Advanced DynamicSystem Simulation: Model Replication and Monte Carlo Studies, 2nd EditionISBN: 9781118397350
280 pages
April 2013

Description
A unique, handson guide to interactive modeling and simulation of engineering systems
This book describes advanced, cuttingedge 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 DynamicSystem Simulation, Second Edition revamps and updates all the material, clarifying explanations and adding many new examples. A bundled CD contains an industrialstrength 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 realworld engineering systems, this volume:
 Presents a newly revised systematic procedure for differenceequation modeling
 Covers runtime vector compilation for fast model replication on a personal computer
 Discusses parameterinfluence studies, introducing very fast vectorized statistics computation
 Highlights Monte Carlo studies of the effects of noise and manufacturing tolerances for controlsystem modeling
 Demonstrates fast, compact vector models of neural networks for control engineering
 Features vectorized programs for fuzzyset controllers, partial differential equations, and agroecological modeling
Advanced DynamicSystem 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.
Table of Contents
PREFACE xiii
CHAPTER 1 DYNAMICSYSTEM MODELS AND SIMULATION 1
SIMULATION IS EXPERIMENTATION WITH MODELS 1
11 Simulation and Computer Programs 1
12 DynamicSystem Models 2
13 Experiment Protocols Define Simulation Studies 3
14 Simulation Software 4
15 Fast Simulation Program for Interactive Modeling 5
ANATOMY OF A SIMULATION RUN 8
16 DynamicSystem Time Histories Are Sampled Periodically 8
17 Numerical Integration 10
18 Sampling Times and Integration Steps 11
19 Sorting DefinedVariable Assignments 12
SIMPLE APPLICATION PROGRAMS 12
110 Oscillators and Computer Displays 12
111 SpaceVehicle Orbit Simulation with VariableStep Integration 15
112 PopulationDynamics Model 17
113 Splicing Multiple Simulation Runs: BilliardBall Simulation 17
INRODUCTION TO CONTROLSYSTEM SIMULATION 21
114 Electrical Servomechanism with MotorField Delay and Saturation 21
115 ControlSystem Frequency Response 23
116 Simulation of a Simple Guided Missile 24
STOP AND LOOK 28
117 Simulation in the Real World: A Word of Caution 28
References 29
CHAPTER 2 MODELS WITH DIFFERENCE EQUATIONS, LIMITERS, AND SWITCHES 31
SAMPLEDDATA SYSTEMS AND DIFFERENCE EQUATIONS 31
21 SampledData DifferenceEquation Systems 31
22 Solving Systems of FirstOrder Difference Equations 32
23 Models Combining Differential Equations and SampledData Operations 35
24 Simple Example 35
25 Initializing and Resetting SampledData Variables 35
TWO MIXED CONTINUOUS/SAMPLEDDATA SYSTEMS 37
26 Guided Torpedo with Digital Control 37
27 Simulation of a Plant with a Digital PID Controller 37
DYNAMICSYSTEM MODELS WITH LIMITERS AND SWITCHES 40
28 Limiters, Switches, and Comparators 40
29 Integration of Switch and Limiter Outputs, Event Prediction, and Display Problems 43
210 Using SampledData Assignments 44
211 Using the step Operator and Heuristic IntegrationStep Control 44
212 Example: Simulation of a BangBang Servomechanism 45
213 Limiters, Absolute Values, and Maximum/Minimum Selection 46
214 OutputLimited Integration 47
215 Modeling Signal Quantization 48
EFFICIENT DEVICE MODELS USING RECURSIVE ASSIGNMENTS 48
216 Recursive Switching and Limiter Operations 48
217 Track/Hold Simulation 49
218 MaximumValue and MinimumValue Holding 50
219 Simple Backlash and Hysteresis Models 51
220 Comparator with Hysteresis (Schmitt Trigger) 52
221 Signal Generators and Signal Modulation 53
References 55
CHAPTER 3 FAST VECTOR–MATRIX OPERATIONS AND SUBMODELS 57
ARRAYS, VECTORS, AND MATRICES 57
31 Arrays and Subscripted Variables 57
32 Vector and Matrices in Experiment Protocols 58
33 TimeHistory Arrays 58
VECTORS AND MODEL REPLICATION 59
34 Vector Operations in DYNAMIC Program Segments: The Vectorizing Compiler 59
35 Matrix–Vector Products in Vector Expressions 61
36 IndexShift Operation 63
37 Sorting Vector and SubscriptedVariable Assignments 64
38 Replication of DynamicSystem Models 64
MORE VECTOR OPERATIONS 65
39 Sums, DOT Products, and Vector Norms 65
310 Maximum/Minimum Selection and Masking 66
VECTOR EQUIVALENCE DECLARATIONS SIMPLIFY MODELS 67
311 Subvectors 67
312 Matrix–Vector Equivalence 67
MATRIX OPERATIONS IN DYNAMICSYSTEM MODELS 67
313 Simple Matrix Assignments 67
314 TwoDimensional Model Replication 68
VECTORS IN PHYSICS AND CONTROLSYSTEM PROBLEMS 69
315 Vectors in Physics Problems 69
316 Vector Model of a Nuclear Reactor 69
317 Linear Transformations and Rotation Matrices 70
318 StateEquation Models of Linear Control Systems 72
USERDEFINED FUNCTIONS AND SUBMODELS 72
319 Introduction 72
320 UserDefined Functions 72
321 Submodel Declaration and Invocation 73
322 Dealing with SampledData Assignments, Limiters, and Switches 75
References 75
CHAPTER 4 EFFICIENT PARAMETERINFLUENCE STUDIES AND STATISTICS COMPUTATION 77
MODEL REPLICATION SIMPLIFIES PARAMETERINFLUENCE STUDIES 77
41 Exploring the Effects of Parameter Changes 77
42 Repeated Simulation Runs Versus Model Replication 78
43 Programming ParameterInfluence Studies 80
STATISTICS 84
44 Random Data and Statistics 84
45 Sample Averages and Statistical Relative Frequencies 85
COMPUTING STATISTICS BY VECTOR AVERAGING 85
46 Fast Computation of Sample Averages 85
47 Fast Probability Estimation 86
48 Fast ProbabilityDensity Estimation 86
49 SampleRange Estimation 90
REPLICATED AVERAGES GENERATE SAMPLING DISTRIBUTIONS 91
410 Computing Statistics by Time Averaging 91
411 Sample Replication and SamplingDistribution Statistics 91
RANDOMPROCESS SIMULATION 95
412 Random Processes and Monte Carlo Simulation 95
413 Modeling Random Parameters and Random Initial Values 97
414 SampledData Random Processes 97
415 “Continuous” Random Processes 98
416 Problems with Simulated Noise 100
SIMPLE MONTE CARLO EXPERIMENTS 100
417 Introduction 100
418 Gambling Returns 100
419 Vectorized Monte Carlo Study of a Continuous Random Walk 102
References 106
CHAPTER 5 MONTE CARLO SIMULATION OF REAL DYNAMIC SYSTEMS 109
INTRODUCTION 109
51 Survey 109
REPEATEDRUN MONTE CARLO SIMULATION 109
52 EndofRun Statistics for Repeated Simulation Runs 109
53 Example: Effects of GunElevation Errors on a 1776 Cannnonball Trajectory 110
54 Sequential Monte Carlo Simulation 113
VECTORIZED MONTE CARLO SIMULATION 113
55 Vectorized Monte Carlo Simulation of the 1776 Cannon Shot 113
56 Combined Vectorized and RepeatedRun Monte Carlo Simulation 115
57 Interactive Monte Carlo Simulation: Computing Runtime Histories of Statistics with DYNAMICSegment DOT Operations 115
58 Example: Torpedo Trajectory Dispersion 117
SIMULATION OF NOISY CONTROL SYSTEMS 119
59 Monte Carlo Simulation of a Nonlinear Servomechanism: A NoiseInput Test 119
510 Monte Carlo Study of ControlSystem Errors Caused by Noise 121
ADDITIONAL TOPICS 123
511 Monte Carlo Optimization 123
512 Convenient Heuristic Method for Testing Pseudorandom Noise 123
513 Alternative to Monte Carlo Simulation 123
References 125
CHAPTER 6 VECTOR MODELS OF NEURAL NETWORKS 127
ARTIFICIAL NEURAL NETWORKS 127
61 Introduction 127
62 Artificial Neural Networks 127
63 Static Neural Networks: Training, Validation, and Applications 128
64 Dynamic Neural Networks 129
SIMPLE VECTOR ASSIGNMENTS MODEL NEURON LAYERS 130
65 NeuronLayer Declarations and Neuron Operations 130
66 NeuronLayer Concatenation Simplifies Bias Inputs 130
67 Normalizing and ContrastEnhancing Layers 131
68 Multilayer Networks 132
69 Exercising a NeuralNetwork Model 132
SUPERVISED TRAINING FOR REGRESSION 134
610 MeanSquare Regression 134
611 Backpropagation Networks 137
MORE NEURALNETWORK MODELS 140
612 FunctionalLink Networks 140
613 RadialBasisFunction Networks 142
614 NeuralNetwork Submodels 145
PATTERN CLASSIFICATION 146
615 Introduction 146
616 Classifier Input from Files 147
617 Classifier Networks 147
618 Examples 149
PATTERN SIMPLIFICATION 155
619 Pattern Centering 155
620 Feature Reduction 156
NETWORKTRAINING PROBLEMS 157
621 LearningRate Adjustment 157
622 Overfitting and Generalization 157
623 Beyond Simple Gradient Descent 159
UNSUPERVISED COMPETITIVELAYER CLASSIFIERS 159
624 TemplatePattern Matching and the CLEARN Operation 159
625 Learning with Conscience 163
626 CompetitiveLearning Experiments 164
627 Simplified AdaptiveResonance Emulation 165
SUPERVISED COMPETITIVE LEARNING 167
628 The LVQ Algorithm for TwoWay Classification 167
629 Counterpropagation Networks 167
EXAMPLES OF CLEARN CLASSIFIERS 168
630 Recognition of Known Patterns 168
631 Learning Unknown Patterns 173
References 174
CHAPTER 7 DYNAMIC NEURAL NETWORKS 177
INTRODUCTION 177
71 Dynamic Versus Static Neural Networks 177
72 Applications of Dynamic Neural Networks 177
73 Simulations Combining Neural Networks and DifferentialEquation Models 178
NEURAL NETWORKS WITH DELAYLINE INPUT 178
74 Introduction 178
75 The DelayLine Model 180
76 DelayLineInput Networks 180
77 Using Gamma Delay Lines 182
STATIC NEURAL NETWORKS USED AS DYNAMIC NETWORKS 183
78 Introduction 183
79 Simple Backpropagation Networks 184
RECURRENT NEURAL NETWORKS 185
710 LayerFeedback Networks 185
711 Simplified RecurrentNetwork Models Combine Context and Input Layers 185
712 Neural Networks with Feedback Delay Lines 187
713 Teacher Forcing 189
PREDICTOR NETWORKS 189
714 OffLine Predictor Training 189
715 Online Trainng for True Online Prediction 192
716 Chaotic Time Series for Prediction Experiments 192
717 Gallery of Predictor Networks 193
OTHER APPLICATIONS OF DYNAMIC NETWORKS 199
718 TemporalPattern Recognition: Regression and Classification 199
719 Model Matching 201
MISCELLANEOUS TOPICS 204
720 BiologicalNetwork Software 204
References 204
CHAPTER 8 MORE APPLICATIONS OF VECTOR MODELS 207
VECTORIZED SIMULATION WITH LOGARITHMIC PLOTS 207
81 The EUROSIM No. 1 Benchmark Problem 207
82 Vectorized Simulation with Logarithmic Plots 207
MODELING FUZZYLOGIC FUNCTION GENERATORS 209
83 Rule Tables Specify Heuristic Functions 209
84 FuzzySet Logic 210
85 FuzzySet Rule Tables and Function Generators 214
86 Simplified Function Generation with Fuzzy Basis Functions 214
87 Vector Models of FuzzySet Partitions 215
88 Vector Models for Multidimensional FuzzySet Partitions 216
89 Example: FuzzyLogic Control of a Servomechanism 217
PARTIAL DIFFERENTIAL EQUATIONS 221
810 Method of Lines 221
811 Vectorized Method of Lines 221
812 HeatConduction Equation in Cylindrical Coordinates 225
813 Generalizations 225
814 Simple HeatExchanger Model 227
FOURIER ANALYSIS AND LINEARSYSTEM DYNAMICS 229
815 Introduction 229
816 FunctionTable Lookup and Interpolation 230
817 FastFourierTransform Operations 230
818 Impulse and Freqency Response of a Linear Servomechanism 231
819 Compact Vector Models of Linear Dynamic Systems 232
REPLICATION OF AGROECOLOGICAL MODELS ON MAP GRIDS 237
820 Geographical Information System 237
821 Modeling the Evolution of Landscape Features 239
822 Matrix Operations on a Map Grid 239
References 242
APPENDIX: ADDITIONAL REFERENCE MATERIAL 245
A1 Example of a RadialBasisFunction Network 245
A2 FuzzyBasisFunction Network 245
References 248
USING THE BOOK CD 251
INDEX 253
Author Information
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.