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Stochastic Dynamics and Control

E-BookPDFDRM AdobeE-Book
426 Seiten
Englisch
Elsevier Science & Techn.erschienen am10.08.2006
This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress processes are also presented. Classical feedback control, active damping, covariance control, optimal control, sliding control of stochastic systems, feedback control of stochastic time-delayed systems, and probability density tracking control are studied. Many control results are new in the literature and included in this book for the first time. The book serves as a reference to the engineers who design and maintain structures subject to harsh random excitations including earthquakes, sea waves, wind gusts, and aerodynamic forces, and would like to reduce the damages of structural systems due to random excitations.

? Comprehensive review of probability theory, and stochastic processes
? Random vibrations
? Structural reliability and fatigue, Non-Gaussian fatigue
? Monte Carlo methods
? Stochastic calculus and engineering applications
? Stochastic feedback controls and optimal controls
? Stochastic sliding mode controls
? Feedback control of stochastic time-delayed systems
? Probability density tracking controlmehr
Verfügbare Formate
BuchGebunden
EUR180,00
E-BookPDFDRM AdobeE-Book
EUR170,00

Produkt

KlappentextThis book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress processes are also presented. Classical feedback control, active damping, covariance control, optimal control, sliding control of stochastic systems, feedback control of stochastic time-delayed systems, and probability density tracking control are studied. Many control results are new in the literature and included in this book for the first time. The book serves as a reference to the engineers who design and maintain structures subject to harsh random excitations including earthquakes, sea waves, wind gusts, and aerodynamic forces, and would like to reduce the damages of structural systems due to random excitations.

? Comprehensive review of probability theory, and stochastic processes
? Random vibrations
? Structural reliability and fatigue, Non-Gaussian fatigue
? Monte Carlo methods
? Stochastic calculus and engineering applications
? Stochastic feedback controls and optimal controls
? Stochastic sliding mode controls
? Feedback control of stochastic time-delayed systems
? Probability density tracking control
Details
Weitere ISBN/GTIN9780080463988
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format HinweisDRM Adobe
Erscheinungsjahr2006
Erscheinungsdatum10.08.2006
Seiten426 Seiten
SpracheEnglisch
Dateigrösse3171 Kbytes
Artikel-Nr.2745113
Rubriken
Genre9200

Inhalt/Kritik

Inhaltsverzeichnis
1;Front cover;1
2;Table of contents;6
3;Preface;16
4;Chapter 1. Introduction;18
4.1;1.1. Stochastic dynamics;18
4.2;1.2. Stochastic control;19
5;Chapter 2. Probability Theory;26
5.1;2.1. Probability of random events;26
5.2;2.2. Random variables;27
5.3;2.3. Probability distributions;28
5.4;2.4. Expectations of random variables;28
5.5;2.5. Common probability distributions;30
5.6;2.6. Two-dimensional random variables;35
5.7;2.7. n-Dimensional random variables;37
5.8;2.8. Functions of random variables;39
5.9;2.9 Conditional probability;46
5.10;Exercises;47
6;Chapter 3. Stochastic Processes;50
6.1;3.1. Definitions;50
6.2;3.2. Expectations;51
6.3;3.3. Vector process;52
6.4;3.4 Gaussian process;53
6.5;3.5. Harmonic process;54
6.6;3.6. Stationary process;55
6.7;3.7. Ergodic process;57
6.8;3.8. Poisson process;62
6.9;3.9. Markov process;65
6.10;Exercises;66
7;Chapter 4. Spectral Analysis of Stochastic Processes;68
7.1;4.1 Power spectral density function;68
7.2;4.2. Spectral moments and bandwidth;71
7.3;4.3. Process with rational spectral density function;76
7.4;4.4. Finite time spectral analysis;78
7.5;Exercises;79
8;Chapter 5. Stochastic Calculus;82
8.1;5.1. Modes of convergence;82
8.2;5.2. Stochastic differentiation;84
8.3;5.3. Stochastic integration;91
8.4;5.4. Ito calculus;98
8.5;Exercises;107
9;Chapter 6. Fokker-Planck-Kolmogorov Equation;110
9.1;6.1. Chapman-Kolmogorov-Smoluchowski equation;110
9.2;6.2. Derivation of the FPK equation;111
9.3;6.3. Solutions of FPK equations for linear systems;116
9.4;6.4. Short-time solution;118
9.5;6.5. Path integral solution;119
9.6;6.6. Exact stationary solutions;121
9.7;Exercises;135
10;Chapter 7. Kolmogorov Backward Equation;138
10.1;7.1. Derivation of the backward equation;138
10.2;7.2. Reliability formulation;141
10.3;7.3. First-passage time probability;142
10.4;7.4. Pontryagin-Vitt equations;143
10.5;Exercises;144
11;Capter 8. Random Vibration of SDOF Systems;146
11.1;8.1. Solutions in the mean square sense;146
11.2;8.2. Solutions with Ito calculus;152
11.3;Exercises;156
12;Chapter 9. Random Vibration of MDOF Discrete Systems;160
12.1;9.1. Lagrange's equation;160
12.2;9.2. Modal solutions of MDOF systems;163
12.3;9.3. Response statistics;168
12.4;9.4. State space representation and Ito calculus;171
12.5;9.5. Filtered white noise excitation;176
12.6;Exercises;178
13;Chapter 10. Random Vibration of Continuous Structures;180
13.1;10.1. Distributed random excitations;180
13.2;10.2. One-dimensional structures;181
13.3;10.3. Two-dimensional structures;196
13.4;Exercises;203
14;Chapter 11. Structural Reliability;204
14.1;11.1. Modes of failure;204
14.2;11.2. Level crossing;204
14.3;11.3. Vector process;217
14.4;11.4. First-passage reliability based on level crossing;219
14.5;11.5. First-passage time probability - general approach;221
14.6;11.6. Structural fatigue;226
14.7;11.7. Dirlik's formula for fatigue prediction;231
14.8;11.8. Extended Dirlik's formula for non-Gaussian stress;232
14.9;Exercises;241
15;Chapter 12. Monte Carlo Simulation;244
15.1;12.1. Random numbers;244
15.2;12.2. Random processes;246
15.3;12.3. Stochastic differential equations;252
15.4;12.4. Simulation of non-Gaussian processes;256
15.5;Exercises;259
16;Chapter 13. Elements of Feedback Controls;260
16.1;13.1. Transfer function of linear dynamical systems;260
16.2;13.2. Concepts of stability;262
16.3;13.3. Effects of poles and zeros;265
16.4;13.4. Time domain specifications;266
16.5;13.5. PID controls;267
16.6;13.6. Routh's stability criterion;269
16.7;13.7. Root locus design;271
16.8;Exercises;272
17;Chapter 14. Feedback Control of Stochastic Systems;274
17.1;14.1. Response moment control of SDOF systems;274
17.2;14.2. Covariance control;277
17.3;14.3. Generalized covariance control;278
17.4;14.4. Covariance control with maximum entropy principle;287
17.5;Exercises;294
18;Chapter 15. Concepts of Optimal Controls;296
18.1;15.1. Optimal control of deterministic systems;297
18.2;15.2. Optimal control of stochastic systems;306
18.3;15.3. Linear Quadratic Gaussian (LQG) control;310
18.4;15.4. Sufficient conditions;316
18.5;Exercises;316
19;Chapter 16. Stochastic Optimal Control with the GCM Method;318
19.1;16.1. Bellman's principle of optimality;318
19.2;16.2. The cell mapping solution approach;319
19.3;16.3. Control of one-dimensional nonlinear system;323
19.4;16.4. Control of a linear oscillator;329
19.5;16.5. Control of a Van der Pol oscillator;333
19.6;16.6. Control of a dry friction damped oscillator;336
19.7;16.7. Systems with non-polynomial nonlinearities;341
19.8;16.8. Control of an impact nonlinear oscillator;347
19.9;16.9. A note on the GCM method;351
19.10;Exercises;353
20;Chapter 17. Sliding Mode Control;354
20.1;17.1. Variable structure control;354
20.2;17.2. Concept of sliding mode;357
20.3;17.3. Stochastic sliding mode control;365
20.4;17.4. Adaptive stochastic sliding mode control;373
20.5;Exercises;375
21;Chapter 18. Control of Stochastic Systems with Time Delay;378
21.1;18.1. Method of semi-discretization;379
21.2;18.2. Stability and performance analysis;381
21.3;18.3. An example;383
21.4;18.4. A note on the methodology;387
21.5;Exercises;388
22;Chapter 19. Probability Density Function Control;390
22.1;19.1. A motivating example;391
22.2;19.2. PDF tracking control;392
22.3;19.3. General formulation of PDF control;394
22.4;19.4. Numerical examples;396
22.5;Exercises;397
23;Appendix A. Matrix Computation;400
23.1;A.1. Types of matrices;400
23.2;A.2. Blocked matrix inversion;401
23.3;A.3. Matrix decomposition;402
23.4;A.4. Solution of linear algebraic equations and generalized inverse;404
24;Appendix B. Laplace Transformation;408
24.1;B.1. Definition and basic properties;408
24.2;B.2. Laplace transform of common functions;410
25;Bibliography;412
26;Subject Index;424mehr