IUTAM Symposium on Nonlinear Stochastic Dynamics and Control (eBook)

Preface 6
Contents 9
Part 1 Response and Reliability of Nonlinear Stochastic Systems 16
Nonlinear Stochastic Ecosystem of Two Competing Species 17
Introduction 17
Characteristics of Deterministic Nonlinear System 18
Stochastic Nonlinear Model 19
Gaussian White-Noise Model 20
Randomized Sinusoidal Process Model 24
Conclusions 26
References 26
Energy Transition Rate at Peptide-Bond Using Stochastic Averaging Method 27
Introduction 27
PB Breaking in ESC and Its Stochastic Dynamical Model 28
Energy Transition Rate in the Case of Fermi Resonance 31
PB Breaking Rate Affected by Oxygen Ion 33
Conclusions 36
References 37
A New Method for the Probabilistic Solutions of Large-Scale Nonlinear Stochastic Dynamic Systems 38
Introduction 38
Problem Formulation 39
Subspace Method 40
Numerical Analysis 43
Conclusions 47
References 47
Nonstationary Probability Densities of Nonlinear Multi-Degree-of-Freedom Systems under Gaussian White Noise Excitations 48
Introduction 48
Approximate Nonstationary Probability Density 49
An Illustrative Example 52
Conclusions 56
References 57
Feature Extraction within the Fei-Tsui Arch Dam under Environmental Variations 58
Introduction 58
Measurement Systems of the Fei-Tsui Arch Dam 59
System Identification from Seismic Response Data 61
Deformation Monitoring from Long-Term Data 63
Conclusions 66
References 67
About Some Schemes of Study for Systems with Different Forms of Time Aftereffect 68
Introduction 68
Neutral Systems with Multiple Constant Delays 69
Scheme of Study 70
Equations for Moments 73
Examples 74
Conclusions 76
References 77
Reliability of Linear and Nonlinear Dynamic Systems under Multiplicative and Additive Noise 78
Introduction 78
Path Integration Approach to Reliability 79
Numerical Examples 81
A Linear Oscillator with Multiplicative and Additive Noise 81
A Duffing Oscillator with Multiplicative and Additive Noise 85
Conclusions 87
References 87
Numerical Solution of Fokker-Planck Equation for Nonlinear Stochastic Dynamical Systems 89
Introduction 89
Path Integration Method 90
Finite Difference Method 95
Conclusions 98
References 98
An Approximate Approach for Nonlinear System Evolutionary Response Spectrum Determination via Wavelets 99
Introduction 99
Harmonic Wavelet-Based Stochastic Process Representation and EPS Estimation 100
Harmonic Wavelet Transform 100
Locally Stationary Wavelet Process Representation 101
EPS Estimation 103
Harmonic Wavelet-Based Statistical Linearization 104
Nonlinear Response EPS Determination 104
Duffing Oscillator Application 106
Conclusions 107
References 107
On Information/Entropy Flow in Stochastic Dynamical Systems 109
Introduction 109
Entropy and Relative Entropy for SDS 110
Entropy in Liouvillian Systems 111
Entropy Rate of Systems with External Random Excitation 111
Relative Entropy for True and Idealized Models 115
Non-stationary Dynamics 115
Vibratory System with Time-Varying Parameters 116
Conclusions 118
References 118
Finite Dimensional Markov Process Approximation for Time-Delayed Stochastic Dynamical Systems 119
Introduction 119
The FDMP Method 121
Applications 122
FPK Equation 123
Moment Equations 123
Reliability 124
First-Passage Time Probability 125
Pontryagin-Vitt Equations 125
Conclusion 126
References 127
Response Analysis of Nonlinear Multi-degree of Freedom Systems to Non-Gaussian Random Excitations 129
Introduction 129
Nonlinear Systems under Gaussian Excitations 130
Nonlinear Systems under Non-Gaussian Excitations 132
Recursive Expressions for Systems under Non-Gaussian Random Excitations 132
Non-Gaussian Random Excitation Models 133
Time Co-ordinate Transformation 133
Adaptive Time Scheme 134
System with Asymmetric Nonlinear Stiffness 134
Two Dof System with Asymmetric Stiffness 135
Computed Results and Discussion 135
Concluding Remarks 138
References 138
Stationary and Nontationary Response Probability Density Function of a Beam under Poisson White Noise 139
Introduction 139
Linear Oscillations of a Beam under Transversal Poisson Pulses 140
Nonlinear Oscillations of a Beam under Transversal Poisson Pulses 144
Solution of Higher Order t 145
Conclusions 147
References 147
Steady State Analysis of Stochastic Systems with Multiple Time Delays 149
Introduction 149
Delay Fokker-Planck Equations 150
Approximate Stationary Solution 152
Case Study and Numerical Simulations 154
References 157
Stochastic Averaging of Strongly Nonlinear Oscillators under Poisson White Noise Excitation 159
Introduction 159
Stochastic Averaging Method 160
Example 165
Conclusions 166
References 167
Part 2 Stability, Bifurcation and Chaos of Nonlinear Stochastic Systems 168
Marginal Instability and Intermittency in Stochastic Systems 169
Introduction 170
Systems with Slow Variations of Parameters 170
Systems with Rapid Variations of Parameters 175
Conclusions 179
References 179
A Practical Strategy to Study Stochastic Chaos 181
Introduction 181
Implement of Orthogonal Polynomial Approximation 182
Typical Phenomena of Stochastic Chaos 184
Example 1 - Stochastic Chaos in Duffing Oscillator 184
Example 2 - Control of Chaos by Random Noise or Chaotic Driving 184
Example 3- Synchronization Induced by Common Noise 186
Conclusions 190
References 190
Fractal Basin Boundaries and Chaotic Dynamics in the Randomly-Driven Henon-Heiles Oscillator 192
Introduction 192
Noisy Exit Basins in the H-H Oscillator 193
Noisy Chaotic Dynamics 195
Conclusions 198
References 199
Moment Lyapunov Exponent for a Three Dimensional Stochastic System 200
Introduction 200
Equations 201
Asymptotic Analysis 203
Solution of the Eigenvalue Problem 206
Numerical Results and Conclusions 207
References 209
Bifurcation Analysis of Stochastic Non-smooth Systems 210
Introduction 210
Damping Induced Bifurcation 212
Excitation Induced Bifurcation and Sensitivity to Initial Conditions 214
Sensitivity to Initial Condition 215
Conclusions 218
References 218
Part 3 Resonance and Synchronization of Nonlinear Stochastic Systems 219
Synchronization Behavior of a Clustered Neuronal Network in a Noisy Environment 220
Introduction 220
Mathematical Model 221
Main Results 222
Summary 226
References 227
Stochastic Parameter Resonance of Road-Vehicle Systems and Related Bifurcation Problems 228
Introduction to the Problem 228
Spectral Analysis of Road-Vehicle Systems 229
Covariance Analysis of Road-Vehicle Systems 230
Extensions to Nonlinear Car Vibrations 231
Asymptotic Stability of Stationary Car Vibrations 233
Conclusions 234
References 235
A Review of Parameter-Induced Stochastic Resonance and Current Applications in Two-Dimensional Image Processing 236
Review of Parameter-Induced Stochastic Resonance 236
2D-PSR System and the Corresponding Fokker-Planck Equation 238
Theory of 2D-PSR for Degraded Image Processing 240
Example of 2D-PSR Image Restoration 242
Example of 2D-PSR Pattern Recognition of Remote Sensing Image 243
Conclusions 245
References 245
Part 4 Control of Nonlinear Stochastic Systems 246
Design of Damper Viscous Properties for Semi-active Control of Asymmetric Structures 247
Introduction 247
Device Sizing for Seismic Excited Frame Structures 248
Reference Linear Active Control Feedback 250
Semi-active Control Design 251
Semi-active Control Strategies 253
Implementation on a Prototype Structure 255
Conclusion 256
References 256
Iterative Procedures in Application of the LQGP Approach to the Duffing Oscillator 257
Introduction 257
Problem Formulation 258
Quasi-Optimal Nonlinear Control Problem 259
Procedure Convergence for the Duffing Oscillator 260
Example 262
Conclusions 264
References 264
Stochastic Optimal Time-Delay Control and Stabilization of Quasi-Integrable Hamiltonian Systems 267
Introduction 267
Formulation of Stochastic Optimal Time-Delay Control 268
Conversion to Stochastic Optimal Control Problems without Time-Delay 268
Time-Delay Feedback Stabilization 271
Example 272
Conclusions 276
References 276
Part 5 Modeling of Stochastic Dynamical Systems and Stochastic Excitations 277
Modeling of Stochastic Dynamic Excitations and the Probability Density Evolution Theory for Nonlinear Stochastic Dynamics 278
Introduction 278
Physical Stochastic Modeling of Dynamic Excitations 279
Basic Thoughts of Physical Stochastic Systems 279
Physical Stochastic Models: Exemplified by Fluctuating Wind 280
Stochastic Responses of Nonlinear Structures via Probability Density Evolution Equation 284
Fundamentals of the Probability Density Evolution Method 284
Numerical Implementation Procedure 285
Numerical Examples 285
Conclusions 286
References 287
On the Consideration of Model Uncertainties in Model Updating of Dynamic Systems 288
Introduction 288
Bayesian Model Updating 289
The Prediction Error in Bayesian Updating 290
Numerical Example 292
Updated Structural Parameters 294
Posterior Modal Properties 295
Posterior Prediction Error 296
Conclusions 296
References 296
Stochastic Reduced Order Models for Uncertain Infinite-Dimensional Geometrically Nonlinear Dynamical Systems- Stochastic Excitation Cases 298
Introduction 298
Reduced Order Modeling of Geometrically Nonlinear Structures 299
Basis Functions Selection 299
Form of the Reduced Order Model Equations 300
Identification of the Stiffness Coefficients 301
Nonparametric Uncertainty Modeling 302
Effects of Uncertainty on a Cantilevered Structure 303
Summary 306
References 307
Part 6 Structural Health Monitoring 308
Decentralized Random Decrement Technique for Data Aggregation and System Identification in Wireless Smart Sensor Networks 309
Introduction 309
Random Decrement Technique 311
RDT-Based Decentralized Data Aggregation 312
Implementation and Experimental Validation of RDT-Based Decentralized Data Aggregation on WSSNs 314
Conclusions 317
References 317
A Wave-Based Approach for Seismic Response Analyses of High-Rise Buildings 319
Introduction 319
Modeling of Wave Motion in Buildings 320
Applications in Earthquake Engineering 323
Uniform Shear-Beam Model 323
Stochastic Wave-Motion Model 326
Conclusions 329
References 329
Author Index 330