Advanced Dynamic–system Simulation – ion Techniques and Monte Carlo Simulation

GRANINO A. KORN, PhD, is a Principal of G.A. and T.M. Korn Industrial Consultants, specializing in software and design systems for interactive simulation of dynamic systems and neural networks. Dr. Korn, a Fellow of the IEEE, has received numerous awards for his innovative research, including the Alexander von Humboldt Prize and the Society for Computer Simulation s Technical Award for Excellence.

Foreword. 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. HOW A SIMULATION RUN WORKS. 1 6. Sampling 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. 1 11. Space vehicle Orbits. Variable step Integration. 1 12. Multi run Study. 1 13. Flight Simulation. 1 14. Modeling Population Dynamics, Chemical Reaction Rates Simulation in Ecology. CONTROL SYSTEM EXAMPLES. 1 15. An Electrical Servomechanism with Motor field delay and Saturation. 1 16. Control system Frequency Response, Parameter influence Studies, and Parameter. Optimization. 1 17. Simulation of a Simple Guided Missile. (a) A Guided Torpedo. (b) The Complete Simulation Program. WHAT DO WE DO WITH ALL THIS?. 1 18. 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. APPLICATIONS OF LIMITERS AND SWITCHES. 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 Switcing 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. (c) Example: $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$. 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 9. Repeated run Monte Carlo Simulation. (a) Taking Statistics on Repeated Simulation Runs. (b) Sequential Monte Carlo Studies. 4 10 Example: Effects of Gun elevation Errors on the1776 Cannon. 4 11. 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 12. Statistical Relative Frequencies, Sample Ranges, and other Statistics. 4 13. 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 14. 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. 5 10. A Convenient Heuristic Method for Testing Pseudrandom Noise. 5 11. An Alternative to Monte Carlo Simulation. (a) Introduction. (b) Dynamic Systems with Random Perturbations. (c) Mean Square Errors in Linear Systems. References. Chapter 6. Other Applications of Vector Models. SIMPLE NEURAL NETWORK MODELS. 6 1. Introduction. 6 2. Neural network Layers. A VECTORIZED STUDY WITH LOGARITHMIC PLOTS. 6 1. $$$$. 6 3. Pulsed neuron Replication. Network Layers and Activation Functions. Biological Neurons and Pulsed neuron Networks. A Radial basis function Layer. Neurons with Vector shift Memory. Examples of Applications. Special Operations: Competitive Learning and Principal Components. MODELING FUZZY LOGIC FUNCTION GENERATORS. Heuristic Function Generation: Rule table Step Functions. Fuzzy Logic fits Continuous Functions to Rule Tables. Vector shift Generation of Fuzzy set Functions. Example: (a) Fuzzy logic Control System. (b) Servomechanism with Rule table Controller. PARTIAL DIFFERENTIAL EQUATIONS. Introduction. The Vectorized Method of Lines. Heat Conduction Problems. Simple Heat Exchangers. Transmission line Simulation. REPLICATION OF AGRO ECOLOGICAL MODELS ON MAP GRIDS. The SAMT/DESIRE System. A Simple Application. References. Chapter 7. Tricks and Treats: Special Functions and Operators. CONDITIONAL RUN TERMINATION AND if STATEMENTS. 7 1. The Run termination Operator. 7 2. if Statements in DYNAMIC Program Segments. TIME HISTORY FUNCTION STORAGE AND TIME DELAY SIMULATION. 7 3. store and get Operations. 7 4 A Crossplotting Application with two DYNAMIC Program Segments: The Pilot ejection Problem. 7 5 Time delay Simulation. 7 6. Time history Storage and Recovery Using Binary Files. COMPILED PROGRAMS NEED NOT BE SIMULATION MODELS. Fast Graph Plotting. (a) A Simple Function Plot. (b) Plotting Array Values. Fast Array Manipulation. Interpreted Difference Equations. COMPLEX NUMBER OPERATIONS AND INTERPRETER GRAPHICS. 6 Complex Quantities in the Interpreter Program. Interpreter Graphics, Complex number Plots, and Conformal Mapping. FAST FOURIER TRANSFORMS AND FREQUENCY RESPONSE PLOTS. Fast Fourier Transforms. Application: Control system Frequency response Plots. Simultaneous Transformation of Two Real Arrays. Cyclical Convolutions. References.