Bayesian Methods for Structural Dynamics and Civil Engineering

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2010-04-05
  • Publisher: Wiley

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Bayesian Methods for Structural Dynamics introduces recently developed Bayesian methods and applications to several areas of engineering. Readers are provided a through grounding in the theory, and shown concrete examples to promote easier understanding. The first two chapters give a general introduction and literature review of the applications of Bayesian methods in different disciplines of engineering, while giving simple examples of static systems to illustrate the concepts. Yuen goes on to introduce time-domain approaches for unmeasured input, which can be applied to multi-degree-of-freedom linear systems subjected to stationary or non-stationary input, as demonstrated with earthquake ground motion. The author presents the Bayesian spectral density approach in the fourth chapter, using hydraulic jump to demonstrate the methodology and providing comparisons of applicability between time-domain and frequency-domain approaches. In chapter five, Yuen addresses the problem of model parameter identification through eigenvalue-eigenvector measurements, with applications to finite-element model updating and structural health monitoring. Chapter 6 considers the problem of selection of model class for system identification, and introduces Markov Chain Monte Carlo simulation and Metropolis-Hastings algorithm. Model class selection is then illustrated by problems in air-quality prediction, artificial neural networks, and seismic attenuation.

Author Biography

Ka-Veng Yuen is an Associate Professor of Civil and Environmental Engineering at the University of Macau. His research interests include random vibrations, system identification, structural health monitoring, modal/model identification, reliability analysis of engineering systems, structural control, model class selection, air quality prediction, non-destructive testing and probabilistic methods. He has been working on Bayesian statistical inference and its application since 1997. Yuen has published over sixty research papers in international conferences and top journals in the field. He is an editorial board member of the International Journal of Reliability and Safety, and is also a member of the ASCE Probabilistic Methods Committee, the Subcommittee on Computational Stochastic Mechanics, and the Subcommittee on System Identification and Structural Control of the International Association for Structural Safety and Reliability (IASSAR), as well as the Committee of Financial Analysis and Computation, Chinese Association of New Cross Technology in Mathematics, Mechanics and Physics. Yuen holds an M.S. from Hong Kong University of Science and Technology and a Ph.D. from Caltech, both in Civil Engineering.

Table of Contents

Prefacep. xi
Acknowledgementsp. xiii
Nomenclaturep. xv
Introductionp. 1
Thomas Bayes and Bayesian Methods in Engineeringp. 1
Purpose of Model Updatingp. 3
Source of Uncertainty and Bayesian Updatingp. 5
Organization of the Bookp. 8
Basic Concepts and Bayesian Probabilistic Frameworkp. 11
Conditional Probability and Basic Conceptsp. 12
Bayes' Theorem for Discrete Eventsp. 13
Bayes' Theorem for Continuous-valued Parameters by Discrete Eventsp. 15
Bayes' Theorem for Discrete Events by Continuous-valued Parametersp. 17
Bayes' Theorem between Continuous-valued Parametersp. 18
Bayesian Inferencep. 20
Examples of Bayesian Inferencep. 24
Bayesian Model Updating with Input-output Measurementsp. 33
Input-output Measurementsp. 33
Bayesian Parametric Identificationp. 34
Model Identifiabilityp. 35
Deterministic versus Probabilistic Methodsp. 40
Regression Problemsp. 43
Linear Regression Problemsp. 43
Nonlinear Regression Problemsp. 47
Numerical Representation of the Updated PDFp. 48
General Form of Reliability Integralsp. 48
Monte Carlo Simulationp. 49
Adaptive Markov Chain Monte Carlo Simulationp. 50
Illustrative Examplep. 54
Application to Temperature Effects on Structural Behaviorp. 61
Problem Descriptionp. 61
Thermal Effects on Modal Frequencies of Buildingsp. 61
Bayesian Regression Analysisp. 64
Analysis of the Measurementsp. 66
Concluding Remarksp. 68
Application to Noise Parameters Selection for the Kalman Filterp. 68
Problem Descriptionp. 68
Kalman Filterp. 68
Illustrative Examplesp. 71
Application to Prediction of Particulate Matter Concentrationp. 77
Introductionp. 77
Extended-Kalman-filter based Time-varying Statistical Modelsp. 80
Analysis with Monitoring Datap. 87
Conclusionp. 98
Bayesian Spectral Density Approachp. 99
Modal and Model Updating of Dynamical Systemsp. 99
Random Vibration Analysisp. 101
Single-degree-of-freedom Systemsp. 101
Multi-degree-of-freedom Systemsp. 102
Bayesian Spectral Density Approachp. 104
Formulation for Single-channel Output Measurementsp. 105
Formulation for Multiple-channel Output Measurementsp. 110
Selection of the Frequency Index Setp. 115
Nonlinear Systemsp. 116
Numerical Verificationsp. 116
Aliasing and Leakagep. 117
Identification with the Spectral Density Approachp. 122
Identification with Small Amount of Datap. 126
Concluding Remarksp. 127
Optimal Sensor Placementp. 127
Information Entropy with Globally Identifiable Casep. 128
Optimal Sensor Configurationp. 129
Robust Information Entropyp. 130
Discrete Optimization Algorithm for Suboptimal Solutionp. 131
Updating of a Nonlinear Oscillatorp. 132
Application to Structural Behavior under Typhoonsp. 138
Problem Descriptionp. 138
Meteorological Information of the Two Typhoonsp. 140
Analysis of Monitoring Datap. 142
Concluding Remarksp. 152
Application to Hydraulic Jumpp. 152
Problem Descriptionp. 152
Fundamentals of Hydraulic Jumpp. 153
Roller Formation-advection Modelp. 153
Statistical Modeling of the Surface Fluctuationp. 154
Experimental Setup and Resultsp. 155
Concluding Remarksp. 159
Bayesian Time-domain Approachp. 161
Introductionp. 161
Exact Bayesian Formulation and its Computational Difficultiesp. 162
Random Vibration Analysis of Nonstationary Responsep. 164
Bayesian Updating with Approximated PDF Expansionp. 167
Reduced-order Likelihood Functionp. 172
Conditional PDFsp. 172
Numerical Verificationp. 174
Application to Model Updating with Unmeasured Earthquake Ground Motionp. 179
Transient Response of a Linear Oscillatorp. 179
Building Subjected to Nonstationary Ground Excitationp. 182
Concluding Remarksp. 186
Comparison of Spectral Density Approach and Time-domain Approachp. 187
Extended Readingsp. 189
Model Updating Using Eigenvalue-Eigenvector Measurementsp. 193
Introductionp. 193
Formulationp. 196
Linear Optimization Problemsp. 198
Optimization for Mode Shapesp. 199
Optimization for Modal Frequenciesp. 199
Optimization for Model Parametersp. 200
Iterative Algorithmp. 200
Uncertainty Estimationp. 201
Applications to Structural Health Monitoringp. 202
Twelve-story Shear Buildingp. 202
Three-dimensional Six-story Braced Framep. 205
Concluding Remarksp. 210
Bayesian Model Class Selectionp. 213
Introductionp. 213
Sensitivity, Data Fitness and Parametric Uncertaintyp. 216
Bayesian Model Class Selectionp. 219
Globally Identifiable Casep. 221
General Casep. 225
Computational Issues: Transitional Markov Chain Monte Carlo Methodp. 228
Model Class Selection for Regression Problemsp. 229
Linear Regression Problemsp. 229
Nonlinear Regression Problemsp. 234
Application to Modal Updatingp. 235
Application to Seismic Attenuation Empirical Relationshipp. 238
Problem Descriptionp. 238
Selection of the Predictive Model Classp. 239
Analysis with Strong Ground Motion Measurementsp. 241
Concluding Remarksp. 249
Prior Distributions - Revisitedp. 250
Final Remarksp. 252
Relationship between the Hessian and Covariance Matrix for Gaussian Random Variablesp. 257
Contours of Marginal PDFs for Gaussian Random Variablesp. 263
Conditional PDF for Predictionp. 269
Two Random Variablesp. 269
General Casesp. 273
Referencesp. 279
Indexp. 291
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