Advanced Dynamic-system Simulation: Model-replication Techniques and Monte Carlo Simulation

Advanced Dynamic-system Simulation......Page 4
Contents......Page 8
Preface......Page 16
1-1. Computer Modeling and Simulation......Page 20
1-2. Differential-equation Models......Page 21
1-3. Interactive Modeling—Experiment Protocol and Simulation Studies......Page 22
1-5. OPEN DESIRE and DESIRE......Page 23
1-6. Sampling the DYNAMIC Segment Variables......Page 24
(b) Improved Integration Rules......Page 29
1-8. Sampling Times and Integration Steps......Page 30
(a) A Linear Harmonic Oscillator......Page 31
1-11. Space Vehicle Orbits—Variable-step Integration......Page 34
1-12. A Population-dynamics Model......Page 37
1-13. Splicing Multiple Simulation Runs: Billiard-ball Simulation......Page 39
1-14. An Electrical Servomechanism with Motor Field Delay and Saturation......Page 41
1-15. Control-system Frequency Response......Page 43
(a) A Guided Torpedo......Page 44
(b) The Complete Simulation Program......Page 47
1-17. Simulation Studies in the Real World: A Word of Caution......Page 48
REFERENCES......Page 49
2-1. Sampled-data Difference Equation Systems......Page 51
2-2. “Incremental” Form of Simple Difference Equations......Page 53
2-3. Combining Differential Equations and Sampled-data Operations......Page 54
2-4. A Simple Example......Page 55
2-6. The Guided Torpedo with Digital Control......Page 57
2-7. Simulation of a Plant with a Digital PID Controller......Page 59
(b) Switching Functions and Comparators......Page 61
2-9. Numerical Integration of Switch and Limiter Outputs, Event Prediction, and Display Problems......Page 64
2-11. Using the step Operator and Heuristic Integration-step Control......Page 65
2-12. Example: Simulation of a Bang-bang Servomechanism......Page 66
2-13. Limiters, Absolute Value, and Maximum/Minimum Selection......Page 68
2-15. Modeling Signal Quantization......Page 69
(a) Introduction......Page 70
(b) Track-hold Simulation......Page 71
(d) Simple Backlash and Hysteresis Models......Page 72
(e) The Comparator with Hysteresis (Schmitt Trigger)......Page 73
2-17. Signal Generators and Signal Modulation......Page 75
REFERENCES......Page 77
3-1. Arrays, Subscripted Variables, and State-variable Declarations......Page 78
(a) Vector Assignments and Vector Expressions......Page 79
(b) Vector Differential Equations......Page 80
(c) Vectorization and Model Replication—Significant Applications......Page 81
(a) Definition......Page 82
3-4. Vector Sampled-data Assignments and Vector Difference Equations......Page 83
3-6. Index-shifted Vectors......Page 85
(b) Euclidean, Taxicab, and Hamming Norms......Page 86
(a) Maximum/Minimum Selection......Page 87
3-9. Matrix Operations in Experiment-protocol Scripts......Page 88
3-10. Matrix Assignments and Difference Equations in DYNAMIC Program Segments......Page 89
3-12. Vectors in Physics Problems......Page 90
3-14. Linear Transformations and Rotation Matrices......Page 91
3-15. State-equation Models for Linear Control Systems......Page 93
3-16. User-defined Functions......Page 94
(a) Submodel Declaration and Invocation......Page 95
3-18. Dealing with Sampled-data Assignments, Limiters, and Switches......Page 97
REFERENCES......Page 98
4-1. Exploring the Effects of Parameter Changes......Page 99
(a) A Simple Repeated-run Study......Page 100
(b) Model Replication......Page 101
(c) Dealing with Multiple Parameters......Page 103
(b) Measures of System Effectiveness......Page 104
(c) Crossplotting Results......Page 105
(e) Iterative Parameter Optimization......Page 106
4-4. Random Processes and Monte Carlo Simulation......Page 107
(a) Taking Statistics on Repeated Simulation Runs......Page 108
(c) Example: Effects of Gun-elevation Errors on the 1776 Cannon......Page 110
(a) Vectorized Monte Carlo Study of the 1776 Cannon Shot......Page 112
4-8. Statistical Relative Frequencies, Sample Ranges, and Other Statistics......Page 115
(a) A Simple Probability-density Estimate......Page 116
(b) Triangle and Parzen Windows......Page 117
(c) Computation and Display of Parzen Window Estimates......Page 118
4-10. Combining Vectorized and Repeated-run Monte Carlo Simulation......Page 119
REFERENCES......Page 122
(a) A Platform for Sampled-data Experiments......Page 124
(c) Recursive Sampled-data Addition and Time Averaging......Page 125
(a) Deriving “Continuous” Noise from Periodic Pseudorandom Samples......Page 126
5-5. Gambling Returns......Page 128
5-6. A Continuous Random Walk......Page 131
5-7. The 1776 Cannonball with Air Turbulence......Page 132
5-8. Monte Carlo Simulation of a Nonlinear Servomechanism: A Noise-input Test......Page 135
5-10. Monte Carlo Optimization......Page 138
(a) Introduction......Page 140
(c) Mean Square Errors in Linearized Systems......Page 141
REFERENCES......Page 142
6-1. Neural-network Models and Pattern Vectors......Page 144
6-2. Simple Vector Operations Model Neural-network Layers......Page 145
6-3. Normalizing and Contrast-enhancing Neuron Layers......Page 146
6-4. Multilayer Networks......Page 147
(b) Using Pattern-row Matrices......Page 148
REGRESSION AND PATTERN CLASSIFICATION......Page 149
6-7. Pattern Classification......Page 150
6-9. The LMS Algorithm......Page 151
(a) Problem Statement and Experiment-protocol Script......Page 152
(b) Network Model and Training......Page 153
(c) Test Runs and A Posteriori Probabilities......Page 156
(a) The Backpropagation Algorithm......Page 157
(b) Discussion......Page 159
(a) Basis-function Expansion and Linear Optimization......Page 160
(b) Radial Basis Functions......Page 163
6-14. Template-pattern Matching......Page 165
(a) Simple Competitive Learning......Page 166
(b) Learning with Conscience......Page 167
(a) Pattern Classification......Page 168
(b) Vector Quantization......Page 169
6-17. Simplified Adaptive-resonance Emulation......Page 170
6-18. Biologically Plausible Competition: Correlation Matching......Page 172
6-19. Supervised Competitive Classifiers: The LVQ Algorithm......Page 173
6-21. Neural Networks and Memory......Page 174
(a) Vector Model of a Tapped Delay Line......Page 176
(b) Simple Linear Filters......Page 177
(d) A Nonlinear Predictor Trained with Backpropagation......Page 178
6-23. The Gamma Delay Line Layer......Page 181
6-24. Pulsed-neuron Models......Page 182
6-25. A Simple Integrate and Fire Model......Page 183
6-26. Neuron-model Replication......Page 185
REFERENCES......Page 187
7-2. Vectorized Simulation with Logarithmic Plots......Page 190
7-3. Rule Tables Specify Heuristic Functions......Page 191
(a) Fuzzy Sets and Membership Functions......Page 193
(d) Normalized Fuzzy-set Partitions......Page 194
7-5. Fuzzy-set Rule Tables and Function Generators......Page 197
(a) Gaussian Bumps—Effects of Normalization......Page 198
(b) Triangle Functions......Page 199
7-8. Vector Models for Multidimensional Fuzzy-set Partitions......Page 200
(a) Problem Statement......Page 201
(b) Experiment Protocol and Rule Table......Page 202
(c) DYNAMIC Program Segment and Results......Page 203
7-10. The Method of Lines......Page 205
(b) Using Differentiation Operators......Page 207
(c) Numerical Problems......Page 210
7-13. Generalizations......Page 211
7-14. A Simple Heat-exchanger Model......Page 213
7-16. Modeling the Evolution of Landscape Features......Page 216
REFERENCES......Page 218
A-1. Example of a Radial-basis-function Network......Page 220
A-2. A Fuzzy-basis-function Network......Page 222
A-3. The CLEARN Algorithm......Page 224
REFERENCES......Page 225
STREAMLINED OPERATION OF DESIRE PROJECTS UNDER LINUX......Page 229
Index......Page 232