzzy control principle is described by Figure 1. 3.2. Design of indoor temperature fuzzy control. In indoor temperature control system, the input variables are indoor temperature T and indoor the changing rate of temperature dT , the output variable is regulation of temperature dU, their fuzzy linguistic variables sets are as follows: T = (NB (very low), NM (more lower), NS (low), ZR (moderate), PS (high), PM (higher), PB (very high)); dT = (NB (rapid decline), NM (lower middle), NS (lower trace), ZR (moderate), PS (trace up), PM (medium temperature), NB (full cooling)); dU = (NB (full heating), PM (medium heat), PS (trace heating), ZR (without heating), NS (micro-cooling), NM (moderate increase), PB (rapid rise))

Figure 1. Indoor temperature fuzzy control principle 1922 T. WANG, L. LI AND S. TONG Table 1. Fuzzy control rule H HH T H NB NM NS ZR PS PM PB dT HH NB PB NM PM NS PS ZR PS ZR NS PS NS PM NM PB NB

Establish the following 49 IF-THEN rules, which are shown by Table 1. The membership functions of T and dT are chosen as interval type-2 fuzzy sets, primary membership functions are Gaussian-types with uncertain means, their upper and lower membership functions are (x−17)2 {  − 2  e 200 , x ≤ 17 − (x−23) 200 ≤ ··· ≤ ≤ e , x 20 µPM (T ) = 1 , 17 x 23 , µ (T ) = (x−17)2 ......  2 PM −  − (x−23) e 200 , x ≥ 20 200 ≥  e , x 23 (x−3.5)2 {  − 2  e 50 , x ≤ 3.5 − (x−6.5) 50 ≤ ··· ≤ ≤ e , x 5 µPS(dT ) = 1 , 5 x 6.5 , µ (dT ) = (x−3.5)2 ......  2 PS −  − (x−6.5) e 50 , x ≥ 5 e 50 , x ≥ 6.5 Given the measurements of input variables T = 18◦C and dT = 3K, according to interval type-2 FLS described in Section 2, where ∩ and ∗ operators are both taken as Min, Type-reducer and Centroid of type-reduction are adopted. The inference diagram is described by Figure 2. The computations are follows µ (T = 18) = 0.8825, µ (T = 18) = 1, PM PM µ (dT = 3) = 0.7827, µ (dT = 3) = 0.9950, PS PS µ (T = 18) = 0.5461, µ (T = 18) = 0.8825, PS PS µ (dT = 3) = 0.6670, µ (dT = 3) = 0.9560. ZR ZR T = 18 and dT = 3 response to the ﬁred rules are

R1 : If T = PM and dT = PS, Then dU = NM;

R2 : If T = PS and dT = ZR, Then dU = NS.

Figure 2. The inference diagram ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1923 Firing set can be calculated as follows: f 1 = min{µ (T = 18), µ (dT = 3)} = 0.7828, PM PS 1 { } f = min µPM (T = 18), µPS(dT = 3) = 0.9950, f 2 = min{µ (T = 18), µ (dT = 3)} = 0.5461, PS ZR 2 { } f = min µPS(T = 18), µZR(dT = 3) = 0.8825 The output of each rule is 1 { 1 ¯1 } 2 { 2 ¯2 } Rout = min [f , f ], µNM (dU) ,Rout = min [f , f ], µNS(dU) The reasoning result is shown in Figure 2. The ﬁnal output is: { 1 2 } µout = max Rout,Rout By type-reduction, we have C = [y1, y1] = [−11.5, −8.5],C = [y2, y2] = [−6.5, −3.5], G˜1 l r G˜2 l r 1 1 2 2 1 1 2 2 fl = f , fl = f , fr = f , fr = f 1 1 1 2 2 1 2 2 ∗ − ∗ − fl yl + fl yl f yl + f yr 0.9950 ( 11.5) + 0.5461 ( 6.5) yl = = = = −9.73 1 2 1 2 fl + fl f + f 0.9950 + 0.5461 2 1 1 2 2 1 1 2 ∗ − ∗ − fr yr + fr yr f yl + f yr 0.7827 ( 8.5) + 0.8825 ( 3.5) yr = = = = −5.85 1 2 1 2 fr + fr f + f 0.7827 + 0.8825

yTR = [−9.37, −5.85]. By defuzzification, we obtain y + y (−9.73) + (−5.85) y(x) = l r = = −7.79K 2 2 If we variable the indoor temperature and the rate changing of indoor temperature, we can calculate the different temperature regulation according to the above process of the computing. Table 2 is given four control results responding to different T and dT . Table 2. The indoor temperature, the changing rate of indoor temperature and regulation of temperature

T dT dU −18◦C −12 K +12.62K −7◦C −6 K +7.46 K 8◦C −3 K −0.3 K 14◦C 11 K −12.21K

4. Conclusions. This paper first presents a type-2 fuzzy logic system, which includes fuzzifier, rule base, fuzzy inference engine, and output processor. The output processor includes type-reducer and defuzzifier, it generates 1-type fuzzy set output and the antecedent or consequent sets in IF-THEN are type-2 fuzzy sets. Based on type-2 FLS, a fuzzy control algorithm is developed to control the indoor temperature regulation problem, and achieve a desired control effect.

Acknowledgment. This work was supported by National Natural Science Foundation of China, the Outstanding Youth Funds of Liaoning Province (No. 2005219001) and Educational Department of Liaoning Province (No. 2006R29 and No. 2007T80). 1924 T. WANG, L. LI AND S. TONG

REFERENCES [1] L. X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Prentice-Hall, Englewood Cliﬀs, NJ, 1994. [2] L. Wang, Fuzzy Control Theory and Application, National Defense Industry Press, Beijing, 1997. [3] M. Mizumoto, Note on the arithmetic rule by Zadeh for fuzzy reasoning methods, Cybernetics and Systems, vol.12, pp.247-306, 1981. [4] N. Karnik and J. M. Mendel, Centroid of a type-2 fuzzy set, Information Sciences, vol.132, pp.195- 220, 2001. [5] N. N. Karnik and J. M. Mendel, Type-2 fuzzy logic systems, IEEE Trans. on Fuzzy Systems, vol.6, no.6, pp.643-658, 1999. [6] Q. Liang and J. M. Mendel, Interval type-2 fuzzy logic systems: Theory and design, IEEE Trans. on Fuzzy Systems, vol.8, no.5, pp.535-550, 2000. [7] T. Wang, Y. Chen and S. C. Tong, Type-2 fuzzy reasoning model and algorithms, International Journal of Innovative Computing, Information and Control, vol.4, no.10, pp.2451-2460, 2008. [8] R. Mart´ınez,O. Castillo and L. T. Aguilar, Optimization of interval type-2 fuzzy logic controllers for a perturbed autonomous wheeled mobile robot using genetic algorithms, Information Sciences, vol.179, pp.2158-2174, 2009. [9] T. C. Lin, M. J. Kuo and C. H. Hsu, Robust adaptive tracking control of multivariable nonlinear systems based on interval type-2 fuzzy approach, International Journal of Innovative Computing, Information and Control, vol.6, no.3, pp.941-962, 2010. [10] S. Y. Li and X. X. Zhang, Fuzzy logic controller with interval-valued inference for distributed parameter system, International Journal of Innovative computing, Information and Control, vol.2, no.6, pp.1197-1208, 2006. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1925-1930

TRAFFIC FLOW FORECASTING AND SIGNAL TIMING RESEARCH BASED ON ANT COLONY ALGORITHM

Wenge Ma1, Yan Yan2 and Dayong Geng1 1Institute of Electrical Engineering Liaoning University of Technology Jinzhou 121001, P. R. China [email protected] 2Department of Automation Liaoning Petrochemical Vocational and Technology College, P. R. China Received February 2010; accepted April 2010

Abstract. In view of actual traffic status of China and the typical intersection layout, to research the optimizing algorithm of signal timing of urban intersection is based on real-time mixed traffic volume under 2∼6 changeable phases. Firstly, according to an examined directional traffic flows, short-term traffic flow is forecasted with unified method of the artificial intelligence and the forecast model. Then, ant colony algorithm is used to carry on the dynamic timing to optimize isolated. This model becomes more adaptability on intersection control. It can reduce delay measurements, and enhance traffic capacity. Keywords: Mixed traffic of motor, Bicycle and pedestrian, Changeable phases, Short- term traffic flow forecasting, Ant colony algorithm

1. Introduction. The mixed traffic flow of motor, bicycle and pedestrian is an important feature in our city’s traffic. It is very different from the application condition of HCM. For foreign pop controllers at homes they are lack of effective modifying design about mixed traffic and objectively have no control effect [1]. Look at the Chinese economic development, mixed traffic will exist for a long time. So the research of effective controlling means to fit mixed traffic feature in our city is very necessary. Used for reference of the domestic theory research results, based on the traffic flow operating characteristic of our city’s intersection, design a system of mixed traffic flow single-point timing. In this paper, we propose a traffic flow forecasting method that is combine multiple predict model with artificial intelligence technology, use ant colony algorithm to optimizing timing, and give the steps of the optimizing algorithm, and the simulation result of MATLAB indicated that the method is better than the conventional timing control. 2. Establish Model. 2.1. Isolated intersection traffic network. Traffic flow distribution in isolated intersection is shown in Figure 1. It is a multi-lane intersection. For easy to analysis, we hypothesized that there are four lanes on one-way, they are left-turn appropriative lane, through appropriative lane, both through and right-turn lane, bikeway. 2.2. Phasic selection and man-machine non-conflict. Generally, the less phases of intersection, the higher utilization rate; and the more phases, the less time of green light in each phase, the more losing time [1]. In this system, we used 2-6 changeable phases traffic state setting. The states of signal lamp is shown in Figure 2. For easy to explanation, we only talk about easterly and western signal lamp states (state 1-3), the same as southern and north. Considering the intersection of mixed traffic of motor, bicycle and pedestrian, when the left-turn and through are in the same phase, it is easy to develop conflict between left-turn bike and same-phase, opposite-phase motor vehicle, if more traffic on left-turn. In the 1925 1926 W. MA, Y. YAN AND D. GENG

Figure 1. Intersection network diagram membership

Figure 2. The states of signal lamp conflict-point finally result in crowded traffic. To solve this conflict, this system designed left-turn appropriative lane (state 2), and left-turn bike flow is the decision value that can decide the system enter this state or not. It can be enter state 2 when the first phase detect the quantity of non-motorized vehicle (µn) and motor vehicle (n) must accord with the follow condition: µn ≥ n (µ is the bike conversion coefficient [2]) or else over the state (as a supporting measures, this state can take non-motorized vehicle green signal “delay” and “early break” [3], to shun conflict between non-motorized vehicle and motor vehicle); It can be enter state 3 when the system detect the quantity of pedestrian are more than 3, or else over this state (as a measures, this state can take pedestrian green signal “delay” and “early break”, to shun conflict between pedestrian and vehicle). Detected twice if the quantity of pedestrian were still less than 3, then in the third dynamic period load state 3. In doing so, within one period, there maybe 2 phases running (state 1, 5) and 3-6 phases running.

2.3. Selection of object function. Consider in this paper, we make delay time and traﬃc capacity as optimize object function. Average vehicle delay (s) of i phase is: { / [ ] /( )} ∑ 2 ∑ 2 di = qsyi(1 − Y ) × [c(1 − ti/c) ] (1 − yi) + 1 − Li/c Li/c (1)

Eﬀective traﬃc capacity (P CU/h) of i phase is:

qc = 2qstik/c (2) where qs is the saturation volume of the intersection, P CU/h; ti is the effective green time of i phase, s, Li is the loss time of i phase, s, yi is the percentage of traffic flow and ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1927 saturation volume on i phase; c is the reference period of intersection, s, k is the flow rate of intersection. Optimize timing model as follows: ∑ minZ (ti, c) = (di − qc)

s.t tmin ≤ ti ≤ tmax, 1 ≤ i ≤ n; ∑n (3) ti+ Li ≤ cmax, 1 ≤ i ≤ n; i=1

smin ≤ ti/qs ≤ smax, 1 ≤ i ≤ n;

where tmin, tmax are maximal and minimal eﬀective green time; smin, smax are the saturation of maximal and minimal; cmax is maximal reference period.

3. Traffic Flow Forecasting. The precondition and key of control algorithm actual- ization is that forecast traffic flow real-timely and exactly, because, in intelligent traffic system, known traffic flow in each lane is the precondition of timing method. Considering the process of traffic flow have obvious randomicity, non-determinacy and nonlinear, this paper pose a method that is combine multiple predict model with artificial intelligence technology. This method is full exert the merit of other model, obviously, this method can win the better forecast result. The steps of this method as follows: Step 1: Model filtration: There are ARIMA model [4], BP Neural Network [5], Non- parameter Regression model [6] and Support Vector Regression model [7] as pending selective model. Go on to use the current traffic flow forecasting model or not that depended current traffic and previous forecast effect. If the model is not used, we can also take another model which maybe have the better predict effect. Step 2: Set parameter: For Non-parameter Regression model when we decided to use it, it’s parameters can be set by current and previous data. Other models can accorded forecast location, flow, period of time and forecast period to setting state space of parameter and according historical data can off-line setting a number of model parameter. Step 3: Forecasting correction: Save the results of traffic flow forecasting to according database in control system, when forecasted period of time is over, figure out forecast windage of each model through detect practical flow of different position. At the same time, save the forecast windage to database and that can update evaluation knowledge in knowledgebase, also can as a new select basis. If detect result indicated that the forecast errors are greater than the threshold, the traffic process and environment have taken tremendous changes, so the current model or parameter is wrong. And then, need reset model parameter by new data.

4. Timing Design Base on Ant Colony Algorithm. Ant colony algorithm is a bionic algorithm. There will leaved a chemical substances called pheromone where the ant pass by, other ants can apperceive pheromone and move to the high concentration, so it formed positive feedback. Ant colony algorithm imitate this process, as: the feasible solution of the question is represented by ant’s rout, the ant research the feasible solution independently in solution space, the higher solution’s quality, the more pheromone, as algorithm advance, pheromone is increasing in the rout which must have better solution, then the more ant choose it, finally, under positive feedback, the whole ants are collected on the rout which have the best solution, of course the best solution is found. Use penalty function method which can translate nonlinear optimize model build in 2.3 into unrestraint optimize problem, the evaluation function of each ant is defined ηi, the 1928 W. MA, Y. YAN AND D. GENG transition function is defined as follow:

∆ηij = |ηi − ηj| (4) So the transition probability from i to j is: { / ∑ α β α β ∈ k τijηij τisηis (j, s allowedk) pij (t) = (5) 0 (otherwise) where τij(t) is pheromone intensity of (i, j) in time t; ηij is visibility; α and β are function coefficient of control pheromone and visibility. The steps of optimizing algorithm: k Step 1: Initialization: Stochastic release 20 ants, give initial value to τij(t) and ∆τij. Step 2: Within t, create a lamp time t(k) stochastically, and count the evaluation function ∗ ∗ ηi, and take the best one to η , at the same time take t to t . Step 3: Build around: Take the initial position of each ant into tabu list, use probability k pij(t) search target j partially. Take ant k to aim j, and put j into tabu list, until the list filled. Step 4: Update pheromone partially: Take ant k from the end to initial position, count longness which ant k pass by in one period, for branch (i, j) in tabu list, counting k ∆τij. Step 5: Update pheromone globally: Update pheromone of all sides when all ants walked a circle, for branch (i, j) execute: ∑ k τij (t + ∆t) = ρτij (t) + ∆τij (t) (6) (ρ is ratio of pheromone), compared around length, find the shortest one, clear tabu list, go back to (2). Step 6: Until meet the stop condition, stop iteration. Step 7: Output the best η∗ and t∗.

Losing time of green time phase is 3s, take ρ = 1/2, tmin=15s, tmax=75s, cmax=240s, ∗ smin=0.65, smax=0.95 to timing optimized model, qs is known, so t of i phase is solved, dynamic period is the sum of t∗ that compose with 2-4 phase. This paper use empirical trial method to insure algorithm’s fast converge.

5. Simulation.

5.1. Simulation flow. Use MATLAB to compile simulation program about timing control method of isolated intersection mixed traffic flow. Hypothesis traffic flow of intersection obey Poisson distribution, and the traffic flow rate is invariable. Simulation flow is shown in Figure 3.

5.2. Experimental determination. Hypothesis the max ﬂow of one lane is 4000/h. Choose 7 λ of Poisson distribution are: λ1 (motor 1800, non 480, pedestrian 80); λ2 (motor 2100, non 680, pedestrian 130); λ3 (motor 2400, non 880, pedestrian 180); λ4 (motor 2700, non 1080, pedestrian 240); λ5 (motor 3000, non 1280, pedestrian 320); λ6 (motor 3300, non 1480, pedestrian 400); λ7 (motor 3600, non 1680pedestrian 500). Simulation time is 60min, record delay time at least 50 times. For timing control, select 7 periods of time 4 phases control (north and south left-turn 10-20s, north and south through and right-turn 30-50s, east and west left-turn 30-40s, east and west through and right-turn 30-40s), and this method is also use Poisson distribution. Simulation results as shown in Table 1. From Table 1 we known that, average vehicle delay is decreased eﬀectively under this timing design plan. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1929

Figure 3. Triangular-type membership

Table 1. The comparison of simulation result

Average vehicle delay (s) λ group Optimized Timing control 1 19.6 20.2 2 23.2 26.3 3 26.8 28.9 4 28.7 34.1 5 32.1 36.6 6 31.9 36.8 7 32.6 37.2

6. Conclusions. In this paper, build a model of maxed traﬃc ﬂow, the sequence of short-term forecasting is decide that the stand-by phase is used or not in this system, ant colony algorithm is used to solve model. From simulation and estimate, the time of all forecasting and timing is about 14s.

REFERENCES

[1] Y. L. Pei, X. C. Jiang and B. H. Liu, Signal timing designing system under mixed traﬃc conditions, Journal of Harbin Institute of Technology, vol.38, no.4, pp.586-588, 2006. [2] C. G. Jiang, Research on the Theory and Application of Vehicle-bicycle Conﬂict at Intersections, Ph.D. Thesis, Jilin University, Changchun, 2005. 1930 W. MA, Y. YAN AND D. GENG

[3] X. G. Yang, M. Z. Sun and H. J. Zhang, Design Guide of Urban Road Traffic, China Communications Press, Beijing, 2003. [4] M. Voort, M. Dougtherty and S. Watson, Combining Kohonen maps with ARIMA time series models to forecast traffic flows, Transportation Research, vol.5, no.4, pp.307-318, 1996. [5] N. Shang, A BP neural network method for short-term traffic flow forecasting on crossroads, Com- puter Applications and Software, vol.23, no.2, pp.32-35, 2006. [6] X. L. Zhang and G. G. He, The combined forecasting approach based on non-parametric regression for short-term traffic flow of roads with parking spaces, Systems Engineering, vol.24, no.12, pp.21-25, 2006. [7] Z. S. Yao, C. F. Shao and Y. L. Gao, Research on methods of short-term traffic forecasting based on support vector regression, Journal of Beijing Jiaotong University, vol.30, no.6, pp.23-26, 2006. [8] H. B. Duan, Principle and Application of Ant Colony Algorithm, Science Press, Beijing, 2005.

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ADAPTIVE CONTROL FOR MISSILE SYSTEMS WITH PARAMETER UNCERTAINTY

Zhiwei Lin1, Zheng Zhu1, Yuanqing Xia1 and Shuo Wang2

1Department of Automatic Control Beijing Institute of Technology Beijing 100081, P. R. China { linzhiwei; xia yuanqing }@bit.edu.cn; [email protected] 2Institute of Automation Chinese Academy of Sciences Beijing 100080, P. R. China [email protected] Received February 2010; accepted April 2010

Abstract. This paper is devoted to attitude control of a nonlinear missile model. Com- bining the back-stepping technique, the corresponding sliding mode controller is designed to guarantee the state variables of the closed loop system to converge to the reference state with the help of the adaptive law by estimating the total uncertainties. Also, simulation results are presented to illustrate the eﬀectiveness of the control strategy. Keywords: Sliding mode control, Back-stepping, Adaptive control, Missile attitude control Nomenclature x, y, z Displacement components X, Y, Z Atmospheric drag, side and lift force Jx,Jy,Jz Moments of inertia Mx,My,Mz Aerodynamic moments wx, wy, wz Angular velocity components Vx,Vy,Vz V elocity components δx, δy, δz Deflection angles ϑ, ψ, γ P itch angle, yaw angle and roll angle α, β Angle of attack and sideslip angle ∗ ∗ ∗ mx, my, mz Atmospheric moment coefficients q Quaternion g Gravity acceleration m Missile mass V Missile speed P T hrust force ρ Atmospheric density Ma Mach number Sref Reference area L Reference length Sometimes, the arguments of a function will be omitted in the analysis when no confusion can arise.

1. Introduction. There have been a great many researches on control designs for missiles with highly nonlinear characteristics using nonlinear control techniques. In [1], the problem of attitude control of missiles is considered as a special tracking problem which

1937 1938 Z. LIN, Z. ZHU, Y. XIA AND S. WANG is investigated by using Fliess functional expansion. This approach has much higher accuracy comparing with several existing linearization-based approaches by treating the output directly, which can avoid accumulated errors eﬀectively. In [2], an inverse optimal adaptive control law is designed to solve the attitude tracking problem of a rigid spacecraft with an uncertain inertia matrix and external disturbances. Especially, asymptotic attitude tracking can be achieved in the presence of uncertain external disturbances which are bounded. In [3], attitude control is converted into a global stabilization problem of a particular type of nonlinear systems involving both disturbances and mass parameter uncertainties. An adaptive controller is designed to accomplish the stabilization problem and has achieved asymptotic rejection of a class of external disturbances by designing a compensator. In [4], large-angle attitude control of spacecraft is considered. Linear matrix inequality techniques are introduced to the design of attitude controllers to guarantee the global stabilization and robust disturbance attenuation. Therefore, in this paper, we consider the problem of attitude control for a missile system making using of adaptive method, sliding-mode control and back-stepping approach. By means of the adaptive law, the uncertainties can be estimated. A sliding mode controller is designed combining the back-stepping technique to force the state variables of the closed loop system to converge to the reference state.

2. Problem Statement and Preliminaries. Consider the missile system described by quaternions [5]       q˙0 −q1 −q2 −q3    −  wx  q˙1  1  q0 q3 q2      =   wy (1) q˙2 2 q3 q0 −q1 wz q˙3 −q2 q1 q0     w˙ x ((Jy − Jz)wywz + Mx)/Jx     w˙ y = ((Jz − Jx)wxwz + My)/Jy (2) w˙ z ((Jx − Jy)wxwy + Mz)/Jz where     δx wx wy wz M m δx + m wx + mx wy + m wz x 1 x x x   2  δy α˙ z αz wy wx  My = ρV Sref L my δy + my α˙ z + my αz + my wy + my wx (3) 2 α˙ α M δz y y wz wx z mz δz + mz α˙ y + mz αy + mz wz + mz wx { Vy αy = − arctan Vx (4) α = − arctan Vz z Vx { q = q0 + q1i + q2j + q3k 2 2 2 2 (5) q0 + q1 + q2 + q3 = 1 T Assumption 2.1. In missile Equations (1) – (2), both the states [q0, q1, q2, q3] and T T [wx, wy, wz] can be measured. The velocity [Vx,Vy,Vz] and displacement components [x, y, z]T needed in (1) – (2) can be measured as well, and they are involved in the following equations           V˙ P − X 2(q q + q q ) 0 w −w V x 1 0 3 1 2 z y x  ˙    −  2 − 2 2 − 2   −    Vy = Y g q0 q1 + q2 q3 + wz 0 wx Vy (6) ˙ m − − Vz Z 2(q2q3 q0q1) wy wx 0 Vz       2 2 − 2 − 2 − x˙ q0 + q1 q2 q3 2(q1q2 q0q3) 2(q1q3 + q0q2) Vx    2 − 2 2 − 2 −    y˙ = 2(q0q3 + q1q2) q0 q1 + q2 q3 2(q2q3 q0q1) Vy (7) − 2 − 2 − 2 2 z˙ 2(q1q3 q0q2) 2(q0q1 + q2q3) q0 q1 q2 + q3 Vz ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1939 √ 2 2 2 V = Vx + Vy + Vz (8) In this paper, the control objective is to force the attitude state to track the reference T quaternion yr. The state vector to be controlled is the quaternion vector [q0, q1, q2, q3] , T and the control input is deflection angle vector [δx, δy, δz] . In order to depict the missile model explicitly, we define         q0 [ ]   wx x Vx δx  q1        X1 =   ,X2 = wy ,X3 = y ,X4 = Vy ,U = δy q2 wz z Vz δz q3 Then system (1)-(2) can be expressed in the following ˙ X1 = F1(X1)X2 ˙ X2 = F2(X2) + F3(X1,X2,X3,X4) + B(X1,X3,X4)U (9) where   −q −q −q  1 2 3  1  q0 −q3 q2  F1(X1) =   (10) 2 q3 q0 −q1 −q2 q1 q0   (Jy − Jz)wywz/Jx   F2(X2) = (Jz − Jx)wxwz/Jy (11) (Jx − Jy)wxwy/Jz   wx wy wz (mx wx + mx wy + mx wz)/Jx w 1 2  α˙ z αz y wx  F3(X1,X2,X3,X4) = ρV Sref L (my α˙ z + my αz + my wy + my wx)/Jy (12) 2 α˙ y αy wz wx (mz α˙ y + mz αy + mz wz + mz wx)/Jz   δx mx /Jx 0 0 1 2  δy  B(X1,X3,X4) = ρV Sref L 0 my /Jy 0 (13) 2 δz 0 0 mz /Jz The main problem in system (9) is the uncertainty existing in the atmospheric moment ∗ ∗ ∗ coefficients mx, my and mz. The moment coefficients are dependent on the mach number Ma, and mach number Ma is also a variable tied to the states X1, X2, X3, X4. However, ∗ ∗ ∗ in practical missile systems, the coefficients mx, my and mz cannot be known exactly, there is always model uncertainty existing in the atmospheric moment coefficients of the missile. Therefore, the structure of system (9) poses a specific difficulty because both of F3 and B became unknown due to the dynamic uncertainty existing in the atmospheric moment coefficients. In order to treat the mass uncertainty, we define an uncertain variable H(t) as following.

H(t) = F3(X1,X2,X3,X4) + B(X1,X3,X4)U − B0U (14) where 1 B = ρV 2S LΦ| (15) 0 2 ref Ma=const and Φ| is defined as Ma=const   δx mx /Jx 0 0 |  δy  | Φ Ma=const = 0 my /Jy 0 Ma=const (16) δz 0 0 mz /Jz 1940 Z. LIN, Z. ZHU, Y. XIA AND S. WANG Then, system (9) can be rewritten as ˙ X1 = F1(X1)X2 ˙ X2 = F2(X2) + H(t) + B0U(t) (17) Remark 2.1. Since the dynamic uncertainty exists in the atmospheric moment coeffi- ∗ ∗ ∗ cients mx, my and mz, both F3 and B in (9) became unknown to us, which makes the control design more complicated. Instead, via selecting appropriate constant mach number δx δy δz Ma, we obtain the coefficients mx , my and mz which can be used as the certain part B0 and divide the uncertain part into the variable H(t). In this way, the dynamic uncertainty existing in (9) can be lumped together as the total uncertainty H(t), which reduced the complicity of control design.

3. Back-stepping Sliding Mode Control Design.

3.1. The back-stepping procedure. Back-stepping control design is one of the nonlinear feedback methods for controlling nonlinear systems. It is based on Lyapunov theory and capable of solving complicated nonlinear systems. The back-stepping method makes the design of the feedback control strategy systematic: it consists of a recursive determination of a virtual Lyapunov-based control signal and obtaining the actual control law until the last step. With this characteristics, the back-stepping technique is more ﬂexible in designing controllers for high-order nonlinear system models. As mentioned above, the back-stepping technique consists of a step-by-step construction of a new system with states ei = Xi − Xr,i, where Xr,i is the desired value for state Xi. We start by deﬁning the tracking error

e1 = X1 − Xr,1 (18) with Xr,1 = yr which is the reference value for Xr,1, having dynamics ˙ e˙1 = X1 − y˙r = F1(X1)X2 − y˙r (19)

In Equation (19), X2 is viewed as a virtual control input used to impose the following desired dynamics   k 0 0 0  1  − −  0 k2 0 0  e˙1 = K1e1 =   e1 (20) 0 0 k3 0 0 0 0 k4

The design matrix K1 is chosen as k1 > 0, k2 > 0, k3 > 0, k4 > 0 to ensure the asymptotic stability of (20). Therefore, combining (19) and (20) gives

F1(X1)X2 =y ˙r − K1e1 (21) Solving for (21), we obtain the virtual control input: −1 − Xr,2 = F1L (X1)(y ˙r K1e1) (22) −1 where F1L (X1) denotes the left inverse matrix of F1(X1). 3×3 Remark 3.1. F1(X1) has four R subdeterminants in (10), the values of these subdeterminants are respectively q0, q1, q2 and q3. The column rank of F1(X1) is reduced only in the case of q0 = q1 = q2 = q3 = 0, otherwise, the column rank of F1(X1) is full if any of qi satisﬁes qi =6 0. Note (5), there is no possibility for q0 = q1 = q2 = q3 = 0 simultaneously. Thus F1(X1) is full column rank which implies the existence of the left inverse matrix of F1(X1). ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1941 3.2. Sliding mode control. It is well known that sliding mode control (SMC) is a robust method to control nonlinear and uncertain systems which has attractive features to keep the systems insensitive to the uncertainties on the sliding surface [6, 7]. The primary advantages of sliding model control are: i) fast response and good transient performance; ii) its robustness against a large class of perturbations or model uncertainties; and iii) the possibility of stabilizing some complex nonlinear systems which are diﬃcult to stabilize by continuous state feedback laws. As usual in the sliding mode technique, the control forces the system evolution on a certain surface which guarantees the achievement of the control requirements. A natural choice is the sliding surface

S = e2 = X2 − Xr,2 (23) Now consider the following reaching law S˙ = −τS − σ sgn(S) where

τ = diag[τ1, τ2, τ3]

σ = diag[σ1, σ2, σ3] T sgn(S) = [sgn(S1), sgn(S2), sgn(S3)]

τi > 0, σi > 0 where Si is the ith component of S(t). Thus, the derivative of S can be also rewritten as follows ˙ ˙ ˙ S = X2 − Xr,2 ˙ = F2(X2) + H(t) + B0U(t) − Xr,2 = −τS − σ sgn(S) (24) Solving for U(t) in equality (24) gives the control law −1 − − − − ˙ U(t) = B0 ( τS σ sgn(S) F2(X2) H(t) + Xr,2) (25) Note that the control law (25) consists of the uncertainty H(t) which are not completely known to us, it could not be applied to the practice systems. Adaptive control method is a natural choice to deal with uncertain parameters and has been widely applied. In order to obtain the uncertainties, therefore, we will apply the adaptive approach to estimate them. Before introducing the adaptive controller, the following assumption is needed. Assumption 3.1. The uncertainty H(t) is assumed to be bounded and satisfy the following condition

kH(t)k ≤ c + kkXξ(t)k = ρ (26) T T T where Xξ(t) = [X1 X2 ] , c and k are unknown bounds which are not easily obtained due to the complicated structure of the uncertainties in practical control systems. 3.3. Adaptive method. Based on the defined sliding surface, a sliding mode controller is designed such that the system state is moved from the outside to the inside of the region, and finally remains inside the region in spite of the uncertainties. In order to reach the sliding condition, the uncertainties need to be estimated and rejected. Define a adaptive control law   S(t) k k kS(t)k ρ,ˆ ifρ ˆ S(t) > up(t) = (27)  S(t) 2 k k ≤ ρˆ , ifρ ˆ S(t) 1942 Z. LIN, Z. ZHU, Y. XIA AND S. WANG and the adaptation update laws are ˆ ρˆ =c ˆ(t) + k(t)kXξ(t)k (28) ˙ cˆ(t) = p1(−0cˆ(t) + kS(t)k) (29) ˆ˙ ˆ k(t) = p2(−1k(t) + kS(t)kkXξ(t)k) (30) ˆ where p1, p2, , 0, 1 are design parameters andc ˆ, k,ρ ˆ are used to estimate the bounds c, k, ρ in (26) respectively. With the uncertainty H(t) estimated by the adaptive law, the control law (25) is modified as ˆ −1 − − − − ˙ U(t) = B0 ( τS σ sgn(S) F2(X2) up(t) + Xr,2) (31)

Remark 3.2. The up(t) in (27) is most important. It shows that adaptive input can estimate (or track) the total action of the uncertainty H(t). As adaptive input is the estimation for the total action of the uncertainty, in the feedback, it is used to compensate for the uncertainty.

4. Stability Analysis. In this section, the stability of the closed-loop system can be established by the following theorems. Before proving the theorems, the following deﬁnition is recalled. Deﬁnition 4.1. [8] Consider the nonlinear system, x˙ = f(x, u), y = h(x) where x is a state vector, u is the input vector and y is the output vector. The solution is uniformly ultimately bounded (UUB) if for all x(t0) = x0, there exists ε > 0 and T (ε, x0), such that kx(t)k < ε, for all t ≥ t0 + T . Theorem 4.1. With the sliding surface given by (23), the trajectory of the closed-loop system (17) can be driven onto the sliding surface with the control law (31), and evolves in a neighborhood around the sliding surface. Proof: Consider the following Lyapunov function: [ ] 1 T 1 2 1 ˜2 Vs = S (t)S(t) + c˜ + k (32) 2 p1 p2 wherec ˜ = c − cˆ(t) and k˜ = k − kˆ(t). Its time derivation is

˙ T ˙ 1 ˙ 1 ˜ˆ˙ Vs = S (t)S(t) − c˜cˆ − kk (33) p1 p2 If kS(t)kρˆ > , with the control law deﬁned in (31) and adaptation laws deﬁned in (28)-(30), we have

˙ T T T Vs(t) = S (t)[−τS − σ sgn(S)] − S (t)up + S (t)H(t) − c˜(−0cˆ + kS(t)k) ˜ ˆ −k(−1k + kS(t)kkXξ(t)k) T ˆ ≤ S (t)(−τS − σ sgn(S)) − kS(t)k(ˆc + kkXξ(t)k) + kS(t)k(c + kkXξ(t)k) −c˜(− cˆ + kS(t)k) − k˜(− kˆ + kS(t)kkX (t)k) 0 1 ( ) ξ ( ) 1 2 1 2 1 = ST (t)(−τS − σ sgn(S)) − cˆ − c − kˆ − k + ( c2 + k2) 0 2 1 2 4 0 1 1 ≤ −Σ3 (τ S2 + σ |S |) + ( c2 + k2) (34) i=1 i i i i 4 0 1 ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1943 If kS(t)kρˆ ≤ , with the control law deﬁned in (31) and adaptation laws deﬁned in (28)-(30), we obtain kS(t)k2 V˙ (t) ≤ ST (t)(−τS − σ sgn(S)) − ρˆ2 + kS(t)k(c + kkX (t)k) s ξ k k2 T S(t) 2 ˜ˆ = S (t)(−τS − σ sgn(S)) − ρˆ + kS(t)kρˆ + 0c˜cˆ + 1kk ( √ ) ( ) kS(t)k 2 1 2 = ST (t)(−τS − σ sgn(S)) − √ ρˆ − + − cˆ − c 2 4 0 2 ( ) 1 2 1 − kˆ − k + ( c2 + k2) 1 2 4 0 1 1 ≤ −Σ3 (τ S2 + σ |S |) + + ( c2 + k2) (35) i=1 i i i i 4 4 0 1 √ ˙ δ It can be concluded now from (34) and (35) that Vs(t) < 0 if kSk > or |Si| > 4τmin δ 2 2 , where δ = 0c + 1k + , τmin = min(τi) and σmin = min(σi). The decrease of 4σmin √ δ Vs(t) eventually drives the the trajectories of the closed-loop system into kSk ≤ 4τmin δ and |Si| ≤ . Therefore, the the trajectories of the closed-loop system is bounded 4σmin ultimately as ( √ ) ( ) δ δ lim S(t) ∈ kSk ≤ ∩ |S | ≤ (36) →∞ i t 4τmin 4σmin which is a small set containing the origin of the closed-loop system. Since τi and σi are positive parameters to be tuned, appropriate τi and σi can be ˙ selected large enough such that Vs < 0 when Vs(t) is out of a certain bounded region which contains equilibrium point. Of course, the design parameters , 0, 1 determine the band of the bounded region, we can chose , 0, 1 small enough in order to guarantee the motion along the sliding surface nearly. Theorem 4.2. With the trajectory of the closed-loop system (17) evolves in a boundary layer around the sliding surface, the output tracking can be accomplished with virtual control input (22). In order to illustrate the reference state tracking, Lyapunov functional is chosen as follows: 1 V = eT e 1 2 1 1

The derivative of V1 with equality (22) is ˙ T V1 = e1 e˙1 T − = e1 (F1(X1)X2 y˙r) T − = e1 (F1(X1)(e2 + Xr,2) y˙r) T − = e1 ( K1e1 + F1(X1)e2) − 3 2 T = Σi=4(kie1i) + e1 F1(X1)e2 (37)

where e1i is the ith component of e1. We have proved that S(t) approaches and remains in the bounded layer in ﬁnite time, which means e2 is bounded. Thus, by selecting positive ki ˙ large enough, we obtain V1 < 0 when V1(t) is out of a certain bounded region. Therefore, e1 is uniformly ultimately bounded by which X1 tracking the reference yr is guaranteed. 1944 Z. LIN, Z. ZHU, Y. XIA AND S. WANG 5. Conclusions. In this paper, the problem of attitude control for a vertical launching missile system which is nonlinear in aerodynamics has been investigated. The adaptive law is applied for estimating the total uncertainties. A sliding mode controller is designed combining the back-stepping technique to force the state variables of the closed loop system to converge to the reference state. Detailed simulation results have been presented to illustrate the developed theory. Acknowledgment. The work of Yuanqing Xia was supported by the National Natural Science Foundation of China under Grant (60974011), Program for New Century Ex- cellent Talents in University of Peoples Republic of China (NCET-08-0047), the Ph.D. Programs Foundation of Ministry of Education of China (20091101110023), and Program for Changjiang Scholars and Innovative Research Team in University, and Beijing Munic- ipal Natural Science Foundation (4102053), respectively.

REFERENCES [1] Y. Yao, B. Yang, F. He, Y. Qiao and D. Cheng, Attitude control of missile via Fliess expansion, IEEE Transactions on Control Systems Technology, vol.16, no.5, pp.959-970, 2008. [2] W. Luo, Y. C. Chu and K. V. Ling, Inverse optimal adaptive control for attitude tracking of spacecraft, IEEE Transactions on Automatic Control, vol.50, no.11, pp.1639-1654, 2005. [3] Z. Chen and J. Huang, Attitude tracking and disturbance rejection of rigid spacecraft by adaptive control, IEEE Transactions on Automatic Control, vol.54, no.3, pp.600-605, 2009. [4] L. L. Show, J. C. Juang and Y. W. Jan, An LMI-based nonlinear attitude control approach, IEEE Transactions on Control Systems Technology, vol.11, no.1, pp.73-83, 2003. [5] Z. H. Yuan and X. F. Qian, Control Flight Mechanics and Computer Simulation, National Defense Industry Press, Beijing, 2001. [6] J. Fei and F. Chowdhury, Robust adaptive sliding mode control for triaxial gyroscope, Journal of Innovative Computing, Information and Control, vol.6, no.6, pp.2439-2448, 2010. [7] W. Xiang and Y. Huangpu, Sliding mode control for a new hyperchaotic dynamical system, ICIC Express Letters, vol.4, no.2, pp.547-552, 2010. [8] H. K. Khalil, Nonlinear Systems, Englewood Cliﬀs, Prentice-Hall, NJ, 2002. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1945-1949

APPLICATION OF PLANT GROWTH SIMULATION ALGORITHM ON SMT PROBLEM

Tong Li1,2, Weiling Su2 and Jiangong Liu2

1Management College Hangzhou Dianzi University Hangzhou 310018, P. R. China [email protected] 2Economics and Management College Dalian University Dalian 116622, P. R. China Received February 2010; accepted April 2010

Abstract. Plant Growth Simulation Algorithm (PGSA) is an intelligence optimization algorithm, which treats plant phototropism growth pattern as its heuristic criterion. Ac- cording to the changes of object function, PGSA determines growth information (auxin concentration), treats solution space of optimal problem as artificial plant growing environment, and sets up probability growth model for artificial plant through deduction mode of plant system (L-system). After solving optimization problem, engineering technology problem, integer programming and other classical problems, application of PGSA on SMT in this paper is demonstrated with the most satisfied result, by comparing the solutions with ant algorithm and simulated annealing algorithm. Keywords: Plant growth simulation algorithm, Intelligence algorithm, Steiner minimum tree

1. Introduction. With the rapid development of information technology, both in theory and applications, intelligence algorithm has made remarkable achievements. Intelligence algorithm is a cross-science major, which includes subjects such as mathematics, computer science, electrical machinery, physics, communication, physiology and evolutionary theory and so on. Its core idea is formatted by the jointed development of connectionist, distributed artificial intelligence and self-organizing system theory. PGSA proposed by the first author of this article in the literature [1,2], is based on the core idea of intelligent computing and plant-phototropism as heuristic criteria of intelligent algorithm. PGSA makes solution space of the optimization problem as an environment of plant growth simulation. According to the changes of the objective function in determining the growth of information (auxin concentration), (L-system) we established the probability of the simulation of plant growth model through the deductive model plant systems. In recent years, the algorithm has been used in combinatorial optimization, nonlinear integer programming as well as engineering optimization problems. During the application process, the various scholars compared PGSA solutions with genetic algorithms, ant algorithms, simulated annealing algorithm, particle swarm optimization, co-evolutionary algorithm, Tabu search algorithms in the classical problems in their respective fields, and PGSA gradually shows its outstanding stability, accuracy and global search capability. Literature [3] has done a summary on PGSA: “The theoretical analysis and simulation results show that compared with genetic algorithm as the representative of modern heuristic algorithms, plant growth simulation algorithm (PGSA) has the following advantages: ➀ PGSA dealt with objective function and constraints separately without encoding and decoding, avoiding the calculation of the new structure with the

1945 1946 T. LI, W. SU AND J. LIU objective function, so there was no punishment coefficient, cross-rates, select issues, and so on, good stability of solutions; ➁ PGSA has a search mechanism with ideal direction and randomicity balance which is determined by morpheme concentration, so the global optimal solution is found quickly”. 2. Description of the SMT Problem. The following definition of the network refers to the map or weighted graph. Definition 2.1. Set P is a finite set of points, N = (V,E) is a network with vertex set V, edge set E. If the V ⊇ P , claimed that N to P Steiner network. In particular, if V = P , claimed that the generation of N to P network. Definition 2.2. Set i and j are two vertices in the network N. If between i and j, there is the existence of at least k internal vertices of disjoint (or edge disjoint) path. That is to say i and j are partial k-connected (or partial k-edge-connected). Definition 2.3. If the network N in any two vertices are local k-connected (or partial k- edge-connected), it’s called that the network N is k-connected (or partial k-edge-connected). Definition 2.4. The length of the network N is defined as the sum length of each side. For a given finite point set P and a positive integer k, called the ratio of the length of P the shortest k-edge-connected Steiner network and P the shortest k-edge-connected generation network is the k-Steiner ratio, denoted by lk(P).

If the minimum spanning tree (MST) recorded the length as LM (P ), Steiner minimum tree (SMT) denoted the length as LS(P ), when after given the set of points, then the LM (P ) ≥ LS(P ) (U.S. Bell companies had collect long-distance telephone charges by LM (P ), and later a user raised objections that this calculation is not conducive to the user fees and shall be LS(P ) to charge), so then there is a question: What is the diﬀerence between the two? So in 1968, Gilbert and Pollack proposed a conjecture: to the Euclidean√ plane, any ﬁnite set of points, LS(P ) and LM (P ) ratio (Steiner ratio) is not less than 3/2. This√ conjecture is called G-P guess, which is well-known as Steiner ratio conjecture. As the 3/2 ≈ 0.866, so to SMT as a substitute for MST, it can be up to 13.4% reduction in the distance.

3. SMT Problem PGSA Design. Suppose there are n growth points (S1, S2, ..., Sn), we calculate each plant auxin concentration value (P1, P2, Pn) according to mathematical models in literature [2], we ﬁnd that P1 + P2 + ... + Pn = 1. Computer systems continue to generate random numbers, which can be thought as small balls which are cast towards the area [0,1], these random numbers as to keep the interval [0,1] on the thrown ball, the small balls fall in the probability space P1, P2, ..., Pn, the growth points relative to certain state space above will have preferential growing rights.

Figure 1. Auxin concentration probability space

Set (x, y, α) for the randomly selected Steiner point (plant growth simulation point) of the current state. x and y is its position coordinate, α is the point of growth point, the section length is d, the top of angle in increments is δ. “[” stands for what is the current information on record about the node (a branch of the bifurcation point) of the information saved, the first branch is painting firstly; and “]” that is the meaning of will ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1947 “[” moment of recorded information released, when one branch is finished, “]” will be a node on the information (on a bifurcation of the state) out, and then continue to draw from the bifurcation point of the first two branches. The meaning of other symbols are: F: in the current direction of the growth in length and d, the top of the state becomes (x0, y0, α), where, x0=x+d cosα, y0=y+d sinα. +: Counter-clockwise rotation at an angle δ, the top of the state becomes (x, y, α + δ). Here, the provisions of counter clockwise is positive. –: Clockwise rotation at an angle δ, the top of the state becomes (x, y, α − δ). The plant growth simulation algorithm of SMT is as follows: (1) Using the MST value which computes limited set of points P by Prim algorithm; (2) According to the MST to generate a new SMT topology, construct the initial Steiner n-point (S1, S2, ..., Sn); (3) Calculations (S1, S2, ..., Sn) auxin concentration:

f(Si) Pi = ∑n f(Si) i=1

And f(·) is the sum of Si and the length of adjacent edges; (4) P (i + 1) ← P (i + 1) + P (i), P (i) ← P (i)/P (n); (5) if P (i) < random [0,1]< P (i + 1) then F ← Si; (6) The initial state ω: F, Rotation angle: δ = 90◦ Growth rule: F → F[−F][+F] F The new growth points are the Si(1), Si(2), Si(3) (7) Si ←min{f(Si), f(Si(1)), f(Si(2)), f(Si(3))}; (8) If a continuous n (eg. 200) times iteration no new branches grow, then the end of plant growth, or else return (3).

4. SMT Numerical Experiment. Plant growth simulation algorithm in solving the SMT problem takes the Steiner ratio LS(P )/LM (P ) as the standard and carries on a precision of comparison with the ant algorithm. (AA), the simulated annealing algorithm (SA) in the literature [9], the experiment uses the case in the test database STEINLIB which internationally announces, computing the results compared in Table 1. Algorithm uses Matlab programming in the Windows XP platform running through, in the test the computer is Celeron (R) CPU 3.06GHz, 1.00GB of memory. PGSA in STEINLIB each test instance were carried out 15 times, including the best results and the worst results. The error is no more than 0.017%, showing that the prominent algorithm is stability. From the results above 8 STEINLIB test instance calculations we can see, Steiner minimum tree is obviously more superior than those of the ant colony algorithm (AA) and the simulated annealing algorithm (SA). In particular, the ﬁrst test instance of the SMT getting by PGSA enhances 10% precision compared to AA and the SA.

5. Conclusions. Simulation of plant growth algorithm (PGSA) as a global optimization algorithm of bionic, looks the probability of plant growth dynamic mechanism of plant phototropism as the optimization mechanism, solving optimization problems. Also the algorithm has shown the strong global search capability. Since the algorithm chooses the initial point under relaxed requirements, it is diﬀerent from other methods which is direct to determine the needs of some of the parameters, thus PGSA has good solution of stability. The application of PGSA on SMT problems shows that PGSA has some good characters such as high accuracy, good stability and strong application. 1948 T. LI, W. SU AND J. LIU Table 1. Comparison of partial instance data and calculation results in STEINLIB

P : (0.03 0.50); (0.20 0.60); (0.37 0.50); (0.37 0.30); (0.20 0.20); (0.03 0.30); (0.63 0.50); (0.80 0.60); (0.97 0.50); (0.97 0.30); (0.80 0.20); (0.63 0.30) PGSA AA SA L (P )/L (P ) S M 0.9346679 0.9777726 0.9751919 Steiner points: (0.1425,0.5000); (0.2000,0.4005); (0.1420,0.3000); (0.3125,0.4005); (0.6876,0.4004); (0.8000,0.4004); (0.8580,0.3000); (0.8576 0.5000)

P : (0.10 0.26); (0.25 0.72); (0.38 0.66); (0.53 0.66); (0.65 0.72); (0.80 0.85); (0.68 0.70); (0.61 0.58); (0.61 0.43); (0.68 0.30); (0.80 0.17); (0.65 0.28); (0.45 0.35); (0.25 0.27); (0.10 0.17); (0.23 0.30); (0.30 0.50); (0.23 0.70) PGSA AA SA L (P )/L (P ) S M 0.9791903 0.9841913 0.9802707 Steiner points: (0.2343,0.7156); (0.3323,0.6449); (0.2335,0.2765); (0.6758,0.7139); (0.5871,0.6486); (0.5972, 0.3863)

P : (0 0.40); (0 0.50); (0.03 0.60); (0.10 0.65); (0.20 0.60); (0.20 0.48); (0.30 0.40); (0.37 0.45); (0.39 0.60); (0.45 0.65); (0.50 0.65); (0.54 0.60); (0.54 0.48); (0.63 0.40); (0.70 0.50); (0.72 0.60); (0.80 0.68); (0.89 0.65); (0.90 0.51); (0.90 0.41) PGSA AA SA L (P )/L (P ) S M 0.9767640 0.9906618 0.9907826 Steiner points: (0.0001,0.4999); (0.0632,0.5780); (0.0564,0.5958); (0.1686,0.5613); (0.3007,0.4146); (0.6247,0.4436); (0.8004,0.6775) ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1949 Acknowledgment. This project was supported by China National Natural Science Foun- dation (70371051), China Post-doctor Foundation (2005038588).

REFERENCES [1] T. Li, C. Wang, W. Wang and W. Su, A global optimization bionics algorithm for solving integer programming-plant growth simulation algorithm, Systems Engineering – Theory and Practice, vol.25, no.1, pp.76-85, 2005. [2] T. Li and Z. Wang, Application of plant growth simulation algorithm on solving facility location problem, Systems Engineering – Theory and Practice, vol.28, no.12, pp.107-115, 2008. [3] C. Wang and H. Cheng, A plant growth simulation algorithm and its application in power transmission network planning, Electric Power Systems, vol.31, no.7, pp.24-28, 2007. [4] B. Lintermann and O. Deussen, Interactive modeling of plants, IEEE Computer Graphics and Ap- plications, vol.19, no.1, pp.56-65, 1999. [5] R. Cordone and M. Trubian, An exact algorithm for the node weighted Steiner tree problem, A Quarterly Journal of Operations Research, vol.6, pp.136-147, 2006. [6] T. C. Bruen and D. Bryant, A subdivision approach to maximum parsimony, Annals of Combina- torics, vol.12, no.1, pp.45-51, 2008. [7] V. D. Kukin, Evolutionary model for the steiner tree problem with ﬂow-dependent weights, Journal of Computer and Systems Sciences International, vol.47, no.3, pp.447-454, 2008. [8] M. Brazil and M. Zachariasen, Steiner trees for ﬁxed orientation metrics, Journal of Global Opti- mization, vol.8, 2008. [9] H. Jin, L. Ma and Z. Wang, Intelligent optimization algorithms for euclidean steiner minimum tree problem, Computer Engineering, vol.32, no.10, pp.201-203, 2006. [10] T. Li and W. Su, A Single-Stage Integer Programming Algorithm with the Two Principle and Appli- cation, Science Press, Beijing, 2007.

ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1951-1957

A CONTROLLER DESIGN FOR T-S FUZZY MODEL WITH RECONSTRUCTION ERROR

Hugang Han1 and Yanchuan Liu2

1Department of Management Information System Prefectural University of Hiroshima 1-1-71 Ujina-higashi, Minami-ku, Hiroshima 734-8558, Japan [email protected]

2College of Electromechanics and Information Engineering Dalian Nationalities University 18 Liaohexi Road, Development Area, Dalian 116600, P. R. China [email protected]

Received February 2010; accepted April 2010

Abstract. In this paper, the reconstruction error between the real system to be controlled and its T-S fuzzy model is considered, and fuzzy approximators are employed to cope with the reconstruction error. As to the fuzzy approximators, parameters in which are updated by adaptive law. As a result, the regular T-S fuzzy controller which takes no consideration of the reconstruction error is a special case of the controller proposed in this paper. The proposed controller can guarantee the state of the closed-loop system uniformly bounded while maintaining all signals involved stable. In order to make the state of the system converge at a region around the equilibrium points quick, discussion of relaxing conservatism of the proposed controller is also provided. Keywords: Reconstruction error, T-S fuzzy model, Adaptive law, System stability

1. Introduction. Recently, the stability issue about the T-S fuzzy systems has been extensively studied. However, only a few results concerning the modeling error, which usually is referred to as reconstruction error, between the real system to be controlled and its T-S fuzzy model, are reported. Basically, the reconstruction error is caused by the uncertainties in the real (nonlinear) system including external disturbance, and the transformation from the real system to the T-S fuzzy model. The control design is carried out based on the fuzzy model by the so-called parallel distributed compensation (PDC) scheme. Then, sufficient conditions for the system stability are provided in the sense of Lyapunov by solving certain linear matrix inequalities (LMIs). In [1], they concluded some LMI conditions to confine the influence of the reconstruction error to a certain region. More popularly, the reconstruction error is treated by involving some norm- bounded matrices with certain structure properties in each local T-S fuzzy model such asx ˙(t) = (Ai + ∆Ai)x(t) + (Bi + ∆Bi)u(t) where Ai,Bi are certain known matrices with some appropriate dimensions, and ∆Ai, ∆Bi represent the norm-bounded matrices [2, 3]. In [4], Zhang and his colleagues considered an external disturbance term in addition to the norm-bounded matrices in each local T-S fuzzy model such asx ˙(t) = (Ai +∆Ai)x(t)+ Biu(t) + Di, where Di denotes the external disturbance. Very recently, a more general uncertainty involved in the T-S fuzzy model such asx ˙(t) = (Ai + ∆Ai)x(t) + (Bi + ∆Bi)u(t) + Di was considered, and an adaptive fuzzy controller was proposed based on the model [5]. However, the norm-bounded matrices are not easy to be estimated since the mathematical model of the real system is unavailable in most cases, and often being

1951 1952 H. HAN AND Y. LIU set large to safely cover the reconstruction error. At the same time, the large norm- bounded matrices inserted in each local T-S fuzzy model may lead the final LMIs to being conservative. On the other hand, parameterized fuzzy system which is expressed as a series of radial basis functions (RBF) expansion has excellent approximation properties [6], and such properties can be used as (fuzzy) approximator to deal with some unknown functions in the plant [7]. This motivate us to employ the fuzzy approximator to cope with reconstruction error in each local T-S fuzzy model. In this paper, in order to effectively deal with the reconstruction error, each local T-S fuzzy model is formed ofx ˙(t) = Aix(t) + Biu(t) + fi(t), where fi(t) denotes the reconstruction error and will be approximated by the fuzzy approximator. Based on the T-S fuzzy model an adaptive controller, which has two parts: one is obtained by solving certain LMIs (fixed part) and the another one is acquired by the fuzzy approximator in which the related parameters are tuned by adaptive law (variable part), is proposed.

2. Problem Statement.

2.1. Fuzzy approximator. Fuzzy model addresses the imprecision of the input and output variables directly by defining them with fuzzy sets in the form of membership functions. Now, we consider a fuzzy model with singleton consequent wi, product in- T ference, Gaussian membership function µ i (xj) in the antecedent with variable x = Aj [x1, x2, ··· , xn], and central average defuzzifier, hence, such a fuzzy model can be expressed as a series of RBF expansion [6], ∑r F(x) = φi(x) · wi (1) i=1 ∏ n j=1 µAi (xj ) ∑ ∏ j where r is the number of fuzzy rules; φi(x) = r n with µAi (xj) being a i=1 j=1 µAi (xj ) j [ (j ) ] x −ξi 2 − j j i Gaussian membership function, defined by µAi (xj) = exp i where ξj indicates j σj i the position, and σj indicates the extent of the membership function. We now can show an important property on the fuzzy system.

Theorem 2.1. [6] For any given real continuous function f on the compact∑ set U ∈ Rn F ∗ r · ∗ and arbitrary , there exists an optimal fuzzy system expansion (x) = i=1 φi(x) wi such that sup |f − F ∗(x)| ≤ (2) x∈U { ∗ { ∗ | ··· } | − where wi is the optimal parameter being wi i = 1, 2, , r = arg minw∈Rr supx∈U f ∑ } r · ∗| i=1 φi(x) wi . This theorem states that the fuzzy system (1) is an approximator on a compact set. In this paper, we use term, fuzzy approximator, to refer to such a fuzzy system. Since ∗ the fuzzy approximator is characterized by parameter wi, the optimal F does contain an ∗ optimal vector wi . 2.2. System and its T-S fuzzy model. Consider the following nonlinear system: x˙(t) = g(x(t), u(t)), (3) where x(t) ∈ Rn is the vector of state variables; u(t) ∈ Rm, the vector of control inputs; g ∈ Rn, a suﬃciently smooth nonlinear function in the state x(t) and aﬃne in u(t). The ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1953 system can be expressed in terms of the T-S fuzzy model as follows. i ··· i Plant Rule i : IF θ1(t) is M1 and and θp(t) is Mp,

THENx ˙(t) = Aix(t) + Biu(t) + fi(x(t)), i ··· ··· i where θj(i = 1, 2, r, j = 1, 2, , p) is a variable in the antecedent; Mj , fuzzy set with membership function µ i (θj); Ai and Bi, constant matrices being of appropriate Mj T n dimensions; fi = [fi1, fin, ··· , fin] ∈ R , unknown residual function (reconstruction error) which occurs in the process of linearizing the nonlinear systemx ˙ = g(x, u) into a linear modelx ˙ = Aix + Biu. In most cases, such a residual function is neglected, and consequently the control performance by the controller based on the T-S fuzzy model without fi may not be as good as we expected. The overall fuzzy model is of the following form accordingly: ∑r { } x˙(t) = αi(t) Aix(t) + Biu(t) + fi(x(t)) , (4) i=1 where ∑ ∏ ∑ wi(t) ≥ r p i αi(t) = r 0, αi(t) = 1, wi(t) = µj(θj(t)). i=1 wi(t) i=1 j=1

In this paper, the residual function fi is taken into consideration by using the fuzzy n approximator described in Section 2.1. The fuzzy approximator rules for fi ∈ R are expressed as follows. k ··· k Approximator Rule k : IF x1(t) is Fi1 and and xn(t) is Fin,

THEN Fi = wik,

k T where F is a fuzzy set with membership function µ k (xj); wik = [wi1k, wi2k, ··· , wink] , ij Fij n singleton consequent vector corresponding with the unknown residual function fi ∈ R in the T-S fuzzy model. The overall fuzzy approximator is of the following form:

∑zi Fi(x(t)) = φik(x(t)) · wik, (5) k=1 where ∏ n ∑zi µF k (xj(t)) ∑ j=1∏ ij φik(x(t)) = zi n , φik(x(t)) = 1. (6) k=1 j=1 µF k (xj(t)) ij k=1 ∑ F ∗ zi · According to Theorem 2.1, there is the optimal fuzzy approximator i = k=1 φik(x) ∗ wik for the unknown function fi: F ∗ ∗ fi(x(t)) = i (x(t)) + εi , (7) ∗ F ∗ where εi is the error between function fi and its optimal fuzzy approximator i . To F ∗ ∗ ∗ construct i for approximating fi, the values of the parameter vectors wik and εi are required. Unfortunately, they are unavailable. Normally, the unknown parameter vectors ∗ ∗ wik, and εi are replaced by their estimationsw ˆik(t), andε ˆi(t), respectively [7]. Then the estimations are stably tuned based on some adaptive law, which will be provided later on.

2.3. Control objective. The control objective is to design the following PDC controller for the T-S fuzzy model (4). j ··· j Control Rule j : IF θ1(t) is M1 and and θp(t) is Mn

THEN u(t) = Kjx(t) + Φj(t), 1954 H. HAN AND Y. LIU

n where Kj ∈ R (j = 1, 2, ··· , r) is the gain vector to be designed, and Kjx(t) is viewed as a ﬁxed part corresponding to the regular PDC controller without consideration of the reconstruction error fi in the T-S fuzzy model, while Φj(t) is a variable part: ( ) ∑zj T · Φj(t) = Bj φjk(x(t)) wˆjk(t) +ε ˆj(t) , (8) k=1 in order to deal with the reconstruction error, wherew ˆjk(t), andε ˆj(t) are estimations ∗ ∗ F ∗ of the optimal parameters wjk, and εj related to the optimal fuzzy approximator j for unknown function fj in the T-S fuzzy model. The overall state feedback control law is ﬁnally represented as { ( )} ∑r ∑zj T · u(t) = αj Kjx(t) + Bj φjk(x(t)) wˆjk(t) +ε ˆj(t) . (9) j=1 k=1

The aim of this paper is to design r local linear state feedback law (9) for the T-S fuzzy model (4) such that the state of the closed-loop control system is uniformly bounded while maintaining all signals involved stable.

3. Main Results.

3.1. Controller design. The controller proposed in this paper can be summarized as a theorem.

Theorem 3.1. For a given fuzzy model (4) with unknown residual function and its fuzzy approximator, if there exist a certain symmetric matrix Q > 0, matrices Mj such that the following LMIs:

T T T || T ||2 AiQ + BiMj + QAi + Mj Bi + (zi + 1)I + (zj + 1) BiBj I < 0, (10) (i, j = 1, 2, ··· , r) hold, then the controller (9) with

−1 Kj = MjQ , (11) ∑r ˙ − − T −1 ··· wˆjk(t) = βwΓwwˆjk(t) αjΓwφjkBj αiBi Q x(t), (k = 1, 2, , zj) (12) i=1 ∑r ˙ − − T −1 εˆj(t) = βεΓεεˆj(t) αjΓεBj αiBi Q x(t), (13) i=1 where scalars βw, βε and matrices Γw, Γε with compatible dimensions are design parameters, will make the state of the closed-loop system uniformly bounded while maintaining all signals involved stable. At the same time, the solutions exponentially converge at rate η to a ball centered at the equilibrium point with radius r, where η is given in (19), (16), (18), and r is given in (23), (19), and (20).

Proof: Deﬁne a Lyapunov function candidate as follows. ( ) ∑r ∑zj T T −1 T −1 V (t) = x(t) P x(t) + w˜jk(t)Γw w˜jk(t) +ε ˜j (t)Γε ε˜j(t) , (14) j=1 k=1 ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1955 T −1 ∗ − ∗ − where P = P = Q > 0,w ˜jk(t) = wjk wˆjk(t),ε ˜j(t) = εj εˆj(t). The time derivative of V (t) on any trajectory of the closed-loop system is ( ∑r ∑r ˙ ≤ T T T T V (t) αiαjx Ai P + PAi + Kj Bi P + PBiKj i=1 j=1 ) || T ||2 + (zi + 1)PP + (zj + 1) BiBj PP x ( ) ∑r ∑r ∑zi ∑zj (15) || ∗||2 || ∗||2 || ∗ ||2 || ∗ ||2 + αiαj εi + εj + wik + wjk i=1 j=1 k=1 k=1 ∑r ∑zj ∑r ∑zj ∑r ∑r − T ∗T ∗ − T ∗T ∗ βw w˜jkw˜jk + βw wjk wjk βε ε˜j ε˜j + βε εj εj . j=1 k=1 j=1 k=1 j=1 j=1

Here, using the fact that Mj = KjQ, and by pre- and post-multiplying (10) by P , it follows that − T T T || T ||2 Sij := Ai P + PAi + Kj Bi P + PBiKj + (zi + 1)PP + (zj + 1) BiBj P P < 0. (16) Therefore, from (15) and (16) it yields

∑r ∑zj ∑r ˙ − T S − T − T V (t) < x x βw w˜jkw˜jk βε ε˜j ε˜j + γ j=1 k=1 j=1 ∑r ∑zj ≤ − S −1 T − −1 T −1 λmin( )λmax(P ) x P x βwλmin(Γw) w˜jkΓw w˜jk j=1 k=1 (17) ∑r − −1 T −1 βελmin(Γε) ε˜j Γε ε˜j + γ { j=1 ( )} ∑r ∑zj − T T −1 T −1 − = η x P x + w˜jkΓw w˜jk +ε ˜j Γε ε˜j + γ = ηV (t) + γ, j=1 k=1 where ∑r ∑r S = αiαjSij > 0, (18) i=1 j=1 { S −1 −1 −1 −1 } η = min λmin( )λmax(Q ), βwλmin(Γw), βελmin(Γε) > 0, (19) ( ) ∑r ∑r ∑zi ∑zj || ∗||2 || ∗||2 || ∗ ||2 || ∗ ||2 γ = αiαj εi + εj + wik + wjk i=1 j=1 k=1 k=1 (20) ∑r ∑zj ∑r || ∗ ||2 || ∗||2 + βw wjk + βε εj . j=1 k=1 j=1 Finally, from (17) we have ( ) γ γ V ≤ + V (0) − e−ηt, (21) η η where V (0) = V (t)|t=0. Since that η > 0, the second block on the right side of (21) tends to 0 when t → ∞. Therefore, we can get that there exists T such that for t ≥ T it satisfies kxk ≤ r, (22) 1956 H. HAN AND Y. LIU where ( ) 1 γ 2 r = λ−1 (Q−1) . (23) min η This completes the proof. Remark 3.1. Compared with the LMIs condition (10), the counterpart in the regular case, where the residual function fi in (4) is taking no consideration, is in the form of T T T AiQ + BiMj + QAi + Mj Bi < 0. (24) Although the LMIs above are more feasible than the LMIs in (10) at first sight, controller following (24) may not guarantee the system stability in the worst case, since the error between the system (3) and its T-S fuzzy model occurs. 3.2. Relaxing conservatism. In the Theorem 3.1, it is desirable to have the largest η and the smallest r so that the system state x can shrink most quickly in a ball centered at the equilibrium points with radius r. From (19), we observe that a smaller Γw,Γε, and a bigger S, Q, βw, βε can help make a larger η. At the same time, from (20) and (23) we know that a smaller Q, βw, βε are advantageous to a smaller r, which is in conflict with some parameters for increasing η. Therefore, we only have room for making η big by doing something on Γw,Γε, and S as follows.

• Choosing a smaller Γw, and Γε. In the adaptive law (12), (13), since Γw, and Γε are free design parameters, basically they can be chosen arbitrarily small. However, there is a limit that smaller Γw,Γε can lead to a bigger η, since η is determined by ﬁnding the smallest one in a group of terms. • Making −Sij small. It is clear that a smaller −Sij is equivalent to a bigger S in (18).

Unlike design parameters Γw,Γε, making −Sij small cannot be done by choosing some papameters directly. Here, we formulate the requirement: −Sij → min as the following generalized eigenvalue minimization under LMI constraint: min λ

s.t. − Sij + M1 < λM2 (25) where M1, M2 > 0 are arbitrarily given matrices with compatible dimensions. Therefore, the following corollary yields in consideration of relaxing conservatism in the Theorem 3.1. Corollary 3.1. For a given fuzzy model (4) with unknown residual function and its fuzzy approximator, and given matrices M1, M2 > 0 with compatible dimensions, if there exist a certain symmetric matrix Q > 0, matrices Mj such that the following LMIs: {min λ subject to LMI (10), T T T || T ||2 M M (26) AiQ + BiMj + QAi + Mj Bi + (zi + 1)I + (zj + 1) BiBj I + 1 < λ 2, hold, then the feedback control gain Ki obtained in (11)-(13) will make the state of the closed-loop system uniformly bounded while maintaining all signals involved stable. At the η same time, the state exponentially converge at a bigger rate 2 to a ball centered at the equilibrium points with radius r deﬁned by (19), (20) and (23).

4. Conclusions. In this paper, in order to eﬀectively deal with reconstruction error between the real system to be controlled and its T-S fuzzy model, an adaptive controller was proposed. Compared with the regular controller when using T-S fuzzy model, the proposed controller puts a variable part updated by an adaptive law besides the ﬁxed one obtained by solving certain LMIs. In addition, a discussion of how to relax the LMIs for the controller was provided. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1957

REFERENCES [1] K. Tanaka, T. Ikeda and H. O. Wang, Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stabilizability, H∞ control theory, and linear matrix inequalities, IEEE Trans. Fuzzy Syst., vol.4, pp.1-13, 1996. [2] Y.-Y. Cao and Z. Lin, Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation, IEEE Trans. on Fuzzy Systems, vol.11, no.1, pp.57-67, 2003. [3] B. Chen, X. Liu, S. Tong and C. Lin, Guaranteed cost control of T-S fuzzy systems with state and input delays, Fuzzy Sets Syst., vol.158, pp.2251-2267, 2007. [4] F. Zhang, Q.-G. Wang and T. H. Lee, Adaptive and robust controller design for uncertain nonlinear systems via fuzzy modeling approach, IEEE Trans. Syst., Man, and Cybern., vol.34, no.1, pp.166- 178, 2004. [5] H. Han, Adaptive fuzzy controller for a class of uncertain nonlinear systems, J. of Japan Society for Fuzzy Theory and Intelligence Informatics, vol.21, no.4, pp.577-586, 2009. [6] L.-X. Wang and J. M. Mendal, Fuzzy basis functions, universal approximation, and orthogonal least-squares learning, IEEE Trans. Neural Networks, vol.3, pp.807-814, 1992. [7] H. Han, C.-Y. Su and Y. Stepanenko, Adaptive control of a class of nonlinear systems with nonlin- early parameterized fuzzy approximators, IEEE Trans. on Fuzzy Systems, vol.9, no.2, pp.315-323, 2001. [8] C. Lin, Q.-G. Wang, T. H. Lee and Y. He, Design of observer-based H∞ control for fuzzy time-delay systems, IEEE Trans. on Fuzzy Systems, vol.16, no.2, pp.534-543, 2008.

ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1959-1964

AN ANALYSIS FOR PARAMETER CONFIGURATION TO FIND A TRIGGER OF CHANGE

Rika Ito1 and Kenichi Kikuchi2 1Japan Aerospace Exploration Agency (JAXA) 7-44-1, Jindaiji-higashi Chofu Tokyo, Japan [email protected] 2Toho University 2-2-1, Miyama, Funabashi, Chiba, Japan [email protected] Received February 2010; accepted April 2010

Abstract. The use of PC cluster systems composed of many PCs is largely spread in these days. For system administrator, it is important to improve system usage keeping proper fair-share policy. However, this optimization problem is difficult to solve. In addition, it is more difficult to search a trigger to change a parameter because the job execution changes by user’s job submission or period. Therefore, we search a trigger for parameter change by analysis of elapsed time. So in this paper, we performed various analysis in view of elapsed time and report the results. Keywords: PC cluster, NQS, Parameter configuration, Optimization, Job scheduler, Resource management

1. Introduction. The use of PC cluster systems composed of many PCs is largely spread and the advanced grid computing technology came to be of practical use by a network performance progress and researched in these days [3,4,7]. For system administrators of such a distributed system, the improvement of usage efficiency of system resource is one of the biggest themes. Generally speaking, distributed systems as PC cluster or grid computing, are shared by a large number of users. So it is also important to build a proper fair-share policy for users. Each user has specific and unique needs, and this can lead to competition between users for system resource. On the other hand, from system management standpoint, it is necessary to endeavor actively towards an improvement in usage efficiency. A conflict is generated between these two factors. The technology to solve this problem is a function called job scheduling. It is offered as system management software and is called a Job scheduler. Job scheduler is software that dynamically allocates submitted jobs to a hardware resource. When a scheduler receives a submitted job, it allocates jobs to hardware resource sequentially based on policies. These policies are configured with an array of preset values (parameters), such as job priority and the number of concurrent executable jobs per user, etc. This establishes an efficient batch processing system for PC clusters or grid computing. There are many research activities and reports for job scheduler [2,8]. There are some schedulers commercially available. NQS (Network Queuing System – Fujitsu Limited) is famous. When there is no surplus in the allocated system resource, the submitted job will be put in a queue. However, the case may happen that a job remains in a queue without execution even when there is free resource, because the parameter configuration of job scheduler is not appropriate. Along with the increase of CPUs, it is getting more important and more serious. However, once the system administrator configures the parameter, they can’t examine whether it is appropriate or not, because the system usage pattern in the past cannot be reproduced. So the system administrators have to determine it by themselves

1959 1960 R. ITO AND K. KIKUCHI with limited experience. In addition we can’t predict how system usage pattern changes, and when we should change a parameter. If there is some sign of system usage pattern, it is easier for us to ﬁnd an optimal parameter conﬁguration for future usage pattern by that sign. Therefore, in this paper, we have performed some trial experiments focusing on analysis of the past log data, the elapsed time as one of signs and we report the results.

2. System Outline and NQS.

2.1. System speciﬁcations. Table 1 is a speciﬁcation of a national Japanese institute called RIKEN. The stripe of parallelization is three types, 32CPU, 64CPU and 128CPU. And the longest run time is two types, short (10 hours) and long: (72 hours). Therefore, queue classes are following six classes. Short queue: S-032, S-064 and S-128 Long queue: L-032, L-064 and L-128

Table 1. System speciﬁcation

CPU Intel Pentium Xeon 3.06GHz Nodes 1024 (2048CPU) Peak Performance 12.4TFLOPS Memory 4GB/node, 2GB/node HDD 146GB/node OS Linux (Red Hat Version 8) Scheduler NQS (Fujitsu Version 1.0, NQS-JM)

2.2. NQS simulator speciﬁcation. NQS is a job scheduler. It is originally developed under Numerical Aerodynamics Simulation (NAS) of NASA. And Fujitsu enhanced it and ported onto Sun OS and VPP environment. Currently it works on Solaris and Linux (Red hat) environments, and is widely used.

Figure 1. NQS simulator

We constructed NQS simulator which behaves as NQS does. The main reason of this simulator is to reproduce the past usage patterns without executing jobs on the real operating environment. We use statistics information of the past usage. In construction of a simulator, we confirmed that the past behavior was reproduced by inputting past statistics information into NQS simulator. The specification of NQS simulator is NQS (Fujitsu)-Ver.1.0 and NQS-JM. When the past log data and parameter configuration are input, the simulator perform a simulation depending on parameter configuration. And we can obtain the results, the starting time, the finishing time, the waiting time of each job, etc.

3. Numerical Experiment. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1961 3.1. Evaluation. In these numerical experiments, our evaluation is System Usage Effi- ciency (SUE). We focused on the elapsed time. Here elapsed time means the wall time from beginning the job to finishing the job. As a system usage, we use SUE. SUE shows system usage efficiency (%) in a period as following equations. SUE = S/V × 100 V : 1024 CPUs × time (seconds). S: The number of CPU’s × Spent time[s] in which the job was actually executed during the period.

3.2. Elapsed time category. In this section, we performed numerical experiments focusing on analysis of the elapsed time of each job. We sampled data of twelve months, from January 2006 to December 2006. We examined each elapsed time by the following categorization. The elapsed time is categorized in seven categories. For example, category (1) is a group of jobs with less than 5000 seconds elapsed time. The distribution of elapsed time of jobs of each month was shown in Figure 2. A bar is tabulated frequencies. It shows elapsed time of each job fall into each of seven categories. These categories are defined by length of elapsed time. We define the number of all jobs in a month as 100% and the number of jobs in each category is shown by percentage. Figure 2 shows how many percentages of each category are kept for twelve months. For example, in January, the percentage of category (1) is near 70%, and category (2) is about 3%. When the percentage of category (1) is large, it means there are many jobs that finished within less than 5000 seconds.

Figure 2. Histogram of elapsed time

3.3. Tree types of categorization of six months. We focus on 6 months, January, February, March, April, October and November. We categorize these 6 months into one of 3 types by their properties of elapsed time. The categorizations are as following Table 2. Type 1 is a group that has many jobs with short elapsed time. Type 2 is a group that has many jobs of long elapsed time. Type 3 is a group of a similar distribution of elapsed time. We consider that if the property of an elapsed time is similar, we can handle these data similarly. In Type 3, the long elapsed time and short one are mixed. Figure 3 shows there are histograms from Type 1 to Type 3. Many jobs were finished within 5000 seconds in Type 1. On the contrary, more than 60% of jobs of Type 2 took 30000 seconds. The distribution of histogram of October is similar to November. This is Type 3. We compared these three types by numerical experiments in order to search a trigger for the parameter configuration change. We certified whether we can improve the system usage in Type 1 – Type 3 by parameter change. We present results of our numerical experiments. 1962 R. ITO AND K. KIKUCHI Table 2. Type and months

Type 1 January & March Type 2 February & April Type 3 October & November

Figure 3. Histogram of Figure 4. Randomized six months local search

3.4. Parameter change analysis.

3.4.1. Parameter change algorithm. It is difficult to know when we should change the parameter, because the pattern of job submission always changes. In addition, the performance may fall down by changing it too frequently. So we performed numerical experiments with two kinds of interval to change it. One is 3 days and the other is 7 days. For example, in case of 3 days, we change the parameter configuration on every 3 day. In case of 7 days, we change it on every 7 day. In convenience, we call them ‘3 day’ and ‘7 day’ respectively here. We obtain an optimal parameter configuration every 3 day (7 day) among the past log data, using a mathematical method, Randomized Local Search. Ran- domized Local Search is one of heuristic methods and extended by Local Search [1,5,6]. In this method, we determine an initial solution and generate a neighborhood around it. We search in that neighborhood to find better solution. If we can find a better solution than the initial solution, we overwrite that solution by a temporary solution. We generate a new neighborhood around that temporary solution, and search in it. We repeat these operations for times to obtain an optimal solution (see Figure 4). (Experimental procedure) We perform the following procedure on every 3 (or 7) days. (1) The current parameter configuration is selected as an initial parameter configuration. (2) The jobs are executed virtually by this initial parameter configuration using simulator for the past log data. (3) We generate a new parameter configuration (neighborhood) based on the initial parameter configuration and we perform a simulation to obtain system usage efficiency for the past log data. The past log data are the number of CPU, elapsed time etc. If this new parameter is better than an initial parameter, we decide this one as a temporary configuration. We repeat these procedure 50 times and finally we select best parameter configuration as an optimal parameter configuration. (4) We apply this optimal configuration as an initial parameter configuration for the next period. (5) We repeat these procedures every 3 days (7 days) until the end of month changing parameter configuration. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1963 From procedure (1) to (3), we used Randomized Local Search. By this mathematical method, parameter configurations can be generated easily and it is easy to obtain optimal solution among the candidates. For example, on 3rd March 2006, we can find optimal parameter configuration for the past executed jobs in 2nd March by using simulator. After finding an optimal parameter configuration for the past log data, we apply that parameter configuration for the next waiting jobs in a queue. We examined the system usage efficiency on every three day from 8th to 26th in Type 1 – Type 3. We show system usage efficiency (SUE) of experiments in Table 3 – Table 8. We begin to show them with Type 1.

Figure 5. Procedure from (1) to (3)

3.4.2. Experimental results. According to Table 3, in January, the result of 3 day is better than that of 7 day as for a total average. In March, that of 3 day is about 1 % better than 7 day as for a total average. As for Type 1, 3 day is better than 7 day. Table 3. SUE of type 1 Table 4. SUE of type 2

200601 206503 200602 200604 day 3 days 7 days 3 days 7 days day 3 days 7 days 3 days 7 days 8 36.283 36.283 68.541 68.541 8 57.239 57.271 85.236 85.236 11 46.192 46.192 95.468 96.137 11 61.105 63.878 85.866 85.806 14 53.422 53.422 95.880 95.553 14 52.392 43.543 79.101 79.101 17 35.736 35.611 93.343 93.586 17 58.209 67.643 60.243 64.012 20 72.346 72.339 91.782 89.238 20 59.816 59.816 69.012 68.837 23 56.604 56.617 97.393 93.010 23 53.429 53.429 74.294 74.387 26 64.969 64.969 98.164 98.381 26 62.700 62.700 76.567 76.487 Ave. 52.222 52.205 91.510 90.635 Ave. 57.841 58.326 75.760 76.267

Table 5. SUE of type 3

200510 200511 day 3 days 7 days 3 days 7 days 8 79.288 80.618 75.976 77.084 11 86.485 87.229 93.943 93.841 14 90.865 92.815 84.384 88.716 17 75.404 76.545 61.844 60.099 20 80.239 74.738 69.051 65.228 23 83.577 84.132 82.229 83.870 26 83.784 87.443 93.917 94.389 Ave. 82.797 83.360 80.192 80.461

Next we show the result of February and April in Table 4. In February, 7 day is better than that of 3 day in total average. In April, 7 day are better than by 0.5%. As for Type 2, the parameter change of 7 day is more efficient than 3 day. 1964 R. ITO AND K. KIKUCHI In case of Type 3, the system usage of 7 day parameter change is better than 3 day. These experiments show that 3 day is better than 7 day in Type 1. And it is considered that the time of parameter change affects on SUE. 3.5. Experimental discussion. According to these analysis, it was shown that there are differences of system usage efficiency by the time when parameter configuration changes. This means that a time of parameter change is related to improvement of system usage. By our experiments, these experiments are observed in two view points. The first view is a categorization of type. The second view point is a density. As for Type 1, 3 day is better than 7 day. Type 1 is a group of short elapsed time. The short jobs finished quickly, so a state of job execution is often apt to change. Therefore in this case, it is effective to change parameter configuration frequently. On the contrary, in Type 2, the state of job execution does not change frequently. Therefore, frequent parameter change doesn’t always effective in Type 2. In Type 3, 7 day parameter change is better than 3 day in both of months. In Type 3, the situation is more complicated but there are many percentages of jobs with elapsed time of more than 25000 seconds. So it is considered that 7 day is more efficient than 3 day in these months. Second view point is a density. In case of a month with high percentage, the difference between 3 day and 7 day is easy to be seen. In case of high usage percentage, it is possible that there are many waiting jobs in a queue. Therefore, it is more significant to tune a parameter configuration appropriately such as March or April. However, it is considered first view and second view are complicatedly related and each point affects on the result. So we need to perform more analysis for future optimization. However, it was verified that parameter change has an impact upon the system usage efficiency through numerical experiments. 4. Conclusion. We performed analysis to search a trigger of parameter change to improve system usage efficiency through numerical experiments. By this analysis, it was verified that a time when we change parameter configuration affects on the system usage efficiency. In case of a month with elapsed time of various lengths are mixed, it is considered to more difficult to search timing to change parameter configuration. In future work, we will perform more precise experiments and analysis for applying it in dynamics system for the actual practical use in future work.

REFERENCES [1] E. Aarts and J. K. Lenstra, Local search in combinatorial optimization, John Wiley & Sons, 1997. [2] D. G. Feitelson, Packing schemes for gang scheduling, Proc. of the 1st Workshop on Job Scheduling Strategies for Parallel Processing, New York, pp.89-110, 1995. [3] P.-F. Dutot, M. A. S. Netto, A. Goldman and F. Kon, Scheduling moldable BSP tasks, Proc. of the 11th Workshop on Job Scheduling Strategies for Parallel Processing, pp.160-175, 2005. [4] V. Hamscher, U. Schwiegelshohn, A. Streit and R. Yahyapour, Evaluation of job-scheduling strategies for grid computing, Proc. of the 1st IEEE/ACM International Workshop on Grid Computing, LNCS, vol.1971, pp.191-202, 2000. [5] E. Polak, Optimization: Algorithms and Consistent Approximations (Applied Mathematical Sci- ences), Springer-Verlag, New York, 1997. [6] C. R. Reeves, Modern Heuristic Techniques for Combinatorial Problems, Mcgraw Hill Book Co Ltd., New York, 2000. [7] S. Gerald, K. Rajkumar, R. Arun and S. Ponuswamy, Scheduling of parallel jobs in a heterogeneous multi-site environment, JSSPP, 2003. [8] Y. Zhang, H. Franke, J. Moreira and A. Sivasubramaniam, An integrated approach to parallel scheduling using gang scheduling, backﬁlling and migration, IEEE Trans. Parallel and Distributed, Syst., vol.14, no.3, pp.236-247, 2003. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1965-1972

COMPLEXITY REDUCTION ALGORITHM FOR ENHANCEMENT LAYER OF H.264/SVC

Kentaro Takei, Takafumi Katayama, Tian Song and Takashi Shimamoto

Computer Systems Engineering, Department of Institute of Technology and Science Graduate School of Engineering Tokushima University Minami-Jyosanjima 2-1, Tokushima City 770-8506, Japan { kentaro t; ringo1986; tiansong; simamoto }@ee.tokushima-u.ac.jp Received February 2010; accepted April 2010

Abstract. The inter-layer prediction of H.264/SVC can help to improve the coding efficiency as well as the computation complexity. This paper presents a low complexity algorithm for inter-layer prediction. Proposed algorithm focuses on the reduction of the candidate modes by making use of the correlations of the encoding cost between the base layer and enhancement layers. For macroblock with colocated macroblock coded by IN- TRA or INTER type, two algorithm are proposed, respectively. Both algorithm efficiently decrease the redundant candidate modes by estimating from the base layer coding information. The experiment results show that proposed algorithm can significantly reduce redundant computation complexity with almost no coding efficiency loss. Keywords: H.264, Scalable video coding, Inter-layer

1. Introduction. In recent years, encoding standard which can achieve the scalability has increasing requirement due to the diversification of the network environment and the applications. Enhancing to the succeed H.264/AVC, a scalable extension is standardized as H.264/SVC [1] in 2007. A reference software is also developed by the joint video team (JVT) for SVC [2, 3]. The objective of H.264/SVC is to enable the generation of a unique bitstream that can adapt to various bit-rate, transmission channel and display capabilities. In H.264/SVC, three scalabilities: spatial scalability, temporal scalability, and quality scalability are finally recommended in the final draft [4, 5, 6]. However, due to it’s high implementation complexity, the complexity reduction becomes a research point. Some previous works are proposed to reduce the complexity of temporal scalability by adaptively reduce the redundant encoding mode or efficiently construct the GOP (Group of Pictures) [9, 10]. The resolution diversity of current display devices motivates the improvement for spatial scalability. The spatial scalability is realized by introducing multiple display resolutions within a single bit-stream. Therefore, the information of the input sequences and the selected modes in the base layer can be used to estimate the optimal mode in the enhancement layers, which is called inter-layer coding [3]. In the inter-layer prediction, three new modes have been introduced using the motion vectors, residuals, and intra information from the base layer to select the best coding mode in the enhancement layers. Using these new modes, inter-layer predictions can not only achieve scalable features but also improve the coding efficiency. However, the inter-layer modes have to perform multiple times rate-distortion optimization (RDO) process, by which very high computational complexity is induced. In particular, the residual prediction mode has to perform twice of the RDO process which

1965 1966 K. TAKEI, T. KATAYAMA, T. SONG AND T. SHIMAMOTO doubles the computational complexity of the normal RDO process of H.264/AVC. A previous work introduced an efficient architecture to reduce the implementation complexity by changing the processing order [7]. However, the computational complexity reduction is not considered from the viewpoint of candidate modes reduction. Another work achieved a very high complexity reduction rate by decreasing some of the candidate modes for H.264/SVC [8]. It is no doubt that the higher enhancement layer it is, the higher video quality is required. However, the improvement of their work is on the basis of the sacri- fice of the video quality for enhancement layer. Our previous work gave an efficient mode reduction method to decrease the encoding complexity [11]. However, the complexity reduction rate is not efficient enough.

2. Inter-Layer Prediction Modes. In order to employ base layer coding information for spatial enhancement layer coding, additional macroblock modes have been introduced in spatial enhancement layers. Three techniques to realize inter-layer prediction have been recommended in H.264/SVC, namely inter-layer motion prediction, inter-layer intra prediction, and inter-layer residual prediction. Therefore, addition to the traditional coding modes of H.264/AVC, several new modes are introduced in H.264/SVC. Figure 1 shows the total modes of H.264/SVC.

H.264/AVC modes H.264/S VC modes INTRA modes

ABCD I MABCD MABCDE FGH J I I K aJverage J K L L K L mode0 mode1 mode0 mode1 mode2 mode3 MABCD MABCD MABCD MABCDEFGH I I I I J J J J MABCD K K K K I L L L L J average K mode4 mode5 mode6 mode7 L I n t er -l a y er I n t r a mode mode8 mode2 mode3 INTTRRAA44xx44 ININTTRRAA1166xx16

16x16 16x8 8x16 16x16 16x8 8x16

Inter-layer INTER modes 8x8 8x4 4x8 4x4 residual modes 8x8 8x4 4x8 4x4

Figure 1. Coding modes of H.264/SVC

The same as H.264/AVC, generally INTRA and INTER types of coding modes are used. INTER type modes utilize the correlation in temporal direction and INTRA type modes utilize the correlation in spatial direction to decrease the redundant components. H.264/SVC employs an rate-distortion optimization (RDO) procedure which is very com- putationally expensive. This RDO process evaluates all possible modes to select the best one with the smallest rate-distortion cost (RDC). The evaluation of RDC can be described by the following equation.

J(s, c, Mode|QP, λmode) = SSD(s, c, Mode|QP ) + λmode · R(s, c, Mode|QP ) (1) where QP is the macroblock quantization parameter, λmode is the lagrangian multiplier, SSD is the sum of square differences between the original block luminance signal denoted by s and its reconstructed signal denoted by c, and R (s, c, Mode|QP ) is the number of ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1967 generated bits of a certain encoding mode. It includes the bits for the macroblock header, motion vector, and the DCT coefficients for the given block. Inter-layer residual prediction is one of the coding modes which are introduced by the inter-layer prediction to not only realize spatial scalability but also improve the coding efficiency. Because the motion vectors in the base layer and enhancement layer tend to have similar motion vectors, the up-sampled residual block also tends to have similar residuals with the corresponding block. When the residual prediction is used, the residuals of the corresponding 8×8 block in the base layer is block-wise up-sampled using a bilinear filter and used as prediction data for the residuals of the enhancement layer macroblock. On the other hand, inter-layer intra prediction mode uses up-sampled intra coded macroblock as a prediction mode in enhancement layer coding.

3. Proposed Algorithm. The motivation of this work is try to reduce the implementation complexity of enhancement layer by cut down the redundant candidate modes of H.264/SVC. By eﬃciently using the encoding information of base layer we propose two low complexity algorithms for enhancement layer encoding. One algorithm is proposed for the co-located macroblock of which is INTRA type coded in base layer and the other one is for INTER type coded, respectively.

3.1. Macroblock with co-located block is INTRA type coded in base layer. Two methods are proposed for the complexity reduction of the macroblock with colocated block is INTRA type coded in base layer.

3.1.1. INTRA mode selection method. The coeﬃcients of one block in base layer commonly have very similar frequence components in the enhancement layer because the sequence of base layer are generated from down-sampled enhancement layer. In this work, we make use of this feature to cut down the candidate INTRA coding modes of enhancement layer. We use the RDC of the selected INTRA mode (RDCbasebest) as a reference value. When RDCbasebest is a 4×4 pixels mode, it is considered that there are much high frequence components. Therefore, we can get rid of the 16×16 pixels modes from candidate modes. When RDCbasebest is a 16×16 pixels mode, all 4×4 pixels modes are also out of consideration.

3.1.2. INTER mode skip method. Generally, because there are very similar frequence components in the base layer and enhancement layer, if the base layer is encoded by INTRA type mode the enhancement layer tends to be encoded by INTRA mode. However, sometimes INTER type modes are selected in the case of there is less correlations between base layer and enhancement layer. In this work, after the best INTRA mode RDCEnh INT RAbest is selected, it is compared with the RDC of skip mode which have the lowest computation complexity. If the RDCEnh INT RAbest is smaller than that of SKIP mode, then the RDO will be terminated.

3.1.3. Flow chart for INTRA mode decision. Figure 2 shows the ﬂow chart for INTRA mode decision algorithm. As Figure 2 shows, in the ﬁrst step RDCbasebest is used to get rid of one candidate type mode between 4×4 and 16×16 pixels block. Then, the RDO for SKIP mode is performed and the RDC of SKIP mode is compared with RDCEnh INT RAbest. If RDCEnh INT RAbest is smaller than that of SKIP mode, all the other INTER type modes will be excluded from the candidate modes.

3.2. Macroblock with co-located block is INTER type coded in base layer. Four methods are proposed for macroblock with co-located block is INTER type coded in base layer to reduce the redundant coding modes. 1968 K. TAKEI, T. KATAYAMA, T. SONG AND T. SHIMAMOTO

start

Yes RDCbasebest == RDCbaseintra4x4

RDO(INTRA16x16,ILIP) RDO(INTRA4x4,ILIP) ᯹᯾ᰄ᯵ᰂ RDO( 16x16)

RDCTBM < Yes RDCenh_16x16 No

RDO (all Inter mode)

The best Intra mode

Figure 2. Flow chart for macroblock with co-located block is INTRA type coded in base layer

3.2.1. SKIP mode decision. When the macroblock is encoded by INTER type in base layer, there are high probability for the co-located macroblock in the enhancement layer to be encoded by INTER type. Moreover, because the resolution of enhancement layer are higher than the base layer, the predicted motion vector (PMV) tends to have higher precision to select the search center and the SKIP mode have more chances to be selected. In this work, the RDC for SKIP mode (RDCEnh skip) and 16×16 mode (RDCEnh 16×16) is used to evaluate the precision of PMV. When

RDCEnh skip < RDCEnh 16×16 (2) is satisfied, it is considered that PMV is precisely selected and the RDO for INTER mode is terminated. In this work, RDO for three traditional modes: Skip, Direct, 16×16 modes are performed at first. If the encoding cost of skip mode or the direct mode are smaller than that of the 16×16 mode the best mode of these three modes are defined as a temporary best mode (TBM). If the 16×16 mode has the smallest encoding cost, the RDO for all the other modes have to be performed. 3.2.2. Inter-layer residual prediction (ILRP) skip. ILRP mode is selected when there are high correlation between base layer and enhancement layer. If the correlation can be precisely predicted, redundant candidate modes can be efficiently reduced. In this work, ∆ RDC is used which can be defined as |RDC − RDC | ∆RDC = base enh (3) RDCbase ∆ RDC is used as a threshold (TH) and is set to 0.05 in this work on the basis of many simulation results. 3.2.3. Candidate modes reduction for ILRP. Due the strong correlation between the base layer and enhancement layer, generally the same mode will be selected. Even sometimes different mode may be selected it is able to be predicted. For example, when the TBM ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1969 is 16×16 mode there should have no more high frequence components in the macroblock. Therefore, it is hardly to be considered to select 4×4 mode. In this work, we further cut down the candidate modes for ILRP as shown in Table 1. Table 1. ILRP candidate modes

TBM SVC candidate mode 16×16 mode 16×16, 16×8, 8×16 16×8 mode 16×16, 16×8, 8×16, 8×8 8×16 mode 8×4, 4×8, 4×4 8×8 mode 4×8 mode 16×8, 8×16, 8×8 8×4 mode 8×4, 4×8, 4×4 4×4 mode

3.2.4. INTRA mode skip. When the co-located macroblock in base layer is encoded by INTER mode with a very small RDC, it has more chance to be encoded by INTER type mode. The probability can also be predicted from the base layer by using the RDC of the best mode in base layer. When

RDCbase best > RDCenh INT ERbest (4) is satisfied the INTRA mode is considered can be cut down from the candidate modes for enhancement layer. 3.2.5. Flow chart of the proposed algorithm. All of the four approches are carefully considered and a efficient complexity reduction algorithm is proposed for macroblock with co-located block is INTER type coded in base layer. The flow chart is shown in Figure 3. First, the RDO for SKIP mode and 16×16 mode are performed. If the RDC of SKIP mode is smaller than that of 16×16, all other INTER type modes is cut down from candidate modes. In the case that the RDC of SKIP mode is bigger than that of 16×16 mode, the other INTER modes have to perform RDO. Then, the best mode is selected as TBM. Next, ∆RDC is calculated using the best mode of base layer and the TBM. If the ∆RDC is smaller than TH, a proposed SVC candidate modes which is list in Table 1 are used. In th case when the RDCTBM is smaller than RDCILRP SKIP , all the candidate modes in Table 1 are cut down. In the end, the RDCbase best and RDCenh INT ERbest is compared to decide if or not it is necessary to perform RDO for INTRA modes.

4. Simulation Results. In order to evaluate the proposed algorithm, it is implemented in the reference software JSVM [12]. The R-D curves of some test sequences are shown in Figure 4-Figure 5. From these R-D curves it is clear that the proposed algorithm induces almost no video quality loss. The simulation results of the proposed algorithm are shown in Table 4. ∆Bitrate, ∆T ime, and ∆PSNR in Table 4 shows the results in comparison with the JSVM. As Table 4 shows, the proposed algorithm can achieve improved complexity reduction rate than previous work. As for the PSNR and bitrate decrease, the proposed algorithm induced almost no video quality loss.

5. Conclusion. In this paper, a low complexity algorithm for inter-layer prediction is proposed. Proposed algorithm focused on the reduction of the candidate modes by making use of the correlations of the encoding cost between the base layer and enhancement layers. For macroblock with co-located macroblock coded by INTRA or INTER type, two algorithm are proposed, respectively. Both algorithm eﬃciently decreased the redundant 1970 K. TAKEI, T. KATAYAMA, T. SONG AND T. SHIMAMOTO

start

RDO(Skip,Inter16x16)

RDCenh_Skip < Yes RDCenh_Inter16x16 No RDO (all Inter mode)

TBM selection

ᠪ Yes RDC

Yes RDCTBM < RDCILRP_skip No

SVC candidate mode

RDCenh_TBM < Yes RDCbase No RDO (all Intra mode)

Best mode

Figure 3. Flow chart for macroblock with co-located block is INTER type coded in base layer ᎨᎲᎰᏀᎶ ፻ ፻፼ ፻ ፹፺ Ꭴ ᎉ

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Figure 4. R-D curves for akiyo and football candidate modes by estimating from the base layer coding information. The experiment results show that proposed algorithm can signiﬁcantly reduce redundant computation complexity with almost no coding eﬃciency loss. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1971

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Figure 5. R-D curves for container and bus

Table 2. Simulation results (QP = 28)

sequence ∆PSNR[dB] ∆bitrate[%] ∆time[%] [8] Proposed [8] Proposed [8] Proposed mother −0.06 0.00 0.13 0.09 −66.0 −67.4 foreman −0.14 0.04 0.09 −1.26 −53.7 −55.2 container −0.02 −0.01 0.21 0.03 −68.7 −71.1 tempete −0.06 −0.03 0.71 0.62 −54.0 −57.7 silent −0.04 0.00 0.48 0.04 −62.1 −67.8 mobile N/A −0.04 N/A 0.24 N/A −50.4 football N/A −0.01 N/A 0.22 N/A −45.4

REFERENCES

[1] J. Reichel, H. Schwarz and M. Wien, Scalable Video Coding-Join Draft 4, ISO/IEC JTC1/SC29/ WG11/JVT-Q201, Nice, France, 2005. [2] H. Schwarz, D. Marpe and T. Wiegand, Overview of the scalable H.264/MPEG-4 AVC extension, Proc. of IEEE International Conference on Image Processing, pp.161-164, 2006. [3] H. Schwarz, D. Marpe and T. Wiegand, Overview of the scalable video coding extension of the H.264/AVC standard, IEEE Trans. on Circuits and Systems for Video Technology, vol.17, no.9, pp.1103- 1120, 2007. [4] H. Schwarz, D. Marpe and T. Wiegand, Joint draft ITU-T rec. H.264—ISO/IEC 14496-10/Amd.3 scalable video coding, Doc. JVT-X201, Geneva, 2007. [5] C. A. Segall and G. J. Sullivan, Spatial scalability within the H.264/AVC scalable video coding extension, IEEE Trans. on Circuits and Systems for Video Technology, vol.17, no.9, pp.1121-1135, 2007. [6] H. Schwarz, D. Marpe and T. Wiegand, Hierarchical B pictures, Joint Video Team, Doc. JVT-P014, Poznan, Poland, 2005. [7] H. Li, Z. G. Li and C. Y. Wen, Fast mode decision algorithm for inter-frame coding in fully scalable video coding, IEEE Trans. on Circuit and System for Video Technology, vol.16, no.7, 2006. [8] B. Lee, M. Kim, S. Hahm, C. Park and K. Park, A fast mode selection scheme in inter-layer prediction of H.264 scalable extension coding, Proc. of IEEE International Symposium on Broadband Multimedia Systems and Broadcasting, pp.1-5, 2008. [9] T. Song, S. Matsuoka, Y. Morigami and T. Shimamoto, Coding eﬃciency improvement with adaptive GOP selection for H.264/SVC, International Journal of Innovative Computing, Information and Control, vol.5, no.11(B), pp.4155-4165, 2009. 1972 K. TAKEI, T. KATAYAMA, T. SONG AND T. SHIMAMOTO

[10] T. Hamamoto, T. Katayama, T. Song and T. Shimamoto, Low complexity mode selection method for hierarchical B-picture of H.264/SVC, ICIC Express Letters, vol.3, no.4(A), pp.1179-1184, 2009. [11] Y. Morigami, T. Song, T. Katayama and T. Shimamoto, Low complexity algorithm for inter-layer residual prediction of H.264/AVC, Proc. of International Conference on Image Processing, 2009. [12] J. Reichel, H. Schwarz and M. Wien, Joint scalable video model 9 (JSVM 9), Joint Video Team, Doc. JVT-V202, 2007. [13] G. Bjontegaard, Calculation of average PSNR diﬀerences between RD-curves, The 13th VCEG Meet- ing, Doc. VCEG-M33, Austin, 2001. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1973-1978

MODELING OF ENTERPRISES RISK MANAGEMENT AND ITS ROBUST SOLUTION METHOD

Min Huang1, Yanli Huo2, Chunhui Xu2 and Xingwei Wang1

1College of Information Science and Engineering Key Laboratory of Integrated Automation of Process Industry, Ministry of Education Northeastern University Shenyang 110004, P. R. China [email protected] 2Faculty of Social Systems Science Chiba Institute of Technology Chiba 275-0016, Japan Received February 2010; accepted April 2010

Abstract. Uncertainties of business environment bring not only opportunities but also more risks for the enterprise. This paper focuses on the enterprise risk programming problem with uncertain cost for risk control. To reduce the risk effectively, the concept of risk control degree is proposed. To reduce the influences of the uncertainty of the cost for risk control on the solution of the problem, Robust Optimization (RO) method pretends to deal with the uncertainty of the cost for risk control and the robust risk programming model is established. The numerical experiments suggested the effectiveness of the proposed method which eliminates the impact of uncertainty with a negligible increase in risk level. Keywords: Risk programming, Uncertainty, Robust optimization, Risk control degree

1. Introduction. Risk management is the key problem to overcome in an enterprise in order to ensure success. The ability to master risk and manage the inevitable uncertainty associated with evaluating future outcomes is a key to sustainable competitive advantage [1]. Risk programming, an important stage of risk management, is the process used to determine the risk management strategy and to realize concrete measures and means. In this process, the known risk is eliminated as soon as possible. In the case of risks that cannot be eliminated, their characteristics may be changed so that the probability and loss of them are limited. Under a certain risk investment, the global risk level of the enterprise in minimized [2]. Some researchers are proposed for risk programming problem [3,4]. However, the cost for risk control is supposed to be deterministic for each risk, which is not the case in the real world. Hence, in this paper, the research focuses on the enterprise risk programming problem with uncertain cost for risk control. Also, in previous studies [4,5] of risk programming, only two statuses (each risk with and without risk control measurement) are considered. In this way, when fund remain is not sufficient for controlling one risk, and will not controlled and fund will be wasted. So, the concept of risk control degree is proposed to effectively reduce the risk. Therefore, the risk programming model for determine the risk control degree with uncertain cost for risk control is proposed. In order to reduce the influence of the uncertainty of the cost for risk control on the solution of the problem, Robust Optimization (RO) method [6,7] is used to deal with the impact of data uncertainty on the feasibility of solutions. When the variability parameter in changing, this approach can guarantee the feasibility of solution with high probability, and it can provide a probability that guarantee robust feasible solution. The numerical analysis suggested the feasibility of the method.

1973 1974 M. HUANG, Y. HUO, C. XU AND X. WANG 2. Problem Description and the Model of Risk Programming. The risk is graded into n rank from small to large. Suppose each risk has one control measure and can be treated with certain risk control degree, that is, risk state may be in one of three states by determine the risk control degree, no treatment (risk control degree equals 0); partial treatment (risk control degree is between 0 and 1) and complete treatment (risk control degree equals 1). In today’s rapidly changing world, the information about the risks of enterprises is more relay on the subjective information, which is suitable to be described by fuzzy theory other than stochastic theory [4]. Suppose the fuzzy description of each risk factors of each risk with no treatment and with complete treatment under the risk control measure are known. When the risk factors are dealt with the risk control measure with certain control degree, the fuzzy description of the corresponding risk factors will change to the low risk status. The cost for risk control measure is uncertainty and the costs of the diﬀerent control measures are diﬀerent. As the total investment for the risk control is limited, the risk programming problem here is to minimize the global risk level by optimally deciding the risk control degree for each of the risk constrained by the certain risk investment, which can be described as follows: ∑n ~ min ak(X)k (1) k=0 ∑m s.t. c˜ixi ≤ E (2) i=1

xi ∈ [0, 1] i = 1, 2, ··· , m; (3) ~ 0 where X = (x1, ··· xi, ··· xm) , E is the total investment for the risk control; i is the index of the risk; k is the index of risk rank; m is the risk numbers; n is the risk rank numbers; ~ ~ ak(X) is the membership degree to k level risk for X,c ˜i is the cost of strategy for risk i, which is the uncertainty one. Supposec ˜i ∈ [ci − cˆi, ci +c ˆi]. xi is the risk control degree of risk i, xi ∈ [0, 1], 0 means no treatment for risk i, 1 means complete treatment for risk i, others means partial treatment for risk i. Formula (1) is the objective function, which means the global risk status of enterprise under a set of risk control degree combination, and is obtained by fuzzy comprehensive evaluation based risk evaluation method [5]. Figure 1 illustrates the hierarchical model for risk evaluation. It can be seen that the risk evaluation is carried out from local to global that is from the bottom to the top. That is: when a combination of risk control degree is given, all the fuzzy description of risk factors in layer 3 can be determined by the following equation:

fik(xi) = aikxi + bik i = 1, 2, . . . , m; k = 0, 1,..., 8 (4) fik(xi) is the membership degree to k rand risk for risk i; aik is the coeﬃcient of risk management to k rank risk for risk i (change of risk states with complete treatment); bik is the membership degree to k rank risk with no treatment of risk i. And then the risk of the process under sub-goal in layer 2 can be evaluated. Further, the risk of sub-goals under the overall objective level 1 can be evaluated. Finally, the fuzzy description of overall risk level in level 0 is obtained and the crisp value of the overall risk level is given by Formula (1). Formula (2) is cost constraints which means that the actual total cost of risk control should not be more than the total risk investment budget. Formula (3) is the range of the risk control degree for each risk.

3. Robust Optimization Model of the Risk Programming. Considering the uncertainty of the cost for risk control, it is reasonable to estimate the mean value and mean deviation ofc ˜i as ci andc î. Then,c ˜i can be described as interval value [ci − cî, ci +c î]. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1975

Figure 1. The hierarchical model for risk evaluation

To deal with this uncertainty of cost for risk control, Robust Optimization (RO) [6,7] model for the problem is proposed. Let J = {i/cˆi > 0} be the uncertainty set. Then |J| is the number of the uncertainty parameters. Let robustness level Γ ∈ [0, |J|], bΓc is the maximum integer less than Γ. The role of the parameter Γ in the constraints is to adjust the robustness of the proposed method against the level of conservatism of the solution. The parameter Γ controls the level of robustness in the constraint. Therefore, the RO model of the risk programming is proposed as follows: ∑n ~ min ak(X)k (5) k=0 { } ∑m ∑ s.t. cixi + max cˆjxj + (Γ − bΓc)c ˆtxt ≤ E (6) {S∪{t} | S⊆J,|S|≤bΓc,t∈J\S} i=1 j∈S

xi ∈ [0, 1] i = 1, 2, ··· , m; (7) where S is a subset of J, |S| is the number of elements in set S, |S| ≤ bΓc. The second item of Formula (6) is to reduce the probability bound of constraint violation. Clearly, this probability is depending on Γ. By strong duality [7], the RO model of risk programming can be rewrite as follows: ∑n ~ min ak(X)k (8) k=0

∑m ∑|J| s.t. cixi + pi + Γz ≤ E (9) i=1 i=1

pi + z ≥ cˆixi i = 1, 2, ··· , |J| (10) z ≥ 0 (11)

pi ≥ 0 i = 1, 2, ··· , |J| (12)

xi ∈ [0, 1] i = 1, 2, ··· , m; (13) It is clear that this model has m+|J|+1 decision variables, m+1+2|J|+1 constraints. To deal with this model, ILOG [8] optimization software is used.

4. Numerical Experiments. In this section, numerical experiment is used to discuss the performance of the proposed method. ILOG software is used to solve the proposed model. The main performance measures used to evaluate the proposed method are defined as follow: 1976 M. HUANG, Y. HUO, C. XU AND X. WANG (1). Probability Bound of Constraint Violation (write as PB) is defined as follows [7]: ( ) Γ − 1 B(n, Γ) ≈ 1 − φ √ (14) n where n is the number of fluctuations parameters, Γ is the robust level. (2). Obj is the value of the objective. (3). Average Cost (AC) is the fund (fixed cost) which is used to select control measures. (4). Objective Change (ObjC) is defined as follows:

ObjC = (Obj − Obj0)/Obj0 (15)

where Obj is the objective when Γ > 0, Obj0 is the objective when Γ = 0. (5). Average Cost Change (ACC ) is deﬁned as follows:

ACC = (AC0 − AC) /AC0 (16)

AC is the average cost when Γ > 0, AC0 is the average cost when Γ = 0. The numerical example involves 5 sub-goals, 5 sub-processes and 30 risks. The weight of sub-goal, process and risk are given in Table 1, and the cost of each risk control is given in Table 2. The risk investment is 30000 RMB. It has 51 decision variables and 72 constraints in this robust optimization model. Table 1. The weight of sub-goals, processes and risk

Weight 0.3sub-goal1 0.15sub-goal2 0.15sub-goal3 0.22sub-goal4 0.18sub-goal5 0.2 (risk1) 0.5 (risk5) 0.8 (risk16) Process1 0.5 0.3 (risk10) 0.3 0.2 (risk4) 0.1 1.0 (risk2) 0.2 0 0 0.2 (risk23) 0.5 (risk13) 0.3 (risk12) 0.2 (risk3) 0.5 (risk8) Process2 0.3 0.5 0.2 1.0 (risk6) 0.2 1.0 (risk29) 0.3 1.0 (risk20) 0.8 (risk17) 0.5 (risk9) 0.8 (risk7) Process3 0.05 1.0 (risk15) 0 0 0.3 0 0 0.2 1.0 (risk27) 0.2 (risk28) 0.9 (risk18) 0.75 (risk19) Process4 0.15 0.2 0.2 1.0 (risk11) 0.4 1.0 (risk14) 0.3 1.0 (risk24) 0.1 (risk21) 0.25 (risk22) Process5 0 0 0 0 0.2 1.0 (risk25) 0.2 1.0 (risk26) 0.2 1.0 (risk30) Note: 0 stand for that there is no risk under the processes of sub-goals

Table 2. Cost of each risk control risk 1 2 3 4 5 6 7 8 9 10 cost 800 1300 2500 2000 3000 800 300 1500 800 2000 risk 11 12 13 14 15 16 17 18 19 20 cost 1000 300 300 2000 3000 300 1200 2800 2000 1300 risk 21 22 23 24 25 26 27 28 29 30 cost 1300 1100 1500 2100 300 1200 700 300 1800 1600

It is clear that the overall risk level is 3.976243 when no risk control measures are selected for enterprise. The best combination of risk control degrees is 101011011110010.111 1110001111011; the overall risk level is 2.7962825 and the costs 30000 RMB without considering the ﬂuctuations in the cost of risk control. Figure 2 shows the change of PB, Obj, AC and ACC with Γ, when the ﬂuctuation degree is 30%, that is Cˆ = 30%C. Figure 2 shows that PB and AC decrease, Obj, ObjC and ACC increase with the increasing of Γ. This is because the bigger Γ, the more volatility parameters are taken into account, so the actual funds used to deal with risk will relatively reduce, which cause the increasing of the risk level of the overall enterprise. It is clear that the rate of change ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1977

Figure 2. The performance measures changing with Γ of ObjC is far less than that of PB. Although the optimal solution under uncertain situations is sub-optimal solution of the determine situations, it meet the uncertainty with a large probability. Therefore, we can use this method to solve the problem of uncertainty with a negligible increment in risk level. Figures 3 to 5 shows the change of ObjC and ACC with the change of Γ and different fluctuations number when the fluctuation degree is 10%, 20% and 30% respectively.

Figure 3. The change of ObjC and ACC while the ﬂuctuation degree is 10%

Figure 4. The change of ObjC and ACC while the ﬂuctuation degree is 20%

Figures 3∼5 show that ObjC and ACC increase when the ﬂuctuation degree or number of uncertain parameters increases. This is because the greater the ﬂuctuation degree or the more the uncertain parameters, the more cost is needed to eliminate the impact of such factors. That is less cost is used to control risk, and the overall risk level is higher.

5. Conclusions. This paper the concept of risk control degree is proposed and robust optimization method to deal with the uncertainty of the cost for risk control strategies, 1978 M. HUANG, Y. HUO, C. XU AND X. WANG

Figure 5. The change of ObjC and ACC while the ﬂuctuation degree is 30% which can give a robust solution that remains to be feasible with a high probability under control cost uncertainty, numerical experiments illustrated that, so the robust versions of risk management method provide a good risk management tool for the enterprise. Acknowledgment. This work is supported by the National Natural Science Founda- tion of China under Grant Nos. 70671020, 70721001, 70931001 and 60673159, Special- ized Research Fund for the Doctoral Program of Higher Education under Grant No. 20070145017, the Fundamental Research Funds for the Central Universities under Grant Nos. N090504006 and N090504003, Science and Technology Research Fund of Bureau of Education of Liaoning Province.

REFERENCES [1] J. Deloach and N. Temple, Enterprise-Wide Risk Management: Strategies for Linking Risk and Opportunity, Financial Times Prentice Hall, 2000. [2] Y. Y. Haimes, Risk Modeling, Assessment, and Management, 2nd Edition, Wiley, New York, 2004. [3] C. Romero, Risk programming for agricultural resource allocation: A multidimensional risk approach, Annals of Operations Research, vol.94, no.1-4, pp.57-68, 2000. [4] M. Huang, F. Lu and X. Wang, GA based stochastic risk programming for virtual enterprise, Proc. of the 2nd IEEE Conference on Industrial Electronics and Applications, pp.949-954, 2007. [5] M. Huang, Y. Huo, C. Xu and X. Wang, Research on virtual enterprise robust risk programming method, ICIC Express Letters, vol.3, no.4, pp.1131-1136, 2009. [6] D. Bertsimas and M. Sim, Robust discrete optimization and network ﬂows, Mathematical Program- ming, vol.98, no.1-3, pp.49-71, 2003. [7] D. Bertsimas and M. Sim, The price of robustness, Operations Research, vol.52, no.1, pp.35-53, 2004. [8] ILOG, ILOG CPLEX 10.1User’s Manual, ILOG S.A., Gentilly, France, 2006. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1979-1984

FUNDAMENTAL STUDY OF CLUSTERING IMAGES GENERATED FROM CUSTOMER TRAJECTORY BY USING SELF-ORGANIZING MAPS

Asako Ohno1, Tsutomu Inamoto2 and Hajime Murao3

1Department of Life Design Shijonawate Gakuen Junior College Hojo, 4-10-25, Daito, Osaka 574-0011, Japan [email protected] 2Graduate School of Law Kobe University Rokkodai, 2-1, Nada, Kobe 657-8501, Japan [email protected] 3Graduate School of Intercultural Studies Kobe University Tsurukabuto, 1-2-1, Nada, Kobe 657-8501, Japan [email protected] Received February 2010; accepted April 2010

Abstract. This paper presents the details of a fundamental study of analyzing a customer trajectory by clustering the constituents of the customer trajectory sequence into two types: one, the constituents working as a source of the features of a group of customer trajectory sequences in a given period that we call a time slot and the other, the constituents working as a source of personal features of each of the customers. Removing personal features from a group of customer trajectory sequences provides us new knowledge that is less affected by the difference among sampled data and is expected to be utilized for planning sales strategies that target customers shopping in specific time slots and for evaluating the effectiveness of these strategies. In this paper, we introduce definitions and procedures of the proposed method of clustering the constituents of customer trajectory sequences. Keywords: Customer trajectory analysis, Knowledge discovery, Self-organizing map

1. Introduction. In the past few decades, the point-of-sale (POS) system has been utilized as one of the essential technologies for companies planning more effective marketing strategies by providing information of when and which products the customers purchase while the information before purchasing is black boxed. Recently, knowing or controlling the behaviors of customers before a purchase by analyzing customer trajectories has become a new trend in this field; such an analysis is expected to provide providers or re- tailers with important information to predict the latent needs and wants of the customers as well as to carry out a basket analysis [1]. We call the sequence data that represents a series of customer behaviors beginning from his/her entrance into the store and ending with his/her exit “a customer trajectory sequence (CTS)”. There are some studies that record a number of CTSs by using wireless systems such as radio frequency identification (RFID) [2], which is a wireless identification system that uses radio waves and tags, and attempt to utilize the discovered knowledge for store layout optimization, inventory management, customer behavior prediction, or sales optimization. By analyzing CTSs in detail, we may also classify customers into different types of groups on the basis of the information extracted from their CTSs and provide them special sales promotions.

1979 1980 A. OHNO, T. INAMOTO AND H. MURAO However, at present, CTS analysis seems to be in its earliest days. Larson et al. [3] generated some hypothesis by clustering customers into different types by using a clustering method based on K-means. Yada [4] stated that useful frameworks of the customer trajectory analysis and the application of this analysis have not yet been sufficiently discussed. It is common to classify customers on the basis of their properties such as age, sex, occupation, hobby, or loyalty. Although this information is useful for predicting future sales or trends that appear in each of the customer groups, it heavily relies on the above mentioned customer properties. It seems more rational to provide sales promotions to a wide range of customers than to small customer groups classified according to the customer properties. If we could extract a new feature that appears in common among customers who had never been grouped together, suppliers might find a wide, new semantic customer group that have never seen or dreamed of, and could provide new sales promotions to them. The appearance of the new customer group may inspire suppliers to invent new concept of products. In this paper, we used an XML database of CTS recorded by using RFID at one of the supermarkets in Japan [4]. Through a preliminary analysis of the CTS and hourly purchasing records at the store, we generated a hypothesis that there are some differences in customer behavior between daytime and night time; same as the ones between weekdays and weekends or between different seasons. CTS may contain features that come from its customer’s personal preference or habit as noise. Generally, this noise is treated as important resource of information when we want to discover knowledge related to the properties of the customers. However, when we want to extract features related to a group of CTS; such as the ones belong to the time slot “daytime”, the noise should be removed. We assume that a CTS contains two types of information: the one works as a part of the features of the time slot group to which it belongs and the other works as part of the features of each of the customers that we treat as noise in this study. To extract features from CTS, we divide CTS into a number of customer trajectory sub sequences (CTSSs). We assume that some of the CTSSs work as the feature of the customer and others work as that of the time slot group. We attempt to extract information which characterizes the feature of the time slot group by clustering some CTSSs that work as resource of the feature of its time slot group across the boundaries of CTS recorded for customers who have different properties each others. Here, we call a set of CTSSs that are observed within in a certain time range or “time slot” during the store hours, “a time slot group”. Each of the CTSSs is a member of both one CTS and one time slot group. The objective of this study is to detect a source of features that differentiate the tendency of a time slot group from that of the other groups by analyzing the CTSSs, that is, the constituents of a CTS recorded by using RFID. This information can be utilized to evaluate the effectiveness of sales promotions or demonstrations. This advantage allows the stores to plan sales strategies tailored to each of the time slots. The contribution of this paper is to propose the methodology of clustering constituents of a CTS and to report the results of our fundamental experiment using a small set of CTSs. There are many ways to divide and classify CTSs. Here, we simply divide a CTS at a fixed time interval, generate an image from for every CTSS, and classify the images by using self-organizing maps. The rest of this paper is organized as follows: we give a detailed explanation of our method in Section 2, report on the experiment in Section 3, and then conclude the paper in Section 4.

2. Proposed Method.

2.1. Overview. A CTS consists of one or more CTSSs. A CTSS is a member of a CTS as well as of a time slot group. We presume that some of the CTSSs may work as a source of ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1981 the features of a time slot group and the others may work as noise, that is, the features of a customer: preference; habit; or properties such as age, sex, and occupation. In particular, we divide the CTS into a number of CTSSs, transform each of the CTSSs into images to simplify the information, and then input the images to a self-organizing map (SOM) [5] to classify the images across the boundaries among diﬀerent customer properties. Thus, we attempt to classify CTSSs into two groups and discover new knowledge that has not been obtained before; that is, the features of a time slot group are formed by a number of CTSSs, each of which belongs to diﬀerent CTSs. We use a part of the trajectory database recorded by using RFID at one of the in-city supermarkets in Japan by a data mining research group [4]. They attached RFID tags to each of the carts and attached receivers at several places in the storeroom so that they could record every single change in the customer trajectories from the customers’ arrival to check out.

2.2. Deﬁnitions.

2.2.1. Time slots and time slot groups. The store hours of the supermarket are 9:00 to 23:00. We have divided this time range into intervals of an hour each and called these intervals “time slots”. There are a number of CTSSs in one time slot. We define a set of CTSSs in one time slot as “a time slot group”. Each of the CTSSs is one of the constituents of a time slot group as well as of the CTS. CTSSs represent the features of the corresponding time slot when they are treated as members of a family, that is, a time slot group. The results of a preliminary analysis of the hourly sales amount in this supermarket showed that the sales amount changed each hour. The lowest value appears in the time slots of 9:00 and 23:00, hereinafter represented as “TS9” and “TS23”, and the highest values are observed in TS17. There are two peaks in sales amount; in TS11 and in TS17. From another preliminary analysis, we found that the mean sojourn time of the customers in daytime is tend to be longer than that of the ones in night time even if the customers visited the supermarket on different days. Therefore, we presume that there are some time-sensitive differences in customer behavior.

2.2.2. Trajectory components. The CTS provides information related to which parts of the shop ﬂoor a customer visited and to which part he/she moved next and how long he/she stayed at each of the parts. A CTS consists of a number of “trajectory components”, each of which represents a part of a customer behavior, such as the part of the customer, state (suspension or migration), or duration of the state recorded by RFID. A CTS of customer Cc in TSTh is represented as { }

Cc(Th) = p1(x1, y1, s1, d1), ··· , pl(xl, yl, sl, dl), ··· , pLc (xLc , yLc , sLc , dLc ) . (1) Th Th Th Th Th where, p (x , y , s , d ) (1 ≤ l ≤ Lc ) is a trajectory component, which is a part of C (T ), l l l l l Th c h and Lc is the number of trajectory components. p(x, y, s, d) is the minimum unit of Th information recorded by RFID and consists of the coordinate values of x and y that indicate a customer’s part in the storeroom, and d represents the duration of one of the two states: migration (Mig.) or suspension (Sus.), represented as s.

s ∈ {0, 1} (2) where 0 indicates Mig. and 1 indicates Sus.

2.3. Detailed procedures. 1982 A. OHNO, T. INAMOTO AND H. MURAO

2.3.1. Preparation. We divide all CTS data per hour to form the time slot groups Th(h ∈ H := {9, 10, ··· , 23}). Each time slot group consists of a set of CTSSs that belong to different customers. If one CTS belongs to more than two time slots, we treat the instances as different CTSs that belong to different time slots. For example, a customer c c Cc(c ∈ C := {1, ··· ,N }, N is the number of customers) has been in the store from 10:50 AM to 11:05 AM, and his/her trajectory sequence Cc(Th) is divided into two sequences; the former sequence is treated as a set of trajectory components Cc(T10) that is a member of Call(T10), and the latter is Cc(T11), a member of Call(T11). Here, Call(Th) denotes the c maximum number of customers in Th and 0 ≤ c ≤ all ≤ N , all ∈ C. Then, we divide Cc in Th into a number of sub sequences by a constant tp(1 ≤ tp) tp is decided on the basis of the mean sojourn time of a set of CTS data. In this paper, we define tp = 12s.

2.3.2. Generation of input images. In order to classify the constituents of Cc(Th), we first divide Cc(Th) into a number of CTSSs. Cc(Th) discretized by a constant tp is represented as { } ··· ··· i Cc(Th) = Cc(Th)1, ,Cc(Th)i, ,Cc(Th)Nc (3) i Here, Cc(Th)i is an i-th CTSS of Cc(Th), and Nc is the number of CTSSs. A CTSS is formed as a unit of a number of trajectory components within tp seconds to generate a number of images that represent information as the constituents of a CTS. A CTSS C (T ) consists of trajectory components pc,i(x , y , s , d ) and is represented as c h i { l l l l l } c,i ··· c,i ··· c,i Cc(Th)i = p1 (x1, y1, s1, d1), , pl (xl, yl, sl, dl), , pL (xL, yL, sL, dL) (4) c,i Here, L is the number of trajectory components, and pl (xl, yl, sl, dl) is the state of a customer at the l-th trajectory component in a CTSS; (x, y), a pair of coordinate values, indicates the customer’s part; sl indicates a state at the time, Mig. and Sus. are represented as 0 or 1, respectively; and dl indicates the duration of the state. Next, we calculate c,i c,i c,i c,i the amount of displacement δ1,l(dxl , dyl ) from the starting part (x1 , y1 ) recorded as c,i the trajectory component p1 (x1, y1, s1, d1) at the top of the CTSS Cc(Th)i to the coordi- c,i c,i c,i nate (xl , yl ) representing the part of pl (xl, yl, sl, dl) by the following equation and use c,i c,i it as the coordinate value of (xl , yl ). c,i c,i − c,i c,i c,i − c,i dxl = xl x1 , dyl = yl y1 (5) c,i c,i We reset the coordinate value of the starting point (x1 , y1 ) to (0, 0). Then, we plot c,i c,i the relative coordinate value (xl , yl ) as a dot√ if sl = 0 and as a circle if sl = 1 on the 2 i-th image. The size of a circle is the value of (sl) . All dots and circles except the one c,i c,i on the starting part are connected to the ones on the previous parts (xl−1, yl−1). Each of the dots and circles is represented in a different color according to the position it is included in. c,i c,i The size of the image generated from a CTSS depends on the value of dxl , dyl . Here, c,i ∈ {− ··· } c,i ∈ {− ··· } we define this value to be dxl 300, , +300 , dyl 300, , +300 , and the resulting image size is 601 * 601 pixels.

3. Experiment. 3.1. Settings. A set of customer trajectory data is saved as an XML database, and each of the data can be identiﬁed by customer IDs, the recorded time, and the recorded dates. We simpliﬁed the original data to a set of CTS for this study as shown in Figure 1. Each of the lines represents a customer trajectory component that consists of the following information: customer ID, recorded time, p(x, y, s, d) that are the coordinate values of x and y representing the parts, “areas” represent the labels for parts, “s” refers to the states, and “d” are duration times. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1983

Figure 1. Example of simpliﬁed trajectory data Table 1. Properties of input data

Customer ID time slot group sojourn time 1 TS10 10:09:38 to 10:23:30 2 TS10 10:11:19 to 10:31:28 3 TS17 17:02:05 to 17:14:53 4 TS17 17:02:39 to 17:10:48

Figure 2. Examples of input images

As input data for this experiment, we use the CTS data of four customers in TS10 and TS17 on the same day, as listed in Table 1. We divide all CTSs into a number of CTSSs and transform them into images to make a set of images representing one CTS. Each column of the table shows the information of the input data: the customer ID of the CTS, the time slot to which the CTS belongs, and the sojourn times. Figure 2 shows the examples of the input images generated from the CTSSs of C1(T10) and C3(T17). 3.2. Results. Figures 3 and 4 show the result of SOM classiﬁcations. In Figure 3, the CTSS of customer 1 labeled as C1(T10) and that of customer 2 labeled as C2(T10) exhibit some similarities such as a small cluster at the bottom-left of the map. The map is divided into two large clusters by diagonal lines starting from the top-left and ending at the bottom-right of the map. In Figure 4, we also ﬁnd some similarities such as small clusters at the bottom-right corners of the maps and some clusters at the top and bottom of the maps. These maps are also divided into two large clusters by diagonal lines starting from the bottom-left corner of the maps and ending at the top-right corner.

4. Conclusion. We proposed a new method for the customer trajectory analysis. In the proposed method, we treat CTSSs as a member of the time slot group that works as the resources of the features of each of the time slots. There have been very few studies analyzing this type of data and focusing on the features of the time slot group. In this paper, we clustered the images generated from the CTSSs that are part of a CTS recorded by using RFID at one of the supermarkets. From the result of the fundamental 1984 A. OHNO, T. INAMOTO AND H. MURAO

Figure 3. Results of SOM classiﬁcations. Input images are generated from CTSSs of customer 1 (TS10), customer 2 (TS10), respectively.

Figure 4. Results of SOM classifications. Input images are generated from CTSSs of customer 3 (TS17), and customer 4 (TS17), respectively. experiment, the proposed method seemed to have the potential of discovering a new type of knowledge by classifying CTSSs by SOM. The goal of the study is to classify CTSSs into two groups: the ones that work as sources of information that are essential to form the features of each of the time slots and the others that work as sources of the features of each of the customers that we treat as noise in this study. As our future work, we plan to conduct further experiments with a large-scale data set, classify a number of time slot groups in different SOMs, and compare the results to discover the typical tendency of CTSSs that appear in specific time slots. Acknowledgment. We would like to express our sincere gratitude to Prof. Yada for providing us with the customer trajectory data and insightful comments to authors.

REFERENCES [1] M. J. A. Berry and G. Linoﬀ, Data Mining Techniques: For Marketing, Sales, and Customer Support, Wiley, 1997. [2] K. Ahsan, H. Shah and P. Kingston, RFID applications: An introductory and exploratory study, International Journal of Computer Science Issues, vol.7, no.3, pp.1-7, 2010. [3] J. S. Larson, E. T. Bradlow and P. S. Fader, An exploratory look at supermarket shopping paths, Internal Journal of Research in Marketing, vol.22, pp.395-414, 2005. [4] K. Yada, String analysis technique for shopping path in a supermarket, Journal of Intelligent Infor- mation Systems, http://www.springerlink.com/content/021821100p670473/, 2010. [5] T. Kohonen, Self-Organizing Maps, Springer-Verlag Berlin Heidelberg, 1995. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1985-1990

INTERFACE CIRCUIT FOR SINGLE ACTIVE ELEMENT RESISTIVE SENSORS

Amphawan Julsereewong1, Prasit Julsereewong1, Tipparat Rungkhum1 Hirofumi Sasaki2 and Hiroshi Isoguchi3 1Faculty of Engineering King Mongkut’s Institute of Technology Ladkrabang Ladkrabang, Bangkok 10520, Thailand { kcamphaw; kjprasit }@kmitl.ac.th; [email protected] 2Professor Emeritus Tokai University 9-1-1, Toroku, Kumamoto 862-8652, Japan [email protected] 3Kumamoto Prefectural College of Technology Kikuyou-machi 869-1102, Japan [email protected] Received February 2010; accepted April 2010

Abstract. This article presents an effective method to realize interface circuit for single active element resistive sensors. The realization is composed of op-amp in conjunction with current conveyors. Surpassing the previous circuit using only single current conveyor, the proposed configuration affords significant improvement in accuracy. PSPICE simulation results are used to confirm the performance of the proposed circuit. Keywords: Interface circuit, Resistive sensor, Single active element, Linearization, Cur- rent conveyor, Op-amp

1. Introduction. Resistive sensors are commonly used to measure physical quantities such as pressure, force, strain, temperature, and fluid flow. Their interface circuits are usually realized as bridge configuration. A conventional voltage-mode Wheatstone bridge (VMWB) as shown in Figure 1(a) is widely used to measure small resistance changes [1]. It can be arranged in a quarter (single-element varying), half (two-element varying), or full (all-element varying) configuration based on the number of bridge arms including sensitive elements. In order to improve the VMWB, a current-mode Wheatstone bridge (CMWB) as shown in Figure 1(b) has been reported [2]. Three major advantages of this approach over the traditional VMWB are reducing bridge elements, summation of sensors’ effects, and common mode cancellation. Table 1 summarizes output signals of both traditional VMWB and CMWB in single-element and all-element varying configurations. If the bridge is balanced at a known point (R0), the amount of deviation from the balanced condition (4R), as indicated by output signal, indicates the amount of change in the parameter being measured. It can be seen that for single-element varying case the resulting outputs of both bridges are nonlinear function of the ratio 4R/R0. Therefore, a linearization technique is required in the case where only one resistor is sensitive to the variation of measured parameter. In current-mode, the linearization circuit based on second generation current conveyor (CCII) has been proposed [2]. Unfortunately, an accuracy of the linearization circuit is limited by the equivalent resistance at input port X (Rx) of the CCII. In this article, the circuit method to improve the linearization circuit as proposed by [2] is described. The high loop gain of an op-amp can be utilized to minimize the limitation

1985 1986 A. JULSEREEWONG, P. JULSEREEWONG, ET AL. caused by Rx of the CCII, when the op-amp works in conjunction with the CCII [3]. Based on the improved linearization structure, the proposed interface circuit is realized for single active resistive sensors such as a Resistance Temperature Detector (RTD) or strain gage. It employs op-amp and CCIIs, which are easily implemented in integrated circuit form. The eﬀectiveness of the proposed conﬁguration arranged in single-element varying is evident by PSICE simulation results.

i1 'i R1 R2 Instrumen- R Current i1 i2 Current i tation 1 o V + ref v Differencing Amplifer - 1 + 'v - v2 Amp. v o i2 Circuit (gain: A ) (gain: A ) I R3 R V I 4 ref RL R2

(a) conventionalI VMWB (b) CMWB [2]

Figure 1. Bridge conﬁgurations

Table 1. Output signals of traditional VMWB and CMWB

Conﬁguration Traditional VMWB CMWB conditions output conditions output ∓4R ±4R Single-element R1 = R2 = vo = ( )AV Vref R1 = R0 io = ( )AI Iref 4R0±24R 2R0±4R varying R3 = R0 and R2 = and R4 = R0 ± 4R R0 ± 4R ±4R ±4R All-element R1 = R4 = vo = ( )AV Vref R1 = io = ( )AI Iref R0 R0 varying R0 ∓ 4R R0 ∓ 4R and and R2 = R2 = R3 = R0 ± 4R R0 ± 4R

2. Circuit Descriptions. CCII is one of versatile building blocks in analog circuit design [4]. Basically, the CCII as shown in Figure 2 is a three-port active element, whose characteristics can be described by the following matrix equation,       iy 0 0 0 vy       vx = 1 0 0 ix (1) iz 0 ±α 0 vz where the plus and minus signs of the current transfer ratio α(= 1 − εi, εi is the current transfer error from port X to port Z) denote a positive CCII (CCII⊕) and a negative CCII (CCIIΘ), respectively. To examine the performance of the CCII-based linearization circuit as shown in Figure CC CC 3, the eﬀects of its non-idealities such as εi, Rx, and Voff are studied, where Voff denotes an oﬀset voltage produced at port X when vy = 0. By using routine circuit analysis, the output current i is related to the reference current I by o ( ref ) − − − CC (R1 R2 Rx)Iref Voff io = (1 − εi) (2) R2 + Rx ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1987

From (2), it is evident that Rx is one of major factors that contribute to an inaccuracy of the circuit as shown in Figure 3.

Y v y iy CCII Z v X iz z vx ix

Figure 2. Circuit symbol of the CCII

Iref

R1 Y io R CCII + Z 2 Rx X

Iref

Figure 3. Practical linearization circuit based on the equivalent circuit of CCII [2]

R 10kȍ Iref b

Vcc Vss ȍ R1 Ra 100k + v Ioff y1 Y i A1 z1 - CCII + Z X i v 1 1 o x i X x2 CCII - 2 Z vo R2 Rx Y Buffer ix1 R3

Iref

Figure 4. Proposed interface circuit for single active element resistive sensors

To minimize the error due to Rx of the CCII, the proposed interface circuit uses op- amp A1 and CCII⊕1 in a hybrid configuration as shown in Figure 4. Both input ports of CCII⊕1 are placed in the negative feedback loop of A1. The high loop gain of A1 ensures that the current ix1 does not depend on Rx. The presence of the resistors Ra = 100 kΩ and Rb = 10 kΩ is there to balance the bridge before measurements are taken by altering the balance of current at port X of CCIIΘ2. From routine circuit analysis, io can be stated as ( ) − − opamp (R1 R2)Iref Voff io = (1 − εip)(1 − εin) (3) R2 where εip and εin are the current transfer errors of CCII⊕1 and CCIIΘ2, respectively, and opamp Voff is an offset voltage of A1. It can be seen that Rx is neglected by the high loop gain of A1. In addition, a small current Ioff can be added or subtracted from the virtual earth opamp input of CCIIΘ2. This means that Voff can be cancelled by an appropriate external current applied by varying Rb. Then after the offset value correction, io can be rewritten as ( ) R1 − R2 io = (1 − εip)(1 − εin) Iref (4) R2 1988 A. JULSEREEWONG, P. JULSEREEWONG, ET AL. Considering at output terminal, the buffered output voltage v can be given by ( )o R1 − R2 vo = R3io = (1 − εip)(1 − εin) R3Iref (5) R2 In practice, when available IC AD844 providing a buffered output terminal is used as the CCII, thus vo can be easily obtained without any additional circuitry. Moreover, R3 is utilized as a gain control resistor. This implies that the gain error caused by εip and εin can be compensated by slightly tuning R3. Then after the gain error correction, the final output value is ( ) R1 − R2 vo = R3Iref (6) R2 In single-element varying configuration, conditions of the elements are R1 = R0 ± 4R and R2 = R0, thus vo can be expressed as 4R vo = ± R3Iref (7) R0 From (7), it is apparent that the output voltage is linearly related to 4R. Therefore the proposed interface circuit as shown in Figure 4 can be used for single active resistive sensors such as RTD or strain gage. For 4R = 0, the output can be balanced by adjusting Rb accordingly until the output is equal to zero.

3. PSPICE Simulation Results. To verify the operational characteristic of the proposed circuit in comparison with the previous circuit in [2], the schemes in Figure 3 and Figure 4 were simulated by PSPICE program. The AD844 and LF358 devices were used as CCIIs and op-amps, respectively. Simulations were carried out for RTD and strain gage types of single active element resistive sensors [5]. To mimic the action of the platinum RTD producing a positive change in resistance for a positive change in temperature [6], a nominal value of 100 Ω (Pt100) was assumed for R0, and Iref = 1 mA and R3 = 1 kΩ were chosen in order to set the gain factor to 1. The measured results for a temperature variation from –50 ◦C to 150 ◦C, in steps of 10 ◦C are plotted in Figure 5. From Figure 5(a), it is evident that the results of the proposed circuit agree well with the calculated values with a maximum variation less than 0.6%, whereas the results from [2] show a maximum variation more than 30%. It is obvious that the accuracy improvement of measuring resistance changes can be achieved using the proposed realization method. Figure 5(b) displays the results of the proposed circuit without compensation and its linear regression. The nonlinearity errors measured using a best fit straight-line for absolute minimum squared error are approximately equal to zero. It is shown that using the proposed interface circuit provides the linear dependence of output voltage versus resistance variation. In the case of simulation for measuring small resistance changes in strain gage, the nominal value of 120 Ω was assumed for R0 and the resistance was allowed to vary by no more than 1%, where Iref = 1 mA and R3 = 50 kΩ were chosen in order to set the gain factor to 50. The measured results obtained are shown in Figure 6, where the resistance variation ratio x = 4R/R0. It can be observed that the output of the circuit in Figure 3 [2] includes the small offset and large gain errors whereas the output of the proposed circuit without compensation includes the large offset and very small gain errors. However, reducing offset and gain errors in the output of the proposed interface circuit can be easily done by supplying the small current Ioff and slightly adjusting the gain R3, respectively.

4. Conclusions. The interface circuit using op-amp and CCIIs has been described in this article. The proposed circuit is perfectly suitable for single active element resistive sensors. By comparing the proposed circuit with the previous resistance bridges arranged in single-element varying, the following advantages can be achieved. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1989

600

500 - - - Ideal x x x Circuit in Figure 3 [2] 400 o o o Proposed Interface Circuit ) V m

( 300

e g a t l

o 200 V

t u p t

u 100 O

-100

-200 -50 -25 0 25 50 75 100 125 150 Input Temperature (Deg. C) (a) Outputs from the circuit in [2] and the proposed circuit versus input temperature

-3 x 10 750 1

500 0.5 )

) Output Voltage % V (

m r (

Nonlinearity Error o r e r g E a

t l y t o

250 0 i r V a

t e u n i p l t n u o O N 0 -0.5

-250 -1 -50 -25 0 25 50 75 100 125 150 Input Temperature (Deg. C) (b) Outputs from the proposed circuit without compensation and nonlinearity error versus input temperature

Figure 5. Results of simulation for RTD Pt100

600 ______Ideal 400 --*----*-- Circuit in Figure 3 [2] --x----x-- Proposed Circuit (No compensation) + + + Proposed Circuit (Offset compensation) )

V 200 o o o Proposed Circuit (Offset and Gain compensations) m (

e g a t l

o 0 V

t u p t u

O -200

-400

-600 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x (%)

Figure 6. Results of simulation for 120 Ω strain gage 1990 A. JULSEREEWONG, P. JULSEREEWONG, ET AL. (1) reducing bridge elements in comparison with the traditional VMWB (2) linear characteristic in comparison with the traditional VMWB and CMWB (3) better accuracy in comparison with the linearization circuit as proposed in [2] (4) ease of balance the bridge before measurements (5) ease of oﬀset and gain error compensations PSPICE simulation results in excellent agreement with the theoretical values have been obtained.

REFERENCES [1] T. L. Floyd, Electric Circuits Fundamentals, Pearson Education International, New Jersey, 2004. [2] S. J. Azhari and H. Kaabi, AZKA cell, the current-mode alternative of wheatstone bridge, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol.47, no.9, pp.1277-1284, 2000. [3] S. J. G. Gift, Hybrid current conveyor-operational amplifier circuit, Int. J. of Electron., vol.88, no.12, pp.1225-1235, 2001. [4] A. Julsereewong, V. Riewruja, H. Sasaki, K. Fujimoto and M. Yahara, A negative proportional characteristic VCO using CCIIs and NAND RS-flip flop, ICIC Express Letters, vol.2, no.1, pp.35-40, 2008. [5] NJATC, Fundamental of Instrumentation, Delmar Cengage Learning, United States of America, 2008. [6] ASTM, Annual Book of ASTM Standards, vol. 14.03 Temperature Measurement, United States of America, 1998. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1991-1996

ANALYTIC SOLUTION OF SHOCK WAVES EQUATION WITH HIGHER ORDER APPROXIMATION

Valentin A. Soloiu1, Marvin H.-M. Cheng2 and Cheng-Yi Chen3 1School of Science and Technology Georgia Southern University PO Box 8045, Statesboro, GA 30460, USA [email protected] 2Department of Mechanical and Aerospace Engineering West Virginia University PO Box 6070, Morgantown, WV 26506, USA [email protected] 3Department of Electrical Engineering Cheng-Shiu University 840, Chengcing Rd., Niaosong Township, Kaohsiung County 833, Taiwan [email protected] Received February 2010; accepted April 2010

Abstract. The advection equation has been investigated by using lower order finite- difference numerical schemes based on the control volume method. This paper aims to develop an efficient approximation method with higher order terms. The proposed mathematical model is proved to be time efficient and is capable to provide smooth output. The simulation results have been compared with the approximation schemes proposed by other researchers. Keywords: Control volume method, Wave propagation, Shock wave

1. Introduction. Conservation laws are common features of individual theories of con- tinuum physics. The laws are supplemented by constitutive relations which characterize the particular medium in question by relating the values of the main vector field to the flux field. Assume that these relations are expressed by smooth forms, and consequently the conservation laws lead to nonlinear hyperbolic partial differential equations. The hyperbolic partial differential equation can be used in simulation for various phenomena, such as shock waves. The equation has been investigated widely by using finite-differences numerical schemes based on the control volume formulation with lower order terms. Shock waves occur in explosions, traffic flow, engine operations, airplanes breaking the sound barrier and so on. A lot of different research groups have investigated such a problem. Typically, they are modeled by nonlinear hyperbolic partial differential equations [1, 2, 3]. In this study, a finite difference method based on a control volume formulation is used to obtain higher order and accurate numerical schemes for integration of advection equation. The simulation results with the proposed method schemes were compared with the classical finite difference, QUICK numerical scheme, proposed by Lenoard [4].

2. Numerical Scheme with the First Order Approximation. The model hyperbolic equation is the wave equation. In one spatial dimension, that is φtt + cφxx = 0. If a ﬁrst order Taylor series expansion in x and t is applied, the hyperbolic partial diﬀerential equation can be discretized and approximated by ∂φ ∂φ + c = 0, c ∈ < (1) ∂t ∂x

1991 1992 V. A. SOLOIU, M. H.-M. CHENG AND C.-Y. CHEN where c is a constant. With the ﬁrst order backward diﬀerence approximation, the equation can be represented as

n+1 − n n φj = (1 Cr) φj + Crφj−1, (2) where Cr is the Courant number, which is deﬁned as ∆t C = c . (3) r ∆x Thus, from the upwind expansion in space and forward expansion in time, one can obtain

n+1 n n n 2 2 ∂φ ∂φ φ − φ φ − φ − ∂ φ ∆t ∂ φ ∆x + c = j j + c j j 1 − · + c · + HOT. (4) ∂t ∂x ∆t ∆x ∂t2 2! ∂x2 2! The approximation of this equation can be aﬀected by the the second partial derivative terms. That is ∂2φ ∆t ∂2φ ∆x ∂2φ 1 ϕ (x, t) = − · + c · = c · (−c∆t + ∆x) , (5) ∂t2 2! ∂x2 2! ∂x2 2 where HOT denotes the higher order terms. If the Courant number Cr is equal to 1, the second derivative terms can be eliminated since −c∆t + ∆x = 0. This yields

n+1 n n n ∂φ ∂φ φ − φ φ − φ − + c = j j + c j j 1 + HOT. (6) ∂t ∂x ∆t ∆x

If Cr is smaller than 1, ϕ (x, t) becomes a diffusion term that provides a smoother solution. Once Cr is greater than 1, ϕ (x, t) becomes antidiffusive and the calculation results accen- tuate any irregularities that exist. In other words, the approximation becomes divergent and instable when Cr is greater that 1. The dissipation of wave amplitude always occurs when Cr < 1 but the magnitude of this dissipation can be reduced by using smaller ∆x. The results of wave simulation propagation are plotted in Figure 1. However, though the diffussion term provides a stable result, the accuracy of the approximation is not satisfactory. Thus, the first order partial derivative approximation needs to be modified for better accuracy.

0.8

0.6

0.4 Amplitude

0.2

0 0 20 40 60 80 100 120 140 160 180 200 ∆ x

Figure 1. Approximation result of the first order numerical schme (Cr = 0.4,N = 900) ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1993 3. Numerical Scheme with Higher Order Approximation. The poor accuracy of the first order approximation suggests a higher order numeric model. With the numerical approximation scheme (QUICK) proposed by Leonard [4], the accuracy can be greatly improved (Figure 2). However, the numerical scheme is unstable when Cr is relatively large (Cr ' 0.5). It is only stable when the Courant number is small enough (Cr ' 0.05). However, the required amount of time steps N becomes large when Cr is too small. Therefore, a efficient and stable approximation scheme is desired.

3 3

2 2

1 1

0 Amplitude 0

Amplitude

-1 -1

-2 -2 0 20 40 60 80 100 120 0 20 40 60 80 100 120 x x (a) (b)

Figure 2. Approximation result using QUICK scheme (a) Cr = 0.5,N = 200; and (b) Cr = 0.05,N = 900

3.1. Finite diﬀerence approximation. To provide a better approximation, an iteration approach method is used in this section. In the case of one-dimensional convection equation with c as constant in Equation (1), the conservative control volume formulation can be written as

∂φ ∂ (cφ) = − (7) ∂t ∂x

n For the control volume centered at ∆x/4 left from φi , the diﬀerence grids of the higher order expansion scheme is shown as Figure 3, where n denotes the nth time step. By integrating Equation (7) from left boundary to right boundary of the control volume, we obtain ∫ ∫ r ∂φ r ∂ (cφ) dx = − dx. (8) l ∂t l ∂x

This equation can be approximated by ﬁnite diﬀerence grids with the following equation [5]. That is

n+1 − n − n − n φi φi = Cr (φr φl ) . (9) 1994 V. A. SOLOIU, M. H.-M. CHENG AND C.-Y. CHEN

t x 4

n 1 n 1 n 1 n 1 n 1 i 2 i 1 i i 1 i 2

n n n n n n i 2 i 1 i i 1 i 2 x

n n l r

Figure 3. Partition grids of the nth time step

The equation of the finite difference method can be further expanded to ( ) ( ) ( ) ∆x ∂φ n 1 ∆x 2 ∂2φ n n n − r r φi = φr + 2 4 ∂x i+ 1 2! 4 ∂x i+ 1 ( ) ( 4) 4 3 3 n − 1 ∆x ∂ φr 3 + HOT, (10) 3! 4 ∂x i+ 1 ( ) 4 ( ) ( ) n 2 2 n n n 3∆x ∂φr 1 3∆x ∂ φr φi+1 = φr + + 2 4 ∂x i+ 1 2! 4 ∂x i+ 1 ( ) ( 4) 4 3 3 n 1 3∆x ∂ φr + 3 + HOT. (11) 3! 4 ∂x 1 i+ 4 By combining these two equations, the value of the function at the right boundary of the control volume can be obtained, which is ( ) 3φn + φn 3 ∂2φ n n i i+1 − r 2 φr = 2 ∆x + HOT. (12) 4 32 ∂x 1 i+ 4 If the difference grids are expanded to i − 1 and i + 2, the difference terms become ( ) ( ) ( ) 5∆x ∂φ n 1 5∆x 2 ∂2φ n n n − r r φi−1 = φr + 2 + HOT, (13) 4 ∂x i+ 1 2! 4 ∂x i+ 1 ( ) 4 ( ) ( ) 4 7∆x ∂φ n 1 7∆x 2 ∂2φ n n n − r r φi+2 = φr + 2 + HOT, (14) 4 ∂x 1 2! 4 ∂x 1 i+ 4 i+ 4 which yield −7φn + 105φn + 35φn − 5φn φn = i−1 i i+1 i+2 . (15) r 128 The same approach can be applied to obtain the value of the function at the left boundary of the control volume. That is −7φn + 105φn + 35φn − 5φn φn = i−2 i−1 i i+1 . (16) l 128 Thus, the value of each point within the grids between the left and right boundaries can be derived, C ( ) φn+1 = φn − r 7φn − 112φn + 70φn + 40φn − 5φn . (17) i i 128 i−2 i−1 i i+1 i+2 ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1995 3.2. Simulation results. During the simulation, a square wave is used as the input signal. The magnitude of this signal starts from 0 and the amplitude is 1. To evaluate the performance of different Cr, several criteria are used. The terminology of these criteria used in the simulation is illustrated in Figure 4. The wave jump represents the period required for the signal jump from 0% to 99% of the amplitude. Wave dimension is defined as the total period of the wave form that jumps from 0% to 100% then return to 0%. The wave vibration amplitude represents the diffence between the maximum and minimum overshoots. Figure 5 demonstrates the simulation results of Cr = 0.4 and Cr = 0.5. Clearly, the propagation speed of Cr = 0.5 is faster than Cr = 0.4. The shape of the wave form is altered due to the accumulation of higher order harmonics.

Wave vibration amplitude

Wave jump

Wave dimension

Figure 4. Proﬁle of a shock wave after approximation

C = 0.4 1.2 r C = 0.5 1 r 0.8 0.6 0.4 Amplitude 0.2 0 −0.2 −0.4 0 20 40 60 80 100 120 140 160 180 200 x

Figure 5. Simulation results of the shock waves with Cr = 0.4 and 0.5

Figure 6 illustrates the comparisons of wave jumps, wave vibration amplitudes, and wave dimensions between Cr = 0.4 and 0.5. In Figure 6(a), it is clear that higher Cr yields steeper jumps. The wave dimension also increases as the step time increases (Figure 6(c), which implies that the approximation has clearer diﬀusion phenomenon with lower Courant numbers. However, from Figure 6(b), the wave vibration amplitudes change from a decreasing asymptotic trend to an increasing one as Cr increases. Such changes make the diﬀusive approximation to an antidifussive behavior. Therefore, a numerical analysis is required to derive the appropriate Courant number for fast, smooth, and accurate output. With the method proposed in this study, Cr is suggested to be 0.46 for stable and smooth approximation outputs. Figure 7 demonstrates the comparison of the approximation output between Lenoard’s QUICK scheme and the proposed method. The proposed method demonstrates a better capability to provide a more stable and smooth result. 1996 V. A. SOLOIU, M. H.-M. CHENG AND C.-Y. CHEN

20 0.4 75

70 15 0.3 65

10 0.2 60 C = 0.4 r Wave jump C = 0.5 55 r 5 C = 0.4 0.1 C = 0.4 r r Wave vibration amplitude Wave vibration amplitude 50 C = 0.5 C = 0.5 r r 0 0 45 0 200 400 600 0 200 400 600 0 200 400 600 Time steps Time steps Time steps (a) (b) (c)

Figure 6. Comparison of the performance of Cr = 0.4 and 0.5 with (a) wave jump; (b) wave vibration amplitude; and (c) wave dimension

QUICK proposed by Leonard 1.2 Iteration method proposed 1

0.8

0.6

Amplitude 0.4

0.2

−0.2 0 20 40 60 80 100 120 140 160 ∆ x

Figure 7. Comparison between Leonard’s method and proposed approximation method

4. Conclusions. The numerical scheme proposed in this study demonstrats the capability to capture the shape of the shock waves even with very steep conﬁgurations. This numerical approximation scheme also proves to be more stable for higher Cr numbers than the QUICK method proposed by Leonard. With Cr close to 0.5, it is clear that the proposed numerical scheme performs better in the aspect of vibration than Leonard’s scheme. However, this method includes more numerical diﬀusion for high number of time steps. More studies are required for more accurate simulation results for shock wave propagation. Acknowledgment. The authors gratefully acknowledge the contribution and helpful comments of Mr. M. Todorescu.

REFERENCES [1] F. M. Allan and K. Al-Khaled, An approximation of the analytic solution of the shock wave equation, Journal of Computational and Applied Mathematics, vol.192, no.2, pp.301-309, 2006. [2] J. Behrens, Atmospheric and ocean modeling with an adaptive ﬁnite element solver for the shallow- water equations, Applied Numererical Mathematics, vol.26, no.1-2, pp.217-226, 1998. [3] A. Bermudez and M. Elena Vazquez, Upwind methods for hyperbolic conservation laws with course terms, Computational Fluids, vol.23, pp.1049-1071, 1994. [4] B. P. Leonard, A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Computer Methods in Applied Mechanics and Engineering, vol.19, no.1, pp.59-98, 1979. [5] K. Nishiwaki, Advanced Heat Transfer and Fluid Dynamics, Ritsumeikan University, Kyoto, Japan, 1995. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 1997-2001

FUZZY OPINION SURVEY BASED ON INTERVAL VALUE

Lily Lin1, Huey-Ming Lee2 and Jin-Shieh Su3

1Department of International Business China University of Technology 56, Sec. 3, Hsing-Lung Road, Taipei 116, Taiwan [email protected]

2Department of Information Management 3Department of Applied Mathematics Chinese Culture University 55, Hwa-Kung Road, Yang-Ming-San, Taipei 11114, Taiwan { hmlee; sjs }@faculty.pccu.edu.tw Received February 2010; accepted April 2010

Abstract. In this study, we propose a fuzzy group opinion survey analysis based on interval value to do aggregated assessment analysis, apply signed distance method to defuzzify the aggregative assessment. Since the proposed model answered with interval value not a point value agrees with the human thinking, the ﬁnal value is more appropriate, objective and unbiased than just the point value assessment. Keywords: Survey, Fuzzy logic, Linguistic variable

1. Introduction. Statistical analysis via sampling survey is a powerful market research tool to acquire the useful information. Traditionally, we compute statistics with sample data by questionnaires according to the thinking of binary logic. But, this kind of result may lead to an unreasonable bias since the human thinking is full with fuzzy and uncertain. After fuzzy sets theory was introduced by Zadeh [10] to deal with problem in which vagueness was present, linguistic value could be used for approximate reasoning within the framework of fuzzy sets theory [11] to eﬀectively handle the ambiguity involved in the data evaluation and the vague property of linguistic expression, and normal triangular fuzzy numbers are used to characterize the fuzzy values of quantitative data and linguistic terms used in approximate reasoning. Lee and Chiang [1] applied signed distance to solve the optimal solution of the production inventory model in the fuzzy sense. Lin and Lee [2,3,5] applied a value m which belongs to the closed interval [0, 1] to represent the reliability or membership grade in the fuzzy sense of marking item and presented the fuzzy sense on sampling survey to do aggregated assessment analysis. In [4], Lin and Lee analyzed sampling survey answered by interval value. Lin and Lee [6] presented two comprehensive algorithms for group assessment with the linear order fuzzy linguistic to do aggregative assessment analysis. Shieh et al. [7] used the interval-value fuzzy sets to evaluate the International Joint Ventures. Shieh et al. [8] applied fuzzy genetic algorithms to solve a fuzzy inventory with backorder. In this study, we propose a fuzzy group assessment analysis for sampling survey based on interval values. The proposed fuzzy evaluation algorithm is easy to do the aggregative evaluated score on each main item and the aggregative score.

2. Preliminaries. For the proposed algorithm, all pertinent deﬁnitions of fuzzy sets are given below [9-12].

1997 1998 L. LIN, H.-M. LEE AND J.-S. SU Definition 2.1. If X is a collection of objects denoted generically by x then a fuzzy set A˜ in X is a set of ordered pairs: ˜ { | ∈ } A = (x, µA˜(x)) x X (1) ˜ µA˜(x) is called the membership function of x in A which maps X to the closed interval [0, 1] that characterizes the degree of membership of x in A˜. Definition 2.2. Triangular Fuzzy Numbers: Let A˜ = (p, q, r), p < q < r, be a fuzzy set on R. It is called a triangular fuzzy number, if its membership function is  x−p ≤ ≤  q−p , if p x q µ (x) = r−x , if q ≤ x ≤ r (2) A˜  r−q 0, otherwise From the signed distance, d(A,˜ 0),˜ of the fuzzy set A˜ to 0˜ defined by Yao and Wu [9], we have the following propositions. ˜ ˜ Proposition 2.1. Let A1 = (p1, q1, r1) and A2 = (p2, q2, r2) be two triangular fuzzy numbers, and k > 0, then, we have 0 ˜ ˜ (1 ) A1 ⊕ A2 = (p1 + p2, q1 + q2, r1 + r2) 0 ˜ (2 ) kA1 = (kp1, kq1, kr1) ˜ ˜ Proposition 2.2. Let A1 = (p1, q1, r1) and A2 = (p2, q2, r2) be two triangular fuzzy numbers, and k ∈ R, then we have 0 ˜ ˜ ˜ ˜ (1 ) d(A1 ⊕ A2, 0)˜ = d(A1, 0)˜ + d(A2, 0)˜ 0 ˜ ˜ (2 ) d(kA1, 0)˜ = kd(A1, 0)˜ Proposition 2.3. Let A˜ = (p, q, r) be a triangular fuzzy number. Then, based on the maximum membership grade principle, we have (10) if A˜ is not an isosceles triangle, then defuzzified A˜ by the signed distance method is appropriate than by the centroid method; (20) if A˜ is an isosceles triangle, then defuzzified A˜ by the signed distance method is the same as by the centroid method. 3. Aggregative Evaluation for Fuzzy Survey with Interval Value. 3.1. Aggregative evaluation for opinion survey form. In most cases, questionnaire opinion survey consists of many subjects and questions, let’s say, main items and sub- items. For instance, one specific questionnaire regarding satisfactory level may include main survey items such as satisfactory level for product, service and price etc., also sub- items may exist under each main item. We may describe them as follows: main items: D1,D2,...,Dp with weights: a1, a2, . . . , ap, respectively ∑p subject to: 0 ≤ aj ≤ 1, j = 1, 2, . . . , p and aj = 1 j=1

sub-items: Di1,Di2,...,Dimi under main item Di, i = 1, 2, . . . , p

with weights: ai1, ai2, . . . , aimi , respectively ∑mi subject to: 0 ≤ aij ≤ 1, i = 1, 2, . . . , p; j = 1, 2, . . . , mi and aij = 1 j=1 Suppose that there are m evaluators, saying, E1,E2,...,Em, to assess the aggregative sampling survey for the main items and sub-items. Let Mijq denotes the assessment of the sub-item Dij given by the evaluator Eq. But, it is hard to determine the value of point Mijq. Therefore, we replace Mijq by the closed interval [Mijq − ∆ijq1,Mijq + ∆ijq2], where 0 < ∆ijq1 < Mijq, 0 < ∆ijq2, i.e., we use [Mijq − ∆ijq1,Mijq + ∆ijq2] to represent the assessment of the sub-item Dij given by the evaluator Eq. We describe the above as shown in Table 1. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 1999

Table 1. Contents of the proposed assessment form for the evaluator Eq

Main item Item weight Sub-item Sub-item weight Interval value D1 a1 D11 a11 [M11q − ∆11q1,M11q + ∆11q2] D12 a12 [M12q − ∆12q1,M12q + ∆12q2] ...... − D1m1 a1m1 [M1m1q ∆1m1q1,M1m1q + ∆1mq2] D2 a2 D21 a21 [M21q − ∆21q1,M21q + ∆21q2] D22 a22 [M22q − ∆22q1,M22q + ∆22q2] ...... − D2m2 a2m2 [M2m2q ∆2m2q1,M2m2q + ∆2m2q2] ...... Dp ap Dp1 ap1 [Mp1q − ∆p1q1,Mp1q + ∆p1q2] Dp2 ap2 [Mp2q − ∆p2q1,Mp2q + ∆p2q2] ...... − Dpmp apmp [Mpmpq ∆pmpq1,Mpmpq + ∆pmpq2]

3.2. Aggregative evaluation algorithm. Step 1 : In Table 1, we let 1 ∑m m = M ij m ijq q=1 1 ∑m ∆ = ∆ ijt m ijqt q=1 be the average of Mijq and ∆ijqt for these m assessed data, t = 1, 2; i = 1, 2, . . ., p; j = 1, 2, . . ., mi. Since mij ∈ [mij − ∆ij1, mij + ∆ij2], there is a triangular fuzzy number

m˜ ij = (mij − ∆ij1, mij, mij + ∆ij2) (3) corresponding to the closed interval [mij − ∆ij1, mij + ∆ij2], for i = 1, 2, . . ., p; j = 1, 2, . . ., mi. Then, we may re-write the Table 1 as Table 2.

Table 2. Contents of the main item Di represented interval value by triangular fuzzy number

Main-Item Item-weight Sub-item Sub-item-weight Triangular fuzzy number Di ai Di1 ai1 (Mi1q − ∆i1q1,Mi1q,Mi1q + ∆i1q2) Di2 ai2 (Mi2q − ∆i2q1,Mi2q,Mi2q + ∆i2q2) . . . . − Dimi aimi (Mimiq ∆imiq1,Mimiq,Mimiq + ∆imiq2)

Step 2: By the ﬁrst stage Let ˜ ⊕ ⊕ ⊕ Ni = (ai1m˜ i1) (ai2m˜ i2) ... (aimi m˜ imi ) (4) for i = 1, 2, . . . , p. 2000 L. LIN, H.-M. LEE AND J.-S. SU Defuzzify (4) by signed distance, we have ∑mi 1 ∑mi d(N˜ , 0)˜ = a m + a (∆ − ∆ ) (5) i ij ij 4 ij ij2 ij1 j=1 j=1 ˜ Then, the value of d(Ni, 0)˜ is the aggregative evaluation score of the main item Di. We ˜ let Si = d(Ni, 0),˜ for i = 1, 2, . . . , p. Step 3: By the second stage We let ∑p T = aiSi (6) i=1 Then, we have that the aggregative evaluation score is [ ] p p ∑ ∑ ∑li 1 ∑li T = a · S = a a m + a (∆ − ∆ ) (7) i i i ij ij 4 ij ij2 ij1 i=1 i=1 j=1 j=1

4. Example Implementation. Assume that there are two evaluators to assess the aggregative benefit rate of the facility site selection [3], and average of the assessed data, such as the weights of main items, weights of sub-items as shown in Table 3. Then, by the proposed algorithm as shown in Section 3, we have (1) The benefit rates of the main items, Labor, Geograph, Economic, Reward and Politics are 0.3175, 0.6225, 0.585, 0.595 and 0.51, respectively. (2) The aggregative benefit rate of the facility site selection is 0.33675.

Table 3. Contents of the example

Item Sub-itemTriangular fuzzy Main-Item Sub-item weight weight number D1: Labor 0.3 D11: Salary level 0.6 (0.1, 0.25, 0.35) D12: Manpower level 0.4 (0.3, 0.45, 0.55) D2: Geograph 0.2 D21: Usage condition level of factory 0.7 (0.5, 0.6, 0.7) D22: Nearing market level of delivery 0.3 (0.5, 0.7, 0.8) D3: Economic 0.2 D31: The index of industry production 0.4 (0.7, 0.85, 0.9) D32: The index of industry modern times 0.6 (0.25, 0.45, 0.55) D4: Reward 0.15 D41: Reward obtain level 0.6 (0.55, 0.65, 0.75) D42: Institution perform level. 0.4 (0.4, 0.5, 0.65) D5: Politics 0.15 D51: Regulatory restrictions level 0.6 (0.35, 0.5, 0.65) D52: Investment subsidy level 0.4 (0.35, 0.55, 0.65)

5. Conclusions. In this study, we propose a model to do the group assessment for opinion survey answered with interval value, and evaluating algorithm based on the signed distance method. Since the proposed model answered with interval value not a point value agrees with the human thinking, the ﬁnal value is more appropriate, objective and unbiased than just the point value assessment. Moreover, if there is only one evaluator existing, the proposed model is also appropriate to assess. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2001 Acknowledgment. The authors gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

REFERENCES [1] H.-M. Lee and J. Chiang, Fuzzy production inventory based on signed distance, Journal of Infor- mation Science and Engineering, vol.23, pp.1939-1953, 2007. [2] L. Lin and H.-M. Lee, Fuzzy assessment method on survey analysis, Expert Systems with Applications, vol.36, pp.5955-5961, 2009. [3] L. Lin and H.-M. Lee, A new algorithm for applying fuzzy set theory to the facility site selection, International Journal of Innovative Computing, Information and Control, vol.5, no.12(B), pp.4953- 4960, 2009. [4] L. Lin and H.-M. Lee, Using signed distance for analyzing sampling survey assessment answered with interval value, ICIC Express Letters, vol.3, no.4(B), pp.1185-1189, 2009. [5] L. Lin and H.-M. Lee, Evaluation of survey by linear order and symmetric fuzzy linguistics based on the centroid method, International Journal of Innovative Computing, Information and Control, vol.5, no.12(B), pp.4945-4952, 2009. [6] L. Lin and H.-M. Lee, Group assessment based on the linear fuzzy linguistics, International Journal of Innovative Computing, Information and Control, vol.6, no.1, pp.263-274, 2010. [7] T.-S. Shieh, J.-S. Su and H.-M. Lee, Fuzzy decision making performance evaluation for international joint venture, ICIC Express Letters, vol.3, no.4(B), pp.1197-1202, 2009. [8] T.-S. Shieh, J.-S. Su and H.-M. Lee, Applying fuzzy genetic algorithms to solve a fuzzy inventory with backorder, International Journal of Innovative Computing, Information and Control, vol.6, no.1, pp.229-237, 2010. [9] J.-S. Yao and K. Wu, Ranking fuzzy numbers based on decomposition principle and signed distance, Fuzzy Sets and Systems, vol.116, pp.275-288, 2000. [10] L. A. Zadeh, Fuzzy sets, Information and Control, vol.8, pp.338-353, 1965. [11] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Information Sciences, vol.8, pp.199-249, pp.301-357 (II), 1975, vol.9, pp.43-58 (III), 1976. [12] H.-J. Zimmermann, Fuzzy Set Theory and Its Applications, 2nd Edition, Kluwer Academic Publish- ers, Boston, 1991.

ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 2003-2008

CERTIFICATE OF AUTHORIZATION WITH WATERMARK PROCESSING IN COMPUTER SYSTEM

Nai-Wen Kuo, Huey-Ming Lee and Tsang-Yean Lee

Department of Information Management Chinese Culture University 55, Hwa-Kung Road, Yang-Ming-San, Taipei 11114, Taiwan { neven; hmlee; tylee }@faculty.pccu.edu.tw Received February 2010; accepted April 2010

Abstract. We propose the safe treatment of the certificate of authorization in computer system. We insert the watermark in the certificate of authorization. We set encryption data tables and use them to encrypt the combined file of the certificate of authorization and watermark to produce these files of cipher text. Both of the owner and grantee keep their encrypted files. When both sides want to confirm, we use their keys to decrypt both files. If the certificate of authorization and watermark are the same, then they are correct. The processes that the certificate of authorization is encrypted and decrypted will be safer. Keywords: Watermark, Encrypt, Decrypt

1. Introduction. Shannon [1] discussed the theory of security system in 1949. In general, the functions of security system are security, authenticity, integrity, non-repudiation, data confidentiality and accessed control [2,3]. In 1974, IBM proposed an algorithm to review. In 1977, NBS (National Bureau of Standards, U.S.A) [5,6] suggested this proposed algorithm as data encryption standard (DES). NIST (National Institute of Standards and Technology) [7,8] proposed secure hash standard (SHS). Matsui [4] proposed linear cryptanalysis to attack DES type security system. Lee [9] used the basic operations of computer to design encryption and decryption algorithm. We set encryption data table (EDT) and use it to produce cipher text. We insert EDT to cipher text. The owner and grantee information are inserted to certificate data base. When the certificate processes through encryption and decryption, it is more secure. In this study, we have the certificate of authorization with the selected watermark in both of owner and grantee. We use the different keys to encrypt the combine files to produce the different file of cipher text and keep each file in the owner and grantee sides. When we want to confirm, we use their keys to decrypt both files to get two kinds of certificate of authorization and watermark. If they are the same, they are correct.

2. The Proposed Method Description. The proposed method is to process the certificate of authorization (COA) in computer system. We insert the selected watermark to COA and print two copies to be kept in the owner and grantee sides. We combine the COA and watermark to one file. We use different keys to encrypt the combined file to produce two files of cipher text. These files are kept by owner and grantee. When we want to confirm, we decrypt two files with each key to produce two kinds of COA and watermark. If these two copies of files are the same, the certificate of authorization is true. We explain tables, database and processes as follows.

2.1. File and database.

2003 2004 N.-W. KUO, H.-M. LEE AND T.-Y. LEE 2.1.1. Build watermark (WM) data base. If we have new watermark ﬁle, we update watermark data bases as Table 1. Table 1. Watermark data base

Serial No. Length WM content

2.1.2. Build file. (1) File of the primitive certificate of authorization (COA); (2) Select watermark from watermark data base; (3) The position of watermark; (4) Combine the above two files and print two copies. The papers are kept in owner and grantee sides. The combined of COA and watermark is as Table 2. Table 2. Combined file

Certiﬁcate of Authorization. Watermark

2.1.3. Build certificate database. (1) Get the title of certificate of authorization; (2) Get the book number and date; (3) Get owner-id and password; (4) Get location code (LC) of owner; (5) Get length of encryption data table (LEDT) for owner; (6) Get grantee-id and password; (7) Get location code (LC) of grantee; (8) Get length of encryption data table (LEDT) for grantee; (9) Get length of COA; (10) Get serial number of watermark (WM); (11) We use owner-id and book number as key to create an entry in CDB (Certificate Data Base). The content of CDB is as Table 3. Table 3. Certificate data base (CDB)

Book Owner Owner LC of LEDT of Grantee Grantee LC of LEDT of Length WM Title Date Number -Id Password Owner Owner -Id Password Grantee Grantee COA No.

2.2. Process. To process certificate of authorization, we have the following operations. 2.2.1. Create COA with watermark (CCOAWWM). (1) Get the primitive certificate of authorization; (2) Select the watermark and the position of watermark first, type two copies of the certificate of authorization with watermark and are kept in the owner and grantee sides; (3) Combine the certificate of authorization and watermark to one file. Save them to symbol table; (4) Build encryption data tables (EDT) of owner and grantee; (5) Use these EDT to encrypt symbol table to produce two copies of cipher text; (6) Insert EDT to cipher text and keep the files in the owner and grantee sides; (7) Set up the entry of CDB (certificate database); (8) Get encrypted COA. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2005 2.2.2. Confirm certificate of authorization (CCOA). (1) Get the files of encrypted COA to be kept in the owner and grantee sides; (2) From owner-id and book number as key to find the entry in CDB; (3) Check each field of owner-id, password, grantee-id and password. If correct, we get LC and LEDT of owner and grantee; (4) Use location LC and LEDT of owner and grantee, we extract EDT from cipher text; (5) We use EDT to decrypt the two remaining cipher text and get two copies of COA and watermark. If they are the same then the COA is correct. 2.2.3. Delete certificate of authorization (DCOA). (1) From the owner-id and book number as key to find the entry in CDB; (2) Check each field of owner-id, password, grantee-id and password. If correct, we delete the entry in CDB. 2.2.4. Create certificate database (CCDB). (1) Use the owner-id and book number as key to find the entry in CDB. If it is existed then it is error and exit to check; (2) Input each field of owner-id, password, grantee-id and password to save in CDB; (3) Get LC and LEDT of owner and grantee and save in CDB. 2.2.5. Check certificate database (CKCDB). (1) From the owner-id and book number as key to find the entry in CDB. If it is non-exist, it is error and exit to check; (2) We list each field of owner-id, password, grantee-id, password, LC and LEDT of owner and grantee to check.

3. The Proposed Model. We present the certiﬁcate of authorization process module (COAPM) on the computer system. It contains process COA module (PCOAM) and con- ﬁrm COA module (CCOAM). COAPM module is shown in Figure 1. PCOAM processes to create, delete, list COA. CCOAM processes to check COA.

Figure 1. Framework of the proposed COAPM

3.1. Process COA module (PCOAM). PCOAM has create COA with watermark component (CCOAWMC), delete certificate of authorization component (DCOAC), create certificate database component (CCDBC) and check certificate database component (CKCDBC) is shown in Figure 2. The functions of these components are as the follows. 2006 N.-W. KUO, H.-M. LEE AND T.-Y. LEE

Figure 2. Architecture of the PCOAM

3.1.1. Create COA with watermark component (CCOAWMC). Get the primitive certificate of authorization and watermark. Build encryption data tables (EDT) of owner and grantee. Use these EDT to encrypt symbol table to produce two copies of cipher text; Insert EDT to cipher text and keep the files in the owner and grantee sides; Set up the entry of CDB (certificate database, Get encrypted COA. 3.1.2. Delete certificate of authorization component (DCOAC). We use the owner-id and book number as key to find the entry in CDB. Check each field of owner-id, password, grantee-id and password. If correct, we delete in CDB. 3.1.3. Create certificate database component (CCDBC). We use the owner-id and book number as key to find the entry in CDB. If it is existed then it is error a; Input each field of date, owner-id, password, grantee-id and password to save in CDB. Get LC and LEDT of owner and grantee and save in CDB. 3.1.4. Check certificate database component (CKCDBC). We use the owner-id and book number as key to find the entry in CDB. If it is non-exist, it is error and exit to check. We list each field of owner-id, password, grantee-id, password, LC and LEDT of owner and grantee to check. 3.2. Confirm certificate of authorization module (CCOAM). CCOAM has certificate of authorization conform component (COACC) and is shown in Figure 3. The function of CCOAM is as the follows.

Figure 3. Architecture of the CCOAM

3.2.1. COA confirm component (COACC). Get the files to be kept in the owner and grantee sides. We use owner-id and book number as key to find the entry in CDB. Check each field of owner-id, password, grantee-id and password. If correct, we get LC and LEDT of owner and grantee. Use location LC and LEDT of owner and grantee, we extract EDT from encrypted COA. We use EDT to decrypt the two remaining encrypted COA and get two copies of COA and watermark. If they are the same then the certificate of authorization is correct. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2007 4. The Processes of Producing Encrypted Certificate of Authorization. We present the encryption step and the decryption step as the following. 4.1. Encryption step. Based on Lee [9], we propose the encryption algorithm in the following steps. (1) Set symbol table (ST). Let the length of the certificate of authorization be N Characters and stored as S1S2...SN; Let the length of the watermark be W Characters and stored as S1S2...SW; Combine them to the symbol table (ST) as S1S2...SN.S1S2...SW and the length is P=N+W Characters. (2) Set encryption data table (EDT). Set fields of EDT. It contains format code (FC), direction flag (DF), number of blocks (NB), number of rotated byte (RB), left shift table (LST) and displace offset (DO). Compute the length of EDT as LEST. Store LEDT. (3) Direction change. Get DF from EDT. If DF is set, we reverse the ST to get symbol table after direction (STAD). Get NB from EDT. We insert dummy symbol to STAD and let the length of STAD is multiplier of NB. We divide STAD to NB blocks. (4) Rotate the symbol table. From the beginning block, we repeat to rotate each block left RB bytes and right RB bytes. We get the symbol table after rotation (STAR). (5) Left shift each byte. Get left shift table (LST) from EDT. The value of each half byte represens the count of left shift bit. We left shift each byte of STAR count bits. We get symbol table after shift (STAS). (6) Position exchange. Get displace offset (DO) of EDT. Extract each byte of STAS offset DO bytes and store to symbol table after extract (STAE) to end of data. Decrease DO by 1, repeat above process. Process above until DO equals to 0 and get symbol table after extract (STAE). (7) Create encrypted file. From location code, we compute location point (LP). Insert EDT to the LP of STAE. Get the encrypted certificate of authorization. 4.2. Decryption step. Decryption is the reverse of encryption. The steps of decryption are as follows: (1) Get encryption data table (EDT) from encrypted certificate of authorization; (2) Change the position of remaining data; (3) Left shift each byte of data; (4) Rotate the data; (5) Reverse the content. 4.3. Location code (LC) and location point (LP). Get the location code (LC) and the length of COA) in CDB and length of selected watermark (Let total length be LN). We set the value LP as following rules: (1) If LN >= LC then LP=LC; (2) If LN < LC then LP=mod(LC,LN). The LP is the location to insert EDT to encrypted COA. 4.4. Format code. The fields in EDT have format code (FC), direction flag (DF), number of blocks (NB), rotated byte (RB), left shift table (LST), and displace offset (DO). The FC is in the first place. The different format of EDT is depending on format code as Table 4. The length of FC, DF, NB, RB, DO are fixed. The length of LST may 2008 N.-W. KUO, H.-M. LEE AND T.-Y. LEE be variable. We compute LEST and store it to CDB. These formats are stored in the computer system and used to encrypt and decrypt. Table 4. Encryption data table format (EDTF)

FC FIELD 1, 2, 3, 4, 5 1 DF, NB, RB, LST, DO 2 DF, NB, RB, DO, LST 3 DF, NB, LST, RB, DO 4 ...

5. Conclusion. In this study, we use the basic computing operations to design these encryption algorithms. It doesn’t need any special hardware. Finally, we make some comments about this study. (1) The certificate of authorization may be any combination of letters, graphic and any other figures. (2) It is more safer, because we must know the following to do the decryption: (a) The location code of this certificate of authorization of owner and grantee; (b) The different cipher text content of format code. (3) The encryption data table is store in the cipher text. (4) The encrypted COA is kept in owner and grantee. System does not keep the files. (5) By the algorithms described in Section 4, we can set up the encryption and decryption mechanism by computers as a useful and security procedures.

REFERENCES [1] C. E. Shannon, Communication theory of security systems, Bell System Technical Journal, vol.28, pp.657-715, 1949. [2] D. Denning, Cryptography and Data Security, Addison-Wesley, 1982. [3] O. Goldreich, Foundations of Cryptography: Basic Tools, Cambridge University Press, Cambridge, 2007. [4] M. Matsui, Linear cryptanalysis method for DES cipher, Advances in Cryptology (CRYPTO090), LNCS, vol.765, pp.386-397, 1994. [5] National Bureau of Standards, NBS FIPS PUB 46: Data Encryption Standard, National Bureau of Standards, Department of Commerce, 1977. [6] National Bureau of Standards, NBS FIPS PUB 81: Data Modes of Operation, U. S. Department of Commerce, 1980. [7] National Institute of Standards and Technology (NIST), FIPS PUB 180: Secure Hash Standard (SHS), 1993. [8] National Institute of Standards and Technology (NIST), NIST FIPS PUB 185: Escrowed Encryption Standard, 1994. [9] T.-Y. Lee and H.-M. Lee, Encryption and decryption algorithm of data transmission in network security, WSEAS Trans. on Information Science and Applications, vol.3, no.12, pp.2557-2562, 2006. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 2009-2014

WEIGHTED SIMILARITY RETRIEVAL OF VIDEO DATABASE

Ping Yu Department of Information Management Chinese Culture University 55, Hwa-Kung Road, Yang-Ming-San, Taipei 11114, Taiwan [email protected] Received February 2010; accepted April 2010

Abstract. Recently, the retrieving of video database is relevant to the users’ requests. We have proposed 9DST approach to represent symbolic videos accompanying with the generation algorithms. In this paper, based on the 9DST approach, we proposed the weighted spatial-temporal similarity retrieval approach of videos. Our method deﬁnes a set of user assigned weights, based on the factors of spatial-temporal relations of object pairs in a video, in order to retrieve videos conveniently. By using the 9DST index structure to index the spatial-temporal relations of object pairs of video database and providing various criterion of similarity between videos to match user requirement, our proposed similarity retrieval algorithm has discrimination power about diﬀerent criteria. Keywords: Video databases, Similarity retrieval, 9DLT video model

1. Introduction. With the advances in information technology, videos have been pro- moted as a valuable information resource. Because of its expressive power, videos are an appropriate medium to show dynamic and compound concepts. Recently, there are many researches proposed various kinds of methods to retrieve the information of videos. The video retrieval problem is concerned with retrieving videos that are relevant to the users’ requests from a video database [1]. Over the last decade, many video indexing and retrieval systems have been proposed, for example, OVID, KMED, QBIC, VideoQ, etc. Su [2] used the motion vectors embedded in MPEG bit streams. Hsieh [3] proposed a hybrid motion-based video retrieval system to retrieve desired videos from video databases through trajectory matching. Spatial- temporal visual map (STVM) [4] defined the spatial-temporal visual similarity to rank the text-retrieval results and find new results. Snoek [5] proposed an automatic video retrieval method based on high-level concept detectors Chen [6] used the subtraction of background to automatic extract the moving objects from a video. Lee [7] minimized a cost function to measure the spatial-temporal consistency of an inpainted and the matching source blocks. Chen [8] analyzed temporal information between successive frames from extracting the change region to find the video object. To retrieve desired videos from a video database, one of the most important methods for discriminating videos is the perception of the objects and the spatial-temporal relations that exist between the objects in a video. To represent the spatial and temporal relations between the objects in a symbolic video, many iconic indexing approaches, extended from the notions of 2D string [9] to represent the spatial and temporal relations between the objects in a video, have been proposed. For example, 2D B-string, 2D C-Tree, 9DLT strings, 3D-list, 3D C-string and 3D Z-string [10]. Based on those symbolic video models, some of the retrieval methods also proposed. In this paper, we propose a new similarity approach that defines the weight set of spatial-temporal similarity of the object pairs between the videos. By providing various weights of similarity between pairs of objects in a video to match user query requirement, our proposed similarity retrieval algorithm

2009 2010 P. YU has discrimination power about diﬀerent criteria. Our proposed approach can be easily applied to an intelligent video database management system to infer integrated spatial and temporal relations similarity between videos. Table 1. The deﬁnitions of relations, codes and topologies of object pair in the 9DST Temporal Topology Operators Conditions Values / Codes P < Q E EQ (01000110)2=70 Belong P %Q BP EQ (01000111)2=71 P ]Q BP EP (10001001)2=137 Inside P %*Q BQ EP (10001010)2=138 P ]*Q BQ

Table 2. The 9 direction neighborhood areas and codes of Op in 9D-SPA [11]

Area 4: Area 3: Area 2: (00001000)2=8 (00000100)2=4 (00000010)2=2 Area 5: Area 0: MBR of Op Area 1: (00010000)2=16 (00000000)=0 (00000001)2=1 Area 6: Area 7: Area 8: (00100000)2=32 (01000000)2=64 (10000000)2=128

2. 9DLT video model. In the 9DST approach, we use the projections of objects to represent the spatial-temporal relations between the objects in a video. We propose the 9DST-string (9 Direction Spatial-Temporal string), to record the spatial-temporal information of objects and relations of object pairs respectively. In the 9DST-string, there are 13 relations between time projects, those relations can be represented by seven spatial operators whose operators, conditions and corresponding topology and code of value used in the paper are listed in Table 1, where BP and EP are the beginning point and ending point of time projection of object P . We also modify the direction codes of spatial relation between object pairs: Dpq and Dqp of 9D-SPA image model [11]. Where, Dpq (or Dqp) represents the value assigned to the directional relation between areas of objects Op and Oq with Op (or Oq) as the reference object. Suppose a video V contains n objects (O1,O2, . . ., On), The structure of 9DST-string is deﬁned as following.

Deﬁnition 2.1. The 9DST-string is a 5-tuple (Oi, Oj; TRij; Shij; SRij) where

(1) Oi and Oj is a object pair in a video; (2) TRij is the temporal topological relations between object pair of Oi and Oj; (3) Shij = {“|”} is the set of interval of shots; (4) SRij = {“|”} is the set of spatial relation of the shot Shij. For each Shij, exist one spatial relation. In the SRij contains three codes of object pair. There are two direction relation codes Dij and Dji, and one spatial topological relations code Tij, the values and corresponding codes as showing in the Tables 1 and 2; ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2011 To see how the 9DST-string works, let’s see the example video as shown in Figure 1. The corresponding 9DST-string of the video is shown in Figure 1(b).

(a) Video A contains 3 frames

(b) The corresponding 9DST-string of video A

Figure 1. Example of videos and the corresponding strings of 9DST approach

(a) The 9DST index structure (b) The 9DST index structure only of object pairs of (A, B) and (A, C) of video A

Figure 2. The 9DST index structure and example

3. The 9DST Index Structure. To reduce the search space of similarity retrieval, we propose the 9DST index structure to index the spatial-temporal relation between a pair of objects with video identifications that contain those objects and spatial-temporal relations in the video database. This indexing structure is extended from the 9D-SPA indexing structure [11] to contain spatial-temporal relations. The index structure has three levels indexs to facilitate the video similarity retrieval. The first level index contains all the object pairs of videos in the video database, the second level indexes those spatial- temporal relation of the object pair, and the third level index contains corresponding video identifications which have the spatial-temporal relation of object pairs in the second level index. In the second level index contains three linked list, global temporal relation list “GT”, spatial relation list “SR” and spatial topological relation “STR”. In the “GT” list contains the global temporal relation T ij of object pair in the video. In the “SR” list, each 2012 P. YU node presents the spatial-temporal relation of a shot that contains the direction relation Dij and Dji. In the “STR” list, each node contains the spatial topological relation of shot. The 9DST index structure is showed as in the Figure 2(a). For example, we construct the briefly structure to Video A as showing in Figure 2(b). 4. Similarity Retrieval. First of all, we define the notations used in the similarity retrieval process, then we describes the similarity between object pairs and videos, and final we propose the similarity retrieval algorithm, which uses the weighted directed graph to calculate the similarity between videos. Definition 4.1. If A and B are the object pair in video V, a spatial relation sequence DAB DAB DAB DAB DBA DBA DBA DBA SRS = SR 1,SR 2, . . ., SR n (or SRS = SR 1,SR 2, . . ., SR n) DAB DBA where SR k (or SR k) means that the spatial relation between A and B. We said DAB DBA the SRS PQ (or SRS PQ) is the spatial relation sequence between A and B in the spatial direction relation of video V .

Definition 4.2. If A and B are the object pair in video V, a temporal relation TRAB means the global temporal relation between the time-projection of object A and B in video V . The spatial relation between object A and B may change over time in the video. These changing relations will form a spatial relation sequence. Therefore, we need to compute and record the new spatial relation whenever their spatial relation changes. We already record the individual spatial relations in the 9DST index structure. Therefore, we do not infer the spatial relation of object pairs, but we need to organize the spatial relation sequence to calculate the similarity to the query video. The similarity between videos based on the spatial-temporal relations between objects in the videos, which allow a user to assign different levels of weights to the spatial and temporal relations and to calculate the similarity between videos. Assume that a pair of objects (A, B) in a video V 0 matches a pair of objects (A, B) in another video V . We use the following notations to define the spatial-temporal relations.

Deﬁnition 4.3. Given two spatial relation sequences SRS = SR1,SR2, . . ., SRn and 0 0 0 0 ≥ 0 SRS = SR1,SR2, . . ., SRm where n m > 0, if SRji = SRi, j1 < j2 < . . . < jm, for all i = 1, 2, . . ., m, we can say that SRS0 is a sub-sequence of SRS. The (A, B) is 0 D 0 D 0 called a sd-similar pair between videos V and V , if SRS AB AB and SRS BA AB both are DAB DBA the sub-sequences of SRS AB and SRS AB, respectively. Therefore, if (A, B) is a sd-similar pair, the similarity of SimSDS is equal to 1; otherwise, it is equal to 0. Deﬁnition 4.4. If A and B are the object pair in video V , a spatial topological sequence is a sequence of ST1,ST2, . . ., STn, where STi is the topological relation of the ith spatial relation between A and B. STSAB is the spatial topological sequence between A and B of video V .

Definition 4.5. Given two spatial topological sequences STS = ST1,ST2, . . ., STn and 0 0 0 0 ≥ 0 STS = ST1,ST2, . . ., STm where n m > 0, if STji = STi , j1 < j2 < . . . < jm, for all i = 1, 2, . . ., m, we can say that STS0 is a sub-sequence of STS.(A, B) is called 0 0 a spatially st-similar pair between videos V and V , if STSAB is the sub-sequences of STS STSAB. Therefore, if (A, B) is a spatially st-similar pair, the similarity of Sim is equal to 1; otherwise, it is equal to 0. 0 Definition 4.6. Let TTRAB and TTRAB be the temporal topological relations of object A and that of object B in video V 0 and V ,(A, B) is called a temporally tt-similar pair 0 0 between videos V and V , if the first four bits of TRAB equal to the first four bits of TRAB. Therefore, if (A, B) is a temporally tt-similar pair, the similarity of SimTT is equal to 1; otherwise, it is equal to 0. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2013

0 Definition 4.7. Let TRAB and TRAB be the temporal relations of object A and that of object B in video V 0 and V ,(A, B) is called a tr-similar pair between videos V 0 and V , if 0 TR TRAB = TRAB. Therefore, if (A, B) is a tr-similar pair, the similarity of Sim is equal to 1; otherwise, it is equal to 0. By defining the spatial-temporal similarity between an object pair, we can define different criteria to measure the similarity degree between the object pair. For each criterion, there are two levels of similarity. The similarity between (A, B) in video V 0 and (A, B) in video V can be the combinations of different levels of those criteria. (A, B) is called a similar pair, and objects A and B are called matched objects. Since video data contain very rich spatial-temporal information, users may extract different spatial-temporal levels of information according to their interests. Therefore, we can define the similarity between an object pair (A, B) as follows: SDS STS Similarity(A, B) = WSDS ∗ Sim (A,B) + WSTS ∗ Sim (A,B) TT TR (1) + WTT ∗ Sim (A,B) + WTR ∗ Sim (A,B)

where the sum of WSDS, WSTS, WTT and WTR is equal to one. To find the similarity between videos V 0 and V , we must consider all possible matched object sets from both videos. However, there are a large number of matched object sets, and it seems difficult to find all of them. We solve such a problem by the weighted directed graph and the 9DST index structure. Suppose O = O1,O2, . . ., On, be objects contained 0 0 0 in query video V , where n is the number of objects of V , and O = O1,O2, . . ., On, be 0 0 matched objects in video V , where (Oi,Oi) is an similar object pair, i = 1, 2, . . ., n. We can form a weighted directed graph G = (V,E), where G contains n vertices v1, v2, . . ., vn, 0 → vi denotes object pair (Oi,Oi), a weight function w : E R maps an edge to the real- valued similarity wij between objects Oi and Oj, if objects Oi and Oj is a similar pair, where i < j; otherwise, wij is equal to 0. The video retrieval algorithm is showed as following. Algorithm: similarity retrieval Input: the assigned weights of spatial-temporal similarity, and query videos V and the video database represented by 9DST-string. Output: the similarity ranked video list of V . 1. Construct the 9DST index structure from the 9DST-strings of video database. 2. Compute the temporal relation and spatial relations sequence for each object pair in query video V . 3. Construct the n-vertex weighted directed graph G = (V,E) for video V from 9DST index structure, where n is the number of objects in V , and the weights in an edge is the similarity of the matched object pair between V 0 and V . 4. Compute the ranked similarity from G. 5. Output the similarity ranked video list of V from G. In comparison with the retrieval method of 3D C-string [12], which is used to find the exactly matched object sets, the retrieval method of 9DST can find the partly matched object sets. That is, the proposed retrieval method can provide a more flexible way to retrieve similar videos.

5. Conclusions. We have proposed a new spatial-temporal structure called 9DST to represent symbolic videos. In this paper, we proposed a new video retrieval method based on the 9DST approach. Our proposed approach uses the 9DST index structure to record the temporal and spatial relations of object pairs in the video database. After associating with the weights of similarity to calculate the similarity between objects and constructing the weighted directed graph between videos, we can ﬁnd a list of ranked similar videos of query video. The similarities also provide multi-granularity to meet users’ need that 2014 P. YU based on the diﬀerent weights of spatial-temporal relations. In this paper, we focused on utilizing the visual information to process videos. How to integrate the other video information such as audio with the visual information to represent a video and perform similarity retrieval is worth further study.

REFERENCES [1] N. Sebe, M. S. Lew and A. W. M. Smeulders, Video retrieval and summarization, Computer Vision and Image Understanding, vol.92, pp.141-146, 2003. [2] C.-W. Su, H.-Y. M. Liao, H.-R. Tyan, C.-W. Lin, D.-Y. Chen and K.-C. Fan, Motion ﬂow-based video retrieval, IEEE Trans. on Multimedia, vol.9, no.6, pp.1193-1201, 2007. [3] J.-W. Hsieh, S.-L. Yu and Y.-S. Chen, Motion-based video retrieval by trajectory matching, IEEE Trans. on Circuits and Systems for Video Technology, vol.16, no.3, pp.396-409, 2006. [4] H.-B. Luan, S.-X. Lin, S. Tang, S.-Y. Neo and T.-S. Chua, Interactive spatio-temporal visual map model for web video retrieval, Proc. of the IEEE Int. Conf. on Multimedia and Expo., pp.560-563, 2007. [5] C. G. M. Snoek, B. Huurnink, L. Hollink, M. de Rijke, G. Schreiber and M. Worring, Adding semantics to detectors for video retrieval, IEEE Trans. on Multimedia, vol.9, no.5, pp.975-986, 2007. [6] Y. B. Chen and O. T.-C. Chen, High-accuracy moving object extraction using background subtraction, ICIC Express Letters, vol.3, no.4(A), pp.933-938, 2009. [7] S.-Y. Lee, J.-H. Heu, C.-S. Kim and S.-U. Lee, Object removal and inpainting in multi-view video sequences, International Journal of Innovative Computing, Information and Control, vol.6, no.3(B), pp.1241-1255, 2010. [8] T.-Y. Chen, T.-H. Chen, D.-J. Wang and Y.-C. Chiou, Real-time video object segmentation algorithm based on change detection and background updating, International Journal of Innovative Computing, Information and Control, vol.5, no.7, pp.1797-1810, 2009. [9] S. K. Chang, Q. Y. Shi and C. W. Yan, Iconic indexing by 2D strings, IEEE Trans. on Pattern Analysis and Machine Intelligence, vol.9, pp.413-429, 1987. [10] A. J. T. Lee, P. Yu and H. P. Chiu, 3D Z-string: A new knowledge structure to represent spatial- temporal relations between objects in a video, Pattern Recognition Letter, vol.26, pp.2500-2508, 2005. [11] P. W. Huang and C. H. Lee, Image database design based on 9D-SPA representation for spatial relations, IEEE Trans. on Knowledge and Data Engineering, vol.16, no.12, pp.1486-1496, 2004. [12] A. J. T. Lee, P. Yu and H. P. Chiu, Similarity retrieval of videos by using 3D c-string knowledge representation, Journal of Visual Communication and Image Representation, vol.16, pp.749-773, 2005. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 2015-2019

JOB SCHEDULING OF RETRIEVING DYNAMIC PAGES FROM ONLINE AUCTION WEBSITES ON GRID ARCHITECTURE

Chong-Yen Lee1, Hau-Dong Tsui1,2 and Ya-Chu Tai1

1Department of Information Management 2Graduate Institute of Political Science Chinese Culture University 55, Hwa Kang Road, Yang-Ming Shan, Taipei 11114, Taiwan { cylee; chd2 }@faculty.pccu.edu.tw; [email protected] Received February 2010; accepted April 2010

Abstract. A search engine reads static web pages of web sites periodically. It can take more time to update the page content. Unlike a search engine, searching and updating merchandise information from online auction websites is almost a mission impossible. Text contents of dynamic online auction web pages are time dependent due to the interaction of their users. Merchandises in any online website are classified into five different groups according to bid price, bid frequency, and auction expired time. Some merchandise pages should be visited frequently to get the most updated information. Factors such as network bandwidth used, bottleneck of the network transmission, data redundancy can affect the pages read through the network. A grid architecture considering above factors and an efficient job scheduling method using web page priority is applied to minimize either the number of working computers on the architecture or the time of retrieving all pages. Keywords: Job scheduling, Dynamic pages, Grid architecture, Page visiting priority

1. Introduction. A search engine scans and stores all web pages periodically. All the pages are stored in large databases. Essentially, resulting pages are direct or indirectly retrieved from databases when users use keywords to define their needs [1]. This kind of pages is static web pages. A dynamic web page refers to a web page whose content is constantly updated due to the interaction of its users or is customized in response to its users’ requests. The content could be in a graphic form such as the result generated by Google Earth, or a text form such as the result generated by a search engine. Text content of a dynamic web page is time dependent because the content is majorly retrieved from a large database based on users’ requests and the database is updated frequently. Unlike the search engine which replies requested pages might be days old, the Internet online auction merchandise search engine must return most updated information to its users. Web pages from an online auction website display information including auction prices of merchandises [2]. Pages of popular merchandises updated very often but the others would not be changed for a long time period. All merchandise pages must be retrieved on time to get all newest merchandise information generated from many different auction websites. Grid architecture which integrates computers with different platforms is ideally for use in extracting information on the network [3,4]. An efficient job scheduling method along with reducing network bandwidth used and moderating network transmission bottleneck can decrease time needed for information transmitted through the Internet [5,6]. In order to efficiently obtain updated information from massive quantity of dynamic auction web pages, a grid structure using efficient information extracting scheduling method with page visiting priority is developed.

2015 2016 C.-Y. LEE, H.-D. TSUI AND Y.-C. TAI 2. Characteristics of a Dynamic Auction Website Page. The content of a dynamic auction website page is the information retrieved from a database. The frequency of its content changed depends on the related information in the database updated. There are ﬁve groups of auction merchandises according to the number of bids and bid prices changed. Figure 1 shows the relationship of these ﬁve groups.

Figure 1. Relationship of merchandise groups

The first group (G1) is merchandises that are new. Web pages containing information of G1 merchandises have never been read. Numbers of bids are 0 and their bid prices are kept original. The second group (G2) is “Direct Buy” merchandises. These merchandises are sold if any customer would like to buy them. They need not to be bidden. They are named “Buy It Now”, “Buy”, “Instant Buy”, “Buy Out” or “Buy Now” in some auction websites. The selling prices have not been changed and will not be changed. The third group (G3) is merchandises which information was read but it has not been bidden since their first appearance. The difference between G2 and G3 is bid prices of G3 could be changed. The fourth group (G4) is those merchandises bid prices changed occasionally. The fifth group (G5) is those merchandises with bid prices changed frequently. G3, G4 and G5 groups of merchandises can be further classified into t time intervals I1...It according to their bid time left. Each time intervals is assigned a time weight TWi (1 ≤i≤t, TW1 ≥TW2 ≥ ... ≥TWt). Merchandise in the shorter bid time left interval has larger time weight value. Table 1 is an example of the time weight table. Table 1. Example of time weight table

i Time Interval Ti (seconds) Time Weight (TWi) 1 I1 600 1500 2 I2 1800 600 : : : : t − 1 It−1 86400 8 t It others 3

3. Webpage Visiting Priority Setting. The scheduling method is used to arrange the merchandise webpage information retrieval sequence for all merchandises of auction websites. For G1 merchandises, they are not in the database when the scheduling is initiated. For G2 items, their information need not to be checked since it is stored in the database and will not be modiﬁed. There are three important factors, bid frequency (BF), bid time left (BTL), and the most recent bid time (MRBT), related to the information ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2017 retrieving arrangement. The merchandise with higher bid frequency means that the item is more popular and its selling price is changed rapidly. Bid time left indicates the time that merchandise page is going to terminate. The page with short bit time left needs to be read in advance and more often unless the newest information could be missed before the page is expired. Merchandise weight (MW) is therefore x = BTL(Mi) (1)

MWi = BF (Mi) × TWx (2) where Mi is merchandise i (1 ≤ i ≤ n, n is the total number of G3, G4 and G5 merchandises), BTL is a function which checks the value of Mi’s bid time left and time interval and returns the index value of the time interval, MWi is Mi’s merchandise weight, TWx returns the time weight in the time weight table, BF is a function which returns Mi’s bid frequency value. The page with highest MW value has the highest priority of visiting. MRBT is used to diﬀerentiate priorities of pages with same MW value. Page with least MRBT has highest priority than others.

4. System Architecture. As Figure 2 shows, there are k supplier S1...Sk in the system. Suppliers are online auction websites in the Internet. Discoverer D reads G1 merchandise information from S1...Sk and stores the information in the database. C is the control center in the architecture. W1...Wm are m working computers which accept commands from control server C and retrieve information from S1...Sk.

Figure 2. Page information retrieving grid architecture

• Discoverer D: D scans suppliers S1...Sk for new merchandises (G1). D gets the information of the merchandise, such as name, description, bid expiration time, category, page address, and exam its type either G2 or G3. It will also get additional information list price for G2 merchandises and initial bid price for G3 merchandises. The bid frequency is set to 0. The information is stored in the database. D also communicates with C to exchange the status of each other. D will assign one of the working computers W1...Wm as the control server if C has not responded for a certain time period. • Control Server C: C gets all merchandise information of G3, G4, G5 groups from the database. There are r rounds in a cycle. In every round, it calculates MW values for these merchandises and sorts these items depending on their priorities and 2018 C.-Y. LEE, H.-D. TSUI AND Y.-C. TAI applies round information from the round information table to determine number of merchandises to retrieve their information. Table 2 is an example of the round information table. Table 2. An example of round information table

Round 1 2 3 ... r−1 r Percentages (P) 15% 20% 10% 15% 30%

For round h (1 ≤ h ≤ r),

∑h Number of item scheduled = Total number of items × P j (3) j=1 As in the example, the first round (h=1), C will schedule 15% of merchandises for information retrieval. The second round (h=2), it will schedule 35% of merchandises for information retrieval and so forth. C then categorizes merchandise items using their category information and organizes items in every category into several groups according to the maximum number of items allowed in the brief item information page that the website who provides the items. Groups along with merchandise information are sent to working computer W1...Wm to get most current merchandise information from suppliers S1...Sk. The control server also communicates with D by sending signals to inform D that C is still active and detects the status of D. It will assign one of the working computers to replace D if it has not received response from D for a time period. 5. Experiment. Observing top 10 auction websites [7] during Feb 1, 2010 to Feb 28, 2010, there is an average of 95,998,013 merchandise items per day. 74,061,299 items are “Direct Buy” merchandises (G2) and about 21.27% of total merchandises (20,421,695 items) are bid merchandises (G3). Within bid merchandises, there is 11.80% of them (1,823,892 items) has been bidden (G4+G5). 3,588,821 merchandises are new merchandises (G1) coming into these auction websites per day. The speed of retrieving page information from auction websites is about 3 pages per second. For 3,588,821 G1 merchandises, the discoverer D needs to read 18,390 pages per day from 10 suppliers (number of merchandise items in a page are different with each supplier). So D is capable to perform its job. The round information table set for the experiment is defined as follows. Table 3. Round information table set for the experiment

Round 1 2 3 4 5 Percentages (P) 10% 15% 15% 25% 35%

Pages need to be read and time needed for diﬀerent rounds are listed in Table 4. For a cycle, the total is 316,657 pages to be read. Total time is about 3 hours. For m working computers, it takes 179/m minutes for each working computer to go through a cycle. Table 4. Pages read and time needed for the experiment

Round 1 2 3 4 5 Total Pages need to be read 13,194 32,985 52,776 85,761 131,941 316,657 Time needed in minutes 8 19 30 48 74 179

In our experiment, 4 working computers are engaged. The status of these computers is different over times. It takes average 55 to 60 minutes per working computer to go ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2019 through a cycle. It means that an estimated time is about 1.3 × calculated time in the real environment. The network traffic between the control server and working computers is smooth since it only sends text information to communicate with all working computers. 6. Conclusion. Extracting merchandise information for all merchandises in several online auction websites is impossible to achieve. In our experiment, it takes average 533,322 minutes (about 370 days) to read all 95,998,013 pages from 10 auction websites. The mission becomes possible by applying the setting of webpage visit priority and suitable scheduling method mentioned. Using the method, the time for going through a cycle can be shortened by increasing the number of working computers. In our experiment, we also showed that information of popular merchandises were read every 9 minutes theoretically or 12 minutes practically. The percentages in the round information table can be modified by decreasing the number of percentage of first round and increasing the number of percentage of last round if the information of popular merchandises needs to be read much faster. Enlarge the number of rounds can speed up popular merchandises read as well.

REFERENCES [1] C. Jenkins, M. Kackson, P. Burden and J. Wallis, Searching the world wide web: An evaluation of available tools and methodologies, Journal on Information and Software Technology, vol.39, no.14-15, pp.985-994, 1998. [2] C. Beam and A. Segev, Auctions on the internet: A ﬁeld study, Unpublished Manuscript, vol.11, no.2, pp.1-30, 1998. [3] W.-C. Shih, C.-T. Yang and S.-S. Tseng, A performance-based parallel loop scheduling on grid environments, Journal of Supercomputing, vol.41, no.3, pp.247-267, 2007. [4] C.-T. Yang, K.-W. Cheng and W.-C. Shih, On development of an eﬃcient parallel loop self-scheduling for grid computing environments, Parallel Computing, vol.33, no.7-8, pp.467-487, 2007. [5] C.-Y. Lee, T.-Y. Lee, H. Wu, H.-D. Tsui and J.-B. Huang, A performance optimization of job scheduling model based on grid environment, Proc. of the 4th International Conference on Computer Sciences and Convergence Information Technology, pp.768-773, 2009. [6] H. Wu, C.-Y. Lee, W.-Y. Chen and T.-Y. Lee, Optimization of job schedule model based on grid environment, Journal of Networks, vol.3, no.3, pp.27-33, 2008. [7] TopTenReviews, Inc., 2010 Online Auction Sites Review Comparisons, http://online-auction- sites.toptenreviews.com/, 2010.

ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 2021-2025

AN IMPROVEMENT ON LI AND HWANG’S BIOMETRICS-BASED REMOTE USER AUTHENTICATION SCHEME

Wen-Gong Shieh and Mei-Tzu Wang

Department of Information Management Chinese Culture University 55, Hwa-Kang Road, Yang-Ming-Shan, Taipei, Taiwan { wgshieh; meii }@faculty.pccu.edu.tw Received February 2010; accepted April 2010

Abstract. In this paper, Li and Hwang’s biometrics-based remote authentication scheme is reviewed. And we find that this scheme is vulnerable, even as user’s biometrics has been included with the smart card. The weakness of the scheme due to symmetric formula between two verifiers is exposed when we issue a successful parallel session attack. Surprisingly, except for user ID, our attack is realized even without user’s biometrics, password or smart card. To eliminate this weakness, some modifications have been made for Li and Hwang’s scheme, under our suggestion, which is able to move up to a more secure level compared with its original version. Keywords: Authentication, Smart cards, Symmetric formula, Biometrics, Parallel session attacks

1. Introduction. As more and more network technology is applied to electronic commerce, such as smart cards, much research has focused on how to figure out a robust authentication scheme. The remote mutual authentication scheme is defined as a mechanism that allows users and systems to authenticate each other. An authentication scheme can be as simple as just using password mechanism. But apparently it is not sufficient when we learn that the world has confronted a series of challenges in networked computer systems for recent decades and suffered disastrous losses for them. In early 1993, there were two researchers: Neuman and Stubblebine, who proposed a nonce-based mutual authentication scheme using timestamps [1]. Afterwards, Hwang, Lee, Li, Ko and Chen argued that Neuman and Stubblebine’s method was not robust enough to defend paradox attacks and parallel session attacks. So they recommended some suggestion to improve it [2]. Yang and Shieh proposed two kinds of authentication schemes: timestamp-based and nonce-based authentication scheme in 1999 [3]. Other works about such kind of schemes are studied by Yang, Wang, Chang [4] and Kim, Jeon and Yoo [5]. The identity-based cryptosystems and the following identity-based remote user authentication scheme were studied by Shamir [6], and Hwang and Li [7], respectively. But the latter was soon being found as not secure as stated in [8]. A unilateral authentication scheme using one-way hash function is considered as more efficient than previous ones [9]. Chien et al. [10] further proposed an extremely efficient remote mutual authentication scheme to authenticate the system also. However, Chien et al.’s scheme was found being vulnerable to parallel session attacks due to its symmetric transmitted messages [11]. Lee et al. [12] proposed a nonce-based mutual authentication scheme without timestamps, but it is again unable to withstand parallel session attacks [13]. The purpose of this paper is to investigate whether Li and Hwang’s biometrics-based remote authentication scheme is more secure by its offering additional secure mechanism: biometrics, and further to examine whether there is other potential weakness in it [14]. The similar problem has also been indicated and fixed by Shieh and Wang [15].

2021 2022 W.-G. SHIEH AND M.-T. WANG The remainder of this paper is organized as follows. In Section 2, we review Li and Hwang’s biometrics-based authentication scheme. In Section 3, a scenario of our parallel session attack is illustrated. In Section 4 the weakness of the scheme is analyzed. In Section 5, an improvement is proposed. Finally, we have a brief conclusion in Section 6.

Figure 1. Li and Hwang’s biometrics-based authentication scheme

2. Review of Li and Hwang’s Biometrics-based Remote User Authentication Scheme. Li and Hwang’s biometrics-based remote user authentication scheme is composed of three phases as shown in Figure 1. The ﬁrst phase, called registration phase, allows a user to register to a system by transmitting identifying information, including his/her account IDi, password PWi, and biometrics Bi, to obtain a smart card that is equipped with required information by the system to support later mutual authentication between them when login process is triggered. The information in the smart card includes IDi, fi, ei, and a hash function h, where fi = h(Bi) and ei = h(IDi Xs) ⊕ h(PWi fi). Note that h(IDi Xs) is the shared secret between the user and the system, ei is the encrypted form of the shared secret, Xs is a secret maintained by the system, and the symbols “⊕” and “ ” represent exclusive OR operation and string concatenation operation respectively. The login phase is triggered when the user enters the smart card with his/her biometrics Bi. The smart card then computes h(Bi) using the stored hash function h and check whether it is equal to the stored data fi. If the answer is positive, then the user’s identity is already conﬁrmed and the process is kept going by further asking another input of the user’s password PWi. After reading PWi the smart card extracts the shared secret ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2023

h(IDi Xs), denoted as M1, by performing exclusive OR operation on the encrypted 0 shared secret ei, which is stored in the smart card, and ri, which is computed as h(PWi fi). At that time, the smart card is ready to transmit the message (IDi,M2) to the system, where M2 is the result of the exclusive OR operation on M1 and a random nonce Rc. M2 is a challenge to the system in that only the one who has the shared secret can recover the random nonce Rc. The authentication phase is two ways, called mutual authentication, meaning that the system authenticates the user and vice visa. The authentication phase starts when the system receives the message (IDi,M2) from the user. It first checks the format of IDi. If the format is correct, the process keeps forward by starting to compute the shared secret M3, which is equal to M1, by performing h(IDi Xs). Then it extracts user’s nonce Rc, which is equal to M4 by performing exclusive OR operation on M2 and M3. At that time, the system is ready to transmit message (M6,M5), where M5 = M3 ⊕ Rs, the result of exclusive OR operation on the shared secret and the system’s nonce Rs, and M6 = h(M2 M4), the hash value of the concatenation of M2 and the user’s nonce M4. Note that M5 is a challenge to the smart card and M6 is served as a verifier in the sense that the smart card can use it to determine whether the system is real. Obviously, besides the smart card, only the real system can extract user’s nonce Rc by using the shared secret and compute the value of M6. In addition, M6 cannot be replayed without being detected by the smart card, because the challenge M2 sent by the user has been included in the calculation of M6 by the system. When the system is verified as real by the user with this checking, the other way of authentication begins to start. The smart card extracts the system’s nonce Rs, which is equal to M7, by performing exclusive OR operation on M5 and the shared secret. Then it performs hash operation on the string which is the concatenation of M5 and M7 to obtain M8 = h(M5 M7). The message M8 is transmitted to the system. Similarly, M8 is served as a verifier, because only the real smart card, besides the system, can extract the system’s nonce Rs by using the shared secret and then use Rs to produce a correct response M8. When the system receives the message from the smart card and finds that M8 is equal to its computed value of h(M5 Rs), the smart card is verified as real and the mutual authentication is completed.

3. Our Parallel Session Attack Against Li and Hwang’s Authentication Scheme. It seems that the inclusion of biometrics in Li and Hwang’s biometrics-based remote user authentication scheme makes it more secure, because the illegal user is required to offer another identity, which is hard to falsify, to the system to pass its authentication examination. But not so in this scheme, because it suffers from the weakness of the symmetry property of verifier formula that causes the system being fooled to produce and transmit a message that includes information that the illegal user is required to respond to the challenge issued by the system in earlier session. The consequence is that the illegal user is mistakenly determined as real and can successfully login into the system. Our parallel session attack to Li and Hwang’s biometrics-based remote user authentication scheme is illustrated in Figure 2. Consider that an illegal user knows nothing about the password or biometrics of any legal user except for the correct format of user ID. He/She then chooses arbitrary legal-form user ID and sends the login message (IDi,Y ) to the system, where Y is any legal form of data appearing in the second entry of a login message. After receiving that message, the system will compute and send the message (M6,M5) to the illegal user, where M6 is a verifier that is ignored by the illegal user, because the illegal user is not interested in verifying the system. The data M5, on the other hand, is a challenge and being crucial to the illegal user. M5 is computed as M3 ⊕Rs and viewed as the random nonce Rs encrypted by the shared secret. What the illegal user wants to compute is h(M5 Rs), the response to the challenge issued by the system. The 2024 W.-G. SHIEH AND M.-T. WANG

Figure 2. Our parallel session attack against Li and Hwang’s biometrics- based authentication scheme illegal user does not have the shared secret to extract Rs. But he/she can fool the system to compute the data h(M5 Rs) for him/her as follows. He/she drops M6 and initiates another parallel login session, session 2, by sending a login message (IDi,M5) to the sys- 0 tem. Now the system takes M5 to compute M6, which is a hash value of the concatenation 0 0 ⊕ of M5 and M4. M4 is computed as M5 M3, where M3 is the shared secret and M5 is the random nonce Rs encrypted by the share secret, that is, M3 ⊕ Rs. It is easy to conclude 0 ⊕ ⊕ ⊕ 0 0 that M4 = M5 M3 = M3 Rs M3 = Rs. So, M6 = h(M5 M4) = h(M5 Rs), which is exactly the information that the illegal user is asked to respond to the challenge 0 issued by the system in earlier session. The system also computes M5, but it is ignored by 0 0 the illegal user. When the illegal user receives the message (M6,M5), he/she terminates 0 session 2 and resumes session 1 by sending the message M6 = h(M5 Rs) to the system to respond to the challenge issued by the system at session 1. As such, the illegal user now is mistakenly veriﬁed as real by the system and can successfully login into the system.

4. The Weakness of the Design of Symmetric Verifiers and Symmetric Chal- lenges. From the scenario of our successful parallel session attack against Li and Hwang’s authentication scheme just illustrated above, it is observed that the two alike verifier formulas: M6 = h(M2 M4) = h(M1 ⊕ Rc Rc), and M8 = h(M5 M7) = h(M1 ⊕ Rs Rs), together with the two alike challenges, M2 = M1 ⊕Rc and M5 = M3 ⊕Rs = M1 ⊕Rs, give the chance to the illegal user to have the system compute h(M1 ⊕ Rs Rs) for him/her. From the system’s view, it thinks that it is offering verifier for the illegal users to verify its identity, that is, the system can extract Rc and form the message M6, without recognizing that the verifier it sends is exactly the verifier that the illegal user is asked to respond to the system’s challenge. If the authentication scheme’s two verifiers do not have the same ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2025 structure, that attack cannot be successful. The key point is now clear: the two verifiers must have different structures in order to guard against such parallel session attacks. 5. Improvement to Li and Hwang’s Authentication Scheme. A simple solution to prevent Li and Hwang’s biometrics-based authentication scheme from our attack is to eliminate the symmetric property of the two verifiers: the verifier M6 = h(M2 M4) = h(M1 ⊕ Rc Rc), and the verifier M8 = h(M5 M7) = h(M1 ⊕ Rs Rs), for example, by replacing the latter with M8 = h(M5 M7 + 1) = h(M1 ⊕ Rs Rs + 1). With this modification, the parallel session attack illustrated in Figure 2 cannot be successful. 0 The illegal user obtains M6 from the system at session 2 is computed as (M5 Rs) = h(M1 ⊕ Rs Rs). But what the system expects to receive from illegal user in session 1 is the verifier M8 = h(M5 M7 + 1) = h(M1 ⊕ Rs Rs + 1) other than h(M1 ⊕ Rs Rs). This means that the parallel session attack will not succeed any more. In summary, our improvement to Li and Hwang’s scheme presented in Figure 1 is shown in the following:

• Compute M8 = h(M5 M7 + 1) instead of M8 = h(M5 M7) in the smart card. • Check M8 = h(M5 Rs + 1) instead of M8 = h(M5 Rs) in the system. 6. Conclusions. In this paper, we reviewed Li and Hwang’s biometrics-based authentication scheme and found that biometrics had been included in their scheme in order to strengthen its robustness, as compared with most other authentication schemes. But after detailed scrutiny, a crucial drawback was exposed: the symmetric formulas of the two veriﬁers cause the system at risk of the parallel session attack. We illustrate the scenario of a successful parallel session attack and propose some modiﬁcations to the scheme so as to improve its security level.

REFERENCES [1] B. C. Neuman and S. G. Stubblebine, A note on the use of timestamps as nonce, Operating Systems Rev., vol.27, no.2, pp.10-14, 1993. [2] T. Hwang, N. Y. Lee, C. M. Li, M. Y. Ko and Y. H. Chen, Two attacks on neuman-stubblebine authentication protocols, Information Processing Letters, vol.53, pp.103-107, 1995. [3] W. H. Yang and S. P. Shieh, Password authentication schemes with smart cards, Computers and Security, vol.18, no.8, pp.727-733, 1999. [4] C. C. Yang, R. C. Wang and T. Y. Chang, An improvement of the Yang-Shieh password authentication schemes, Applied Mathematics and Computation, vol.162, pp.1391-1396, 2005. [5] K. W. Kim, J. C. Jeon and K. Y. Yoo, An improvement on Yang et al.’s password authentication schemes, Applied Mathematics and Computation, vol.170, pp.207-215, 2005. [6] A. Shamir, Identity-based cryptosystems and signature schemes, Proc. of the CRYPTO’84, pp.47-53, 1984. [7] M. S. Hwang and L. H. Li, A new remote user authentication scheme using smart cards, IEEE Transactions on Consumer Electronics, vol.46, no.1, pp.28-30, 2000. [8] C. K. Chan and L. M. Cheng, Cryptanalysis of a remote user authentication scheme using smart cards, IEEE Transactions on Consumer Electronics, vol.46, no.4, pp.992-993, 2000. [9] H. M. Sun, An efficient remote user authentication scheme using smart cards, IEEE Transactions on Consumer Electronics, vol.46, no.4, pp.958-961, 2000. [10] H. Y. Chien, J. K. Jan and Y. M. Tseng, An efficient and practical solution to remote authentication: Smart card, Computers and Security, vol.21, no.4, pp.372-375, 2002. [11] C. L. Hsu, Security of Chien et al.’s remote user authentication scheme using smart cards, Computer Standards and Interfaces, vol.26, no.3, pp.167-169, 2004. [12] S. W. Lee, H. S. Kim and K. Y. Yoo, Efficient nonce-based remote user authentication scheme using smart cards, Applied Mathematics and Computation, vol.167, pp.335-361, 2005. [13] W. G. Shieh and M. T. Wang, An improvement on Lee et al.’s nonce-based authentication scheme, WSEAS Transactions on Information Science and Applications, vol.4, no.4, pp.832-835, 2007. [14] C. T. Li and M. S. Hwang, An efficient biometrics-based remote user authentication scheme using smart cards, Journal of Network and Computer Applications, vol.33, pp.1-5, 2010. [15] W. G. Shieh and M. T. Wang, An improvement to Kim-Chung’s authentication scheme, ICIC Express Letters, vol.3, no.4(B), pp.1215-1219, 2009.

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TOWARDS A DYNAMIC AND VIGOROUS SOA ESB FOR C4I ARCHITECTURE FRAMEWORK

Abdullah S Alghamdi, Iftikhar Ahmad and Muhammad Nasir Department of Software Engineering, College of Computer and Information Sciences King Saud University P.O. Box 51178, Riyadh 11543, Kingdom of Saudi Arabia { ghamdi; iftikhar; mnasir }@ksu.edu.sa Received March 2010; accepted May 2010

Abstract. A SOA ESB is a middleware that provides services such as message routing and transformation. Further, it has the capabilities to ease the pains of connecting heterogeneous C4I systems among various defense forces. The purpose of this paper is to propose an approach based on criteria for selecting SOA Enterprise Service Bus (ESB) for C4I architecture framework. This assay mechanism is based on two types of criteria; main criteria and sub-criteria. We used multi-criteria decision making (MCDM) technique for analyzing diﬀerent SOA Enterprise Service Buses (ESBs). The results indicate that Mule and Fiorano ESBs are more dynamic and vigorous for architecting C4I system. Keywords: System of systems (SOS), Service oriented architecture (SOA), Command, Control, Communications, Computers and intelligence (C4I) system, Multi criteria decision making (MCDM), Enterprise services buses (ESBs)

1. Introduction. The growing adoption of C4I systems in defense and civil areas had made it more imperative and attractive. Therefore, this justifies that the defense strate- gists, researchers and system developers are taking much interest in C4I systems. Presently, there are many issues in the integration of heterogeneous C4I systems that may be minimized using SOA ESBs. There are many SOA ESBs available in the market today but the problem is which one is fit for purpose. Therefore, selecting a SOA ESB has become a difficult task because many factors have to be considered. This paper describes an assessing mechanism of six ESBs namely Mule, GlassFish, Fiorano, ServiceMix, Sonic and Fuse keeping in view the C4I System as a base, so as to ascertain which ESB fulfills the requirements of the system of systems (SOS). The assessing mechanism consists of two criteria; main criteria and sub-criteria. We evaluated and rated the SOA ESBs on the basis of main criteria and sub-criteria which are further processed by assigning priorities, and calculating weights. The rest of paper is organized into the following sections, related work, methodology and implementation, results and conclusion. 2. Related Work. The C4I systems are incorporated in various sectors such as; defense, police, investigation, road, rail, airports, oil and gas where command and control scenarios exist. The main focus of these systems is defense applications. The purpose of a C4I system is to help the commander to accomplish his objective in any crucial situation [1]. A SOA ESB provides secure message transfer service between applications and interoperability using web services and related technologies. SOA ESB provides loosely coupled services. This can be used to connect different army wing’s systems to communicate with each other and share certain information. The applications communicate with each other via service invoking in a location independent fashion using SOA ESB. ESB assists as an infrastructure backbone for SOA applications and services and ease enterprise integration. SOA ESB notably reduces cost and time to create new processes through reutilization of existing applications and data. ESB is considered much reliable for delivering messaging

2033 2034 A. S ALGHAMDI, I. AHMAD AND M. NASIR across services even over hardware layer, and in critical circumstances like network or software failure, the shot messages are buffered and secured by ESBs and delivered when the system is up and running again [2]. To make a secured defense system is a great deal in its true sense because of tremendous rise in threats in day-to-day world. At this point of time many SOA ESBs are available to connect different systems and synchronize them so that they can easily communicate with each other [3]. Different ESB vendors provide various ESB products. Thus it is so difficult to choose an ESB in accordance with the set parameters and requirements. Much work has been done in the area of ESBs evaluation with respect to user needs because it is a challenging task. Many researchers used different mechanisms to compare and evaluate them based on certain criteria. But the important criteria are those that lead closely to a particular ESB that fulfills the requirements of SOA application. Researchers usually compare general ESBs, open source ESBs or commercial ESBs. Every researcher imposes his own list of criteria to conduct a certain evaluation and the most commonly base is price. Price is an important factor but it turns futile when open source ESB are compared. One of the distinct works is done by Woolley [4] who applied Vollmer and Gilpin’s evaluation criteria to two open source ESBs, such as Apache Service Mix and Mule Source Mule. He included current offering, strategy, market pressure and integration into the list of criteria. Woolley suggested that Mule ESB is the best and after this Fiorano ESB. Other ESBs were BEA System Equalogic Service Bus, IBM WebSphere Enterprise Service Bus and Apache ServiceMix. Desmet et al. [5] compared two open sources ESBs such as Apache ServiceMix and Mule Source Mule, and also two commercial ESBs like IBM WebSphere Enterprise Ser- vice Bus and BEA Systems Aqualogic Service Bus. This research was on performance. Because of the flexibility ESBs may turn into bottleneck if complicated messages use it with many processes. Hence, the performance is an important criterion for evaluation. They rated Open ESBs first and commercial ESBs after them. ESB rates were based on the performance test results. MacVittie [6] also evaluated commercial ESBs. He used integration, price and core bus feature as evaluation criteria. He rated BEA Aqualogic Service Bus first and second to Oracle SOA Suite. The others were Fiorano, Cape Clear, Tibco Software, IBM WebSphere Enterprise Service Bus, Sonic and Software AG. This is based on information provides by the consumers or was taken from the previous studies. Tobias et al. [7] evaluated open sources enterprise services buses such as Fuse, Mule and Open ESB on the basis of criteria like stateless, stateful, extensibility and failover. They rated Fuse as first and Mule as second and Open ESB as third. Their study revealed the need to identify critical information resources and expose them through loosely coupled, reusable, and composable services for successful composition into workflows. Interoper- ability is an important issue in designing and development process of C4I systems. Other multi-criteria based approaches are used and applied by Alghamdi [8], Chien-Chang Chou [15] and Kunio Shibata et al. [16].

3. Enterprise Service Buses (ESBs). 3.1. Mule ESB. This ESB offers simple development model and lightweight architecture, so integrating, interoperability and creating services are easy and fast. This does not need to replace or change existing system and it can easily work with any existing infrastructure and deploy in any topology with or without an application container. This ESB also provide same performance and reliability challenges that are required for large SOA implementations [9]. 3.2. GlassFish ESB. This ESB provides lightweight integration platform with fast development tools and deploy SOA components with free dependencies and flexibility. This provides an easy way to integrate and provides interoperability. It contains GlassFish ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2035 application server, NetBeans tooling, JBI runtime for deploying solutions, integration engines, adapters for external systems, and simple installer [10]. 3.3. Fuse ESB. This ESB can easily be embedded at endpoints that allow distributed systems to intelligently interact without mandating a centralized server. Further, it has pluggable architecture supports. This allows organizations to use their service solution in their SOA with pluggable architecture [11]. 3.4. Sonic ESB. This ESB simplifies integration and flexible reuse of business components using a standard-based SOA. This allows different army wings to dynamically configure the reliable connection, reconciliation, control of services and their interactions. This also provides intelligent routing with highly scalable service interaction without performance bottleneck or single point of failure. This ESB also provides endpoint connectivity for web services that are reliable, scalable and secure integration of web service-enabled applications [12]. 3.5. Fiorano ESB. This ESB is able to perform middleware infrastructure platform for web-services that supports intelligently directed communication and platform relationship between loosely coupled (SOA) and decoupled (EDA) components. This also provides failover, security, monitoring, load-balancing and other management services using the JMX (Java Management Extensions) standard. This increases process performance with higher message throughput and enhances availability [13]. 3.6. Apache ServiceMix ESB. This is an open ESB that support both SOA and EDA to create a physical enterprise ESB. Further, it provides integration between different applications and support JBI implementation [9]. It also supports a number of binding components such as Java EE Connector Architecture (JCA), ActiveMQ JMS and Jencks etc. This ESB also supports asynchronous communication [14].

4. Methodology and Implementation. The methodology incorporated in this evaluation consists of goal selection, decision of criteria; determine the alternatives, building hierarchy, assignment of priorities, calculation of weights and consistency test. Further, this work is implemented using multi-criteria decision making software. 4.1. Goal selection. First of all, we selected a goal for this work. The goal is selection of dynamic and vigorous SOA ESB for C4I architecture framework. Six ESBs such as Mule, Fiorano, GlassFish, ServiceMix, Sonic and Fuse are selected for assay purpose. 4.2. Decision of criteria. Secondly, we decided criteria and sub-criteria. The main criteria consist of Interoperability’, ‘Extensibility’, ‘Messaging’, ‘Easiness’ and ‘Availability’. The main criteria are further divided into sub-criteria. The criterion ‘Interoperability’ is divided into sub-criteria namely ‘Syntactic’, ‘Semantic’ and ‘Network’. In the same way, the criterion ‘Messaging’ is divided into ‘Reliability’, ‘Security’ and ‘Speed’. The ‘Avail- ability’ is further divided into sub-criteria such as ‘State less’, ‘State full’ and ‘Failover’. The selection of criteria and sub-criteria is based on the works as done by many other researchers [10-14]. 4.3. Determine the alternatives. Thirdly, we determined the alternatives such as Fio- rano, Mule, Sonic. ServiceMix, GlassFish and Fuse. These alternatives are the focus of this work. 4.4. Building hierarchy. The hierarchy is built on the bases of criteria, sub-criteria and alternatives as shown in Figure 1. The goal “selection of dynamic and vigorous SOA ESB for C4I architecture framework” is at top of the hierarchy. The criteria and sub-criteria are shown in the middle. The alternatives are at bottom of the hierarchy but these are not shown due complexity in the diagram. 2036 A. S ALGHAMDI, I. AHMAD AND M. NASIR 4.5. Assignment of priorities. The assignment of priorities is based on the information obtained from previous works [10-14]. The scale used for pairwise comparison is nine points scale as shown as Table 1. 4.6. Calculation of weights. The weights of each node (criteria, and sub-criteria) are calculated on the bases of assigned priorities as shown in Table 1. 4.7. Consistency test. The consistency ratio is calculated based on the weights. If the consistency ratio is less than 10 percent, the inconsistency is acceptable. Otherwise, we need to revise the subjective judgment.

Figure 1. Hierarchy consist of goal, criteria and sub-criteria

Table 1. Weights of main criteria and sub-criteria

Weights Interoperability Extensibility Messaging Easiness Availability Total Local 0.38 0.09 0.23 0.12 0.18 1.00 Global 0.38 0.09 0.23 0.12 0.18 1.00 Interoperability sub-criteria weights Weights Syntactic Semantic Network Total Local 0.33 0.33 0.34 1.00 Global 0.12 0.12 0.14 0.38 Messaging sub-criteria weights Weights Reliability Security Speed Total Local 0.32 0.21 0.47 1.00 Global 0.07 0.05 0.11 0.23 Availability sub-criteria weights Weights State less Sate full Failover Total Local 0.33 0.33 0.34 1.00 Global 0.06 0.06 0.06 0.18

5. Results. Table 1 explains weights of main criteria and sub-criteria like interoperability, messaging and availability. Figure 2 illustrates criteria ranking such as interoperability, messaging, availability, easiness and extensibility. Figure 3 demonstrate ranking between six diﬀerent alternatives such as Mule, Fiorano, ServiceMix, Sonic, GlassFish and Fuse. Mule is rated as best ESB in the application of C4I architecture framework. The Fiorano is rated as second, ServiceMix as third, Sonic as fourth, GlassFish as ﬁfth, and Fuse as sixth in this work. ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2037

Figure 2. Criteia’s ranking

Figure 3. Alternative ranking

6. Conclusions. An MCDM technique has been used to evaluate six ESBs, namely, Mule, Fiorano, ServiceMix, Sonic, GlassFish and Fuse. This evaluation was based on main criteria and sub-criteria. According to this evaluation, it has been found that amongst these six ESBs, Mule and Fiorano are more suitable to tackle the current issues of C4I architecture framework such as interoperability, messaging, availability and easiness.

Acknowledgment. This work is supported by Department of Software Engineering, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia.

REFERENCES

[1] L. W. Yeoh and M. C. Ng, Architecting C4I systems, Proc. of the 2nd International Symposium on Engineering Systems MIT, Cambridge, Massachusetts, 2009. [2] L. Garces-Erice, Building an enterprise service bus for real-time SOA: A messaging middleware stack, Proc. of the 33rd IEEE International Computer Software and Applications Conference, pp.79- 84, 2009. [3] S. Mittal, B. Zeigler, J. L. R. Martin, F. Sahin and M. Jamshidi, Modeling and Simulation for Systems of Systems Engineering, Wiley, 2008. 2038 A. S ALGHAMDI, I. AHMAD AND M. NASIR

[4] R. Woolley, Enterprise Service Bus (ESB) Product Evaluation Comparisons, http://dts.utah.gov/ techresearch/researchservices/researchanalysis/resources/esbCompare061018.pdf, Utah Department of Technology Services, 2009. [5] S. Desmet, B. Volckaert, S. V. Assche, D. V. D. Weken, B. Dhoedt and F. De Turck, Through- put evaluation of diﬀerent enterprise service bus approaches, Proc. of the Conference on Software Engineering Research and Practice, pp.378-384, 2007. [6] K. Vollmer and M. Gilpin, The forrester wave: Enterprise service bus, BEA Systems, http:// whitepa- pers.zdnet.co.uk/0,1000000651,260256988p,00.htm, 2006. [7] L. MacVittie, Review: ESB suites, Networking Computing, CMP Media LLC, http://www.network computing.com/wireless/review-esb-suites.php, 2006. [8] A. S. Alghamdi, Evaluating defense architecture framework for C4I system using analytic hierarchy process, Journal of Computer Science, vol.5, no.12, pp.1075-1081, 2009. [9] A. S. Alghamdi, I. Ahmad and M. Nasir, Evaluating ESB for C4I architecture framework using analytic hierarchy process, Proc. of the 9th International Conference on Software Engineering Research and Practice, Las vegas, NE, 2010. [10] Y. Vasiliev, Beginning Database-Driven Application Development in Java EE Using GlassFish, Springer Link, 2009. [11] A. Badura, B. Sakowicz and D. Makowski, Integration of management protocols based on apache servicemix JBI platform, Proc. of the 10th International Conference on CADSM, pp.381-384, 2009. [12] Sonic ESB, Delivering an Integration Framework for the OpenEdge Enterprise, Progress Software, http://www.progress.com.tr/openedge/urunler/verisayfasi/sonic esb.pdf, 2006. [13] N. Fu, X. Zhou, K. Wang and T. Zhan, Distributed enterprise service bus on JBI, Proc. of the 3rd International Conference on Grid and Pervasive Computing – Workshops, pp.292-297, 2008. [14] K. Kotsopoulos, P. Lei and Y. F. Hu, A SOA-based information management model for next- generation network, Proc. of the International Conference on Computer and Communication En- gineering, pp.1057-1062, 2008. [15] C.-C. Chou, A combined MCDM and fuzzy MCDM approach to selecting the location of the distribution center in the hub port: An empirical study on Hong Kong, Shanghai and Kaohsiung, International Journal of Innovative Computing, Information and Control, vol.6, no.7, pp.3037-3051, 2010. [16] K. Shibata, J. Watada and Y. Yabuuchi, Fuzzy AHP approach to comparison of grant aid for ODA in Japan, International Journal of Innovative Computing, Information and Control, vol.5, no.6, pp. 1539-1546, 2009. ICIC Express Letters ICIC International c 2010 ISSN 1881-803X Volume 4, Number 5(B), October 2010 pp. 2039-2044

JOINT MULTIPLE PARAMETERS ESTIMATION FOR VECTOR-SENSOR ARRAY USING BIQUATERNIONS

Fei Wang, Hailin Li and Jianjiang Zhou

College of Information and Science Technology Nanjing University of Aeronautics and Astronautics Nanjing 210016, P. R. China [email protected] Received March 2010; accepted May 2010

Abstract. As for joint multiple parameters estimation of direction of arrival (DOA) and polarization information of signal source with linear uniform three components vector- sensor array, we define a new biquaternion formalism to model sampled data. In comparison with Bihan’s biquaternion model, we show that our biquaternion model is fit for joint multiple parameters estimation of DOA and polarization information of signal source with linear uniform three components vector-sensor array, but Bihan’s model is not. Then, we construct the Toeplitz matrix with autocorrelation function of our biquaternion model and propose using biquaternion MUSIC algorithm to jointly estimate DOA and polarization information of signal source. Simulations show that our idea is effective. Keywords: Biquaternion, MUSIC, Toeplitz matrix, Vector-sensor

1. Introduction. In recent decade, scientists have paid more and more attention to vector sensor. With vector sensor, we may obtain not only direction of arrival (DOA), but also polarization and magnetization information of signal source. In many applications, such as communication, radar, seismic exploration, radio astronomy, and biomedical system, vector-sensor array is widely used to get more information of signal source and to improve estimation accuracy [1-7]. Because vector sensor can receive multi-components of signal source, people research not only how to extend high resolution method of scalar sensor to vector sensor, but how to establish a new math model and corresponding algorithm to be ﬁt for sampled data of vector sensor. Nehorai, Wong and Li mainly organized sampled data into long vectors and extended array signal processing methods of scalar sensor to vector sensor, such as long vector MUSIC-like (LV-MUSIC) and ESPRIT-like algorithms [1-3]. Bihan and Miron proposed a quaternion model and quaternion MUSIC algorithm of one-dimensional (1D) linear uniform two components vector-sensor array [8]. They also proposed a biquaternion model and biquaternion MUSIC algorithm (BQ-MUSIC) of 1D linear uniform three components vector sensors array [9]. In most cases, three electric dipoles are enough to receive signal source information. Diﬀerent to other models, Bihan’s biquaternion model is essentially to make connection between the three components of signal source, i.e., Bihan’s biquaternion model can be used widely, it can depict data sampled not only by vector sensor including three electric dipoles but also by arbitrary three channels sensors. Unfortunately, Bihan’s method can only extract DOA and polarization parameters at the same time while signal sources number is much smaller than that of array elements (e.g., one source recorded on seven sensors [9]). And polarization information is not accessible with Bihan’s method when signal sources number is relatively large. That is why Bihan advised the use of BQ-MUSIC with polarization information known as accurately as possible [9]. Usually, polarization

2039 2040 F. WANG, H. LI AND J. ZHOU information is unknown in advance. To solve that problem, we define a new biquaternion model. Through analyzing its autocorrelation function, we show that this new biquaternion model is fit for jointly estimating DOA and polarization information of signal source comparing to Bihan’s method. In this paper, Section 2 defines our new biquaternion model. Section 3 depicts our parameters estimation process and discusses the important difference between our estimator and Bihan’s estimator.

2. Biquaternion Model of Linear Uniform Three Components Vector-sensor Array. Consider L narrowband electromagnetic plane waves incident on linear uniform three components vector-sensor array. Define sampled data model as: ∑L ym(n) = (β0l + iβ1l + Iβ2l) · exp(jmθl) + υm(n) (1) l=1 where, m represents the mth array element, 0 ≤ m ≤ M − 1; n represents sampling point, 0 ≤ n ≤ N − 1; β0l, β1l and β2l represent coefficient of each component of the lth signal source, they are complex, e.g., β0l = |β0l| exp(jα0l) and β0l is nonzero; θl = ∆x sin Θ 2πv l ,Θ represents incident angle of the lth signal, η represents light speed, η l v represents signal frequency, ∆x represents space between two adjacent elements and ∆x = λ/2, λ represents signal wavelength; i, j and I represent imagine symbols of biquaternions. And their operational√ rules are ij = −ji = k, i2 = j2 = k2 = −1, jk = −kj = i, ki = −ik = jI = −1, iI = Ii, jI = Ij, kI = Ik. υm(n) represents additive white Gaussian noise (AWGN). Our purpose is to jointly estimate β1l/β0l, β2l/β0l and θl. To show the difference between our model and Bihan’s model, we rewrite Bihan’s math model as followed: ∑L ybm(n) = (iβ0l + jβ1l + kβ2l) · exp(Imθl) + υm(n) (2) l=1 where, all parameters are the same as (1) but the expression of β0l, β1l and β2l, e.g., β0l = |β0l| exp(Iα0l), so do β1l and β2l.

3. Joint Multiple Estimation of Parameters. Let ρ1l exp(jα1l) = β1l/β0l, ρ2l exp(jα2l) = β2l/β0l. Deﬁne ∆ ∗ R(d) = E [ym+d(n)ym(n)] ∑L jα1l jα2l 2 = (1 + iρ1le + Iρ2le )· |β0l| exp(jdθl) (3) l=1 − − · − jα1l − jα2l 2 (1 ρ1le i ρ2le I) + συδ(d) ≤ ≤ − ∗ 2 · where, 0 d D < M 1; ‘ ’ is conjugate symbol; συ represents noise variance; δ( ) represents Dirac function. ∗ ∗ − − jα1l jα2l − jα1l − jα2l Let cl = 1 + iρ1le + Iρ2le . cl is conjugate of cl and cl = 1 ρ1le i ρ2le I. Deﬁne R = UΛUH + υ (4) where   c1 c2 ··· cL − − −  jθ1 jθ2 ··· jθL   c1e c2e cLe  U =  . . . .  (5) . . . . −jDθ1 −jDθ2 −jDθL c1e c2e ··· cLe ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2041

2 2 2 Λ = diag( |β01| |β02| · · · |β0L| ) (6)

2 2 ··· 2 υ = diag( συ συ συ ) (7) ‘H’ is conjugate transpose symbol. Obviously, RH = R, i.e., R is Hermitian biquaternion matrix. As for biquternion matrix, Mehta [10] has proved that if and only if biquaternoin matrix is Hermitian matrix its eigenvalues are real and its eigenvectors are mutual orthogonal. Based on Mehta’s theory, Bihan proposed subspace decomposition method of Hermitian biquaternion matrix named BQ-MUSIC. Since R in (4) is Hermitian biquaternion matrix, we can use BQ-MUSIC to decompose R and get signal subspace and noise subspace. Then, the last important step is to design joint multiple parameters estimator. In the following we[ introduce our estimator.] T jφ jDφ jf1 jf2 Let ξ = 1 e ··· e b = 1 + ib1e + Ib2e . Deﬁne

1 g(b1, f1, b2, f2, φ) = (8) (bξ)H WWH (ξb) where W represents biquaternion noise subspace. Using (8), we can search L spectra peaks, and the corresponding coordinates values of L spectra peaks are estimation results. In fact, restrictions on orthogonal biquaternion vectors made from our model are stricter than that of Bihna’s. It’s also the reason that our method is more eﬀective in jointly estimating multiple parameters. We give an example as followed to show that. According to our and Bihan’s model forms, we deﬁne

Yl = (β0l + iβ1l + Iβ2l) · εl Z = (1 + iγ1 + Iγ2) · ξ (9)

Ybl = (iβ0l + jβ1l + kβ2l) · εbl Zb = (i + jγ1 + kγ2) · ξb (10) where [ ] [ ] − − − − − − ε = 1 e jθl ··· e j(M 1)θl , ε = 1 e Iθl ··· e I(M 1)θl , l [ ] bl [ ] ξ = 1 ξ(1) ··· ξ(M − 1) , ξb = 1 ξb(1) ··· ξb(M − 1) .

Yl and Ybl represent data model of the lth signal deﬁned by this paper and Bihan, respectively. Furthermore, we have H ∗ ∗ ∗ − H YlZ = [(β0l + β1lγ1 + β2lγ2 ) + I(β0lγ2 β2l)] εlξ T (11) + i [(β0lγ1 − β1l) − I (β1lγ2 + β2lγ1)] εlξ

H ∗ ∗ ∗ ∗ YblZ = [(β0l + β1lγ + β2lγ ) + i(β2lγ − β1lγ ) b 1 2 1 2 (12) ∗ − − ∗ H +j(β0lγ2 β2l) + k(β2l β0lγ1 )] εblξb where ‘H’ represents conjugate transpose, ‘∗’ represents conjugate, ‘T ’ represents transpose. Supposing that εl, εbl, ξ, ξb are nonzero complex vectors and εl and εbl are orthogonal T 6 T 6 6 6 to ξ and ξb respectively, εlξ = 0 and εblξb = 0 if θl = 0 and θl = π, i.e., γ1 = β1l/β0l and γ2 = −β2l/β0l if Yl is orthogonal to Z in (6). Equation (11) shows that restrictions on orthogonal biquaternion vectors made from our H model are εlξ = 0, γ1 = β1l/β0l and γ2 = −β2l/β0l, whereas (12) shows that restriction H on orthogonal biquaternion vectors made from Bihan’s model is just εblξb = 0. 2042 F. WANG, H. LI AND J. ZHOU

4. Simulations. We generate (1) with L = 2, M = 4, ∆x = λ/2, β01 = β02 = 1, β11 = ρ11 exp(jα11) = 0.6 exp(j0.2), β21 = ρ21 exp(jα21) = 0.7 exp(j0.3), θl = 0.5π, (Θ1 = ◦ ◦ 30 ), β12 = ρ12 exp(jα12) = 1.1 exp(j0.9), θ2 = 0.57π(Θ2 = 35 ), β22 = ρ22 exp(jα22) = 1.0 exp(j0.8) and noise is AWGN. We simulate our idea at ﬁrst, and then we compare our method with Bihan’s method to illustrate our method clearly. Figure 1 and Figure 2 show estimation results with our method. For each point on the ﬁgures, we run 100 experiments and 500 snapshots of each experiment.

Figure 1. RMSE of each parameter of signal source from 30◦

Figure 2. RMSE of each parameter of signal source from 35◦ ICIC EXPRESS LETTERS, VOL.4, NO.5, 2010 2043 Figure 1 and Figure 2 show root mean square error (RMSE) of estimation of normalized direction angle and polarization parameters of each signal source. θ1 in Figure 1 and θ2 in Figure 2 represent normalized direction angle. ρ11, α11, ρ21, α21 in Figure 1 and ρ12, α12, ρ22, α22 in Figure 2 represent polarization parameters. In Figure 1 and Figure 2, RMSE is not always an increasing trend for some parameter estimation in local, such as θ1 and θ2. The reason is that direction angles estimation is sensitive to polarization parameters estimation results with our method. Next, we compare our method with Bihan’s method. Bihan has mentioned that their method is fit for polarization parameters estimation if sensors number is great bigger than signal sources number (e.g., seven sensors for one signal source [9]). In the following simulations, there are two signal sources but only four sensors so we assume that polarization parameters are known. Figure 3 shows RMSE of direction angel estimation (Θ1,Θ2) with Bihan’s and our method. For each point on this figure, we run 100 experiments and 500 snapshots of each experiment. From Figure 3, we can observe that Bihan’s method is better when SNR is close to 30dB. However, the estimation performance of his method decreases quickly with decreasing SNR, whereas our method is still effective.

Figure 3. RMSE of direction angle with polarization parameters known

5. Conclusions. We propose a novel biquaternion model of sampled data of linear uniform three components vector sensors array. In comparison with Bihan’s method, our method is more eﬀective in joint estimation of direction angle and polarization parameters. However, parameters searching is a heavy computation burden because there are ﬁve unknown parameters (ρ1, α1, ρ2, α2, θ) in Bihan’s and our estimators. So, if we could know some possible values of those parameters in advance, it would be very useful in saving running time.

Acknowledgment. This work is partially supported by the Qualiﬁed Personnel plan of Jiangsu Province (P0952-041). The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation. 2044 F. WANG, H. LI AND J. ZHOU

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ICIC EXPRESS LETTERS AN INTERNATIONAL JOURNAL OF RESEARCH AND SURVEYS

VOLUME 4, NUMBER 5(B), October 2010

CONTENTS (Continued)

Adaptive Control for Missile Systems with Parameter Uncertainty 1937 Zhiwei Lin, Zheng Zhu, Yuanqing Xia and Shuo Wang

Application of Plant Growth Simulation Algorithm on SMT Problem 1945 Tong Li, Weiling Su and Jiangong Liu

A Controller Design for T-S Fuzzy Model with Reconstruction Error 1951 Hugang Han and Yanchuan Liu

An Analysis for Parameter Configuration to Find a Trigger of Change 1959 Rika Ito and Kenichi Kikuchi

Complexity Reduction Algorithm for Enhancement Layer of H.264/SVC 1965 Kentaro Takei, Takafumi Katayama, Tian Song and Takashi Shimamoto

Modeling of Enterprises Risk Management and Its Robust Solution Method 1973 Min Huang, Yanli Huo, Chunhui Xu and Xingwei Wang

Fundamental Study of Clustering Images Generated from Customer Trajectory by Using Self-Organizing Maps 1979 Asako Ohno, Tsutomu Inamoto and Hajime Murao

Interface Circuit for Single Active Element Resistive Sensors 1985 Amphawan Julsereewong, Prasit Julsereewong, Tipparat Rungkhum Hirofumi Sasaki and Hiroshi Isoguchi

Analytic Solution of Shock Waves Equation with Higher Order Approximation 1991 Valentin A. Soloiu, Marvin H.-M. Cheng and Cheng-Yi Chen

Fuzzy Opinion Survey Based on Interval Value 1997 Lily Lin, Huey-Ming Lee and Jin-Shieh Su

Certificate of Authorization with Watermark Processing in Computer System 2003 Nai-Wen Kuo, Huey-Ming Lee and Tsang-Yean Lee

Weighted Similarity Retrieval of Video Database 2009 Ping Yu

Job Scheduling of Retrieving Dynamic Pages from Online Auction Websites on Grid Architecture 2015 Chong-Yen Lee, Hau-Dong Tsui and Ya-Chu Tai

An Improvement on Li and Hwang's Biometrics-Based Remote User Authentication Scheme 2021 Wen-Gong Shieh and Mei-Tzu Wang

Multiple Robot System Applying in Chinese Chess Game 2027 Song-Hiang Chia, Kuo-Lan Su, Sheng-Ven Shiau and Chia-Ju Wu

Towards a Dynamic and Vigorous SOA ESB for C4I Architecture Framework 2033 Abdullah S Alghamdi, Iftikhar Ahmad and Muhammad Nasir

Joint Multiple Parameters Estimation for Vector-Sensor Array Using Biquaternions 2039 Fei Wang, Hailin Li and Jianjiang Zhou

2010 ICIC INTERNATIONAL ISSN 1881-803X PRINTED IN JAPAN

ICIC EXPRESS LETTERS AN INTERNATIONAL JOURNAL OF RESEARCH AND SURVEYS

VOLUME 4, NUMBER 5(B), October 2010

CONTENTS (Continued)

Study of Parameters Selection in Finite Element Model Updating Based on Parameter Correction 1831 Linren Zhou and Jinping Ou

Dynamic Modeling of 3D Facial Expression 1839 Jing Chi

Chaos in Small-World Cellular Neural Network 1845 Qiaolun Gu and Tiegang Gao

Evaluating the Quality of Education via Linguistic Aggregation Operator 1851 Ying Qiao, Xin Liu and Li Zou

Collaborative Filtering Algorithm Based on Feedback Control 1857 Baoming Zhao and Guishi Deng

MVC Algorithm Using Depth Map through an Efficient Side Information Generation 1863 Ji-Hwan Yoo, Young-Ho Seo, Dong-Wook Kim, Manbae Kim and Ji-Sang Yoo

Design of Node with SOPC in the Wireless Sensor Network 1869 Jigang Tong, Zhenxin Zhang, Qinglin Sun and Zengqiang Chen

Research on the Sensorless Control of SPMSM Based on a Reduced-Order Variable Structure MRAS Observer 1875 Lipeng Wang, Huaguang Zhang, Zhaobing Liu, Limin Hou and Xiuchong Liu

Production Planning Based on Evolutionary Mixed-Integer Nonlinear Programming 1881 Yung-Chien Lin, Yung-Chin Lin and Kuo-Lan Su

Hiding Secret Information in Modified Locally Adaptive Data Compression Code 1887 Chin-Chen Chang, Kuo-Nan Chen and Zhi-Hui Wang

Genetic Programming Based Perceptual Shaping of a Digital Watermark in the Wavelet Domain 1893 Asma Ahmad and Anwar M. Mirza

A Competitive Particle Swarm Optimization for Finding Plural Acceptable Solutions 1899 Yu Taguchi, Hidehiro Nakano, Akihide Utani, Arata Miyauchi and Hisao Yamamoto

Design and Implementation of a Novel Monitoring System for Container Logistics Based on Wireless Sensor Networks and GPRS 1905 Kezhi Wang, Shan Liang, Xiaodong Xian and Qinyu Xiong

Spatially Adaptive BayesShrink Thresholding with Elliptic Directional Windows in the Nonsubsampled Contourlet Domain for Image Denoising 1913 Xiaohong Shen, Yulin Zhang and Caiming Zhang

Application of Type-2 Fuzzy Logic System in Indoor Temperature Control 1919 Tao Wang, Long Li and Shaocheng Tong

Traffic Flow Forecasting and Signal Timing Research Based on Ant Colony Algorithm 1925 Wenge Ma, Yan Yan and Dayong Geng

Statistical Layout of Improved Image Descriptor for Pedestrian Detection 1931 Ming Bai, Yan Zhuang and Wei Wang

(Continued)

2010 ICIC INTERNATIONAL ISSN 1881-803X PRINTED IN JAPAN

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