A Novel Data-Driven Framework for Real-Time Ocean Wave Monitoring Using High Frequency Radar Systems

Home , Significant wave height

Nuoyi Zhu

A Dissertation

Submitted to the Faculty

of the

WORCESTER POLYTECHNIC INSTITUTE

in partial fulfillment of the requirements for the

Degree of Doctor of Philosophy

Civil Engineering

March 2018

APPROVED:

Prof. Tahar El-Korfchi, Major Advisor Department of Civil and Environmental Engineering Worcester Polytechnic Institute

Prof. Yeesock Kim, Co-Advisor Department of Civil Engineering and Construction Management California Baptist University

Prof. Leonard Albano, Committee Member Department of Civil and Environmental Engineering Worcester Polytechnic Institute Abstract

Every year, frequent high waves induced by the tsunami, earthquakes, strong wind, and/or other climate change conditions have become one of the major factors of the various coastal disasters in the shoreline. In order to mitigate the coastal disaster, monitoring of ocean surface conditions such as wave heights and periods in real time is of high importance. However, the real-time ocean wave monitoring is a challenging problem, which has not yet been definitively resolved. With this in mind, a novel data-driven framework is proposed for the forecasting, identifying and classifying ocean waves in real-time using high frequency (HF) radar systems.

The first part of the research investigates the effects of the ocean wave forecasting model using the nonlinear auto-regressive and moving average algorithms (ARMA). The second part of the research compares the three different identification features in ocean wave: frequency-based feature, AR-based feature, and ICA-based feature. The third part of the research introduces a classification model to identify the difference of ocean waves using the support vector machine

(SVM) with radial basis function (RBF) kernel function.

To validate the proposed algorithms, the Samcheok City, Gangwond-do, located on the

East Coast of Korea is selected as the study area. A 2-year ocean wave height data from this area is collected using two Wellen radar systems. It is shown that the proposed algorithms have good performance in forecasting, identifying and classifying ocean waves.

It is expected that the proposed system will accurately predict natural hazards and provide adequate warning time for people to evacuate. Hence this framework will directly increase the reliability and functionality of coastal hazard warning systems and contribute to the reduction in the potential for injuries and deaths in natural disasters of the coastal areas.

Acknowledgement

I would like to sincerely thank my advisor Professor Tahar El-Korchi and Professor Yeesock Kim for their guidance, insights, support and friendship throughout my PhD years in WPI. I would like to thank my committee member Professor Leonard Albano for his acceptance in being part of my

PhD committee, and for his time and priceless insights. I would like to thank Professor Kwonmoo

Lee for his time and priceless insights.

I would like to give special thanks to Agata Lajoie, Marylou Horazny, Cynthia Bergeron and

Maryann Watts. They were always there when I needed. I would like to thank my fellow graduate students for their feedback, cooperation and of course friendship. It was great sharing with all of you during last four years.

I would like to thank the Department of Civil and Environmental Engineering at WPI for giving me the chance to pursue my doctorate and for providing the financial support with a teaching assistantship. I would like to thank the Regional Technology Innovation Program from Ministry of Land, Transport and Maritime Affairs of Korean Government for providing the financial support with a research assistantship.

More than all, I would like to thank my family, this could not be done without their support. I am grateful to my mom and my dad, who have provided me through moral and emotional support in my life. I am also grateful to my other family members and friends who have supported me along the way.

Table of Contents

Abstract ...... 2 Acknowledgement ...... 3 Table of Contents ...... 4 List of Figures ...... 7 List of Tables ...... 10 1. Introduction ...... 11 2. Real-time Forecasting of Ocean Wave Signals Using High Frequency Radar Systems ...... 17 2.1 Introduction ...... 17 2.2 Proposed forecasting model ...... 23 2.2.1 Linear ARMA model ...... 24 2.2.2 Proposed nonlinear ARMA model ...... 24 2.2.3 Optimization of model structure and its parameters ...... 25 2.3. Case study ...... 29 2.4. Modeling results and analysis ...... 33 2.4.1 Model parameter setup ...... 33 2.4.2 Performance evaluation ...... 33 2.5. Conclusion ...... 44 3. Change Detection of Ocean Wave Characteristics ...... 45 3.1 Introduction ...... 45 3.1.1 Ocean wave measurement ...... 45 3.1.2 High frequency (HF) radar systems ...... 46 3.1.3 Estimation of wave spectra ...... 47 3.1.4 Short-time Fourier transform (STFT) ...... 49 3.1.5 Feature extraction ...... 50 3.2 Proposed algorithm ...... 53 3.2.1 Short-time Fourier transform (STFT) ...... 53 3.2.2 Fuzzy C-means clustering-based feature extraction approach ...... 58 3.3 Case study ...... 63 3.3.1 Study area ...... 63 3.3.2 Test setup ...... 64

3.3.3 Data set ...... 65 3.3.4 Result analysis ...... 66 3.4 Conclusion ...... 75 4. Regression Models for Ocean Wave Identification Using High Frequency Radar Systems .... 77 4.1 Introduction ...... 77 4.2 Proposed detection model ...... 80 4.2.1 Autoregressive (AR) model ...... 81 4.2.2 Short-time Fourier transform (STFT) ...... 83 4.2.3 Ocean wave characteristic detection ...... 84 4.3 Case study ...... 85 4.4 Modeling result and analysis ...... 89 4.4.1 Model parameter setup ...... 89 4.4.2 AR model performance evaluation ...... 89 4.4.3 Feature analysis ...... 93 4.5. Conclusion ...... 103 5. An ICA-Based Model for Ocean Wave Identification Using High Frequency Radar Systems ...... 104 5.1 Introduction ...... 104 5.2 Proposed detection model ...... 107 5.2.1 Ocean wave feature based on independent component analysis ...... 108 5.2.2 ICA-based ocean wave characteristic feature ...... 110 5.3 Case study ...... 111 5.4 Modeling result and analysis ...... 114 5.4.1 Model parameter setup ...... 114 5.4.2 Feature extraction ...... 114 5.4.3 Feature comparison ...... 116 5.4.4 Validation for IIF feature extraction model ...... 118 5.5 Conclusion ...... 120 6. A PCA-Based SVM Model for Ocean Wave Monitoring Using High Frequency Radar...... 122 6.1 Introduction ...... 122 6.2 Proposed detection model ...... 126 6.2.1 Ocean wave feature based on principal component analysis ...... 126 6.2.2 PCA-based ocean wave characteristic feature ...... 127

6.2.3 Support vector machine (SVM) model for classificaiton ...... 129 6.3 Case Study ...... 131 6.4. Modeling result and analysis ...... 135 6.4.1 Model parameter setup ...... 135 6.4.2 Feature extraction ...... 135 6.4.3 Feature comparison ...... 137 6.4.4 Classification model ...... 139 6.5 Conclusion ...... 143 7. Conclusion ...... 144 7.1 Summary of the concluding remarks ...... 144 7.2 Future research ...... 146 REFERENCE ...... 147

List of Figures

Figure 2-1. Mega-tsunami ...... 17 Figure 2-1. Flow chart of the algorithm ...... 29 Figure 2-3. Study area for ocean radar installation ...... 30 Figure 2-4. Facility of WERA system ...... 31 Figure 2-5. Monitoring points and range ...... 32 Figure 2-6. Installation specification of HF radar ...... 32 Figure 2-7. Modeling results of the proposed ARMA model ...... 34 Figure 2-8. The 1st validation for the proposed ARMA model...... 35 Figure 2-9. The 2nd validation for the proposed ARMA model ...... 36 Figure 2-10. The 3rd validation for the proposed ARMA model ...... 37 Figure 2-11. Residual errors of the modeling result for the proposed ARMA model ...... 38 Figure 2-12. Residual errors of the 1st validation result for the proposed ARMA model ...... 38 Figure 2-13. Residual errors of the 2nd validation result for the proposed ARMA model ...... 39 Figure 2-14. Residual errors of the 3rd validation result for the proposed ARMA model ...... 39 Figure 2-15. QQ plot of the modeling result for the proposed ARMA model ...... 40 Figure 2-16. QQ plot of the 1st validation result for the proposed ARMA model ...... 40 Figure 2-17. QQ plot of the 2nd validation result for the proposed ARMA model ...... 41 Figure 2-18. QQ plot of the 3rd validation result for the proposed ARMA model ...... 41 Figure 3-1. Fourier transform view of STFT ...... 54 Figure 3-2. The discrete STFT as the output of a filter bank consisting of lowpass filters ...... 56 Figure 3-3. The discrete STFT as the output of a filter bank consisting of bandpass filters ...... 57 Figure 3-4. The proposed ocean wave change detection algorithm...... 62 Figure 3-5. Study area for ocean radar installation ...... 63 Figure 3-6. The WERA system ...... 64 Figure 3-7. Monitoring points and range ...... 65 Figure 3-8. Installation specification of HF radar ...... 66 Figure 3-9. Normal ocean wave height ...... 68 Figure 3-10. High wave height ...... 69

Figure 3-11. The STFT results using normal wave height data ...... 69 Figure 3-12. The STFT results using the high wave data ...... 70 Figure 3-13. HFOF(x) vs HFOF(dx) of December and January ocean wave ...... 72 Figure 3-14. Clustering of HFOF(x) and HFOF((dx)): Training ...... 73 Figure 3-15. Clustering of HFOF(x) and HFOF((dx)): Test 1...... 74 Figure 3-16. Clustering of HFOF(x) and HFOF((dx)): Test 2...... 74 Figure 3-17. Clustering of HFOF(x) and HFOF((dx)): Test 3...... 75 Figure 4-1. The flowchart of the proposed model ...... 80 Figure 4-2. Fourier transform view of STFT ...... 84 Figure 4-3. Study area for ocean radar installation ...... 86 Figure 4-4. Facility of WERA system ...... 87 Figure 4-5. Monitoring points and range ...... 88 Figure 4-6. Installation specification of HF radar ...... 88 Figure 4-7. Modeling results for proposed AR model ...... 90 Figure 4-8. The 1st validation for proposed AR model ...... 91 Figure 4-9. The 2nd validation for proposed AR model ...... 92 Figure 4-10. The 3rd validation for AR model ...... 93 Figure 4-11. Comparison of mean value for two groups of data ...... 94 Figure 4-12. Comparison of variance value for two groups of data ...... 94 Figure 4-13. Comparison of feature FCSS for two groups of data ...... 95 Figure 4-14. Comparison of feature FCS for two groups of data ...... 96 Figure 4-15. Comparison of feature ACS for training data ...... 97 Figure 4-16. Comparison of feature ACS for 1st validation data ...... 98 Figure 4-17. Comparison of feature ACS for 2nd validation data ...... 98 Figure 4-18. Comparison of feature ACSS for 3rd validation data ...... 99 Figure 4-19. Comparison of feature ACSS for training data ...... 101 Figure 4-20. Comparison of feature ACSS for 1st validation data ...... 102 Figure 4-21. Comparison of feature ACSS for 2nd validation data ...... 102 Figure 4-22. Comparison of feature ACSS for 3rd validation data ...... 103 Figure 5-1. Study area for ocean radar installation ...... 111

Figure 5-2. Facility of WERA system ...... 112 Figure 5-3. Monitoring points and range ...... 113 Figure 5-4. Installation specification of HF radar ...... 113 Figure 5-5. Normal ocean wave height ...... 115 Figure 5-6. Abnormal wave height ...... 115 Figure 5-7. The identification feature IIF for training data ...... 116 Figure 5-8. The identification feature PIF for training data ...... 117 Figure 5-9. The identification feature IIF for 1st validation data ...... 118 Figure 5-10. The identification feature IIF for 2nd validation data ...... 119 Figure 5-11. The identification feature IIF for 3rd validation data ...... 119 Figure 6-1. Study area for ocean radar installation ...... 132 Figure 6-2. Facility of WERA system ...... 133 Figure 6-3. Monitoring points and range ...... 134 Figure 6-4. Installation specification of HF radar ...... 134 Figure 6-5. Normal ocean wave height ...... 135 Figure 6-6. Abnormal wave height ...... 136 Figure 6-7. The identification feature PIF for training data...... 137 Figure 6-8. The identification feature HFOF for training data ...... 138 Figure 6-9. Comparison of feature ACSS for training data ...... 139 Figure 6-10. The training result of nonlinear SVM classifier using RBF kernel function ...... 140 Figure 6-11. The 1st validation result of nonlinear SVM classifier using RBF kernel function . 141 Figure 6-12. The 2nd validation result of nonlinear SVM classifier using RBF kernel function 142 Figure 6-13. The 3rd validation result of nonlinear SVM classifier using RBF kernel function 142

List of Tables

Table 2-1. Performance evaluation of the proposed estimation model and default model ...... 43 Table 4-1. Results of feature decision for four data sets...... 100

1. Introduction

Since early civilization, coastal areas have been ideal places for human settling as they provided abundant marine resources, fertile agricultural land and possibilities for trade and transport. In the last century, the global trade prosperity led to high population densities and high levels of development in many coastal areas. At present, about 1.2 billion people live in coastal areas globally, and this number is predicted to increase to 1.8 to 5.2 billion by the 2080s due to a combination of population growth and coastal migration. Along with this increase follows major investments in infrastructure and the built environment.

Frequent high waves, induced by the strong wind, tsunami, earthquakes, and/or other climate change conditions, however, pose some great challenges to human habitation. They always cause serious disasters. The huge energy attacks the coastal areas, leading to the full or partial collapse of structures and threats to life safety. For example, the 2004 Indian Ocean tsunami killed at least 230,000 people in 14 countries, ranging from Indonesia, Thailand, Malaysia, to thousands of kilometers away in Bangladesh, India, Sri Lanka, the Maldives, and even as far away as

Somalia, Kenya, and Tanzania in East Africa. Besides the direct loss, such as structural collapse and life safety, high waves may also bring other potential disasters. The 2011 Japan tsunami not only caused 15,891 deaths, more than 2500 people missing and more than one million structures damaged but also disabled the power supply and cooling of three reactors at the Fukushima Daiichi

Nuclear Power Plant, which resulted in a level-7 nuclear meltdown and release of radioactive materials. The serious aftermath is still affecting Japan and the neighboring countries, such as

China and Korea. Frequent high waves have become one of the major factors of the coastal disaster. Therefore, reducing or eliminating the frequent high wave attack would be the essential way to prevent the coastal disaster.

In order to eliminate the frequent high wave attack, routine ocean wave monitoring is extremely necessary. With monitoring, the authorities can alert public in advance to protect lives and property. Also, researchers would gain benefits from a deeper understanding of the ocean wave behavior, especially in calm and stormy weather conditions. What’s more, the government can evaluate the potential impacts on coastal communities.

Ocean wave data collection lays the foundation for the coastal disaster mitigation. Without reliable data, the subsequent analysis and forecasting are made useless. There are several methods for the ocean wave information collection. Two main collection methods are wave buoy and high- frequency (HF) radar systems. A wave buoy is a floating device that drifts with the sea waves. For wave buoys, the collection of ocean wave data is based on the measurement of buoy motion through mounted sensors such as accelerometers and tilt sensors. Therefore, due to its special working condition, it is at high risk of being damaged as the result of losing data. An HF radar is a remote sensing system that is installed on the shoreline and radiates high-frequency radio waves along the sea surface. The radio waves are then scattered back by the ocean waves. These backscattered Doppler waves may result in a strong return of energies at a very precise wavelength and direction. Using the Doppler spectrum, some information about oceanographic parameters is calculated. Because HF radars are installed at the shoreline, damage from various marine activities can be minimized. Considering the convenience and accuracy, high-frequency (HF) radar is the optimal measurement systems. Hence, in this research, the proposed framework is developed based on the HF radar systems.

Several estimation algorithms have been developed to estimate the ocean wave information. Most of them are physics-based modeling methods. To be specific, a physical model about the relationship among the several ocean wave parameters, such as ocean wave height and

12 ocean frequency, is generated based on first- and second-order Doppler power spectrum, which is derived from energy equations. Then the specific parameter is achieved through computation of the physical model. The advantage of the physics-based model is the relationships between observations are clearly described using mathematical equations. Hence, the model is interpretable. However, it is challenging to develop a robust parametric model. On the one hand, there are significant uncertainties associated with the parametric model. As a result, it is almost impossible to derive the parametrical model that can accommodate numerous unknowns. On the other hand, in order to achieve the parameter, it is required to compute a large-scale of complicated nonlinear two-dimensional integral equations without linearization and approximation. Therefore the requirement of computation capacity is strict. With this in mind, the application of a data- driven modeling framework that does not require any physical model would be an alternative solution.

In this dissertation, a novel data-driven framework for ocean wave analysis using HF radar systems is proposed. For the ocean wave analysis, large amounts of data need to be processed in a short period of time due to the rapid change of the ocean wave motion. This framework addresses this critical issue and provides a pipeline for the analysis of complex ocean wave behavior within a limited time. With its emphasis on computational efficiency, the framework makes real-time ocean wave monitoring possible. Specifically, the framework consists of three modules: a forecasting module, a feature extraction module, and a classification module. The forecasting module is the module for ocean wave information prediction. In this study, the specific information is ocean wave height. The purpose of this module is to forecast the ocean wave height that far away from the coast in real-time, based on the existing observations so that the potential of ocean wave behavior can be predicted in advance. If the predicted behavior were unusual, it would be a

13 warning sign to inform the authorities that some attention should be paid. In this framework, the forecasting module is implemented with a modified nonlinear, autoregressive and moving average

(ARMA) model. An ARMA model is a widely used algorithm to model time series systems. Its main idea is that prediction can be represented through the linear combination of historical information. The application of ARMA modules is based on the assumption that the system is linear and time-invariant (LTI). However, the ocean wave system is highly nonlinear, time- varying, and non-stationary. Therefore, the traditional ARMA model may not be a good forecasting method. In addition, traditional ARMA model requires determination of the order (i.e. the number of terms to represent) in advance. The order should be selected properly, otherwise, the model may be either time consuming or not accurate. The proposed model overcomes those drawbacks. First, it includes not only the linear terms but also the nonlinear terms, such as the quadratic and cubic terms, to fit the nonlinear behavior of ocean wave system. Moreover, the model can auto-select the required terms so that it can be both accurate and computationally efficient.

The feature extraction module is for ocean wave characteristics identification. A feature is an individual measurable property or characteristic of a phenomenon being observed. For example, in an ocean wave, it can be ocean wave height and ocean wave frequency. The purpose of a feature would be much easier to understand in the context of a problem. In general, a feature should be encode as much information as possible concerning the task of interest and minimum information redundancy. Theoretically, any property can be a feature. However, a good feature should be a direct measure to express and distinguish differences. It should be neither too general nor unreliable. In this study, feature extraction is a scientific approach to extract or generate the identification property of ocean wave based on realizable observations, such as the ocean wave height. In this study, three different features are introduced: the frequency-based feature, HFOF;

14 the AR-based feature, ACSS; and the ICA-based feature, PIF. The frequency-based feature, HFOF, comes from time-frequency analysis. Time-frequency analysis is widely used for system identification (SI) in structural engineering. However, unlike SI, in this study, the analysis method is short-time Fourier transform (STFT) instead of the traditional Fourier transform. The main reason is that the ocean wave system is a highly nonlinear, time-varying, and non-stationary system, which conflicts with the basic assumption of an LTI system when applying Fourier transform. The frequency-based feature is then developed based on the STFT. It tells not only the frequency property of the ocean wave but also how the property changes with respect to time. The

AR-based feature, ACSS, is extracted from the auto-regressive (AR) model. The AR model is also a good system representation in theory of linear theory. This feature is highlighted with its excellent identification. The ICA-based feature is derived from the independent component analysis (ICA). ICA is a linear transformation method generally used for blind source separation.

It explains the variance property of the ocean wave. Every feature tells the different properties of the ocean wave from different perspectives.

The classification module serves to classify different types of ocean waves based on the identification features. In this study, the classifier is selected as the support vector machine (SVM) with radial basis function (RBF) kernel function. The SVM finds the optimal criteria to separate different types of ocean waves. What’s more, the criteria is well expressed with a mathematical equation. With the RBF kernel function, the SVM classifier can even be applied to the nonlinear classification question. Therefore, the SVM with RBF kernel function provides a robust, systematic criteria to identify the type of ocean wave for each observation.

The proposed algorithms are validated through field data obtained from Samcheok City,

Gangwondo which is located on the east coast of Korea. This area is the optimal choice as it has

15 experienced high wave damage in previous years. Based on the field data, the proposed algorithms are simulated for abnormal ocean wave forecasting, identification, and classification. The field data is ocean wave height data collected from July 1, 2012 to June 30, 2014 using two HF radar systems. The HF radar systems used for this study are WERA (WavE RAdar), developed by the

German company Helzel Messtechnik GmbH in 2000. Each radar system is operated at a frequency band of 24.525MHz with a bandwidth of 150 KHz for 1km lattice spacing resolution.

The azimuths of center beam of the two radar systems are 95.8° and 37.3°, respectively, with the range of ±60° from the central angle.

This dissertation combines five journal papers, listed from Chapters 2 to 6. Chapter 2 outlines the performance of the proposed nonlinear autoregressive and moving average (ARMA) models as a means for ocean wave forecasting of HF radar systems. Chapters 3 to 5 discuss three feature extraction models, frequency-based feature, AR-based feature, and ICA-based feature, that were used to extract and analyze the nonlinear behavior of ocean waves. Chapter 6 details use of the SVM model as the classification model to classify different types of ocean waves in the coastal area. The conclusions and the future work that follows from the research are expressed in Chapter

2. Real-time Forecasting of Ocean Wave Signals Using High Frequency Radar

Systems

2.1 Introduction

Every year high waves in the ocean have caused huge losses of both life and property: Many people have died and/or disappeared due to high waves from all parts of the world. Since high waves suddenly rise, they have also threatened to capsize ships. Such a hydrological process is the most common cause of coastal bridge failure in the world (Wardhana and Hadipriono 2003).

Figure 2-1. Mega-tsunami

(http://stanislauscollege.blogspot.com/2014/11/mega-tsunami.html)

The east coast of Korea is especially exposed to the danger of tsunami because it is close to Japan.

The west coast of Japan embodies many potential areas with a great tsunami that may be triggered by earthquakes (Figure 2-1). In particular, severe damages took place in the region when tsunami

17 occurred in the west of Japan in 1986 and 1993. In particular, the fear of tsunami destruction has increased from the 2011 Great Tsunami of Japan (Mimura et al. 2011). Frequent high waves induced by the tsunami, earthquakes, strong wind, and/or other climate change conditions have become one of the major factors of the deaths of thousands and thousands of people, coastal structure damages, beach erosion and various coastal disasters in the shoreline. In order to decrease the coastal disaster, it is essential to monitor the high waves in real time.

It is challenging to develop an effective method to mitigate the coastal disaster in a systematic way: 1) it is difficult to measure the coastal high waves in the ocean, 2) the wave height, period and current in the shoreline are significantly influenced by the unpredictable ocean waves, and 3) it is very challenging to develop a robust parametric forecasting model that can accommodate numerous unknowns in order to predict the complex behavior of wave forces in the shoreline. With this in mind, we propose novel forecasting models to predict environmental changes in the ocean which is so far away from the shoreline.

As previously discussed, forecasting of ocean wave conditions such as wave heights, currents, and periods is mightily important for coastal hazard mitigation. However, the ocean wave data collection is not readily available for a number of reasons, in particular, sensor installation in the open ocean area. The limited data collection of ocean waves has been a serious impediment to the development of an effective ocean wave forecasting model. However, high-frequency (HF) radar systems can be an alternative system for more reliable measurement of ocean surface waves.

It is generally known that the HF radar system has become one of the most effective ocean wave measurement systems. However, a forecasting model using the real-time HF radar system has not yet been developed conceptually nor thoroughly tested empirically.

Several methods have been proposed for significant wave prediction. The commonly adopted methods can be categorized as three parts: empirical, numerical, and statistical approaches. Empirical methods are simplified wave prediction methods. They usually rely on semi-empirical equations which are based on the interrelationships between dimensionless wave parameters (Kazeminezhad et al., 2005). They can be useful when quick, low-cost estimates are required. Several simple and fast methods have been developed and presented for wave forecasting, such as Wilson (1965), SMB (Bretschneider, 1970), Donelan (Donelan, 1980), Shore

Protection Manual (US Army Corps of Engineers, 1984) and Coastal Engineering Manual (US

Army Corps of Engineers, 2003). In all these models, it is assumed that wave height and period are determined using fetch length and meteorological data such as wind speed and duration

(Kazeminezhad et al., 2005). However, the performance of the empirical models depends on the quantity and quality of the data (Mahjoobi et al., 2008). In addition, traditional empirical methods are mostly based on the normality, linearity, and homoscedasticity assumptions such that the wind and wave directions are the same (Mahjoobi et al., 2008; Kazeminezhad et al., 2005). Thus, these methods would only be accurate in simple and limited cases (US Army 2003, Akpınar et al., 2014).

Numerical methods are theoretical physics-based approaches. The numerical models are generally based on the spectral energy or action balance equations, in a finite difference form throughout a grid placed over the water area (Gelci et al. 1957). This equation shows that the wave spectra evolution are related to the adiabatic effects of advection and refraction, and a source function S which is the sum of physical processes such as wind input, dissipation by breaking, and nonlinear interactions (Janssen, 2008). In the early 1960s, when researchers applied the energy balance equation to spectral wave models, the effects of wave energy advection induced by wind inputs and a rudimentary form of dissipation by white-capping were included, but the nonlinear

19 interactions were not considered. Although these so-called first–generation models were used successfully for many years, considerable doubt has existed as to the precise representation of the mechanism of wave generation. Besides, these models were unable to explain the pronounced overshoot phenomenon of a growing wind sea (Barnett & Wilkerson, 1967). In the early 1970s, through extensive field measurements (Mitsuyasu et al., 1971; Hasselmann et al., 1973), the analysis of the field observations led to a different view of the energy balance: the principle energy source of growing the waves with the low-frequency spectrum is the nonlinear energy transfer from the high-frequency components, rather than the direct wind force. Furthermore, such a nonlinear wave energy transfer has an important bearing on the shape of the spectra, i.e., frequency bandwidth and peaks.

Therefore, in the mid-1970s, it was clear that the nonlinear interaction impacted significantly on spectra evolution. But due to the lack of computing power, it was impossible to directly involve the effect of nonlinear energy transfer in the energy balance equation. However, a universal, quasi-equilibrium spectral distribution could be approximately represented by a single, slowly changing scale parameter in some limited conditions. Thus the so-called second-generation models emerged, based on a parametric description of the wind sea (Hasselmann et al., 1973).

Since then, the second-generation wave models have been used for many years, and even some of them are still working today. However, the models would not work for strongly non-uniform wind fields because of the effect of the advection terms, which are related to the nonlinear energy distribution and a significant error from the quasi-equilibrium spectral distribution. Hence an explicit expression for nonlinear interaction was required for a much broader application.

In the 1980s, with the aid of the improved computers and numerous data on the ocean surface collected from satellites, third-generation models for ocean wave prediction have been

20 developed (Komen et al., 1984). These third-generation models are based on both theoretical and experimental studies by a number of researchers (Phillips, 1957, 1958; Miles, 1957; Snyder et al.,

1981; Hasselmann et al., 1985; Janssen, 1991). Based on third-generation models, Wave Model

(WAM) was proposed for large-scale deep-water applications (WAMDI Group, 1988).

Furthermore, several other models had been developed. WAVEWATCH III, developed by

National Oceanic and Atmospheric Administration (NOAA), has presented hindcast in North Sea.

Unlike the WAM, WAVEWATCH III accounted for unsteady wave-currents interactions (Tolman et al., 2002). The Simulating Waves Near shore (SWAN) model was developed for modeling random, short-crested waves in coastal regions with shallow water and ambient currents (Booij et al., 1999). SWAN has been used successfully in some applications such as hindcast (Ris et al.,

1999) and real-time wave prediction systems for coastal areas (Rogers et al., 2007; Dykes et al.,

2009). Even though the third-generation models can provide an explicit representation of the physical processes relevant for wave evolution, such numerical models can be quite limiting for practical use, however. This is due to the complexity of meteorological data collection and processing (Goda, 2003; Browne et al., 2007). Hence, a new simple but robust modeling framework is needed for ocean wave forecasting.

Statistical methods are very useful for forecasting time series such as the ocean waves. In particular, autoregressive (AR) moving average (MA) is very useful in forecasting the ocean wave signals. Spanos (1983) proposed three different linear AR, MA, and ARMA models for modeling a power spectrum of ocean waves: the Pierson-Moskowitz (PM) spectrum. These models are based on the development of the linear prediction theory, in which the time series of the ocean wave is considered as the output of an autoregressive digital filter to white noise input. As the result, the time series approximation problem was reduced to the determination of the optimal parameter

21 values of the digital filter pulse transfer function. These parameters were determined by minimizing the error dynamic equation, yielding the solution to the nonlinear algebraic equations.

It was shown from the simulation that a good agreement between the estimated spectrum and the target PM spectrum was found. However, in this case, a set of nonlinear algebraic equations must be solved. Therefore, it would be challenging to be applied in real time. Mandal et al. (1992) established a spectral estimation method for modeling marine environmental data. The estimator is a reduced order ARMA model, using the Akaike Information Criterion (AIC), modified Yule-

Walker (MYW) and the model order reduction techniques. They compared the predictions of the proposed model with both the theoretical PM and JONSAWAP spectrums. However, it was demonstrated under some limited conditions, i.e., the wind speed is 10 m/s. Spanos and Zeldin

(1996) presented an efficient method for the two stage ARMA approximation. This method was used to adjust the parameters for a linear ARMA approximation of a random process. The algorithm was applied to the PM spectrum and then the approximation errors of the proposed method were compared with those of the auto-cross-correlation matching (ACM) method. The comparison showed the accuracy of the ocean wave spectrum estimator. However the effectiveness of the approach was demonstrated using a theoretical PM spectrum, not the real ocean wave signals.

All of the aforementioned ARMA models have been applied based on the assumption that the ocean waves under investigation are linear and time-invariant (LTI). In addition, they have only been theoretically proven that the ARMA model is effective in predicting ocean wave spectrum. In fact, ocean waves are highly nonlinear, time-varying, non-stationary signals.

Therefore, it clear that a nonlinear ARMA model with improved accuracy is needed to forecast the real ocean waves in real time. To develop a real-time nonlinear ARMA forecasting model, a

22 logical first step is using a robust real-time sensing system to collect ocean waves information in a systematic way. High frequency (HF) radar systems are employed in this study to collect ocean wave height data in real time. However, robust ARMA models employing the HF radar systems have not been yet developed conceptually nor thoroughly tested empirically. In this study, the proposed nonlinear ARMA model is extensively tested using a variety of different field data collected from the HF radar system. The performance of the proposed model is also evaluated in both quantitative and qualitative ways. Furthermore, the proposed ARMA model performance is compared with the benchmark model outputs.

The organization of the article is as follows: A novel forecasting model is presented in section 2. Section 3 discusses case studies, including case study sites and real-time HF radar systems. The modeling and extensive validation results are presented in section 4. Concluding remarks are given in section 5.

2.2 Proposed forecasting model

In this paper, a novel, autoregressive moving average (ARMA) model is proposed for forecasting of ocean wave height in real time. The nonlinear ARMA model is an integrated model of (ARMA) model, nonlinear cross terms, and an automatic model order selection algorithm. The ocean waves are measured via the HF radar system. After the significant wave heights are extracted, the prediction model is made to estimate the ocean wave height. The prediction error is minimized by using the least squares method.

2.2.1 Linear ARMA model

A linear ARMA model is given by

P Q yn() ayniij (-)  benjen (-)(),  (2.1) ij10

where P and Q represent the AR and MA model orders, respectively. The term e(n) is considered a noise source or a prediction-error term. The parameters ai and bj represent to-be-estimated coefficients of the AR and MA terms, respectively.

2.2.2 Proposed nonlinear ARMA model

The linear ARMA model is powerful in modeling linear systems. However, the prediction of ocean wave height is a highly complex nonlinear problem. Therefore it may not be accurate and efficient to apply the linear model to the nonlinear problems. With this in mind, a nonlinear ARMA model is proposed in this study to estimate the ocean wave height in real time. The nonlinear ARMA model depends on not only its previous output but also the products between the outputs. The nonlinear ARMA (NARMA) model is defined as

PMM yn()(-)()() aynii   bynpynq pq    i11 p  q  p

UUU Q (2.2) cyniynijk( )(  jynk )(  )   denj j (-)(),  en i10 j  i k  j j 

24 where P is the AR model order, M is the quadratic AR model order, U is the cubic AR model order, and Q is the MA model order. To develop this model, the key is to determine the values of ai, bpq, cijk, and dj that provide the best fit to the data. The most widely used method to determine the values is the maximum likelihood method. This method selects the set of values of the model parameters that maximizes the "agreement" of the selected model with the observed data.

Therefore, the method has the advantage among other methods that the estimated parameters are more efficient. However, it still has a drawback that the accuracy of model is totally dependent on the selection of model-order. Because the parameters are estimated after the model-order selection, even though the estimation of parameters is accurate under the setting model-order, it is still unknown whether the model-order is appropriate or not. It is possible that the model becomes inaccurate due to the inappropriate model-order selection. Therefore an automatic selection of model orders is proposed in this paper.

2.2.3 Optimization of model structure and its parameters

In order to accurately and efficiently obtain the nonlinear ARMA model, a new algorithm is introduced. The new algorithm for optimized search criterion, based on the concept of affine geometry, utilizes nonorthogonal projection search criteria. Therefore it may enable the model both accurate and efficient. The first step in this algorithm is to select only the linearly independent vectors from the pool of candidate vectors.

Consider the nonlinear ARMA process defined as in Eq. (2.2). The candidate vectors for search are: y(n-1),…,y(n-P), y(n-1)y(n-1),…,y(n-M)y(n-M), y(n-1)y(n-1)y(n-1),…,y(n-U)y(n-U)y(n-U) and e(n),…, e(n-Q). The candidate vectors can be arranged as the matrix shown below:

ABCD, (2.3)

where

y(0) y (1 P )  y(1) y (2 P )  A  , (2.4) y()() n y n P   y( N 1) y ( N P )

y(0) y (0) y (1 M ) y (1 M )  y(1)(1) y (2 M ) y (2 M )  B  , (2.5) y( n 1) y ( n  1) y ( n  M ) y ( n  M )   y( N 1) y ( N  1) y ( N  M ) y ( N  M )

y(0) y (0) y (0) y (1 U ) y (1 U ) y (1 U )  y(1)(1) y (1) y (2 U ) y (2 U ) y (2 U )  C  , and (2.6) yn(1)(1)(1) yn  yn  ynUynUynU (  )(  )(  )   yN( 1)( yN  1)( yN  1) yNUyNUyNU (  )(  )(  )

e(1) e (1 Q )  e(2) e (2 Q )  D  , (2.7) e()() n e n Q   e()() N e N Q

where 푁 is the total number of data points. With the new candidates of linearly independent vectors, the least squares analysis is performed

T yW(n )g e ( n ), (2.8)

where W = [w0, w1,…, wR] is the selected linearly independent vectors, R is the number of selected linearly independent vectors, and

T gR g0,, g 1, g (2.9)

In Eq. (2.9), gi is the coefficient estimate of the nonlinear ARMA model. The objective is to minimize the equation error, en  , in the least squares sense using the criterion function defined as follows

2 J()(). y n TW N g g (2.10)

The criterion function in Eq. (2.10) is quadratic in θg and can be minimized by taking the a partial derivative with respect to θg, yielding the following least-squares equation

1 ˆ T g  WW Wy(n ). (2.11)

22 With the obtained coefficients, calculate every gwmm, and rearrange the wm in descending order.

Note that the over-bar represents the time average. At this step of the algorithm, the number of candidate vector wm necessary for obtaining proper accuracy needs to be chosen. This approach is taken in order to retain only the wm values that reduce the error value significantly. If either negligible decrease or increase in the error value by adding an additional wm value is found, then those wm values are dropped from the model. Once only those wm values that reduce the error value significantly are obtained, the proposed nonlinear ARMA model terms are estimated using the least squares method, as described by Lu et al (2001). The flow chart of the algorithm is displayed in Figure 2-2.

Figure 2-1. Flow chart of the algorithm

2.3. Case study

In order to verify the effectiveness of the proposed estimation model, Samcheok City, Gangwondo, was selected as a study area. Samcheok City is located on the east coast of Korea (Figure 2-3).

This areas has been on the alert for high wave damages in the previous years.

Figure 2-3. Study area for ocean radar installation

The HF radar used for this study is WERA (WavE RAdar), developed by the German company

Helzel Messtechnik GmbH in 2000. Each radar consists 4 transmitters and 8 receivers with the operation radio frequencies from 5 and 50 MHz. The waves and currents are collected as high as

27km and 48km, respectively. The cell sizes can be determined ranging from 300m to 3km in distance. The data collection interval is between 0.5 second to 10 minutes with a time integration analysis for every 10 minutes. In particular, the collection data can be browsed through web and searched based on time basis (UTC-base). The devices needed for the ocean radar include transmitter (TX) and receiver (RX) antennas, control server, GPS receiver, and accessories (Figure

2-4).

Figure 2-4. Facility of WERA system

In this study, the ocean radars operated at a frequency band of 24.525MHz with a bandwidth of

150 KHz for 1km lattice spacing resolution. The azimuths of center beam of the two radar systems are 95.8° and 37.3° (Figure 2-5), respectively, with the range of ±60° from the central angle (Figure

2-6). The data collection lasted two years from July 1, 2012 to June 30, 2014

Figure 2-5. Monitoring points and range

Figure 2-6. Installation specification of HF radar

2.4. Modeling results and analysis

2.4.1 Model parameter setup

In this section, the effectiveness of the developed model was demonstrated using the HR radar data collected in the field. The ocean wave heights were measured through two HF radar systems. To train the proposed estimation model, a subset of these data were selected. The subset ocean wave height data were measured between December 6, 2012 and December 15, 2012 with a sampling interval of 86 seconds. The number of terms to be searched for the proposed nonlinear ARMA model was selected as: AR = 10, MA =1, quadratic AR = 5 and cubic AR = 5.

2.4.2 Performance evaluation

2.4.2.1 Visual performance analysis

The performance of the forecasting model can be judged by visual inspection. It is easy to capture the overall behavior of the model without conducting extensive quantitative analysis. In this study, the time history plots that compares the field data with the forecasted values are used first. Figure

2-7 shows the selected training results of the proposed nonlinear ARMA model. The solid lines represent the forecasted values and the dotted lines are the measured data. As shown in Figure 2-

7, strong agreements between the nonlinear ARMA model and the HF radar data is found.

Figure 2-7. Modeling results of the proposed ARMA model

To generalize the forecasting capacity of the proposed nonlinear ARMA model, the trained model was tested using another three data sets that were not used for the training process. The measurements used for the testing were collected between January 6, 2013 and January 8, 2013.

Figure 2-8, Figure 2-9 and Figure 2-10 show the first, second, third validation results, respectively.

As shown, the output of the proposed nonlinear ARMA model agrees well with the field data set.

Figure 2-8. The 1st validation for the proposed ARMA model

Figure 2-9. The 2nd validation for the proposed ARMA model

Figure 2-10. The 3rd validation for the proposed ARMA model

The residual plots and quantile-quantile (QQ) plots are also used. Figure 2-11 to Figure 2-14 show the residual error plots for four data sets. The residual errors of all the data sets appear random.

Therefore, there is no reason to suspect that systematic errors are present in the models.

Figure 2-11. Residual errors of the modeling result for the proposed ARMA model

Figure 2-12. Residual errors of the 1st validation result for the proposed ARMA model

Figure 2-13. Residual errors of the 2nd validation result for the proposed ARMA model

Figure 2-14. Residual errors of the 3rd validation result for the proposed ARMA model

Figures 2-15 to Figure 2-18 present the QQ plots of the forecasting model and measured data. If the model and data have the same distribution, the QQ plot will be linear. From Figures 2-15 to

Figure 2-18, all the four QQ plots are closely linear, which means that both models and data sets come from the same distribution.

Figure 2-15. QQ plot of the modeling result for the proposed ARMA model

Figure 2-16. QQ plot of the 1st validation result for the proposed ARMA model

Figure 2-17. QQ plot of the 2nd validation result for the proposed ARMA model

Figure 2-18. QQ plot of the 3rd validation result for the proposed ARMA model

2.4.2.2 Quantitative analysis

In order to quantify the predicted data and measured data, several evaluation indices were used.

The benchmark linear ARMA model was used as a baseline. The first evaluation index, the percent error in maximum values (J1) was used to determine if the forecasting model can produce a similar range of observed data.

max yyi  max ei  J1 100% , (2.12) max yi 

where ye = the forecasting value, y = the data measured in the field, and Nt = the number of data points. The bias (J2, the mean of the residuals) and mean square error (J3) were adopted to determine if the forecasting model tends to overestimate and underestimate the measured data as the second and third indices, respectively.

1 Nt J2  yi y ei  , (2.13) Nt i1

Nt 1 2 J3  yi y ei  . (2.14) Nt i1

The root mean square error (J4) was also calculated to express the error metric in units of m.

Nt 1 2 J4  yi y ei  , (2.15) Nt i1

To see how well the forecasting model captures the variance in the measured data, the coefficient of determination (J5) was used.

Nt 1 2  yyi ei  Nt i1 J5 1 N . (2.16) 1 t 2  yyi   Nt i1

The computation time (J6), which was measured by the computer, illustrated the complexity of the process. Table 2-1 shows the performances of the proposed nonlinear ARMA model, including the comparison of the proposed model and the benchmark ARMA model.

Table 2-1. Performance evaluation of the proposed estimation model and default model

Data Model J1 J2 J3 J4 J5 J6 Proposed Model 0.80% 2.04E-04 3.96E-05 0.0063 0.9996 2.13 Training Benchmark 60.49% 7.38E-01 1.30E-01 0.3611 -0.5729 359.59 Proposed Model 0.19% 8.05E-04 3.09E-04 0.0176 0.9968 0.75 1st validation Benchmark 59.37% 1.18E-01 1.51E-01 0.3882 -0.5491 14.49 Proposed Model 1.82% 4.68E-04 2.98E-04 0.0172 0.9964 0.70 2nd validation Benchmark 69.18% 1.31E-02 1.31E-01 0.3620 -0.5798 18.29 Proposed Model 0.19% 8.05E-04 3.09E-04 0.0176 0.9968 0.73 3rd validation Benchmark 54.72% 1.20E-02 1.52E-01 0.3900 -0.5636 12.92

As shown in Table 1, it is observed from both training and testing processes that the proposed

ARMA model demonstrated good performances in forecasting the complex behavior of ocean waves. According to all the six evaluation indices, the proposed nonlinear ARMA model gives

43 better performance than the benchmark ARMA model, implemented using the MATLAB function

‘arima’. For the proposed model, the J1 metric for all the four cases was very small. Every J1 is within 2.0%. It showed the forecasting model correctly produced a similar range of measured data.

The coefficients of determination (J5) for the proposed model ranged from 0.9964 to 0.9996, indicating strong agreement. As seen in all the 5 indices of errors, most of the training errors were lower than the validation errors.

2.5. Conclusion

In this paper, a novel model was proposed for the forecasting of real time ocean wave height. It was developed through the integration of linear autoregressive moving average (ARMA) models, nonlinear cross terms, the weighted least squares estimation algorithm, an automatic order selection algorithm and the HF radar system. To demonstrate the effectiveness of the proposed forecasting model, two Wellen radar systems were installed in Samcheok City, Gangwond-do in the East Coast of Korea. A randomly selected data set was used for training the proposed nonlinear

ARMA model. Other three data sets that were not used for the training process were used for validating the proposed model. It was observed from both training and testing cases that there are great agreements between the forecasted values and the measured data. It is shown from the extensive modeling processes that the proposed model is effective in predict ocean wave heights.

3. Change Detection of Ocean Wave Characteristics

3.1 Introduction

The real time detection of changes in ocean wave characteristics is a very complex problem which has not yet been definitively resolved. Central to this paper is the development of a novel approach for detecting changes in ocean wave characteristics. This paper presents challenging issues for ocean wave measurement and associated data collection devices. Then, ocean wave spectrum analysis is described, followed by a presentation of the novel ocean feature extraction approach.

3.1.1 Ocean wave measurement

The monitoring of ocean surface conditions such as wave heights and periods is of high importance to ocean research and a variety of related marine activities, such as physical oceanography, wave forecasting, ship routines, and coastal protection. To obtain ocean wave information, a variety of measurement techniques have been developed. The commonly adopted approaches fall into three categories: wave buoys, acoustic Doppler current profilers (ADCP), and high-frequency (HF) radars. A wave buoy is a floating device that drifts with the sea waves. For wave buoys, the collection of ocean wave data is based on the measurement of buoy motion through mounted sensors such as accelerometers and tilt sensors. However, wave buoys sometimes lose data because they are vulnerable to accidental or malicious damage from marine traffic. As a hydro acoustic current meter, ACDP devices measure current speed and direction over a range of sea depth, using the Doppler shift of backscattered acoustic signals (Griffiths et al., 1987; Wilson et al., 1997).

However, the accuracy of ACDP measurements is sensitive to temperature and salinity. A HF radar is a remote sensing system that is installed on the shoreline and radiates high-frequency radio

45 waves along the sea surface. The radio waves are then scattered back by the ocean waves. These backscattered Doppler waves may result in a strong return of energies at a very precise wavelength and direction. By means of the Doppler spectrum, some information about oceanographic parameters is calculated so that the ocean wave spectrum can be estimated. Because HF radars are installed at the shoreline, damage from various marine activities can be minimized. Thus they tend to be more durable than the other options. In addition, it is reported that the ocean wave measurements of HF radars are more accurate than the ocean wave estimates of ADCPs (Teague et al., 2001). Hence, this research selected the HF radar system as the main ocean wave measurement device for which the proposed ocean wave change detection algorithm would be developed.

3.1.2 High frequency (HF) radar systems

Over the past several decades, HF radars have attracted a great deal of attention in the field of ocean surface wave measurements. Barrick et al (1977) at the National Oceanic and Atmospheric

Administration (NOAA) developed the Coastal Ocean Dynamics Application Radar (CODAR) system, the first HF radar for this use. The system estimated the ocean wave height spectrum using ocean surface currents. Paduan and Roesenfeld (1996) used the CODAR to measure surface currents in Monterey Bay. Independently of the CODAR systems, other systems have also been developed. Prandle et al. (1993) developed the Ocean Surface Current Radar (OSCR) system to measure the surface currents in the Straits of Dover. They then used their measurements to conduct tidal analyses. Gurgel et al. (1986) developed a new system called Wellen radar (WERA) (Gurgel et al., 1999). They utilized WERA to measure surface currents and directional spectra of wave heights. The High-Frequency Ground Wave Radar (HF-GWR), designed and operated by Northern

Radar Systems in Canada, was used to estimate surface currents at Cape Race, on the east coast of

Canada (Hickey et al., 1995). The Courants de Surface MEsurés par Radar (COSMER) at the

University of Toulon was deployed in the Normand Breton Gulf to continuously collect sea surface current data (Broche et al., 1987). The Coastal Ocean Surface Radar (COSRAD) at James Cook

University in Australia was placed on the Great Barrier Reef (Heron et al., 1985) to observe sea- wave spectra, surface currents and boundary-layer winds. Takeoka et al. (1995) observed the sea surface of the Bungo Channel by means of High-Frequency Ocean Surface Radar (HFOSR) at the

Okinawa Radio Observatory Communications Research Laboratory (ORO/CRL) in Japan. The

Multi-frequency Coastal Radar (MCR) at the University of Michigan, Ann Arbor, was used as part of the third Chesapeake Bay Outflow Plume Experiment (COPE-3) (Teague et al., 2001). It measured the open ocean and then estimated the eastward and northward components of ocean currents. The Ocean States Measuring and Analyzing Radar (OSMAR2000), developed by Wuhan

University in China, was employed to measure wave spectra, wave heights and wind fields over the Eastern China Sea (Huang et al., 2002). The PortMap system at James Cook University in

Australia was used to map surface currents in Ports and Harbors (Heron et al., 2005). Although the HF radar systems have already widely applied to surface current measurement, research on the real-time estimation of the wave spectrum using HF radar data is still in its early stages.

3.1.3 Estimation of wave spectra

Several methods have been developed to estimate wave spectra. For example, an ocean wave spectrum can be estimated from first- and second-order Doppler spectra (Lipa 1977; Wyatt 1990).

Since Crombie (1955) identified the distinctive features of the sea echo Doppler spectrum, Barrick

(1972a; 1972b) has derived the theoretical formulations for the Doppler spectrum in terms of the

47 ocean wave spectra. It has been proven analytically and experimentally that the first-order spectrum provides the basis for surface current measurements. Based on the theory of the first- order Doppler spectrum, several commercial systems have been applied extensively to provide detailed maps of surface currents in coastal waters. However, the first-order spectrum requires a wide frequency band of operations and thus has a limited coverage area for remote-sensing per station (Barrick 1972a).

The second-order spectrum provides the basis for wave measurement by inverting the integral equation related to ocean wave spectra to the second-order Doppler spectrum. The Doppler spectrum is expressed as integral forms of the wave spectrum based on the HF radio wave scattering theory. Many researchers have successfully solved the inversion problems under certain conditions (Lipa, 1977, 1978; Lipa and Barrick, 1986; Lipa et al., 1990; Wyatt 1990, 2000; Gill and Walsh, 1992; Howell and Walsh, 1993; Gill et al., 1996; Hisaki, 1996; Hashimoto and Tokuda,

1999; Hashimoto et al., 2003; Green and Wyatt, 2006; Hashimoto et al., 2008). However, it is still challenging to derive wave spectra from the second-order Doppler spectrum because of the difficulty in inverting the integral equations. It is also because the lower-energy second-order

Doppler is closer to the noise level and therefore more likely to be contaminated (Lipa and Nyden,

2005). In particular, when the higher order nonlinear effects in the Doppler spectrum are dominant, the accuracy of wave measurements from the spectra may be limited (Wyatt, 1995; 2000).

In order to address these problems, Hisaki (2005; 2006) developed a new method to estimate ocean wave spectra. He integrated the energy balance equations and regularization constraints with the relationship equations between the Doppler and the ocean wave spectra.

However, it is difficult to solve this large-scale, nonlinear least squares problem. The solution of the nonlinear least squares formulation employing the iterative optimization algorithm is sensitive

48 to the initial values of design variables and the weighting factors of the objective function (Hisaki,

2009).

Rather than inverting nonlinear integral equations, Vizinho and Wyatt (2001) proposed the use of the modified-covariance method in order to monitor the rapidly varying oceanographic conditions. The results showed that the proposed spectral-estimation method, based on the autoregressive stochastic model, can provide sufficiently stable spectral estimates using short period data sets. Although this method is suitable for the fast-changing sea clutter environment, the resolution is relatively low when the signal-to-noise ratio is low (Tian et al., 2012). In other words, the quality control of the Doppler spectra and radar-estimated wave data is critical to the accuracy of wave estimations. It is therefore apparent that a much more reliable and accurate method for spectrum estimation of time-varying ocean wave signals should be developed.

3.1.4 Short-time Fourier transform (STFT)

As an alternative framework for spectrum analysis of ocean wave signals, the use of short-time

Fourier transform (STFT) is proposed that transfers random signals to the ordered sum of sinusoids or complex exponentials. STFT was first applied to speech and acoustic signals processing and analysis (Berouti and Makhoul, 1979; Godino-Llorente and Gomez-Vilda 2004). Then it was successfully extended to other application areas related to non-stationary signals, such as biomedical signals (De Boer et al., 1985). STFT is useful in analyzing HF radar data due to fast computation, allowing the real-time monitoring of rapidly-varying ocean wave signals. But there is, to date, no specific study of the application of STFT to ocean wave signals. In this paper, the use of the STFT method is integrated with a real-time feature extraction algorithm for wave detection and the classification of ocean wave characteristics.

The proposed approach is a novel integrated model of several algorithms such as STFT, clustering algorithms, statistical analysis, and feature extraction schemes; thus it is difficult to find similar methods in the literature. In general, it is challenging to develop a robust parametric model that can accommodate numerous unknowns and still predict the complex patterns of ocean wave signals. There are significant uncertainties associated with the parametric model for forecasting varying ocean wave patterns, including the definition of the time-varying ocean waves themselves

(magnitude, periods, and direction), wind velocity, wind duration, fetch, the original state of the sea surface, water depth, and earthquakes, among others. It has been nearly impossible to develop a robust parametric model for a variety of conditions in the field. This is because it is possible to derive a parametric model only when physical phenomena are fully understood. With this in mind, the application of a model-free, data-driven modeling framework that does not require any physical model would be an alternative solution. However, the performance of the proposed model can degrade when there is not feasible data, because the proposed model is data-driven.

3.1.5 Feature extraction

Various algorithms for the detection of characteristic features have been developed by a number of ocean engineering researchers: Oram et al. (2008) developed an edge detection algorithm in order to objectively detect significant edges at different user-defined length scales in remotely sensed images of the ocean’s surface. This algorithm was applied to coincident time series of remotely sensed sea-surface temperature (SST) and chlorophyll-a (CHLA) images to investigate the event-scale dynamics of meso-scale features of Southern California Bight. The results showed that the spatial orientation and time evaluation of these features were similar in both SST and

CHLA. Piedra-Fernández et al. (2010) illustrated a novel effective way of extracting relevant

50 features for ocean structure recognition in satellite image using filtersand Bayesian classifiers.

They applied their method to National Oceanographic and Atmospheric Administration satellite

Advanced Very High Resolution Radiometer (AVHRR) images and detected features of North-

East Atlantic and the Mediterranean, such as upwellings, eddies, and island wakes. The results showed that the proposed methodology reduced the number of features for description by 80%, thus significantly reducing the computational cost. Zhang et al. (2001) proposed a method of classifying ocean processes using observations obtained from an autonomous-underwater vehicle

(AUV). Then, they set up a simulation for distinguishing ocean convection from internal waves. It was found from the simulation that the controllable speed of the AUV can be utilized to classify ocean processes. An integrated scheme for detection, extraction and classification of linear ocean features in synthetic aperture radar (SAR) imaginary was proposed by Wu and Liu (2001). This methodology consisted of using histogram screening for the feature detection, wavelet analysis for feature extraction, and texture analysis for feature classification. Several applications of linear oceanic features were described, including fronts, ice edge, and polar low in the northern Pacific and the Bering Sea. The results indicated that this methodology laid a promising foundation for a more fully automated detection, extraction and classification system. This body of work demonstrates the powerful uses of the feature extraction.

Among all the feature extraction algorithms, some of them are specifically for ocean wave feature selections. Xu (1992) presented a texture analysis approach for extracting ocean wavelengths, directions, and heights in the frequency and spatial domains of ocean wave images.

He applied his algorithm to ocean wave images obtained from a harbor aero-photograph. The analysis results indicated that these approaches were powerful. Dowd et al. (2001) developed a statistical estimation framework for wave-SAR inversion. Their framework allowed the ocean

51 information content of SAR to be quantified on a wavenumber-dependent basis. This regression framework was based on the extraction of directional ocean wave spectra from SAR imagery. They successfully used the framework to extract wave estimates from the SAR spectra, including wave number dependent error estimates and explicit identification of spectral null spaces where SAR contains no wave information. However, these extraction algorithms are based on ocean wave images such as harbor aero-photograph or SAR imagery, rather than HF radar data.

Gill and Walsh (1992) developed a procedure which could be used to extract directional wave-height spectra from HF ocean backscatter received from a four-element square array. The technique was based on a numerical method by solving the integral inversion equation. They tested this algorithm experimentally by comparing radar results for the non-directional wave height spectrum with data provided by a Waverider buoy. They found that for operation in the upper HF band, noise and ocean currents significantly affected the stability of the inversion. Because the method needs a numerical model that requires a high cost of computations, it would not be effective for real-time estimation of ocean wave characteristics detection. With this in mind, in this study proposed a novel ocean wave feature extraction method employing the STFT and statistical analysis. This method is useful in real-time detection of ocean wave characteristics using

HF radar systems. The STFT conducts the real time spectral analysis and then ocean wave characteristics are formulated in terms of the STFT estimation results and significant wave heights using statistical analysis. Next, any changes in ocean wave signals are classified using fuzzy C- means clustering algorithms.

3.2 Proposed algorithm

In this paper, a novel ocean wave detection algorithm is developed. The ocean waves are measured via the HF radar system. After the significant wave heights are extracted, the data are analyzed both in the frequency and time domains. In the frequency domain, spectra are estimated using the

STFT. In the time domain, the expected values and variances are determined. Based on both wave frequency and time-series information, characteristic features are extracted using the fuzzy C- means clustering algorithm for detecting changes in ocean waves in real time.

3.2.1 Short-time Fourier transform (STFT)

When HF radar spectra are analyzed using the Fourier transform, it is common to encounter the problem that the Fourier transform cannot characterize changes in the spectral content of a given signal over time because of the time-varying frequency characteristics. In contrast, the STFT consists of a separate Fourier transform for each instant. Thus it is possible for STFT to provide information on when a signal changes and at which frequency. It is advantageous to combine time series analysis and time-varying frequency-domain analysis under a single analysis framework. In this paper, two different STFT algorithms are introduced for the ocean wave data and then an algorithm is selected.

3.2.1.1 Fast Fourier transform (FFT)-based STFT

The STFT is presented in this section as an extension of the basic Fourier transform definitions of a sequence. The usual short-time Fourier transform representation of a discrete-time signal x (n) is given by

 X n,  x m w n m e jm (3.1) m

where X(n,ω) is the Fourier transform function of discrete-time signal x(n) with time index n and frequency variable ω; w(n) is the window function which determines the portion of the input signal that receives emphasis at a particular time index n; m is the shift variable; and j is the imaginary unit. It can be applied using the following procedure: 1) An appropriate window function, w(m), is selected such that the desirable portion of the time series is shifted by n points; 2) The discrete- time signal x(m) is multiplied by the modified window function; and 3) The Fourier transform of the resulting short-time section is taken to obtain the frequency function X(n, ω) (Figure 3-1) .

Figure 3-1. Fourier transform view of STFT

Analogous to the discrete Fourier transform (DFT), the discrete STFT is obtained from the discrete-time STFT through:

X n, k  X n , | 2  k (3.2) N

where the discrete-time STFT results are sampled with a frequency sampling interval of 2 in N order to obtain the discrete STFT. Substituting Eq. (3.2) into Eq. (3.1), the relation between the discrete STFT and its corresponding sequence x[n] becomes:

2   j km X n, k  x m w n m e N (3.3) m

where k is the frequency index.

3.2.1.2 Digital filter-based STFT process

The STFT can also be viewed as the output of a filtering operation where the window function w[n] plays a key role as an impulse response filter. For the filtering view of the STFT, the value of k at ko is fixed, and Eq. (3.3) is re-written as

 2  j ko m X n, k x m eN w n m  o       (3.4) m 

2  j ko m It can be observed that the STFT represents the convolution of the sequence x[] m e N with the sequence w[n].

2  j ko m N X n, ko   x m e w n (3.5) 

2  j ko n In other words, X (n, ko) at ko each can be obtained by a signal x[n] being modulated with e N , the results of which are passed through a filter whose impulse response is the window function, w[n] (Figure 3-2).

Figure 3-2. The discrete STFT as the output of a filter bank consisting of lowpass filters

A slight variation on the filtering and modulation view of the STFT is obtained by manipulating

Eq. (3.3) into the following form:

22 j koo n j k n NN X(,)[][] n ko  e x n w n e (3.6) 

In this case, the sequence x[n] is passed through the same filter as in the previous case except for

2  j k n a linear phase factor. The filter output is then modulated by e N o (Figure 3-3).

Figure 3-3. The discrete STFT as the output of a filter bank consisting of bandpass filters

Comparing the two views of STFT, in the view of the FFT-based STFT, STFT X (n, ko) is considered a function of frequency index ko with the fixed time index n. For the fixed n, X (n, ko) is simply the normal Fourier transform of the sequence w(n-m)x(m). Hence X (n, ko) is the Fourier transform of a time series of limited time-interval sections. In contrast to the FFT-based STFT, the digital filter-based STFT X (n, ko) is a function of time index n with the fixed frequency index ko.

In particular, with a finite number of frequencies, X (n, ko) can be considered as the output of a filter bank. In other words, X (n, ko) is the collection of sequences, each corresponding within a particular frequency band. In this paper, the FFT-based STFT is used for ocean wave frequency analysis, because the main purpose of this study is to investigate the ocean wave characteristic changes in real-time. The FFT-based STFT allows the analysis of frequency characteristic in a short time-interval.

3.2.2 Fuzzy C-means clustering-based feature extraction approach

As previously mentioned, the goal of this study was to develop a robust real-time decision making model, which identifies dangerous situations in the ocean environment in order to enhance the comprehension and recognition of a local officials/supervisors prior to making a decision. To this end, the ocean wave information is captured using the HF radar system and then processed via the

FFT-based STFT algorithm to extract key features. The processed data is classified into normal and abnormal categories using a fuzzy C-means clustering algorithm. In ocean engineering, there are few applications of fuzzy C-mean clustering. Sousa et al. (2008) developed an algorithm, through the application of fuzzy C-means clustering and validation indexes, to automaticcally identify the areas covered by upwelling waters. They used 16 sea surface temperature (SST) images obtained over the coastal ocean of Portugal and found that the results were consistent with the oceanographic knowledge of the Portuguese upwelling area.

Fuzzy C-means clustering can be formulated as (Dunn in 1973; Bezdek in 1981).

kn m JUCX, , i, j || x j c i || (3.7) ij11

which is subject to

k  ij, 1 (3.8) i1

where µi,j is the membership grades for data point xj in the ith cluster whose values are between 0 and 1; X = (x1,x2,…,xn) is a set of samples; C = (c1,c2,…ck) is a vector of cluster center, which has to be determined; m > 1 is a design parameter; U=[µi,j] is the partition matrix with k × n dimension; n is the number of the data set; and k is the number cluster center. Taking the derivative of Eq.

(3.7) and (3.8) leads to the necessary conditions:

n m i, j x j j1 ci  n m (3.9) ij,  j1

in which

2/(m 1) k ||xc ||   ji ij,  (3.10) p1 ||xcjp ||

The fuzzy C-means clustering procedure is described as follows:

1) Cluster centers are randomly selected and the partition matrix U is generated using Eq. (3.10) such that Eq. (3.8) is satisfied; 2) The cluster centers C are estimated using Eq. (3.9) and the new partition matrix U is updated according to the estimated cluster centers C; and 3) Step 2 is repeated until Eq. (3.7) determines the minimum or the change of partition matrix is in the tolerance.

The relevant features extracted using the fuzzy C-means clustering algorithm are used to develop an effective feature index for the detection of changes in ocean wave characteristics.

A new identification feature is defined through the several processed parameters of wave height time series data x[n]. Although a number of features were considered, the proposed method appeared to be the most effective. The proposed HF radar-based ocean feature (HFOF) extraction is defined as

p Var x n 2 HFOF log | Ck | (3.11) FCM x n k0

where Var (x[n]) is the variance of x[n], FCM(x[n]) is the fuzzy C-means values of x[n], and Ck is the kth Fourier transform coefficients, which can be obtained from x[n] and P is the total number of Fourier transform coefficients. Figure 3-4 shows the proposed change detection algorithm. The proposed algorithm operates by:

Step 1: The ocean wave height and its derivative data are extracted from HF radar systems.

Step 2: A window function is applied to the data in order to truncate it into several same-

length, short-time sequences. The window function also reshapes the signal

sequences. Note that the type and length of the window function are selected based

on the data.

Step 3: Once the short sequences are constructed, the statistical analysis, spectra analysis,

and fuzzy C-means clustering are performed separately to each sequence in order

to obtain the characteristics both in the time and frequency domains. The

performance of the spectral analysis is evaluated through the analysis of

variance (ANOVA) F-test. If the performance is not satisfied (i.e., the F ratio is

smaller than the F critical value), the process goes to Step 2. In other words, “Error”

is defined as F critical value > F ratio. This process is repeated until the

performance is statistically significant. The target F critical value is determined by

the users. In this paper, the target F critical value is chosen as a value of 90%

confidence.

Step 4: The ocean wave features HFOF are extracted. After the normalization of HFOF,

fuzzy C-means clustering is performed again to detect the changed characteristics

of the ocean wave.

Step 5: When the performance of the model is satisfied, the model is validated using other

data sets that are not used for training process. In this paper, the validation was

evaluated by the misclassification rate. If the misclassification rate was higher than

the threshold, the validation was not satisfied and the procedure went to Step 2. If

it was satisfied, the algorithm would stop. The threshold value of misclassification

rate was determined by the user. In this paper, the threshold value was set at 3%.

Figure 3-4. The proposed ocean wave change detection algorithm

3.3 Case study

3.3.1 Study area

To demonstrate the effectiveness of the proposed feature extraction analysis framework, extensive field studies were conducted. Samcheok City, Gangwondo, located in the east coast of South Korea was selected as the study area. It is famous for high waves. In previous years, the city has suffered high wave damage. Therefore, it is absolutely necessary to monitor ocean conditions in this area.

The installation sites of the radar systems were locations with optimal radio-wave transmitting environments for data reliability, good geological conditions as well as good accessibility. Four potential sites were selected (Figure 3-5). Considering the feasibility, adaptability, and maintenance of the radars, two sites at Imwon Harbor and Hujung Beach were selected as installation sites.

Figure 3-5. Study area for ocean radar installation

3.3.2 Test setup

The HF radar used for this study was WERA (WavE RAdar), developed by a German company

Helzel Messtechnik GmbH in 2000. It uses over-the-horizon radar technology to monitor ocean surface currents, waves and wind direction. WERA has 8 channels, composed of 4 transmitters and 8 receivers, and operates with radio frequencies between 5 MHz and 50 MHz. The maximum distances that waves and currents can be collected are 27km and 48km, respectively. Cell sizes can be determined from distances of 300m to 3km. Data collection runs from 0.5 second to 10 minute intervals with a time integration analysis for every 10 minutes.

The devices needed for installing the ocean radar are shown in Figure 3-6, including the transmitter (TX) and receiver (RX) antennas, the control server, the GPS receiver, and accessories.

In particular, TX-SAT is a long-distance wireless antenna. The real-time data of wave height and ocean circulation by WERA are available online. The observed data (current, wave, and wind) can be searched based on time (UTC-base).

Figure 3-6. The WERA system

3.3.3 Data set

The ocean radars in the subject area operated at a frequency band of 24.525 MHz with a bandwidth of 150 KHz for 1 km lattice spacing resolution. The azimuths of the center beam at Imwon Harbor

(Site A) and Hujeong Beach (Site B) are 95.8° and 37.3° (Figure 3-7) with the range of ±60° from the central angle (Figure 3-8). Each site had a 30-minute cycle for wave and current data collection.

The data collection lasted from July 1, 2012 to June 30, 2014.

Figure 3-7. Monitoring points and range

Figure 3-8. Installation specification of HF radar

3.3.4 Result analysis

Figures 3-9 and 3-10 show two different ocean wave height data sets collected from the HF radar.

The data were measured between December 6 and 8, 2012 and between January 6 and 8 2013, respectively. As shown in the figures, it is difficult to visually distinguish the normal and high wave signals using the time domain formation of the time series data. Hence, the time domain signals were transformed into frequency domain signals to better represent the characteristics of the measured signals

3.3.4.1 STFT application

As previously discussed, it is challenging to directly apply the Fourier transform to ocean wave data. However, assuming the signal is stationary in a short time interval, STFT detects frequency

66 changes. When STFT processing is applied to the time series signals, the sampling rate should be carefully considered. According to the Nyquist–Shannon sampling theorem, the sampling frequency should exceed twice the maximum frequency of data (Shannon, 1949). Otherwise it would cause aliasing. For example, the period of a tsunami is between 25 and 50 minutes (Lipa et al., 2011). When a sampling rate of 86 seconds is selected, the sampling frequency (1/86 Hz) is far beyond double the maximum possible frequency of the data (1/750 Hz) and an aliasing problems will not occur. The proposed algorithm can be applied to any type of ocean wave signals, although detection of high wave signals is of interest in this study: the tsunami was selected as a case study of environmental conditions. When needed, the approach can be modified by adjusting the sampling rate of the high frequency radar such that ocean wave signals with shorter periods are analyzed in real time. Figures 3-11 and 3-12 show the STFT results of the ocean wave signals in Figures 3-9 and 3-10, respectively. In this analysis, a Hamming Window with a length of 1024 is selected as a window function. The Nyquest number (N) is 1024. Once the type and the length of the window function are selected, the data is truncated. Then the truncated data is analyzed using STFT. During the STFT analysis of the data, the time window is fixed. The “Frequency” reflects the series of frequency variables that are represented in the ocean wave data. The

“Magnitude” represents the number of the frequency components present in the ocean wave data.

The “Sequence Number” is the order number of the sequence that is truncated by the moving window function, i.e., the sequence number denotes the number of the truncated data that is collected using the moving window function. As shown in Figures 3-11 and 3-12, the magnitudes of all the frequency terms change with time. To be specific, the magnitudes of low frequency components in Figure 3-11 in the latter sequences are higher than those in the former sequences.

Similarly, the magnitudes of high frequency components in Figure 3-12 in the latter sequences are

67 higher than those in the former sequences. It can be inferred from these observations that the amounts of the low frequency components of the ocean wave in Figure 3-9 increase over time, while the high frequency components increase with time in Figure 3-10. Therefore, from the previous analysis, the conclusion can be reached that the STFT method can not only detect the frequency responses of the ocean wave signal, but also display the trend of frequency changes with respect to the time, i.e., both time and frequency information can be acquired simultaneously.

However, it is still challenging to distinguish between the normal wave height signals and the high wave signals in real time. Such an issue could be addressed by integrating the STFT with fuzzy C- means clustering and statistical analysis.

Figure 3-9. Normal ocean wave height

Figure 3-10. High wave height

Figure 3-11. The STFT results using normal wave height data

Figure 3-12. The STFT results using the high wave data

It should be noted that the properties of the STFT would be sensitive to the selection of the window function. To obtain the optimal window function, a variety of simulations were conducted. The outputs of the STFT algorithm with the same type window function but different lengths were compared. The outputs of the STFT algorithm with the longer windows were more concentrated than those of the STFT algorithm with the shorter windows; while the outputs of shorter windows are smoother than those of longer windows. This is because the shorter windows contain less information, and thus result in a lower frequency resolution. The shorter windows will be more localized in time, and thus a greater resolution is allowed for the time domain responses. In contrast, the longer windows contain more information; however, this information is averaged across the entire window duration, thus potentially attenuating any transients or other short-time non- stationary behaviors. The advantage in this case, is that the greater information content might allow a higher resolution.

A second comparison was conducted using outputs with the same length but different types of window functions. It was observed from the comparison that the outputs of the rectangular window were more concentrated than the others only because the other three types are “bell- shaped”. The shape of a window is a signal selected type of window, which can concentrate the center and attenuate the effect of both sides. Thus, the output of the STFT with this type of function may have better behavior in time domain, especially for the transient change. For the rectangular window, it simply truncates the signal and all the information will be averaged across the whole window. Thus it may miss some of the time transients.

3.3.4.2 Proposed feature extraction algorithm

The ocean wave energy is a function of a variety of uncertain parameters: wave height, wave periods, winds, earthquakes, among others. As waves propagate, their energy is transported. The huge energy in high waves has the potential to degrade coastlines, cause devastating property damage and loss of life in a large unpredictable manner. For this reason, it is necessary to monitor the sea state in real time to check whether abnormal ocean waves are occurring. As previously discussed, it is sometimes very difficult to identify the difference between two kinds of ocean waves if they have similar time domain characteristic; however, frequency domain characteristics can also be effectively used to estimate characteristics.

Based on the spectral analysis of the wave height data, the HFOFs from the truncated ocean wave height sequence were extracted through the comparison between two data sets in Figures 3-

9 and 3-10, using Eq. (3.11). The shape and length of the window function is time-invariant in this study, i.e., once the type and the length of the time window are selected, they are fixed. However, it is believed that further experimentation with a time-varying window function, i.e., an adaptive

71 window function, is worthwhile, albeit beyond the scope of this study. For each truncated ocean wave height sequence, two different types of features were analyzed: the HFOF of the ocean wave height x (HFOF(x)) and the HFOF of the ocean wave height derivative dx (HFOF(dx)). The two features of each truncated ocean wave, represented as a result pair, are shown in Figure 3-13.

Figure 3-13. HFOF(x) vs HFOF(dx) of December and January ocean wave

As shown in Figure 3-13, the features of two groups of data are not clearly separable. In order to deal with this issue, a clustering was again performed. Figure 3-14 shows the clustering results of HFOF(x) and HFOF(dx), using the fuzzy C-means clustering algorithm. FCM (HFOF(x)) represents the clustering center of HFOF(x). FCM (HFOF(dx)) is the clustering center of

HFOF(dx). It can be seen from Figure 3-14 that there is a significant difference in the two features between the two groups of data. The misclassification rate of the training data is about 2.08%, which indicates that the classification accuracy is over 97%. Another three data sets, which were

72 not used in the training process, were used to validate the trained model. Figures 3-15 to 3-17 show the validation results. It can be clearly observed that the two sets of wave data have different features. The misclassification rates for three test data are 1.39%, 2.78%, and 1.39%, respectively.

It can therefore be concluded that the proposed algorithm is effective in detecting wave characteristics.

Figure 3-14. Clustering of HFOF(x) and HFOF((dx)): Training

Figure 3-15. Clustering of HFOF(x) and HFOF((dx)): Test 1

Figure 3-16. Clustering of HFOF(x) and HFOF((dx)): Test 2

Figure 3-17. Clustering of HFOF(x) and HFOF((dx)): Test 3

3.4 Conclusion

In this paper, a novel feature extraction model was proposed for real-time ocean wave characteristics detection. It was developed through the integration of the fuzzy C-means clustering algorithm, short-time Fourier transform (STFT), statistical analysis formulas, and spectrum analysis algorithms. To demonstrate the effectiveness of the proposed feature extraction model, a variety of the ocean wave data were collected by two Wellen radar systems installed in Samcheok

City, South of Korea. It was shown from the modeling and the extensive testing processes that the proposed algorithm is effective in extracting characteristic features from different ocean waves.

The objective of the proposed feature extraction model identifies the distribution of extracted features to determine the patterns of varying wave characteristics, i.e., group

75 classification. For example, when the measured data have the same/similar patterns, they will be included in the same cluster boundary. If the ocean wave characteristics change, the feature distribution (i.e., signal patterns) will be different. Note that it is nearly impossible to visually detect different properties between different ocean wave time series in general.

The contribution of this study is as follows: first, a new detection algorithm was developed through the integration of several signal processing algorithms without using a physical model.

Hence it is expected that the new approach provides a novel insight into the analysis of ocean wave characteristics using data-driven methods. Second, this method makes ocean wave detection much more convenient and efficient. Unlike the traditional numerical method, there is no need to solve large scale nonlinear equations. As a result, it does not require high capability of computation.

Third, the proposed algorithm is a fast and convenient method to detect wave characteristics in real time. Hence, it is expected that the proposed system can be used to implement a high wave warning system, which will deliver warnings to people and infrastructure before a high wave is expected to arrive. Therefore, with the warnings, several actions can be taken in advance to protect human life and property.

As a model-free data-driven modeling framework, the capacity of the proposed approach is limited to the quantity and quality of the collected data.

In the future research, it will be necessary to evaluate the effects of different types and lengths of window functions. In addition, the detection algorithm can be updated using an adaptive window function. The proposed algorithm can be also developed to detect the characteristics of other non-stationary ocean features. Combination with other algorithms such as fuzzy logic and neural networks can be realized to improve the ability of the proposed method.

4. Regression Models for Ocean Wave Identification Using High Frequency

Radar Systems

4.1 Introduction

In recent years, the problem of high waves in the ocean has received considerable attention.

Frequent high waves induced by strong wind, tsunami, earthquakes, and other climate change conditions have become one of the significant factors of the coastal disaster, such as human deaths and coastal structure damages. To decrease the coastal catastrophe, it is essential to monitor the high waves in real time.

However, it is challenging to propose a systematic framework to develop the estimation model. Considerable numbers of unpredictable factors significantly influence the wave height, period, and current in the shoreline. These uncertainties make it difficult to formulate an apparent mathematic model, satisfying numerous parameters, to estimate the complex behavior of wave in the coastline. Therefore, it is essential to propose detection models that can be effective to the environmental changes in the ocean in real time.

As previously discussed, detection of the ocean wave characteristics is high importance to the coastal hazard mitigation. For a real-time estimation model, its accuracy and efficiency significantly depend on the ocean waves information, such as wave heights, currents, and periods.

Therefore, the limitation for the acquirement of the ocean wave information may be an obstruction in the development of the estimation model. However, among a large variety of measurement techniques, high-frequency (HF) radar systems can be an optimistic system for reliable measurement of ocean surface waves. It is known that the HF radar system has become one of the most effective ocean wave measurement systems. Although HF radar systems have been widely

77 applied in the real-time ocean wave measurement, the development of the detection model for ocean wave conditions using the real-time HF radar system is still in early stages. With this in mind, a novel real-time feature estimation model using HF radar systems is proposed to detect ocean wave characteristics.

A variety of applications of feature detection have been devoted to ocean engineering.

Oram et al. (2008) developed an algorithm to detect the significant edge in the remotely sensed images of the surface ocean, based on the gradient-based edge detector. This method had the advantage of being less sensitive to noise in the input image and was able to detect significant edges at different user-defined length scales. They applied this algorithm to satellite images to investigate the physical and biological variability of surface waters in the Southern California

Bight. Piedra-Fernández et al. (2010) studied the application of the filter measures and the

Bayesian networks in the satellite image for ocean structure recognition system. They found that the two methods were beneficial for minimizing the number of required irrelevant features, thereby improving the overall interpretation performance and reducing the computation time. They validated their methodology for the National Oceanographic and Atmospheric Administration satellite Advanced Very High Resolution Radiometer (AVHRR) images in detecting and locating several ocean features of interest in the North-East Atlantic and the Mediterranean. The proposed method made it possible to reduce the number of features for description by 80%, thus significantly reducing the computational cost. Zhang et al. (2001) developed a classifier for the oceanographic process using an autonomous-underwater vehicle (AUV). The classifier was based on the relations between the observations from a moving platform and the temporal-spatial spectrum of the surveyed process. They tested the AUV-based classifier in the Labrador Sea. Using the flow velocity data measured in the field, the classifier detected convection’s occurrence. Wu and Liu

(2003) proposed an algorithm to identify, extract, and classify the linear ocean features in synthetic aperture radar (SAR) imaginary. This algorithm was the integration of histogram screening, wavelet analysis, and texture analysis. They validated their algorithm in several features of interest, such as fronts, ice edge and polar low, in the northern Pacific and the Bering Sea. Their simulation results indicated that the algorithm would be a good foundation for the advanced algorithm in the future.

Some of the researchers specifically concentrated on the feature of ocean waves. Xu (1992) presented the feature extraction approach for a harbor aero-photograph. The algorithm, based on both frequency and spatial domain analysis, extracted the ocean wave information including the wavelengths, directions, and heights. The simulation results indicated that the approach was powerful. Gill and Walsh (1992) developed a mathematical framework of directional wave-height spectra extraction for HF ocean backscatter by solving the integral inversion equation. They compared the radar results with data provided by a Waverider buoy and found that the stability was significantly affected by the noise and ocean currents under the upper HF band operation.

The autoregressive (AR) is an advantageous method in feature extraction for time series data, developed based on the linear theory model. Due to the advantage in only requiring the output data, it has been widely used in structural health monitoring for structural damage detection (Nail et al. 2006). However, in the research of ocean wave, AR models are used primarily in ocean wave forecasting (Spanos 1983, Mandal et al. 1992, Spanos and Zeldin 1996). The application of

AR models to the feature analysis of ocean waves is a novel method. There is limited published research on it. With this in mind, in this paper, an innovative feature extraction model based on the AR model is proposed. This model is useful in the real-time detection of ocean wave characteristics using HF radar systems.

4.2 Proposed detection model

In this paper, a novel feature extraction framework for ocean wave characteristics is displayed in

Figure 4-1. The ocean waves are measured via the HF radar system. After the significant wave heights are extracted, the measurements are truncated into several same length sequences to generate real-time data. Then the AR time series model estimates the wave height, based on the truncated data. Once the truncation is completed, the AR coefficients are extracted to identify the ocean wave characteristics.

Figure 4-1. The flowchart of the proposed model

4.2.1 Autoregressive (AR) model

In general, a linear AR model can be represented as

P y()(-)() n ai y n i e n (4.1) i1

th where y(n) is the ocean wave height signal, ai is the i AR coefficient, P is the model orders of the

AR process, and the term e(n) is the residual term.

Consider the AR process defined as in Eq. (4.2). The candidate vectors for search are: y(n-

1),…,y(n-P). The candidate vectors can be arranged as the matrix shown below:

y(0) y (1 P )  y(1) y (2 P )  , (4.2) y()() n y n P   y( N 1) y ( N P )

where 푁 is the total number of data points. With the new candidates of linearly independent vectors, the least squares analysis is performed

T yW(n )g e ( n ), (4.3)

81 where W = [w0, w1,…, wR] is the selected linearly independent vectors, R is the number of selected linearly independent vectors and

T gR g0,, g 1, g (4.4)

In Eq. (4.4), gi is the coefficient estimate of the AR model. The objective is to minimize the equation error e(n), using the least squares criterion function defined as follows

2 J()(). y n TW N g g (4.5)

The criterion function in Eq. (5) can be minimized by taking the partial derivative with respect to

θg as follows

1 ˆ T g  WW Wy(n ). (4.6)

22 With the obtained coefficients, calculate every gwmm which the over-bar represents the time average and rearrange the wm in descending order. Then the number of candidate vector wm would be chosen for the proper accuracy needs. This step aims to select only the wm values that significantly reduce the error. If few changes happened in the error value by adding an additional wm value is found, then those wm values are dropped from the model. Once only those wm values

82 that reduce the error value significantly are obtained, the proposed AR model terms are estimated using the least squares method, as described by Lu et al. (2001).

4.2.2 Short-time Fourier transform (STFT)

The STFT is an extension of the basic Fourier transform definitions of a sequence. The discrete short-time Fourier transform representation of a discrete-time signal x[n] is given by

2   j km X n, k  x m w n m e N (4.7) m

where X(n,k) is the Fourier transform function of discrete-time signal x[n] with time index n and frequency index k; w[n] is the window function which determines the portion of the input signal that receives emphasis at a particular time index n; m is the shift variable; j is the imaginary unit; and N is the Nyquist number. The procedure of STFT is as follows: 1) An appropriate window function, w[n], is selected such that the desirable portion of the time series is shifted by m points;

2) The discrete-time signal x[m] is multiplied by the modified window function; and 3) The Fourier transform of the resulting short-time section is taken to obtain the frequency function X(n, k).

Figure 4-2. Fourier transform view of STFT

From Eq. (4.7), it is clear to see that the STFT consists of a separate Fourier transform for each instance. Thus it is possible for STFT to provide information on when a signal changes and at which frequency. It is advantageous to combine time series analysis and time-varying frequency- domain analysis under a single analysis framework.

4.2.3 Ocean wave characteristic detection

In this paper, several novel identification features for ocean wave characteristics were introduced through the grouping of the AR coefficients. Although some features were considered, the two proposed methods appeared to be the most effective. From many trial and error simulations, it was found that the AR coefficients normalized by the largest value provide the most efficient identification features.

The identification feature through the coefficients of the model can be defined as

P ci logabi i  i  i1 (4.8)

where P is the number of terms that are selected; βi is the coefficient of the model which can be the AR model from Eq. (4.4) or the STFT model from Eq. (4.7); ai, bi and ci are the coefficients corresponded to βi, based on the choice of the model. All the values of the parameters in Eq. (4.8) are determined by the user.

4.3 Case study

To verify the effectiveness of the proposed estimation model, Samcheok City, Gangwondo, was selected as a study area. Samcheok City is located on the east coast of South Korea (Figure 4-3).

This area has been on the alert for high wave damages in the previous years.

Figure 4-3. Study area for ocean radar installation

The HF radar used for this study was WERA (WavE RAdar), developed by a German company

Helzel Messtechnik GmbH in 2000. Each radar consists four transmitters and eight receivers with the operation radio frequencies from 5 and 50 MHz. The waves and currents are collected as high as 27km and 48km, respectively. The cell sizes can be determined to range in distances from 300m to 3km. The data collection interval is between 0.5 seconds to 10 minutes with a time integration analysis for every 10 minutes. In particular, the collection data can be browsed through the web and searched based on a time basis (UTC-base). The devices needed for the ocean radar includes the transmitter (TX) and receiver (RX) antennas, the control server, the GPS receiver, and accessories (Figure 4-4).

Figure 4-4. Facility of WERA system

In this study, the ocean radars operated at a frequency band of 24.525MHz with a bandwidth of

150 KHz for 1km lattice spacing resolution. The azimuths of the center beam of the two radar systems are 95.8° and 37.3° (Figure 4-5), respectively, with the range of ±60° from the central angle (Figure 4-6). The data collection lasted two years from July 1, 2012 to June 30, 2014

Figure 4-5. Monitoring points and range

Figure 4-6. Installation specification of HF radar

4.4 Modeling result and analysis

4.4.1 Model parameter setup

In this section, the effectiveness of the developed model was demonstrated using the HR radar data collected in the field. The ocean wave heights were measured by two HF radar systems. To train the proposed estimation model, a subset of these data was selected. The subset ocean wave height data were measured between December 6, 2012 and December 15, 2012 with a sampling interval of 86 seconds. The model order for the proposed AR model was selected as 50.

4.4.2 AR model performance evaluation

The performance of the forecasting model can be judged by visual inspection. It is easy to capture the overall behavior of the model without conducting the extensive quantitative analysis. In this study, the time history plots that compare the field data with the forecasted values are used first.

Figure 4-7 shows the selected training results of the proposed AR model. The solid lines represent the predicted values, and the dotted lines are the measured data. As shown in Figure 4-7, excellent agreements between the nonlinear AR model and the HF radar data are found.

Figure 4-7. Modeling results for proposed AR model

To generalize the forecasting capacity of the proposed nonlinear AR model, the trained model was tested using other three data sets that were not used for the training process. The measurements used for the testing were collected between January 6, 2013 and January 8, 2013. Figures 4-8 to

4-10 show the first, second, third validation results, respectively. As shown, the output of the proposed nonlinear AR model greatly agrees well with the field data set.

Figure 4-8. The 1st validation for proposed AR model

Figure 4-9. The 2nd validation for proposed AR model

Figure 4-10. The 3rd validation for AR model

4.4.3 Feature analysis

4.4.3.1 Statistical feature

For the time series, the statistical features, such as the mean and the variance, are the standard way to describe the characteristics. Ocean wave height data is a kind of time series data. Thus, the mean and the variance might be the feature of the ocean wave data. Based on the statistical analysis, the mean and the variance from the truncated ocean wave height sequence were extracted through the comparison between two data sets in Figures 4-11 and 4-12. As shown in Figures 4-11 and 4-12, the features of two groups is not separable. Therefore, the variance and mean are not the optimal choice of identification feature for the detection of ocean wave characteristics.

Figure 4-11. Comparison of mean value for two groups of data

Figure 4-12. Comparison of variance value for two groups of data

4.4.3.2 Feature of STFT model

The identification feature through the STFT was applied. The feature, which is defined as FCSS, was determined by the Eq. (4.8). Here, only the 2nd and 3rd coefficient of the STFT was chosen. In other words, a1 was selected as 0. The detail of other parameters in Eq. (4.8) are shown as follows:

nd, rd nd rd ai for 2 and 3 coefficient are selected as 0.8 and 0.3, respectively; bi for 2 and 3 coefficient

nd rd are both selected as 1; ci for 2 and 3 coefficient are selected as 6 and 3, respectively. Figure 4-

13 shows the result of the identification feature of STFT through the comparison between two groups of data.

Figure 4-13. Comparison of feature FCSS for two groups of data

As shown in Figure 4-13, the two groups of data are not clearly separable. To deal this issue, another identification feature of STFT which is two dimensional was used. In this feature, which is defined as FCS, first three coefficients of STFT were considered. The first dimension of the FCS is the same as FCSS defined above. The second dimension of the FCS considered the first coefficient of the STFT, in which a1 equals 0.8; b1 equals 1; c1 equals 6. Figure 4-14 shows the result of feature FCS. As shown in Figure 4-14, it still has the issue that the two groups of data are

95 combined together and not clearly separated. According to Figures 4-13 and 4-14, it may be concluded that feature of STFT is not validation in ocean wave characteristics detection.

Figure 4-14. Comparison of feature FCS for two groups of data

4.4.3.3 Feature of AR model

As shown above, either the feature of statistic or STFT has a good performance on representing the characteristics of ocean waves. With this The feature through the group of AR was applied here. The feature, which is defined as ACS, was determined by the Eq. (4.8). Here, only the 2nd

rd and 3 coefficient of the AR were chosen. In other words, a1 was selected as 0. The detail of other

nd rd parameters in Eq. (4.8) are shown as follows: ai for 2 and 3 coefficient are selected as 0.8 and

nd rd nd rd 0.3, respectively; bi for 2 and 3 coefficient are both selected as 1; ci for 2 and 3 coefficient are selected as 6 and 3, respectively. Figure 4-15 shows the result of identification feature of AR through the comparison between two groups of data.

Figure 4-15. Comparison of feature ACS for training data

It is clear to observe that the two groups of data are clearly separable. The misclassification rate of the training data is about 0.38%, which indicates that the classification accuracy is over 99%.

Another three data sets, which were not used in the training process, were used to validate the training model. Figures 4-16 to 4-18 show the validation results. It can be seen from Figures 4-16 to 4-18 that two wave data have different features of ACS. The classification accuracy for the three validation data is all over 99%.

Figure 4-16. Comparison of feature ACS for 1st validation data

Figure 4-17. Comparison of feature ACS for 2nd validation data

Figure 4-18. Comparison of feature ACSS for 3rd validation data

In order to evaluate the performance of the feature recognition, a hypothesis test was made to test if the results are statistic reliable. From Figures 4-15 to 4-18, there is a significant difference between the mean values of the ACSes obtained from two different group of data. If µACS, Data 1 and µACS, Data 2 are defined as the mean value of the ACSes obtained from two different group of data, respectively. Therefore, a hypothesis test may be set up as follows to determine if their differences are significant:

H0 : µACS, Data 1 = µACS, Data 2

H1 : µACS, Data 1 ≠ µACS, Data 2 (9)

where H0 and H1 are the null and alternate hypothesis, respectively. H0 represents the two wave data has the same feature and H1 represents the two wave data has the different features. The

99 significance level of the test is set at 0.05. Table 4-1 shows the results of the hypothesis for the features. It is observed that for both training and validation data sets the feature decisions to give

H1, which indicates the two data have the different features. Since the p-values are all significantly much less than the significance level of 0.05., the null hypothesis H0 is rejected and the alternate hypothesis H1 is accepted. It can be therefore concluded that the proposed feature ACS is statistical reliable in detecting wave characteristics.

Table 4-1. Results of feature decision for four data sets Data Set Feature decision p-value

Training H1 ≈ 0

Validation 1 H1 ≈ 0

Validation 2 H1 ≈ 0

Validation 3 H1 ≈ 0

Another identification feature of AR model was extracted from two group of data. This feature, defined as ACSS, is a 2 dimensional feature. The first dimension of the ACSS is the same as the

ACS defined above. The second dimension involves the first coefficient of the AR. The detail parameter is selected that a1 equals 0.8; b1 equals 1; c1 equals 6. Figure 4-19 shows the comparison of features ACSS for two different wave data.

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Figure 4-19. Comparison of feature ACSS for training data

From Figure 4-19, it is clear to observe that the two groups of data have different features of ACSS.

Another three data sets, which were not used in the training process, were used to validate the training model. Figures 4-20 to 4-22 show the validation results. It can be seen from Figures 4-20 to 4-22 that there is a big difference between two wave data. It can be proved that the proposed feature ACSS is validated for wave characteristics identification.

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Figure 4-20. Comparison of feature ACSS for 1st validation data

Figure 4-21. Comparison of feature ACSS for 2nd validation data

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Figure 4-22. Comparison of feature ACSS for 3rd validation data

4.5. Conclusion

In this paper, a novel model was proposed for real-time ocean wave feature forscasting. It was developed through the integration of autoregressive (AR) models, the weighted least squares estimation algorithm, an automatic order selection algorithm, and the HF radar system. To demonstrate the effectiveness of the proposed forecasting model, two Wellen radar systems were installed in Samcheok City, Gangwond-do in the East Coast of Korea. A randomly selected data set was used for training the proposed AR-based feature extraction model. Other three data sets that were not used for the training process were used for validating the proposed model. It was observed from both training and testing cases that the proposed model is efficient to predict ocean wave features.

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5. An ICA-Based Model for Ocean Wave Identification Using High Frequency

Radar Systems

5.1 Introduction

In recent years, the problem of high waves in the ocean has received considerable attention.

104 applied in the real-time ocean wave measurement, the development of the detection model for ocean wave conditions using the real-time HF radar system is still in early stages. With this in mind, a novel real-time feature estimation model using HF radar systems is proposed to detect ocean wave characteristics.

A variety of applications of feature detection have been devoted to ocean engineering.

Bight. Piedra-Fernández et al. (2010) studied the application of the filter measures and the

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As an alternative framework for feature extraction of ocean wave signals, independent process analysis (ICA) is statistical technique to decompose the signal into a number of linear independent component. ICA was originally developed in solving the blind source separation (BSS) problem. The application of this principal has been extended to feature extraction, such as the sound and image processing. However, few studies have concentrated on the application of ICA to ocean wave signals. On the other hand, ocean wave signals are similar to sound signals: they both can be treated as a mixed signal composed with a number of source signal. As the successful application on the sound signals, ICA would be a useful tool for ocean wave signals analysis. In

106 this paper, the use of the ICA method is integrated with a real-time feature extraction algorithm for wave detection and the classification of ocean wave characteristics.

In our previous work, we have presented three types of feature extraction algorithms based on short-time Fourier transform (STFT), Autoregressive (AR) model, and principal component analysis (PCA). Compared with these previous work, the proposed algorithm has its advantages, especially in efficiency and simplification. On one hand, the proposed feature is simple and convenient that the independent component can be directly applied as the identification feature.

However, for both the STFT based feature and AR based feature, a specific mathematical formula is required to define the identification feature after STFT coefficients and AR coefficients extraction. On the other hand, the ICA based feature has a much more clear recognition between two different classes of signal. Although the PCA-based feature is as simple as the proposed ICA feature, it is necessary to apply the decision model, such as support vector machine, to build a boundary to separate two different classes after the feature extraction. However, after the ICA based feature extraction, there is a significant difference between two group classes of signal. They can be sseparated visually. Thus, the decision model is not required.

5.2 Proposed detection model

In this paper, a novel feature extraction framework using ICA for ocean wave characteristics is developed. The ocean waves are measured via the HF radar system. After the significant wave heights are extracted, the data set is truncated into several same length sequences in order to generate a time series segment matrix. Once the time series segment matrix built, ICA is applied to extract the independent component. Finally, the ocean wave characteristics are identified through the independent component-based feature.

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5.2.1 Ocean wave feature based on independent component analysis

Independent process analysis (ICA) was first introduced by Jutter and Herault (1991) and clearly stated with the general framework by Comon (1994). ICA had a wide application in solving the blind source separation (BSS) problem. One of the common BSS problems is the "cocktail party problem" that involves the separation of particular speech signals from sample data consisting of people talking simultaneously in a room but with no or very little information about the source signals or how they are mixed. The key idea of the ICA assumes that each statistically independent observed signal is linearly mixed by a set of separate, independent, underlying source signals called independent components, and that each source signal is a realization of some fixed probability distribution at each time point. More precisely, the observed signal x is linear mixture of the underlying sources

x As (5.1) where A is a mixing matrix and s is an underlying source signal needed to be separated. The objective is to find a new matrix W such that the linear transformed data x is an estimation of the underlying sources

sˆ  Wx (5.2)

In other word, the goal of ICA is to find an unmixing matrix W that is an approximation of A-1 so that ssˆ  .

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It is noted that the goal of ICA is to find a linear representation of non-Gaussian data so that the components are statistically independent, or as independent as possible. Compared with PCA, where the goal is to produce unrelated and Gaussian features, this is a much stronger requirement that ICA not only decorrelates the signals (2nd order statistics) but also reduces the higher-order dependences. Therefore unlike PCA, the independent component in ICA is neither orthogonal nor ranked in order. However, it has both pros and cons. On one side, ICA does not require the projection axes to be orthogonal to each other. As the result, the direction of independent component axes in ICA are more flexible than PCA. On the other side, as the independent components are not ranked in order, it is impossible to reduce the dimension of the data based on the order of independent component as the PCA dose. When the data set is huge, it would require huge computation capacity.

Considering the issues mentioned above, in this study, the FastICA algorithm (Hyvärinen & Oja,

2000) is selected as the ICA algorithm. Unlike the typical ICA algorithm, the FastICA algorithm uses the PCA to whiten the data, making the data whitening and the dimensionality decreasing at the same time. Therefore, not only the independent components are ranked in order, but also the computation is efficiencient. The procedure for FastICA is as follows:

1) Center the vector x by subtracting the mean vector so as to make x a zero mean variable; 2)

Whiten the vector x using PCA and decrease the dimensionality; 3) Apply a fixed-point iteration

T scheme to find a unit vector wi so that wi x is the maximum of the nongaussianity, where x is the

T whitened and lower dimensional signal vector; and 4) Each source si can be obtained by wi x.

As the order of the solved independent component reflects the variability, similar to PCA, the proposed ICA can also be a useful technique in dimension reduction that, instead of considering all the variables, only the most significant variables are considered.

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5.2.2 ICA-based ocean wave characteristic feature

For the time series data, such as the ocean wave height data, it has a unique data structure where each time point is often considered a variable and each time series is considered an observation.

As the time dimension increases, the number of variables also increases, in proportion to the time dimension. Therefore, instead of applying feature extraction algorithms directly to the data, some techniques to summarize each time series in a form that has a significantly lower dimension is required. One of the simplest ways is to summarize the time series based on a specific time interval.

In specific, the time series data set, x( t ), t [0, T ] is divided into N number of data series vxtti ( ),  [( i  1) TNiTNi ,( ) ];  1,2, N with equal time interval called segments. The segment vi can be obtained through a moving window function with the length of T/N. Reform the time series segments into the following matrix

푽 = [풗ퟏ 풗ퟐ … 풗푵] (5.3)

Therefore, the dimension of the original data series successfully reduced.

After the dimension reduction of the original data, a feature extraction algorithm is applied to the modified matrix V. As described before, the order of independent components reflects the variability. The first several indexes of independent components contain the most interesting dynamics. In this study, the first two indexes of independent component scores are selected as the identification features. To be specific, the ICA-based identification feature (IIF) is a two- dimension identification feature to identify the different ocean wave characteristic.

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5.3 Case study

In order to verify the effectiveness of the proposed estimation model, Samcheok City, Gangwondo, was selected as a study area. Samcheok City is located in the east coast of South Korea (Figure 5-

1). This areas has been on the alert for high wave damages in the previous years.

Figure 5-1. Study area for ocean radar installation

Two WERA (WavE RAdar) HF radar systems, developed by a German company Helzel

Messtechnik GmbH in 2000, were used for this study. This system includes 4 transmitters and 8 receivers, with radio frequencies ranging from 5 and 50 MHz. The data collection interval is between 0.5 second to 10 minutes with a time integration analysis for every 10 minutes. The waves and currents are able to be collected as high as 27km and 48km, respectively. The cell sizes can be determined ranging in distances from 300m to 3km. The devices needed for the ocean radar

111 includes the transmitter (TX) and receiver (RX) antennas, the control server, the GPS receiver, and accessories (Figure 5-2).

Figure 5-2. Facility of WERA system

In this study, the ocean radars operated at 24.525MHz with a bandwidth of 150 KHz for 1km lattice spacing resolution. The azimuths of center beam of the two radar systems are 95.8° and

37.3° (Figure 5-3), respectively, with the range of ±60° from the central angle (Figure 5-4). The data collection lasted two years from July 1, 2012 to June 30, 2014

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Figure 5-3. Monitoring points and range

Figure 5-4. Installation specification of HF radar

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5.4 Modeling result and analysis

5.4.1 Model parameter setup

In this section, the proposed model is evaluated through the ocean wave height data collected by the HF radar data in the field. To train the proposed estimation model, a three-day subset of these data was selected. The subset ocean wave height data were measured between December 6, 2012 and December 15, 2012 with a sampling interval of 86 seconds.

5.4.2 Feature extraction

In this section, the IIFs are extracted through the comparison between two different groups of ocean wave data. Figures 5-5 and 5-6 shows two different types of ocean wave height data that are used in this training process. The ICA was applied to each of them and the identification feature

IIFs are extracted. Figure 5-7 shows the results from the application of the proposed IIF to the two groups of different ocean wave height data. The horizontal value (IIF1) represents the first index of ICA component, while the vertical value (IIF2) represents the second index of ICA component.

From Figure 5-7, it is clear that the blue points, representing normal wave, gather to the left and the red points, representing the abnormal wave, gather to the right side. As the result, one group of data is separated with the other one and there is no overlap between them. In other words, there is a significant difference in the feature between two groups of data.

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Figure 5-5. Normal ocean wave height

Figure 5-6. Abnormal wave height

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Figure 5-7. The identification feature IIF for training data

5.4.3 Feature comparison

In this section, a comparison was made between the feature extracted from PCA and ICA. Similar to ICA, PCA is also a widely used linear transformation method which transforms a set of possibly correlated variables into a set of linearly unrelated variables called principal components (PCs).

The transformation defines in such way that the first PC has the largest the possible variance, and the every following component has the highest variance under the constraint that it should be orthogonal to the previous components. In other words, the transformation is an orthogonal transformation that the resulting PCs are orthogonal to each other and ranking in order based on the variability. As the resulting PCs are the unique characteristics of a system, they are widely used as an identification feature in feature extraction. Similar to the IIF, the first two PCs extracted from

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PCA of ocean waves are selected as the detection feature, defined as PIF, to identify the ocean waves. Figure 5-8 shows the result of feature PIF using the data as in Figures 5-5 and 5-6.

Figure 5-8. The identification feature PIF for training data

In Figure 5-8, the horizontal axes represents the first index of PCA component whereas the vertical axes represent the second index of PCA component. From Figure 5-8, it is clear to see that even though the features PIF of normal and abnormal wave are different, that is the shape of normal wave plot is convex and the shape of abnormal wave plot is concave, part of plots overlaps each other so that there is no clear boundaries between two groups of data. It means it is impossible to be only visually detected. Therefore it is still possible that the abnormal wave is misclassified to the normal wave or the normal wave is misclassify to the abnormal wave if only based on the feature PIF. In other words, a decision making model is required for post processing to distinguish each other in order to increase the detection accuracy. However, for the IIF features (Figure 5-7),

117 the feature itself can clearly separate two groups of data. As the result, this method is efficient compared with PCA method.

5.4.4 Validation for IIF feature extraction model

In order to validate the results, three other datasets, which are not used in training process, are used to test the model. The results are shown in Figures 5-9 to 5-11. From Figures 5-9 to 5-11, it is clear that two groups of ocean wave data have different features. In other words, the identification feature has a good performance in ocean wave characteristics identification. Therefore, it can be proved that the proposed algorithm is validation.

Figure 5-9. The identification feature IIF for 1st validation data

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Figure 5-10. The identification feature IIF for 2nd validation data

Figure 5-11. The identification feature IIF for 3rd validation data

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5.5 Conclusion

In this paper, a novel model was proposed for real time ocean wave feature identification. It was developed through the integration of independent component analysis (ICA) and the HF radar system. To demonstrate the effectiveness of the proposed forecasting model, two Wellen radar systems were installed in Samcheok City, Gangwond-do in the East Coast of Korea. A randomly selected data set was used for training the proposed ICA based feature identification model. Other three data sets that were not used for the training process were used for validating the proposed model. It was observed from both training and testing cases that the proposed model is effective in ocean wave feature identification.

This study will be the first attempt to systematically apply the ICA into ocean wave characteristics detection based on HF radar systems. Hence it is expected that the new approach provides a novel insight into the analysis of ocean wave characteristics using data-driven methods.

What’s more, this method makes ocean wave detection much more convenient. Unlike the previous data-driven method, there is no need to specifically define the feature. The independent component obtained from the ICA can be directly used as the identification feature. Therefore, the identification feature is simple and direct. Last but not least, the proposed algorithm is a fast and efficient method to detect wave characteristics in real time. On one side, a dimension reduction is implemented during the feature extraction to shrink the data size. On the other side, the identification feature is obvious so that only the feature extraction model is enough and there is no required to use a decision making model. With these two benefits, the processing time dramatically decreases. Hence, it is expected that the proposed system can be used to implement a high wave warning system, which will deliver warnings to people and infrastructure before a high wave is

120 expected to arrive. Therefore, with the warnings, several actions can be taken in advance to protect human life and property.

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6. A PCA-Based SVM Model for Ocean Wave Monitoring Using High

Frequency Radar.

6.1 Introduction

In recent years, the problem of high waves in the ocean has received considerable attention.

122 applied in the real-time ocean wave measurement, the development of the detection model for ocean wave conditions using the real-time HF radar system is still in early stages. With this in mind, a novel real-time feature estimation model using HF radar systems is proposed to detect ocean wave characteristics.

A variety of applications of feature detection have been devoted to ocean engineering.

Bight. Piedra-Fernández et al. (2010) studied the application of the filter measures and the

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The support vector machines (SVM) technique is a widely used method in pattern recognition, especially for the classification problem. Several applications of SVM have already been demonstrated in ocean engineering. Mahjoobi and Mosabbeb (2009) illustrated an approach to predict the significant wave height in Lake Michigan based on the SVM technique. The input data was wave wind data gathered from deep water locations in Lake Michigan and collected by

NDBC. Two different kernel functions, RBF and polynomial, were used in their study. Then they compared the results within the two different kernel functions and with two different ANN models, multi-layer perception (MLP) and RBF, with the same data. The comparison results showed the

RBF kennel-based SVM model performed better than the polynomial kernel-based model and the

124 two ANN models. Malekmohamadi et al. (2011) applied the SVM to forecast wave height in Lake

Superior, using wind data, gathered by National Data Buoy Center (NDBC). Then they compared the forecasting results with other soft computing-based models including Bayesian Networks

(BN), Artificial Neural Networks (ANNs), and Adaptive Neuro-Fuzzy Inference System (ANFIS).

Through several statistical indices evaluations, the results show that SVM can provide acceptable predictions for wave heights. Patil et al. (2012) developed a hybrid genetic algorithm tuned support vector machine regression (GA-SVMR) model to predict the wave transmission of horizontally interlaced multilayer moored floating pipe breakwater (HIMMFPB). The optimal SVM and kernel parameters of the model are determined by genetic algorithm. Six kernel functions were demonstrated including liner, polynomial, RBF, ERBF, spline, and b-spline. The model was trained on the data set obtained from experimental wave transmission of HIMMFPB using regular wave flume at Marine Structure Laboratory, National Institute of Technology, Karnataka,

Surathkal, Mangalore, India. The results are compared within 6 kernel functions and with ANN and ANFIS models in terms of three different indices. The comparison results showed that the b- spline kernel function performs better than the other kernel functions, and the GA-SVMR model performs superior to the other two models. Elbisy (2015) presented a SVM approach, using various kernel functions, to predict the wave parameters (i.e. wave height, wave direction, and peak spectral period) of the Abu Qir Bay coastal zone. The input data is the wind speed and direction data collected by the Coastal Research Institute during 2002 and 2003, and the output variables are the significant wave height. The kernel function was selected as the radial basis function (RBF).

He compared the prediction results with a backpropagation neural network (BPNN) model and a cascade-correlation neural network (CCNN) model. Six indices were used to evaluate the

125 performance of the different models, and the results showed that the SVM (RBF kernel) forecasting results are more accurate than those of the CCNN and BPNN models.

6.2 Proposed detection model

In this paper, a novel principal component analysis (PCA)-based feature extraction framework using SVM for ocean wave characteristics is developed. The ocean waves are measured via the

HF radar system. After the significant wave heights are extracted, the data set is truncated into several same length sequences in order to generate a time series segment matrix. Once the time series segment matrix built, PCA is applied to the extract identification feature. Finally, the ocean wave characteristics are identified through the SVM based on the PCA identification feature.

6.2.1 Ocean wave feature based on principal component analysis

Principle component analysis (PCA), also known as an empirical orthogonal function, was introduced by Pearson (1901) with the concern for with data fitting, and it was independently developed by Hotelling (1933). The central idea of PCA is to reduce the dimensionality of a data set consisting of a large number of interrelated variables, but save the most critical process information, by transforming into a new smaller set of variables called principal components (PC), which are unrelated and retain most of the variation present in all of the original variables. In other words, the PCA transformation changes the number of input data into a set of components according to their importance. In specific, suppose X is the original data set. It can be re- represented as

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풀 = 푷푿 (6.1) where P is a transformation matrix, and Y is the re-represented matrix. The objective is to find the orthonormal matrix P such that the covariance matrix SY of Y is diagonalized and the rows of P are the principal components of X. The transformation matrix P is called PC coefficients. The re- represented matrix Y is the PC scores that are the representation of X in the principal component space. The general procedure for solving PCA is as follows:

1) Subtract the mean for each measurement type from X to get the zero mean matrix X’; 2) calculate the covariance matrix SX’ of X’; 3) find the eigenvectors and eigenvalues of SX’; and 4) form a matrix that each column is an eigenvector of SX’. The order of vector is with respect to the decreasing order of eigenvalues. These vectors are the principal components. This matrix is the transformation matrix P; 5) the re-represented matrix Y can be obtained by Y = PX.

It is possible to examine the covariance matrix SY of Y associated with the principal components that the order of principal components reflects the variability in Y. The first index of principal components accounts for the highest variability. In other words, the most interesting dynamics occur only in the first several dimensions of principal components. Therefore, PCA can be a useful technique in dimension reduction that instead considering all of the variables, the most significant variables are considered.

6.2.2 PCA-based ocean wave characteristic feature

For time series data, such as the ocean wave height data, there is a unique data structure in which each time point is often considered a variable and each time series is considered an observation.

As the time dimension increases, the number of variables also increases, in proportion to the time

127 dimension. Therefore, instead of applying feature extraction algorithms directly to the data, some techniques to summarize each time series in a form that has a significantly lower dimension is required. One of the simplest way was to summarize the time series based on a specific time interval. In specific, the time series data set, x( t ), t [0, T ] is divided into N number of data series vxtti ( ),  [( i  1) TNiTNi ,( ) ];  1,2, N with equal time interval called segments. The segment vi can be obtained through a moving window function with the length of T/N. Reform the time series segments into the following matrix

푽 = [풗ퟏ 풗ퟐ … 풗푵] (6.2)

Therefore, the dimension of the original data series is successfully reduced.

After the dimension reduction of the original data, a feature extraction algorithm is applied to the modified matrix V. Although, there are numerous feature extraction methods, the PCA is the convenient and effective one. It not only can capture the unique characteristics of the data but also reduce the dimension the data, resulting in the reduction of the computation time. Hence, a novel identification feature through the PCA is introduced in this study. As described before, the order of principal components reflects the variability in its PC scores. In this study, the first two indexes of PC scores are selected as the identification features. To be specific, the PCA-based identification feature (PIF) is a two-dimension identification feature. Note that it would not be easy to identify the different ocean wave characteristics due to their complexity. To address this issue, an SVM is applied to the PIFs

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6.2.3 Support vector machine (SVM) model for classificaiton

In machine learning, SVM is a supervised learning method that classify the data by finding the

n separating hyperplane with the largest margin (Burges 1998). Given a set of training vectors xi R , i =1,2,…N, belong to two classes, labeled as yi, where yi {-1,+1}. The equation of the hyperplane is defined as

T f(w , x , b ) w ( x )  bs  0 (6.3)

where x is the input data vector, ϕ(x) is a feature-space transformation, w is the weight vector, and bs is the bias. The optimal separating hyperplane is the one that separates the data so that the points within the same class concentrates on one side and maximum the margin, which is the distance between the closest vectors of the two classes, as well. These closest vectors are called as support vector. In all, the SVMs can be categorized into 2 classes: linear and nonlinear

Linear SVMs can be classified into hard-margin SVMs and soft-margin SVMs. The goal of a hard-margin SVM is to find the classifier which the hyperplane correctly separates two classes of data vectors so that the margin is as large as possible. In order to find the optimal margin classifier, the SVM requires the solution of the following optimization problem:

1 Min J (w )  wT w 2 (6.4) T s . t . yi (wx i b s )  1, i  1,2,..., N

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However, in the real world, the data are often not linearly separable. In this case, the hard-margin

SVM does not terminate. In order to address this issue, the soft-margin SVM introduces a positive slack variable εi. Then, the optimization task is to make the margin as large as possible but at the same time to keep the number of points with ε>0 as small as possible. Therefore, the reformulation of the hard-margin optimization problem is as follows

N 1 T Min J (w )  w w Ci 2 i1 T (6.5) s . t . yi (wx i b s )  1  i , i  1,2,..., N

i  0, iN 1,2,...,

where C is a positive parameter that controls the relative influence of the two competing terms.

Based on the methods of linear SVM, the nonlinear SVM can be generalized. The idea of nonlinear SVM is to allow the SVM to classify the nonlinearly separable vectors. The suggested way is to apply the kernel trick so that the original data xi is transformed into a higher feature space

Φ(xi). The resulting algorithm is similar to linear SVM, except constraints in Eq. (6.5) are replaced with

T yi (wx i  b s )  1  i , i  1,2,..., N (6.6)

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Therefore, every dot product in the linear SVM is replaced by the inner products in the feature space of the form Φ(xi)∙ Φ(xj) in the nonlinear SVM. The function of inner products in the feature space is also called as a kernel function Ks. One benefit of the kernel function is that it can be calculated without knowing Φ(xi) explicitly. In other words, only the kernel function Ks is needed in the algorithm. One widely used example of kernel function is the Gaussian radial basis function

(RBF), which is defined as

2 xxij K( x, x ) exp (6.7) s i j 2 2 

There is no specific rule in kernel function selection. The rule of thumb is to select RBF kernel function. This is because the RBF kernel function can meet most of the situations. With this in mind, the RBF kernel function is used in this SVM classification model.

6.3 Case Study

In order to verify the effectiveness of the proposed estimation model, Samcheok City, Gangwondo, was selected as a study area. Samcheok City is located in the east coast of South Korea (Figure 6-

1). This areas has been on the alert for high wave damages in the previous years.

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Figure 6-1. Study area for ocean radar installation

The HF radar used for this study was WERA (WavE RAdar), developed by a German company

Helzel Messtechnik GmbH in 2000. Each radar consists 4 transmitters and 8 receivers with the operation radio frequencies from 5 and 50 MHz. The waves and currents are collected as high as

27km and 48km, respectively. The cell sizes can be determined ranging in distances from 300m to

3km. The data collection interval is between 0.5 second to 10 minutes with a time integration analysis for every 10 minutes. In particular, the collection data can be browsed through web and searched based on time basis (UTC-base). The devices needed for the ocean radar includes the transmitter (TX) and receiver (RX) antennas, the control server, the GPS receiver, and accessories

(Figure 6-2).

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Figure 6-2. Facility of WERA system

In this study, the ocean radars operated at a frequency band of 24.525MHz with a bandwidth of

150 KHz for 1km lattice spacing resolution. The azimuths of center beam of the two radar systems are 95.8° and 37.3° (Figure 6-3), respectively, with the range of ±60° from the central angle (Figure

6-4). The data collection lasted two years from July 1, 2012 to June 30, 2014

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Figure 6-3. Monitoring points and range

Figure 6-4. Installation specification of HF radar

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6.4. Modeling result and analysis

6.4.1 Model parameter setup

6.4.2 Feature extraction

In this section, the PIFs are extracted through the comparison between two different groups of ocean wave data. Figure 6-5 to 6-6 shows two different types of ocean wave height data that are used in this training process.

Figure 6-5. Normal ocean wave height

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Figure 6-6. Abnormal wave height

Figure 6-7 shows the results from the application of the proposed PIF to the two groups of different ocean wave height data. For each point, the horizontal value represents the first index of PC scores, while the vertical value represents the second index of PC scores. From Figure 6-7, it is clear that, each group of data has some unique characteristics: the shape of normal wave plot is convex and the shape of abnormal wave plot is concave.

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Figure 6-7. The identification feature PIF for training data.

6.4.3 Feature comparison

In our previous research, we developed two other identification feature: frequency based feature,

AR-based feature and ICA-based feature. Comparing those three features, this proposed feature has its unique advantages. The frequency-based feature is developed based on short-term Fourier transform (STFT) and fuzzy c-means clustering algorithms. The frequency-based feature which is called as HFOF, is defined as follows:

p Var x n 2 HFOF log | Ck | (6.8) FCM x n k0

137 where Var (x[n]) is the variance of x[n], FCM(x[n]) is the fuzzy C-means values of x[n], and Ck is the kth Fourier transform coefficients, which can be obtained from x[n] and P is the total number of Fourier transform coefficients. Figure 6-8 shows the result of HFOF feature of wave height and its derivative sequences using the same training data in Figure 6-5 and 6-6. Compared with the proposed feature PIF, the feature HFOF integrates various algorithms. However, the proposed algorithm only applies the PCA, which is much simpler and more directly. What’s more, from

Figure 6-8, it is informed that the HFOF cannot clearly separate two group data. They are messy together. As the result, it is almost impossible to apply the classifier, such as nonlinear SVM model, to separate each other.

Figure 6-8. The identification feature HFOF for training data

The AR-based feature, which is called ACSS, comes from the theory of linear system. It is a nonlinear transformation to the coefficients of AR model. Figure 6-9 shows the result of ACSS feature using the same training data in Figure 6-5 and 6-6. From Figure 6-9, it is clear to see that

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ACSS has a good performance that it accurately separate two different types of ocean wave.

What’s more, these datasets can even linear separable. However, this feature is lacking in the interpretable that it is difficult to describe the physical meaning.

Figure 6-9. Comparison of feature ACSS for training data

Based on the analysis above, on both the feature expression and the feature performance, the proposed algorithm is superior to the existing method.

6.4.4 Classification model

Although good feature can tell the unique property of the data set, it cannot directly to identify to which of a set of categories a new observation belongs. With this mind a classifier that provide a clear decision criteria is necessary. Among lots of classifiers, SVM algorithms are chosen in this study. One of the specific advantage is it can provide a clear and simple boundary between two different groups of data. In this study, an SVM model using rbf kernel function is implemented after the feature extraction to detect whether or not the ocean wave is abnormal. In order for the

139

SVM to separate the training datasets into correct classes with least possible error, its parameters

C and σ must be accurately selected. One of the efficient way to select the parameters is the grid search using cross-validation (Hsu et al., 2000). That is various grid pairs of (C, σ) values are tried and the one with the best cross-validation accuracy is selected. In cross-validation, which is short for v-fold cross-validation, the training set is divided into v subsets of equal size. Sequentially each subset is tested using the each of the candidate classifier trained on the reaming v-1 subsets. Thus the accuracy of the cross-validation is the average percentage of all the v data subsets which are correctly classified. The benefit of this method is that on one side grid-search is straightforward and reliable, on the other side cross-validation efficiently prevents the overfitting problem that the model has a good performance only in the training data sets. In this problem, a three-fold cross- validation is considered among various grid pairs of (C, σ), where C = 2-5, …,25 and σ = 2-5, …,25.

After the most suitable parameters chosen, the data sets can then be classified by a nonlinear SVM classifier using rbf kernel function, which is displayed in Figure 6-8.

Figure 6-10. The training result of nonlinear SVM classifier using RBF kernel function

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From Figure 6-10, the blue bold line is the decision boundary between two groups of data. the nonlinear SVM using rbf kernel function has a good performance. It gives a clear enough boundary between the two groups of data

In order to validate the results, three other datasets, which are not used in training process, are used to test the model. The results are shown in Figures 6-11 to 6-13. From Figures 6-11 to 6-13, it is clear that for all results, the nonlinear SVMs using rbf kernel function have a good performance.

They both clearly identify two different groups of data.

Figure 6-11. The 1st validation result of nonlinear SVM classifier using RBF kernel function

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Figure 6-12. The 2nd validation result of nonlinear SVM classifier using RBF kernel function

Figure 6-13. The 3rd validation result of nonlinear SVM classifier using RBF kernel function

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6.5 Conclusion

In this paper, a novel model was proposed for real time ocean wave feature identification. It was developed through the integration of principal component analysis (PCA), nonlinear SVM and the

HF radar system. To demonstrate the effectiveness of the proposed forecasting model, two Wellen radar systems were installed in Samcheok City, Gangwond-do in the East Coast of Korea. A randomly selected data set was used for training the proposed PCA-SVM feature identification model. Other three data sets that were not used for the training process were used for validating the proposed model. It was observed from both training and testing cases that the proposed model is effective in ocean wave feature identification.

The highlight of this study is as follows: first, this study will be the first attempt to systematically integrate the PCA and SVM into ocean wave characteristics detection based on HF radar systems. Hence it is expected that the new approach provides a novel insight into the analysis of ocean wave characteristics using data-driven methods. Second, this method makes ocean wave detection much more convenient. Unlike the previous data-driven method, there is no need to specifically define the feature. The principal component obtained from the PCA can be directly used as the identification feature. Therefore, the identification feature is simple and direct. Last but not least, the proposed algorithm is a fast and clear method to detect wave characteristics in real time. On one side, there are two steps dimension reduction implemented in the algorithm. As the result, the processing time is decreased. On the other side, a decision making model using SVM applied after the feature extraction. It provides a solid boundary between two different types of ocean wave characteristics. Therefore, it will clearly to inform the degree that two ocean wave has similar characteristics.

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7. Conclusion

7.1 Summary of the concluding remarks

This dissertation proposes the usage of a data-driven method into the area of coastal hazard mitigation: a multiple model framework for real-time ocean wave monitoring. In this context, novel algorithms are developed for forecasting, identification, and classification of different types of ocean waves. Focus is first laid on the prediction of ocean wave. The aim is to develop mathematical models to forecast the ocean wave based on the historical ocean wave sequences.

The proposed model is developed through the integration of an autoregressive and moving average

(ARMA) model with nonlinear terms and weighted least squares algorithms. This method does not require setting the order of model in advance. In other words, the proposed model automatically selects the required terms. Comparison of the traditional ARMA model shows that proposed nonlinear ARMA model is effective and computationally efficient in estimating the ocean wave.

In addition to the novel ocean wave forecasting model, this dissertation also proposes three different models for extracting ocean wave identification features. In this dissertation, three different identification features are introduced: frequency-based feature, AR-based feature, and

ICA-based feature. The frequency-based feature tells the frequency property of the ocean wave.

To obtain this feature, a time- frequency analysis is conducted. To be specific, the short-time

Fourier transform with the fuzzy clustering algorithm is applied to the ocean wave data. The frequency components and the clustering centroid are selected as the identification features. It is demonstrated that the frequency-based identification features have good performance to distinguish the different types of ocean waves, especially those that have the similar time domain characteristics. Although the frequency-based feature is robust to identify different ocean waves, the window function, including the type, the length as well as the overlapping rate, in STFT

144 algorithm is customized. It means these parameters vary from different situations. This variety makes the extraction model difficult to be commercialized. With this in mind, the study of AR- based feature is investigated. The AR-based feature is derived from the AR model. At first, the ocean wave data is input in an AR model, and the first three coefficients of the AR model are extracted. Then the AR feature is built from a transformation of these coefficients. Even though it demonstrates that the AR-based feature has good identification performance, it still has the limitation in the feature interpretation. It is almost impossible to express the physical meaning of the feature. The ICA-based feature can make up this defect. ICA-based feature extraction model is a direct extraction method that ICA is applied to the ocean wave sequence, and the coefficients of first two largest variance independent components are selected as the identification feature.

Based on the demonstrated result, the ICA-based feature is proved to bean effective identification feature.

Finally, the dissertation also introduces a classification model for ocean wave classification. The model is trained to classify different types of ocean wave. The coefficients of the PCA are selected as the identification feature. The support vector machine is selected as the classifier. The kernel function of the classifier is RBF. It is demonstrated that the proposed model can accurately classify two different kinds of ocean wave. The proposed model provides an end- to-end framework that it starts from digging into the unstructured dataset and uncovering the insights to building a prediction model to make classification.

The proposed algorithms are validated through field data obtained from Samcheok City,

Korea. The data is ocean wave data that collected from July 1, 2012 to June 30, 2014 using two

HF radar systems. From the validation results, it shows that the proposed algorithms are demonstrated to be powerful in forecasting, identifying, and classifying the ocean waves.

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As the conclusion, it has been demonstrated from the analytical and experimental study that: 1) the proposed forecasting model is accurate and efficient to forecast ocean wave heights; 2) the proposed feature extraction model is effective in identifying ocean waves; and 3) the proposed classification model is efficient in classifying the different ocean waves.

7.2 Future research

The nonlinear ARMA model addressed in this dissertation has been demonstrated theoretically and numerically. It is recommended to apply more accurate and computationally efficient method like sequence models to forecast the ocean wave. Among them, a model called long short-term memory (LSTM) network is the most widely used. The accuracy of LSTM in time series forecasting has already been proved. As ocean wave data is a time series data, its validation in the ocean wave forecasting can be expected.

The proposed framework can be extended to other applications that needs real-time time series analysis but have a large amount of data set, such as structural health monitoring in civil engineering. Since this framework is data-driven and mainly based on the time series sequence, its successful application can be expected in other areas.

Further research can also investigate on the production realization of the whole framework.

Production realization is the overall tranformation from invention ideas into real products. The proposed framework can be a potentional solution into the coastal hazard early warning system.

Now, there is no mature real-time hazard warning system for the public. However, the success of the AMBER alert provides precious experiences into devloping the real-time warning system produciton. With the high speed development of the internet of thing (IoT), the implement of the proposed framework becomes a reality. Thus, it is a rewarding direction for future reseach.

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