Advanced Dynamic-System Simulation
Model Replication and Monte Carlo Studies
2nd Edition
Published on 1. April 2013
Book
Hardback
280 pages
978-1-118-39735-0 (ISBN)
Description
A unique, hands-on guide to interactive modeling and simulation of engineering systems
This book describes advanced, cutting-edge techniques for dynamic system simulation using the DESIRE modeling/simulation software package. It offers detailed guidance on how to implement the software, providing scientists and engineers with powerful tools for creating simulation scenarios and experiments for such dynamic systems as aerospace vehicles, control systems, or biological systems.
Along with two new chapters on neural networks, Advanced Dynamic-System Simulation, Second Edition revamps and updates all the material, clarifying explanations and adding many new examples. A bundled CD contains an industrial-strength version of OPEN DESIRE as well as hundreds of program examples that readers can use in their own experiments. The only book on the market to demonstrate model replication and Monte Carlo simulation of real-world engineering systems, this volume:
* Presents a newly revised systematic procedure for difference-equation modeling
* Covers runtime vector compilation for fast model replication on a personal computer
* Discusses parameter-influence studies, introducing very fast vectorized statistics computation
* Highlights Monte Carlo studies of the effects of noise and manufacturing tolerances for control-system modeling
* Demonstrates fast, compact vector models of neural networks for control engineering
* Features vectorized programs for fuzzy-set controllers, partial differential equations, and agro-ecological modeling
Advanced Dynamic-System Simulation, Second Edition is a truly useful resource for researchers and design engineers in control and aerospace engineering, ecology, and agricultural planning. It is also an excellent guide for students using DESIRE.
This book describes advanced, cutting-edge techniques for dynamic system simulation using the DESIRE modeling/simulation software package. It offers detailed guidance on how to implement the software, providing scientists and engineers with powerful tools for creating simulation scenarios and experiments for such dynamic systems as aerospace vehicles, control systems, or biological systems.
Along with two new chapters on neural networks, Advanced Dynamic-System Simulation, Second Edition revamps and updates all the material, clarifying explanations and adding many new examples. A bundled CD contains an industrial-strength version of OPEN DESIRE as well as hundreds of program examples that readers can use in their own experiments. The only book on the market to demonstrate model replication and Monte Carlo simulation of real-world engineering systems, this volume:
* Presents a newly revised systematic procedure for difference-equation modeling
* Covers runtime vector compilation for fast model replication on a personal computer
* Discusses parameter-influence studies, introducing very fast vectorized statistics computation
* Highlights Monte Carlo studies of the effects of noise and manufacturing tolerances for control-system modeling
* Demonstrates fast, compact vector models of neural networks for control engineering
* Features vectorized programs for fuzzy-set controllers, partial differential equations, and agro-ecological modeling
Advanced Dynamic-System Simulation, Second Edition is a truly useful resource for researchers and design engineers in control and aerospace engineering, ecology, and agricultural planning. It is also an excellent guide for students using DESIRE.
More details
Other editions
Additional editions
E-Book
02/2013
2nd Edition
Wiley
€94.99
Available for download
E-Book
02/2013
2nd Edition
Wiley
€94.99
Available for download
Person
GRANINO A. KORN, PhD, is Professor of Electrical and Computer Engineering at the University of Arizona and a partner with G.A. and T.M. Korn Industrial Consultants, a company that designs systems for interactive simulation of dynamic systems and neural networks. He is the author of fifteen books, a Fellow of the IEEE, and the recipient of several awards for his work on computer simulation.
Content
PREFACE xiii
CHAPTER 1 DYNAMIC-SYSTEM MODELS AND SIMULATION 1
SIMULATION IS EXPERIMENTATION WITH MODELS 1
(a) Difference-Equation Models 2
(b) Differential-Equation Models 2
(c) Discussion 3
ANATOMY OF A SIMULATION RUN 8
(a) Euler Integration 10
(b) Improved Integration Rules 10
SIMPLE APPLICATION PROGRAMS 12
(a) Linear Oscillator 12
(b) Nonlinear Oscillator: Duffing's Differential Equation 14
INRODUCTION TO CONTROL-SYSTEM SIMULATION 21
(a) Guided Torpedo 24
(b) Complete Torpedo-Simulation Program 26
STOP AND LOOK 28
References 29
CHAPTER 2 MODELS WITH DIFFERENCE EQUATIONS, LIMITERS, AND SWITCHES 31
SAMPLED-DATA SYSTEMS AND DIFFERENCE EQUATIONS 31
(a) Introduction 31
(b) Difference Equations 31
(c) A Minefield of Possible Errors 32
(a) General Difference-Equation Model 32
(b) Simple Recurrence Relations 33
TWO MIXED CONTINUOUS/SAMPLED-DATA SYSTEMS 37
DYNAMIC-SYSTEM MODELS WITH LIMITERS AND SWITCHES 40
(a) Limiter Functions 40
(b) Switching Functions and Comparators 42
EFFICIENT DEVICE MODELS USING RECURSIVE ASSIGNMENTS 48
References 55
CHAPTER 3 FAST VECTOR-MATRIX OPERATIONS AND SUBMODELS 57
ARRAYS, VECTORS, AND MATRICES 57
(a) Improved Modeling 57
(b) Array Declarations, Vectors, and Matrices 57
(c) State-Variable Declarations 58
VECTORS AND MODEL REPLICATION 59
(a) Vector Assignments and Vector Expressions 59
(b) Vector Differential Equations 60
(c) Vector Sampled-Data Assignments and Difference Equations 60
(a) Definition 61
(b) Simple Example: Resonating Oscillators 61
(a) Definition 63
(b) Preview of Significant Applications 63
MORE VECTOR OPERATIONS 65
(a) Sums and DOT Products 65
(b) Euclidean, Taxicab, and Hamming Norms 65
(a) Maximum/Minimum Selection 66
(b) Masking Vector Expressions 66
VECTOR EQUIVALENCE DECLARATIONS SIMPLIFY MODELS 67
MATRIX OPERATIONS IN DYNAMIC-SYSTEM MODELS 67
(a) Matrix Expressions and DOT Products 68
(b) Matrix Differential Equations 68
(c) Matrix Difference Equations 69
VECTORS IN PHYSICS AND CONTROL-SYSTEM PROBLEMS 69
USER-DEFINED FUNCTIONS AND SUBMODELS 72
References 75
CHAPTER 4 EFFICIENT PARAMETER-INFLUENCE STUDIES AND STATISTICS COMPUTATION 77
MODEL REPLICATION SIMPLIFIES PARAMETER-INFLUENCE STUDIES 77
(a) Simple Repeated-Run Study 78
(b) Model Replication (Vectorization) 78
(a) Measures of System Performance 80
(b) Program Design 81
(c) Two-Dimensional Model Replication 81
(d) Cross-Plotting Results 82
(e) Maximum/Minimum Selection 83
(f) Iterative Parameter Optimization 83
STATISTICS 84
COMPUTING STATISTICS BY VECTOR AVERAGING 85
(a) Simple Probability-Density Estimate 86
(b) Triangle and Parzen Windows 87
(c) Computation and Display of Parzen-Window Estimates 88
REPLICATED AVERAGES GENERATE SAMPLING DISTRIBUTIONS 91
(a) Introduction 91
(b) Demonstrations of Empirical Laws of Large Numbers 93
(c) Counterexample: Fat-Tailed Distribution 95
RANDOM-PROCESS SIMULATION 95
(a) Modeling Continuous Noise 98
(b) Continuous Time Averaging 99
(c) Correlation Functions and Spectral Densities 100
SIMPLE MONTE CARLO EXPERIMENTS 100
References 106
CHAPTER 5 MONTE CARLO SIMULATION OF REAL DYNAMIC SYSTEMS 109
INTRODUCTION 109
REPEATED-RUN MONTE CARLO SIMULATION 109
VECTORIZED MONTE CARLO SIMULATION 113
Cannon Shot 113
SIMULATION OF NOISY CONTROL SYSTEMS 119
ADDITIONAL TOPICS 123
(a) Introduction 123
(b) Dynamic Systems with Random Perturbations 123
(c) Mean-Square Errors in Linearized Systems 124
References 125
CHAPTER 6 VECTOR MODELS OF NEURAL NETWORKS 127
ARTIFICIAL NEURAL NETWORKS 127
SIMPLE VECTOR ASSIGNMENTS MODEL NEURON LAYERS 130
(a) Pattern Normalization 131
(b) Contrast Enhancement: Softmax and Thresholding 131
(a) Computing Successive Neuron-Layer Outputs 132
(b) Input from Pattern-Row Matrices 133
(c) Input from Text Files and Spreadsheets 133
SUPERVISED TRAINING FOR REGRESSION 134
(a) Problem Statement 134
(b) Linear Mean-Square Regression and the Delta Rule 135
(c) Nonlinear Neuron Layers and Activation-Function Derivatives 136
(d) Error-Measure Display 136
(a) The Generalized Delta Rule 137
(b) Momentum Learning 139
(c) Simple Example 139
(d) The Classical XOR Problem and Other Examples 140
MORE NEURAL-NETWORK MODELS 140
(a) Basis-Function Expansion and Linear Optimization 142
(b) Radial Basis Functions 143
PATTERN CLASSIFICATION 146
(a) Simple Linear Classifiers 147
(b) Softmax Classifiers 148
(c) Backpropagation Classifiers 148
(d) Functional-Link Classifiers 149
(e) Other Classsifiers 149
(a) Classification Using an Empirical Database: Fisher's Iris Problem 149
(b) Image-Pattern Recognition and Associative Memory 151
PATTERN SIMPLIFICATION 155
(a) Bottleneck Layers and Encoders 156
(b) Principal Components 156
NETWORK-TRAINING PROBLEMS 157
(a) Introduction 157
(b) Adding Noise 158
(c) Early Stopping 158
(d) Regularization 159
UNSUPERVISED COMPETITIVE-LAYER CLASSIFIERS 159
(a) Template Patterns and Template Matrix 159
(b) Matching Known Template Patterns 160
(c) Template-Pattern Training 160
(d) Correlation Training 162
(a) Pattern Classification 164
(b) Vector Quantization 164
SUPERVISED COMPETITIVE LEARNING 167
EXAMPLES OF CLEARN CLASSIFIERS 168
(a) Image Recognition 168
(b) Fast Solution of the Spiral Benchmark Problem 169
References 174
CHAPTER 7 DYNAMIC NEURAL NETWORKS 177
INTRODUCTION 177
NEURAL NETWORKS WITH DELAY-LINE INPUT 178
(a) Linear Combiners 180
(b) One-Layer Nonlinear Network 181
(c) Functional-Link Network 181
(d) Backpropagation Network with Delay-Line Input 182
STATIC NEURAL NETWORKS USED AS DYNAMIC NETWORKS 183
RECURRENT NEURAL NETWORKS 185
(a) Conventional Model of a Jordan Network 185
(b) Simplified Jordan-Network Model 186
(c) Simplified Models for Other Feedback Networks 187
(a) Delay-Line Feedback 187
(b) Neural Networks with Both Input and Feedback Delay Lines 188
PREDICTOR NETWORKS 189
(a) Off-Line Prediction Using Stored Time Series 189
(b) Off-Line Training System for Online Predictors 189
(c) Example: Simple Linear Predictor 190
OTHER APPLICATIONS OF DYNAMIC NETWORKS 199
(a) Introduction 201
(b) Example: Program for Matching Narendra's Plant Model 201
MISCELLANEOUS TOPICS 204
References 204
CHAPTER 8 MORE APPLICATIONS OF VECTOR MODELS 207
VECTORIZED SIMULATION WITH LOGARITHMIC PLOTS 207
MODELING FUZZY-LOGIC FUNCTION GENERATORS 209
(a) Fuzzy Sets and Membership Functions 210
(b) Fuzzy Intersections and Unions 210
(c) Joint Membership Functions 213
(d) Normalized Fuzzy-Set Partitions 213
(a) Gaussian Bumps: Effects of Normalization 215
(b) Triangle Functions 215
(c) Smooth Fuzzy-Basis Functions 216
(a) Problem Statement 217
(b) Experiment Protocol and Rule Table 217
(c) DYNAMIC Program Segment and Results 220
PARTIAL DIFFERENTIAL EQUATIONS 221
(a) Introduction 221
(b) Using Differentiation Operators 221
(c) Numerical Problems 224
FOURIER ANALYSIS AND LINEAR-SYSTEM DYNAMICS 229
(a) Using the Index-Shift Operation with Analog Integration 232
(b) Linear Sampled-Data Systems 235
(c) Example: Digital Comb Filter 236
REPLICATION OF AGROECOLOGICAL MODELS ON MAP GRIDS 237
References 242
APPENDIX: ADDITIONAL REFERENCE MATERIAL 245
References 248
USING THE BOOK CD 251
INDEX 253
CHAPTER 1 DYNAMIC-SYSTEM MODELS AND SIMULATION 1
SIMULATION IS EXPERIMENTATION WITH MODELS 1
(a) Difference-Equation Models 2
(b) Differential-Equation Models 2
(c) Discussion 3
ANATOMY OF A SIMULATION RUN 8
(a) Euler Integration 10
(b) Improved Integration Rules 10
SIMPLE APPLICATION PROGRAMS 12
(a) Linear Oscillator 12
(b) Nonlinear Oscillator: Duffing's Differential Equation 14
INRODUCTION TO CONTROL-SYSTEM SIMULATION 21
(a) Guided Torpedo 24
(b) Complete Torpedo-Simulation Program 26
STOP AND LOOK 28
References 29
CHAPTER 2 MODELS WITH DIFFERENCE EQUATIONS, LIMITERS, AND SWITCHES 31
SAMPLED-DATA SYSTEMS AND DIFFERENCE EQUATIONS 31
(a) Introduction 31
(b) Difference Equations 31
(c) A Minefield of Possible Errors 32
(a) General Difference-Equation Model 32
(b) Simple Recurrence Relations 33
TWO MIXED CONTINUOUS/SAMPLED-DATA SYSTEMS 37
DYNAMIC-SYSTEM MODELS WITH LIMITERS AND SWITCHES 40
(a) Limiter Functions 40
(b) Switching Functions and Comparators 42
EFFICIENT DEVICE MODELS USING RECURSIVE ASSIGNMENTS 48
References 55
CHAPTER 3 FAST VECTOR-MATRIX OPERATIONS AND SUBMODELS 57
ARRAYS, VECTORS, AND MATRICES 57
(a) Improved Modeling 57
(b) Array Declarations, Vectors, and Matrices 57
(c) State-Variable Declarations 58
VECTORS AND MODEL REPLICATION 59
(a) Vector Assignments and Vector Expressions 59
(b) Vector Differential Equations 60
(c) Vector Sampled-Data Assignments and Difference Equations 60
(a) Definition 61
(b) Simple Example: Resonating Oscillators 61
(a) Definition 63
(b) Preview of Significant Applications 63
MORE VECTOR OPERATIONS 65
(a) Sums and DOT Products 65
(b) Euclidean, Taxicab, and Hamming Norms 65
(a) Maximum/Minimum Selection 66
(b) Masking Vector Expressions 66
VECTOR EQUIVALENCE DECLARATIONS SIMPLIFY MODELS 67
MATRIX OPERATIONS IN DYNAMIC-SYSTEM MODELS 67
(a) Matrix Expressions and DOT Products 68
(b) Matrix Differential Equations 68
(c) Matrix Difference Equations 69
VECTORS IN PHYSICS AND CONTROL-SYSTEM PROBLEMS 69
USER-DEFINED FUNCTIONS AND SUBMODELS 72
References 75
CHAPTER 4 EFFICIENT PARAMETER-INFLUENCE STUDIES AND STATISTICS COMPUTATION 77
MODEL REPLICATION SIMPLIFIES PARAMETER-INFLUENCE STUDIES 77
(a) Simple Repeated-Run Study 78
(b) Model Replication (Vectorization) 78
(a) Measures of System Performance 80
(b) Program Design 81
(c) Two-Dimensional Model Replication 81
(d) Cross-Plotting Results 82
(e) Maximum/Minimum Selection 83
(f) Iterative Parameter Optimization 83
STATISTICS 84
COMPUTING STATISTICS BY VECTOR AVERAGING 85
(a) Simple Probability-Density Estimate 86
(b) Triangle and Parzen Windows 87
(c) Computation and Display of Parzen-Window Estimates 88
REPLICATED AVERAGES GENERATE SAMPLING DISTRIBUTIONS 91
(a) Introduction 91
(b) Demonstrations of Empirical Laws of Large Numbers 93
(c) Counterexample: Fat-Tailed Distribution 95
RANDOM-PROCESS SIMULATION 95
(a) Modeling Continuous Noise 98
(b) Continuous Time Averaging 99
(c) Correlation Functions and Spectral Densities 100
SIMPLE MONTE CARLO EXPERIMENTS 100
References 106
CHAPTER 5 MONTE CARLO SIMULATION OF REAL DYNAMIC SYSTEMS 109
INTRODUCTION 109
REPEATED-RUN MONTE CARLO SIMULATION 109
VECTORIZED MONTE CARLO SIMULATION 113
Cannon Shot 113
SIMULATION OF NOISY CONTROL SYSTEMS 119
ADDITIONAL TOPICS 123
(a) Introduction 123
(b) Dynamic Systems with Random Perturbations 123
(c) Mean-Square Errors in Linearized Systems 124
References 125
CHAPTER 6 VECTOR MODELS OF NEURAL NETWORKS 127
ARTIFICIAL NEURAL NETWORKS 127
SIMPLE VECTOR ASSIGNMENTS MODEL NEURON LAYERS 130
(a) Pattern Normalization 131
(b) Contrast Enhancement: Softmax and Thresholding 131
(a) Computing Successive Neuron-Layer Outputs 132
(b) Input from Pattern-Row Matrices 133
(c) Input from Text Files and Spreadsheets 133
SUPERVISED TRAINING FOR REGRESSION 134
(a) Problem Statement 134
(b) Linear Mean-Square Regression and the Delta Rule 135
(c) Nonlinear Neuron Layers and Activation-Function Derivatives 136
(d) Error-Measure Display 136
(a) The Generalized Delta Rule 137
(b) Momentum Learning 139
(c) Simple Example 139
(d) The Classical XOR Problem and Other Examples 140
MORE NEURAL-NETWORK MODELS 140
(a) Basis-Function Expansion and Linear Optimization 142
(b) Radial Basis Functions 143
PATTERN CLASSIFICATION 146
(a) Simple Linear Classifiers 147
(b) Softmax Classifiers 148
(c) Backpropagation Classifiers 148
(d) Functional-Link Classifiers 149
(e) Other Classsifiers 149
(a) Classification Using an Empirical Database: Fisher's Iris Problem 149
(b) Image-Pattern Recognition and Associative Memory 151
PATTERN SIMPLIFICATION 155
(a) Bottleneck Layers and Encoders 156
(b) Principal Components 156
NETWORK-TRAINING PROBLEMS 157
(a) Introduction 157
(b) Adding Noise 158
(c) Early Stopping 158
(d) Regularization 159
UNSUPERVISED COMPETITIVE-LAYER CLASSIFIERS 159
(a) Template Patterns and Template Matrix 159
(b) Matching Known Template Patterns 160
(c) Template-Pattern Training 160
(d) Correlation Training 162
(a) Pattern Classification 164
(b) Vector Quantization 164
SUPERVISED COMPETITIVE LEARNING 167
EXAMPLES OF CLEARN CLASSIFIERS 168
(a) Image Recognition 168
(b) Fast Solution of the Spiral Benchmark Problem 169
References 174
CHAPTER 7 DYNAMIC NEURAL NETWORKS 177
INTRODUCTION 177
NEURAL NETWORKS WITH DELAY-LINE INPUT 178
(a) Linear Combiners 180
(b) One-Layer Nonlinear Network 181
(c) Functional-Link Network 181
(d) Backpropagation Network with Delay-Line Input 182
STATIC NEURAL NETWORKS USED AS DYNAMIC NETWORKS 183
RECURRENT NEURAL NETWORKS 185
(a) Conventional Model of a Jordan Network 185
(b) Simplified Jordan-Network Model 186
(c) Simplified Models for Other Feedback Networks 187
(a) Delay-Line Feedback 187
(b) Neural Networks with Both Input and Feedback Delay Lines 188
PREDICTOR NETWORKS 189
(a) Off-Line Prediction Using Stored Time Series 189
(b) Off-Line Training System for Online Predictors 189
(c) Example: Simple Linear Predictor 190
OTHER APPLICATIONS OF DYNAMIC NETWORKS 199
(a) Introduction 201
(b) Example: Program for Matching Narendra's Plant Model 201
MISCELLANEOUS TOPICS 204
References 204
CHAPTER 8 MORE APPLICATIONS OF VECTOR MODELS 207
VECTORIZED SIMULATION WITH LOGARITHMIC PLOTS 207
MODELING FUZZY-LOGIC FUNCTION GENERATORS 209
(a) Fuzzy Sets and Membership Functions 210
(b) Fuzzy Intersections and Unions 210
(c) Joint Membership Functions 213
(d) Normalized Fuzzy-Set Partitions 213
(a) Gaussian Bumps: Effects of Normalization 215
(b) Triangle Functions 215
(c) Smooth Fuzzy-Basis Functions 216
(a) Problem Statement 217
(b) Experiment Protocol and Rule Table 217
(c) DYNAMIC Program Segment and Results 220
PARTIAL DIFFERENTIAL EQUATIONS 221
(a) Introduction 221
(b) Using Differentiation Operators 221
(c) Numerical Problems 224
FOURIER ANALYSIS AND LINEAR-SYSTEM DYNAMICS 229
(a) Using the Index-Shift Operation with Analog Integration 232
(b) Linear Sampled-Data Systems 235
(c) Example: Digital Comb Filter 236
REPLICATION OF AGROECOLOGICAL MODELS ON MAP GRIDS 237
References 242
APPENDIX: ADDITIONAL REFERENCE MATERIAL 245
References 248
USING THE BOOK CD 251
INDEX 253