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ADVANCED DYNAMIC SYSTEM SIMULATION
Model Replication and Monte Carlo Simulation
Table of Contents
Foreword
Table of Contents
Chapter 1. Introduction to Dynamic-system Simulation
DYNAMIC-SYSTEM MODELS AND COMPUTER PROGRAMS
- 1-1. Computer Modeling and Simulation
1-2. Differential-equation Models
1-3. Interactive Modeling. Experiment Protocol and Multi-run Studies
1-4 Simulation Software
1-5. OPEN DESIRE and DESIRE
HOW A SIMULATION RUN WORKS
1-6. Sampling the DYNAMIC-segment Variables
1-7. Integration Routines
- (a) Euler Integration
(b) Improved Integration Rules
1-8. Sampling Times and Integration Steps
1-9. Sorting Defined-variable Assignments
EXAMPLES OF SIMPLE APPLICATIONS
1-10. Oscillators and Computer Displays
(a) A Linear Harmonic Oscillator
(b) A Nonlinear Oscillator and Duffing's Differential Equation
1-11. Space-vehicle Orbits. Variable-step Integration
1-12. A Population-dynamics Model
1-13. Splicing Multiple Simulation Runs: Billiard-ball Simulation
CONTROL-SYSTEM EXAMPLES
1-14. An Electrical Servomechanism with Motor-field delay and Saturation
1-15. Control-system Frequency Response
1-16. Simulation of a Simple Guided Missile
(a) A Guided Torpedo
(b) The Complete Simulation Program
WHAT DO WE DO WITH ALL THIS?
1-17. Simulation Studies in the Real World: a Word of Caution
REFERENCES
Chapter 2. Models with Difference Equations, Limiters, and Switches
SAMPLED-DATA ASSIGNMENTS AND DIFFERENCE EQUATIONS
2-1. Sampled-data Difference-equation Systems
2-2. "Incremental" Form of Simple Difference Equations
2-3. Combining Differential Equations and Sampled-data Operations
2-4. A Simple Example
2-5. Initializing and Resetting Sampled-data Variables
EXAMPLES OF MIXED CONTINUOUS/SAMPLED-DATA SYSTEMS
2-6. The Guided Torpedo with Digital Control
2-7. Simulation of a Plant with a Digital PID Controller
MODELING LIMITERS AND SWITCHES
2-8. Limiters, Switches, and Comparators
(a) Limiter Functions
(b) Switches and Comparators
2-9. Numerical Integration of Switch and Limiter Outputs, Event Prediction, and Display Problems
2-10. Using Sampled-data Assignments
2-11. Using the step Operator and Heuristic Integration-step Control
2-12. Example: Simulation of a Bang-bang Servomechanism
LIMITERS, SWITCHES, AND DIFFERENCE EQUATIONS
2-13. Limiters, Absolute Values, and Maximum/Minimum Selection
2-14. Output-limited Integration
2-15. Modeling Signal Quantization
2-16. Continuous-variable Difference Equations with Switching and Limiter Operations
(a) Introduction
(b) Track-hold Simulation
(c) Maximum-value and Minimum-value Holding
(d) Simple Backlash and Hysteresis Models
(e) The Comparator with Hysteresis (Schmitt Trigger)
2-17. Signal Generators and Signal Modulation
REFERENCES
Chapter 3. Programs with Vector/Matrix Operations
and Submodels
VECTOR ASSIGNMENTS AND VECTOR DIFFERENTIAL EQUATIONS
3-1. Arrays, Subscripted Variables, and State-variable Declarations
3-2. Vector Operations in DYNAMIC Program Segments. The Vectorizing Compiler
(a) Vector Assignments and Vector Expressions
(b) Vector Differential Equations
(c) Vectorization and Model Replication: Significant Applications
3-3. Matrix-vector Products in Vector Expressions
(a) Definition
(b) A Simple Example: Resonating Oscillators
3-4. Vector Sampled-data Assignments and Vector Difference Equations
3-5. Sorting Vector and Subscripted-variable Assignments
MORE VECTOR OPERATIONS
3-6. Index-shifted Vectors
3-7. Sums, DOT Products, and Vector Norms
(a) Sums and DOT Products
(b) Euclidean, Taxicab, and Hamming Norms
3-8. Maximum/Minimum Selection and Masking
(a) Maximum/Minimum Selection
(b) Masking Vector Expressions
MATRIX OPERATIONS
3-9. Matrix Operations in Experiment-protocol Scripts
3-10. Matrix Assignments and Difference Equations in DYNAMIC Program Segments
3-11. Vector and Matrix Operations using Equivalent Vectors
VECTOR MODELS IN PHYSICS AND CONTROL ENGINEERING
3-12. Vectors in Physics Problems
3-13. Simulation of a Nuclear Reactor
3-14. Linear Transformations and Rotation Matrices
3-15. State-equation Models for Linear Control Systems
USER-DEFINED FUNCTIONS AND SUBMODELS
3-16. User-defined function.
3-17. Submodels
(a) SUBMODEL Declaration and Invocation
(b) Submodels With Differential Equations
3-18. Dealing with Sampled-data Assignments, Limiters, and Switches
REFERENCES
Chapter 4. Parameter-influence Studies, Model Replication, and Monte Carlo Simulation
PARAMETER-INFLUENCE STUDIES AND VECTORIZATION
4-1. Exploring the Effects of Parameter Changes
4-2. Repeated Runs and Model Replication (Vectorization)
(a) A Simple Repeated-run Study
(b) Model Replication
(c) Dealing with Multiple Parameters
4-3. Programming Parameter-influence Studies.
(a) Introduction
(b) Measures of System Effectiveness
(c) Crossplotting Results
(d) Maximum/Minimum Selection
(e) Iterative Parameter Optimization
RANDOM PROCESSES AND RANDOM PARAMETERS
4-4. Random Processes and Monte Carlo Simulation
4-5. Generating Random Parameters and Random Initial Values
MONTE CARLO SIMULATION OF DYNAMIC SYSTEMS
4-6. Repeated-run Monte Carlo Simulation
(a) Taking Statistics on Repeated Simulation Runs
(b) Sequential Monte Carlo Studies
(c) Example: Effects of Gun-elevation Errors on the1776 Cannon
4-7. Vectorized (Model-replicating) Monte Carlo Simulation
(a) Vectorized Monte Carlo Study of the 1776 Cannon Shot
(b) Interactive Monte Carlo Simulation: Computing Time Histories
of Statistics with Compiled DOT Operations
4-8. Statistical Relative Frequencies, Sample Ranges, and other Statistics
4-9. Post-run Probability-density Estimation
(a) A Simple Probability-density Estimate
(b) Triangle and Parzen Windows
(c) Computation and Display of Parzen-window Estimates
4-10. Combining Vectorized and Repeated-run Monte Carlo Simulation
REFERENCES
Chapter 5. Random-process Simulation and
Monte Carlo Studies with Noisy Signals
COMPUTER MODELS OF NOISE PROCESSES
5-1. Noise in DYNAMIC Program Segments
5-2. Sampled-data Random Processes
(a) A Platform for Sampled-data Experiments
(b) A Sampled-data Random-process Model: Coin Tossing
(c) Recursive Sampled-data Addition and Time-averaging
5-3. Modeling Continuous Noise
(a) Deriving "Continuous" Noise from Periodic Pseudorandom Samples
(b) "Continuous" Time Averages
5-4. Problems with Simulated Noise
MONTE CARLO SIMULATION WITH NOISY SIGNALS
5-5. Gambling Returns
5-6. A Continuous Random Walk
5-7. The 1776 Cannonball with Air Turbulence
SIMULATION OF NOISY CONTROL SYSTEMS
5-8. Monte Carlo Simulation of a Nonlinear Servomechanism: a Noise-input Test
5-9. Monte Carlo Study of Control-system Errors Caused by Noise
ADDITIONAL TOPICS
5-10. Monte Carlo Optimization
5-11. A Convenient Heuristic Method for Testing Pseudrandom Noise
5-12. An Alternative to Monte Carlo Simulation
(a) Introduction
(b) Dynamic Systems with Random Perturbations
(c) Mean Square Errors in Linear Systems
REFERENCES
Chapter 6. Vector Models of Neural Networks
NEURAL-NETWORK SIMULATION
6-1. Neural-network Models and Pattern Vectors
6-2. Simple Vector Operations Model Neural-network Layers
6-3. Normalizing and Contrast-enhancing Neuron Layers
6-4. Multilayer Networks
6-5. Exercising the Neural-network Model
(a) Computing Successive Neuron-layer Outputs
(b) Using Pattern Matrices
(c) Pattern Input from Files
REGRESSION AND PATTERN CLASSIFICATION
6-6. Mean-square Regression
6-7. Pattern Classification
NEURAL-NETWORK-TRAINING: PATTERN CLASSIFICATION
6-8. Linear Pattern Classifiers
6-9. The LMS Algorithm
6-10. A Softmax Image Classifier
(a) Problem Statement and Experiment-protocol Script
(b) Network Model and Training
(c) Test Runs and a Posteriori Probabilities
6-11. Associative Memory
NONLINEAR MULTILAYER NETWORKS
6-12. Backpropagation Networks
(a) The Backpropagation Algorithm
(b) Discussion
(c) Examples and Neural-network Submodels
6-13. Radial-basis-function Networks
(a) Basis-function Expansion and Linear Optimization
(b) Radial Basis Functions
.
COMPETITIVE-LAYER PATTERN CLASSIFICATION
6-14. Template-pattern Matching
6-15. Unsupervised Pattern Classifiers
(a) Simple Competitive Learning
(b) Competition with Conscience
6-16. Unsupervised Competitive-learning Experiments
(a) Pattern Classification
(b) Vector Quantization
6-17. Simplified Adaptive-resonance Emulation
6-18. Biologically Plausible Competition: Correlation Matching
SUPERVISED COMPETITVE LEARNING
6-19. Supervised Competitive Classifers: the LVQ Algorithm
6-20. Counterpropagation Networks
NEURAL NETWORKS WITH MEMORY
6-21. Neural Networks and Memory
6-22. Networks with a Delay-line Input Layer
(a) Vector Model of a Tapped Delay Line
(b) Simple Linear Filters
(c) Linear Matched Filters, Signal Classifiers, and Model Matching
(d) A Nonlinear Predictor Trained with Backpropagation6-23.
6-23. The Gamma Delay-line Layer
PULSED-NEURON REPLICATION
6-24. Pulsed-neuron Models
6-25. A Simple Integrate-and-fire Model
6-26. Neuron-model Replication
REFERENCES
Chapter 7. More Applications of Vector Models
A VECTORIZED STUDY WITH LOGARITHMIC PLOTS
7-1. The EUROSIM No. 1 Benchmark Problem
7-2. Vectorized Simulation with Logarithmic Plots
MODELING FUZZY-LOGIC FUNCTION GENERATORS
7-3. Rule Tables specify Heuristic Functions
7-4. Fuzzy-set Logic
(a) Fuzzy Sets and Membership Functions
(b) Fuzzy Intersections and Unions
(c) Joint Membership Functions
(d) Normalized Fuzzy-set Partitions
7-5. Fuzzy-set Rule Tables and Function Generators
7-6. Simplified Function Generation with Fuzzy Basis Functions
7-7. Vector Models of Fuzzy-set Partitions
(a) Gaussian Bumps. Effects of Normalization
(b) Triangle Functions
(c) Smooth Fuzzy-basis Functions.
7-8. Vector Models for Multidimensional Fuzzy-set Partitions
7-9. Example: Fuzzy-logic Control a Servomechanism
(a) Problem Statement
(b) Experiment Protocol and Rule Table
(c) DYNAMIC Program Segment and Results
PARTIAL DIFFERENTIAL EQUATIONS
7-10. The Method of Lines
7-11. The Vectorized Method of Lines
(a) Introduction
(b) Using Differentiation Operators
(c) Numerical Problems
7-12. The Heat-conduction Equation in Cylindrical Coordinates
7-13. Generalizations
7-14. A Simple Heat-exchanger Model
REPLICATION OF AGRO-ECOLOGICAL MODELS ON MAP GRIDS
7-15. A Geographical Information System
7-16. Modeling the Evolution of Landscape Features
REFERENCES
APPENDIX. Additional Reference Material
A-1. Examples of Radial-basis-function and Fuzzy-basis-function Networks
A-2. A Fuzzy-basis-function Network
A-3. The CLEARN Algorithm with crit > 0
Reference Tables
REFERENCES
The Book CD …
… contains complete binary OPEN DESIRE modeling/simulation program packages for personal-computer Linux, many examples, source code, and a comprehensive, indexed Reference Manual. Obtain the Windows version by emailing the author (gatmkorn@aol.com).