Bayesian Methods for Structural Dynamics and Civil Engineering

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.

Contents Preface

Nomenclature

1 Introduction

1.1 Thomas Bayes and Bayesian Methods in Engineering

1.2 Purpose of Model Updating

1.3 Source of Uncertainty and Bayesian Updating

1.4 Organization of the Book

2 Basic Concepts and Bayesian Probabilistic Framework

2.1 Conditional Probability and Basic Concepts

2.2 Bayesian Model Updating with Input-output Measurements

2.3 Deterministic versus Probabilistic Methods

2.4 Regression Problems

2.5 Numerical Representation of the Updated PDF

2.6 Application to Temperature Effects on Structural Behavior

2.7 Application to Noise Parameters Selection for Kalman Filter

2.8 Application to Prediction of Particulate Matter Concentration

3 Bayesian Spectral Density Approach

3.1 Modal and Model Updating of Dynamical Systems

3.2 Random Vibration Analysis

3.3 Bayesian Spectral Density Approach

3.4 Numerical Verifications

3.5 Optimal Sensor Placement

3.6 Updating of a Nonlinear Oscillator

3.7 Application to Structural Behavior under Typhoons

3.8 Application to Hydraulic Jump

4 Bayesian Time-domain Approach

4.1 Introduction

4.2 Exact Bayesian Formulation and its Computational Difficulties

4.3 Random Vibration Analysis of Nonstationary Response

4.4 Bayesian Updating with Approximated PDF Expansion

4.5 Numerical Verification

4.6 Application to Model Updating with Unmeasured Earthquake Ground Motion

4.7 Concluding Remarks

4.8 Comparison of Spectral Density Approach and Time-domain Approach

4.9 Extended Readings

5 Model Updating Using Eigenvalue-Eigenvector Measurements

5.1 Introduction

5.2 Formulation

5.3 Linear Optimization Problems

5.4 Iterative Algorithm

5.5 Uncertainty Estimation

5.6 Applications to Structural Health Monitoring

5.7 Concluding Remarks

6 Bayesian Model Class Selection

6.1 Introduction

6.2 Bayesian Model Class Selection

6.3 Model Class Selection for Regression Problems

6.4 Application to Modal Updating

6.5 Application to Seismic Attenuation Empirical Relationship

6.6 Prior Distributions - Revisited

6.7 Final Remarks

A Relationship between the Hessian and Covariance Matrix for Gaussian Random Variables

B Contours of Marginal PDFs for Gaussian Random Variables

C Conditional PDF for Prediction

C.1 Two Random Variables

C.2 General Cases

References

Index