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Assessment of the Modeling Abilities of Neural Networks Can Be Formed ASSESSMENT OF THE MODELING ABILITIES OF NEURAL NETWORKS by Alvin Ramsey Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the Requirements for the Degree of Master of Science in Mechanical Engineering at the Massachusetts Institute of Technology January 1994 © Massachusetts Institute of Technology 1994 All rights reserved Signature of Author .. lDpartment of Mechanical Engineering January 1994 /t / I I Certified by --- George Chryssolouris -~~ 1 I ,'4ro . essor Thesis Supervisor l l V~rto Accepted by - ............- ... -'-- Professor Ain A. Sonin i A)-:S1'!!3NSr Graduate Committee OFTFrHR A 5,,'RARIE DEDICATION To my mother ( o o3 ) and to my brother ( Bro, on my word, we shall go fishing someday! ). 2 ASSESSMENT OF THE MODELING ABILITIES OF NEURAL NETWORKS by Alvin Ramsey Submitted to the Department of Mechanical Engineering on January 1994 in partial fulfillment of the requirements for the Degree of Master of Science in Mechanical Engineering ABSTRACT The treatment of manufacturing problems, whether in process control, process optimization, or system design and planning, can be helped by input-output models, namely, relationships between input and output variables. Artificial neural networks present an opportunity to "learn" empirically established relationships and apply them subsequently in order to solve a particular problem. In light of the increasing amount of applications of neural networks, the objective of this thesis is to evaluate the ability of neural networks to generate accurate models for manufacturing applications. Various neural network models has been tested on a number of "test bed" problems which represent the problems typically encountered in manufacturing processes and systems to assess the reliability of neural network models and to determine the efficacy of their modeling capabilities. The first type of problem tested on neural networks is the presence of noise in experimental data. A method to estimate the confidence intervals of neural network models has been developed to assess their reliability, and the proposed method has succeeded for a number of the models of the test problems in estimating the reliability of the neural network models, and greater accuracy may be achieved with higher-order calculations of confidence intervals which would entail increased computational burden and a higher requirement of precision for the parametric values of the neural network model. The second type of problem tested on neural networks is the high level of nonlinearity typically present in an input-output relationship due to the complex phenomena associated within the process or system. The relative efficacy of neural net modeling is evaluated by comparing results from the neural network models of the test bed problems with results from models generated by other common modeling methods: linear regression, the Group Method of Data Handling (GMDH), and the Multivariate Adaptive Regression Splines (MARS) method. The relative efficacy of neural networks has been concluded to be relatively equal to the empirical modeling methods of GMDH and MARS, but all these modeling methods are likely to give a more accurate model than linear regression. Thesis Supervisor: Professor George Chryssolouris Title: Associate Professor of Mechanical Engineering 3 ACKNOWLEDGMENTS Many deserves thanks and recognition for helping me develop the work performed for the Laboratory for Manufacturing and Productivity at MIT. I would like to thank my advisor, Professor George Chryssolouris, for his guidance, support, and opportunity to work in his research group. I must also thank Dr. Moshin Lee, Milan Nedeljkovic, Chukwuemeka (Chux) Amobi, and German Soto for their contributions to the work presented in this thesis; they are among the "buddies" of the lab. I like to thank the rest of the buddies: Subramaniam (the original Buddy), Andrew Yablon, Andrew Heitner, Sean Arnold, Eric Hopkins, Wolfram Weber, Johannes Weis, Giovanni Perrone, Dirk Loeberman, Ulrich Hermann, Helen Azrin, Tina Chen, and Steve Marnock. And I finally would like to thank my mother, Kun Cha Ramsey, and my brother, Dan Ramsey, for their continuous support. 4 TABLE OF CONTENTS LIST OF FIGURES .................................................................................. 7 LIST OF TABLES .................................................................................... 9 1. INTRODUCTION ............................................................................... 10 2. NEURAL NETWORKS FOR EMPIRICAL MODELING ................................ 15 2.1. Empirical vs. Analytical Modeling ...................................................... 15 2.2. Neural Network Background ........................................................ 16 2.2.1. The Pursuit of Pattern Recognition .............................................. 17 2.2.2. Backpropagation Neural Networks .............................................. 19 2.2.3 Other Neural Network Architectures ............................................. 22 3. NEURAL NETWORKS IN MANUFACTURING . .......................... 24 3.1. Areas of Applicability ........................................................ 24 3.1.1. Process Control, Diagnostics and Optimization ............................ 24 3.1.2. System Design and Planning .................. .................... 28 3.2. Current Applications of Neural Networks in Manufacturing ........................ 30 4. CONFIDENCE INTERVAL PREDICTION FOR NEURAL NETWORKS........................................................ 37 4.1. Confidence Intervals for Parameterized Models ............. ......................... 37 4.1.1. Selection of the Variance-Covariance Matrix ................................... 40 4.2. Derivation of Confidence Intervals for Models Derived from Noisy Data ......... 41 4.3. Derivation of Confidence Intervals for Neural Networks ............................ 43 5. APPLICATION OF CONFIDENCE INTERVAL PREDICTION FOR NEURAL NETWORKS ............................................... ................. 47 5.1. Test Problem: Multivariate Test Functions . .............................. 47 5.1.2. Neural Network Modeling of the Multivariate Test Functions ............... 48 5.1.3. Neural Network Reliability ................... .................................... 52 5.2. Test Problem: Laser Machining ........................................................ 53 5.2.1.Background ......... .. ......... .. ......... ......................53 5 5.2.2. Neural Network Modeling of Laser Through-Cutting ........................ 56 5.2.2. Neural Network Modeling of Laser Grooving ................................ 57 5.2.3. Neural Network Reliability ......... ........................................... 59 5.3. Test Problem: The Manufacturing of an Automobile Steering Column ........... 59 5.3.1. An Evaluation Framework for Manufacturing Systems ....................... 60 5.3.2. The Manufacturing of an Automobile Steering Column ................ 62 5.3.3. Neural Network Modeling of the Manufacturing of the Steering Column ............................................................................. 70 5.3.4. Neural Network Reliability ............................................. ...... 71 6. RELATIVE PERFORMANCE OF NEURAL NETWORKS .............................. 73 6.1. Linear Regression ................................................................ 73 6.2. Group Method of Data Handling ....................................................... 74 6.3. Multivariate Adaptive Regression Splines ........... ....................... 78 6.3.1. Recursive Partitioning Regression . ............................. 79 6.3.2. Adaptive Regression Splines ........ ...................... 80 6.4. Results of the Various Modeling Approach to the Test Bed Problems ........... 81 6.4.1. Modeling of the Multivariate Test Functions ............................. 82 6.4.2. Modeling of Laser Machining .......... .... ..... .................................85 6.4.2.1. Laser Through-Cutting ..................................................... 85 6.4.2.2.Laser Grooving ........... ........ .. .....................86 6.4.3. Modeling of the Manufacturing of an Automobile Steering Column ........ 87 6.4.4. Overall Assessment of the Relative Modeling Efficacy of Neural Networks .......................................................................... 89 7. CONCLUSION ...................................... 900................... 7.1. Use of Confidence Intervals to Assess Neural Network Reliability ........ 90 7.2. Relative Efficacy of Neural Network Models ......................................... 91 7.3. Summary .................................................................. 92 REFERENCES ...................................................... ........................ 93 6 LIST OF FIGURES Figure 2.1: Example of a linearly separable pattern ................... 1......................18 Figure 2.2: The exclusive OR problem ................... 1....................................19 Figure 2.3: An example of a feedforward neural network .......... .................. 20 Figure 2.4: A 1-1-1neural network with linear input and output nodes ................... 22 Figure 4-1: A 1-1-1 neural network with linear input and output nodes ................... 43 Figure 5-1: 806%confidence intervals for the neural network model of function 1........................................................... 49 Figure 5-2: 800%confidence intervals for the neural network model of function 1 containing noise ......................................................
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