Advanced Dynamic-System Simulation

Now in a fully revised second edition, this work introduces dynamic–system simulation with a main emphasis on OPEN DESIRE and DESIRE software. Offering a complete update of all material, the new edition boasts two completely new chapters on fast simulation of neural networks as well as three appendices on radial–basis–function, fuzzy–basis–function networks, and CLEARN algorithm. A companion CD contains complete binary OPEN DESIRE modeling/simulation program packages for personal–computer LINUX and MS Windows, DESIRE examples, source code, and a comprehensive, indexed reference manual.

PREFACE xiii CHAPTER 1 DYNAMIC–SYSTEM MODELS AND SIMULATION 1 SIMULATION IS EXPERIMENTATION WITH MODELS 1 1–1 Simulation and Computer Programs 1 1–2 Dynamic–System Models 2 1–3 Experiment Protocols Define Simulation Studies 3 1–4 Simulation Software 4 1–5 Fast Simulation Program for Interactive Modeling 5 ANATOMY OF A SIMULATION RUN 8 1–6 Dynamic–System Time Histories Are Sampled Periodically 8 1–7 Numerical Integration 10 1–8 Sampling Times and Integration Steps 11 1–9 Sorting Defined–Variable Assignments 12 SIMPLE APPLICATION PROGRAMS 12 1–10 Oscillators and Computer Displays 12 1–11 Space–Vehicle Orbit Simulation with Variable–Step Integration 15 1–12 Population–Dynamics Model 17 1–13 Splicing Multiple Simulation Runs: Billiard–Ball Simulation 17 INRODUCTION TO CONTROL–SYSTEM SIMULATION 21 1–14 Electrical Servomechanism with Motor–Field Delay and Saturation 21 1–15 Control–System Frequency Response 23 1–16 Simulation of a Simple Guided Missile 24 STOP AND LOOK 28 1–17 Simulation in the Real World: A Word of Caution 28 References 29 CHAPTER 2 MODELS WITH DIFFERENCE EQUATIONS, LIMITERS, AND SWITCHES 31 SAMPLED–DATA SYSTEMS AND DIFFERENCE EQUATIONS 31 2–1 Sampled–Data Difference–Equation Systems 31 2–2 Solving Systems of First–Order Difference Equations 32 2–3 Models Combining Differential Equations and Sampled–Data Operations 35 2–4 Simple Example 35 2–5 Initializing and Resetting Sampled–Data Variables 35 TWO MIXED CONTINUOUS/SAMPLED–DATA SYSTEMS 37 2–6 Guided Torpedo with Digital Control 37 2–7 Simulation of a Plant with a Digital PID Controller 37 DYNAMIC–SYSTEM MODELS WITH LIMITERS AND SWITCHES 40 2–8 Limiters, Switches, and Comparators 40 2–9 Integration of Switch and Limiter Outputs, Event Prediction, and Display Problems 43 2–10 Using Sampled–Data Assignments 44 2–11 Using the step Operator and Heuristic Integration–Step Control 44 2–12 Example: Simulation of a Bang–Bang Servomechanism 45 2–13 Limiters, Absolute Values, and Maximum/Minimum Selection 46 2–14 Output–Limited Integration 47 2–15 Modeling Signal Quantization 48 EFFICIENT DEVICE MODELS USING RECURSIVE ASSIGNMENTS 48 2–16 Recursive Switching and Limiter Operations 48 2–17 Track/Hold Simulation 49 2–18 Maximum–Value and Minimum–Value Holding 50 2–19 Simple Backlash and Hysteresis Models 51 2–20 Comparator with Hysteresis (Schmitt Trigger) 52 2–21 Signal Generators and Signal Modulation 53 References 55 CHAPTER 3 FAST VECTOR&ndash,MATRIX OPERATIONS AND SUBMODELS 57 ARRAYS, VECTORS, AND MATRICES 57 3–1 Arrays and Subscripted Variables 57 3–2 Vector and Matrices in Experiment Protocols 58 3–3 Time–History Arrays 58 VECTORS AND MODEL REPLICATION 59 3–4 Vector Operations in DYNAMIC Program Segments: The Vectorizing Compiler 59 3–5 Matrix&ndash,Vector Products in Vector Expressions 61 3–6 Index–Shift Operation 63 3–7 Sorting Vector and Subscripted–Variable Assignments 64 3–8 Replication of Dynamic–System Models 64 MORE VECTOR OPERATIONS 65 3–9 Sums, DOT Products, and Vector Norms 65 3–10 Maximum/Minimum Selection and Masking 66 VECTOR EQUIVALENCE DECLARATIONS SIMPLIFY MODELS 67 3–11 Subvectors 67 3–12 Matrix&ndash,Vector Equivalence 67 MATRIX OPERATIONS IN DYNAMIC–SYSTEM MODELS 67 3–13 Simple Matrix Assignments 67 3–14 Two–Dimensional Model Replication 68 VECTORS IN PHYSICS AND CONTROL–SYSTEM PROBLEMS 69 3–15 Vectors in Physics Problems 69 3–16 Vector Model of a Nuclear Reactor 69 3–17 Linear Transformations and Rotation Matrices 70 3–18 State–Equation Models of Linear Control Systems 72 USER–DEFINED FUNCTIONS AND SUBMODELS 72 3–19 Introduction 72 3–20 User–Defined Functions 72 3–21 Submodel Declaration and Invocation 73 3–22 Dealing with Sampled–Data Assignments, Limiters, and Switches 75 References 75 CHAPTER 4 EFFICIENT PARAMETER–INFLUENCE STUDIES AND STATISTICS COMPUTATION 77 MODEL REPLICATION SIMPLIFIES PARAMETER–INFLUENCE STUDIES 77 4–1 Exploring the Effects of Parameter Changes 77 4–2 Repeated Simulation Runs Versus Model Replication 78 4–3 Programming Parameter–Influence Studies 80 STATISTICS 84 4–4 Random Data and Statistics 84 4–5 Sample Averages and Statistical Relative Frequencies 85 COMPUTING STATISTICS BY VECTOR AVERAGING 85 4–6 Fast Computation of Sample Averages 85 4–7 Fast Probability Estimation 86 4–8 Fast Probability–Density Estimation 86 4–9 Sample–Range Estimation 90 REPLICATED AVERAGES GENERATE SAMPLING DISTRIBUTIONS 91 4–10 Computing Statistics by Time Averaging 91 4–11 Sample Replication and Sampling–Distribution Statistics 91 RANDOM–PROCESS SIMULATION 95 4–12 Random Processes and Monte Carlo Simulation 95 4–13 Modeling Random Parameters and Random Initial Values 97 4–14 Sampled–Data Random Processes 97 4–15 &ldquo,Continuous&rdquo, Random Processes 98 4–16 Problems with Simulated Noise 100 SIMPLE MONTE CARLO EXPERIMENTS 100 4–17 Introduction 100 4–18 Gambling Returns 100 4–19 Vectorized Monte Carlo Study of a Continuous Random Walk 102 References 106 CHAPTER 5 MONTE CARLO SIMULATION OF REAL DYNAMIC SYSTEMS 109 INTRODUCTION 109 5–1 Survey 109 REPEATED–RUN MONTE CARLO SIMULATION 109 5–2 End–of–Run Statistics for Repeated Simulation Runs 109 5–3 Example: Effects of Gun–Elevation Errors on a 1776 Cannnonball Trajectory 110 5–4 Sequential Monte Carlo Simulation 113 VECTORIZED MONTE CARLO SIMULATION 113 5–5 Vectorized Monte Carlo Simulation of the 1776 Cannon Shot 113 5–6 Combined Vectorized and Repeated–Run Monte Carlo Simulation 115 5–7 Interactive Monte Carlo Simulation: Computing Runtime Histories of Statistics with DYNAMIC–Segment DOT Operations 115 5–8 Example: Torpedo Trajectory Dispersion 117 SIMULATION OF NOISY CONTROL SYSTEMS 119 5–9 Monte Carlo Simulation of a Nonlinear Servomechanism: A Noise–Input Test 119 5–10 Monte Carlo Study of Control–System Errors Caused by Noise 121 ADDITIONAL TOPICS 123 5–11 Monte Carlo Optimization 123 5–12 Convenient Heuristic Method for Testing Pseudorandom Noise 123 5–13 Alternative to Monte Carlo Simulation 123 References 125 CHAPTER 6 VECTOR MODELS OF NEURAL NETWORKS 127 ARTIFICIAL NEURAL NETWORKS 127 6–1 Introduction 127 6–2 Artificial Neural Networks 127 6–3 Static Neural Networks: Training, Validation, and Applications 128 6–4 Dynamic Neural Networks 129 SIMPLE VECTOR ASSIGNMENTS MODEL NEURON LAYERS 130 6–5 Neuron–Layer Declarations and Neuron Operations 130 6–6 Neuron–Layer Concatenation Simplifies Bias Inputs 130 6–7 Normalizing and Contrast–Enhancing Layers 131 6–8 Multilayer Networks 132 6–9 Exercising a Neural–Network Model 132 SUPERVISED TRAINING FOR REGRESSION 134 6–10 Mean–Square Regression 134 6–11 Backpropagation Networks 137 MORE NEURAL–NETWORK MODELS 140 6–12 Functional–Link Networks 140 6–13 Radial–Basis–Function Networks 142 6–14 Neural–Network Submodels 145 PATTERN CLASSIFICATION 146 6–15 Introduction 146 6–16 Classifier Input from Files 147 6–17 Classifier Networks 147 6–18 Examples 149 PATTERN SIMPLIFICATION 155 6–19 Pattern Centering 155 6–20 Feature Reduction 156 NETWORK–TRAINING PROBLEMS 157 6–21 Learning–Rate Adjustment 157 6–22 Overfitting and Generalization 157 6–23 Beyond Simple Gradient Descent 159 UNSUPERVISED COMPETITIVE–LAYER CLASSIFIERS 159 6–24 Template–Pattern Matching and the CLEARN Operation 159 6–25 Learning with Conscience 163 6–26 Competitive–Learning Experiments 164 6–27 Simplified Adaptive–Resonance Emulation 165 SUPERVISED COMPETITIVE LEARNING 167 6–28 The LVQ Algorithm for Two–Way Classification 167 6–29 Counterpropagation Networks 167 EXAMPLES OF CLEARN CLASSIFIERS 168 6–30 Recognition of Known Patterns 168 6–31 Learning Unknown Patterns 173 References 174 CHAPTER 7 DYNAMIC NEURAL NETWORKS 177 INTRODUCTION 177 7–1 Dynamic Versus Static Neural Networks 177 7–2 Applications of Dynamic Neural Networks 177 7–3 Simulations Combining Neural Networks and Differential–Equation Models 178 NEURAL NETWORKS WITH DELAY–LINE INPUT 178 7–4 Introduction 178 7–5 The Delay–Line Model 180 7–6 Delay–Line–Input Networks 180 7–7 Using Gamma Delay Lines 182 STATIC NEURAL NETWORKS USED AS DYNAMIC NETWORKS 183 7–8 Introduction 183 7–9 Simple Backpropagation Networks 184 RECURRENT NEURAL NETWORKS 185 7–10 Layer–Feedback Networks 185 7–11 Simplified Recurrent–Network Models Combine Context and Input Layers 185 7–12 Neural Networks with Feedback Delay Lines 187 7–13 Teacher Forcing 189 PREDICTOR NETWORKS 189 7–14 Off–Line Predictor Training 189 7–15 Online Trainng for True Online Prediction 192 7–16 Chaotic Time Series for Prediction Experiments 192 7–17 Gallery of Predictor Networks 193 OTHER APPLICATIONS OF DYNAMIC NETWORKS 199 7–18 Temporal–Pattern Recognition: Regression and Classification 199 7–19 Model Matching 201 MISCELLANEOUS TOPICS 204 7–20 Biological–Network Software 204 References 204 CHAPTER 8 MORE APPLICATIONS OF VECTOR MODELS 207 VECTORIZED SIMULATION WITH LOGARITHMIC PLOTS 207 8–1 The EUROSIM No. 1 Benchmark Problem 207 8–2 Vectorized Simulation with Logarithmic Plots 207 MODELING FUZZY–LOGIC FUNCTION GENERATORS 209 8–3 Rule Tables Specify Heuristic Functions 209 8–4 Fuzzy–Set Logic 210 8–5 Fuzzy–Set Rule Tables and Function Generators 214 8–6 Simplified Function Generation with Fuzzy Basis Functions 214 8–7 Vector Models of Fuzzy–Set Partitions 215 8–8 Vector Models for Multidimensional Fuzzy–Set Partitions 216 8–9 Example: Fuzzy–Logic Control of a Servomechanism 217 PARTIAL DIFFERENTIAL EQUATIONS 221 8–10 Method of Lines 221 8–11 Vectorized Method of Lines 221 8–12 Heat–Conduction Equation in Cylindrical Coordinates 225 8–13 Generalizations 225 8–14 Simple Heat–Exchanger Model 227 FOURIER ANALYSIS AND LINEAR–SYSTEM DYNAMICS 229 8–15 Introduction 229 8–16 Function–Table Lookup and Interpolation 230 8–17 Fast–Fourier–Transform Operations 230 8–18 Impulse and Freqency Response of a Linear Servomechanism 231 8–19 Compact Vector Models of Linear Dynamic Systems 232 REPLICATION OF AGROECOLOGICAL MODELS ON MAP GRIDS 237 8–20 Geographical Information System 237 8–21 Modeling the Evolution of Landscape Features 239 8–22 Matrix Operations on a Map Grid 239 References 242 APPENDIX: ADDITIONAL REFERENCE MATERIAL 245 A–1 Example of a Radial–Basis–Function Network 245 A–2 Fuzzy–Basis–Function Network 245 References 248 USING THE BOOK CD 251 INDEX 253