Learn the latest techniques in programming sophisticated simulation systemsThis cutting-edge text presents the latest techniques in advanced simulation programming for interactive modeling and simulation of dynamic systems, such as aerospace vehicles, control systems, and biological systems. The author, a leading authority in the field, demonstrates computer software that can handle large simulation studies on standard personal computers. Readers can run, edit, and modify the sample simulations from the text with the accompanying CD-ROM, featuring the OPEN DESIRE program for Linux and Windows. The program included on CD solves up to 40,000 ordinary differential equations and implements exceptionally fast and convenient vector operations.The text begins with an introduction to dynamic-system simulation, including a demonstration of a simple guided-missile simulation. Among the other highlights of coverage are:Models that involve sampled-data operations and sampled-data difference equations, including improved techniques for proper numerical integration of switched variablesNovel vector compiler that produces exceptionally fast programs for vector and matrix assignments, differential equations, and difference equationsApplication of vector compiler to parameter-influence studies and Monte Carlo simulation of dynamic systemsVectorized Monte Carlo simulations involving time-varying noise, derived from periodic pseudorandom-noise samplesVector models of neural networks, including a new pulsed-neuron modelVectorized programs for fuzzy-set controller, partial differential equations, and agro-ecological models replicated at many points of a landscape mapThis text is intended for graduate-level students, engineers, and computer scientists, particularly those involved in aerospace, control system design, chemical process control, and biological systems. All readers will gain the practical skills they need to design sophisticated simulations of dynamic systems.Note: CD-ROM/DVD and other supplementary materials are not included as part of eBook file.
Author(s): Granino A. Korn
Year: 2007
Language: English
Pages: 221
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
