Bayesian methods for structural dynamics and civil engineering

Bayesian methods are a powerful tool in many areas of science and engineering, especially statistical physics, medical sciences, electrical engineering, and information sciences. They are also ideal for civil engineering applications, given the numerous types of modeling and parametric uncertainty in civil engineering problems. For example, earthquake ground motion cannot be predetermined at the structural design stage. Complete wind pressure profiles are difficult to measure under operating conditions. Material properties can be difficult to determine to a very precise level - especially concrete, rock, and soil. For air quality prediction, it is difficult to measure the hourly/daily pollutants generated by cars and factories within the area of concern. It is also difficult to obtain the updated air quality information of the surrounding cities. Furthermore, the meteorological conditions of the day for prediction are also uncertain. These are just some of the civil engineering examples to which Bayesian probabilistic methods are applicable.

Familiarizes readers with the latest developments in the field Includes identification problems for both dynamic and static systems Addresses challenging civil engineering problems such as modal/model updating Presents methods applicable to mechanical and aerospace engineering Gives engineers and engineering students a concrete sense of implementation Covers real-world case studies in civil engineering and beyond, such as: structural health monitoring seismic attenuation finite-element model updating hydraulic jump artificial neural network for damage detection air quality prediction Includes other insightful daily-life examples Companion website with MATLAB code downloads for independent practice Written by a leading expert in the use of Bayesian methods for civil engineering problems

This book is ideal for researchers and graduate students in civil and mechanical engineering or applied probability and statistics. Practicing engineers interested in the application of statistical methods to solve engineering problems will also find this to be a valuable text.

MATLAB code and lecture materials for instructors available at www.wiley.com/go/yuen

Author Notes

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.

Preface	p. xi
Acknowledgements	p. xiii
Nomenclature	p. xv
1 Introduction	p. 1
1.1 Thomas Bayes and Bayesian Methods in Engineering	p. 1
1.2 Purpose of Model Updating	p. 3
1.3 Source of Uncertainty and Bayesian Updating	p. 5
1.4 Organization of the Book	p. 8
2 Basic Concepts and Bayesian Probabilistic Framework	p. 11
2.1 Conditional Probability and Basic Concepts	p. 12
2.1.1 Bayes' Theorem for Discrete Events	p. 13
2.1.2 Bayes' Theorem for Continuous-valued Parameters by Discrete Events	p. 15
2.1.3 Bayes' Theorem for Discrete Events by Continuous-valued Parameters	p. 17
2.1.4 Bayes' Theorem between Continuous-valued Parameters	p. 18
2.1.5 Bayesian Inference	p. 20
2.1.6 Examples of Bayesian Inference	p. 24
2.2 Bayesian Model Updating with Input-output Measurements	p. 33
2.2.1 Input-output Measurements	p. 33
2.2.2 Bayesian Parametric Identification	p. 34
2.2.3 Model Identifiability	p. 35
2.3 Deterministic versus Probabilistic Methods	p. 40
2.4 Regression Problems	p. 43
2.4.1 Linear Regression Problems	p. 43
2.4.2 Nonlinear Regression Problems	p. 47
2.5 Numerical Representation of the Updated PDF	p. 48
2.5.1 General Form of Reliability Integrals	p. 48
2.5.2 Monte Carlo Simulation	p. 49
2.5.3 Adaptive Markov Chain Monte Carlo Simulation	p. 50
2.5.4 Illustrative Example	p. 54
2.6 Application to Temperature Effects on Structural Behavior	p. 61
2.6.1 Problem Description	p. 61
2.6.2 Thermal Effects on Modal Frequencies of Buildings	p. 61
2.6.3 Bayesian Regression Analysis	p. 64
2.6.4 Analysis of the Measurements	p. 66
2.6.5 Concluding Remarks	p. 68
2.7 Application to Noise Parameters Selection for the Kalman Filter	p. 68
2.7.1 Problem Description	p. 68
2.7.2 Kalman Filter	p. 68
2.7.3 Illustrative Examples	p. 71
2.8 Application to Prediction of Particulate Matter Concentration	p. 77
2.8.1 Introduction	p. 77
2.8.2 Extended-Kalman-filter based Time-varying Statistical Models	p. 80
2.8.3 Analysis with Monitoring Data	p. 87
2.8.4 Conclusion	p. 98
3 Bayesian Spectral Density Approach	p. 99
3.1 Modal and Model Updating of Dynamical Systems	p. 99
3.2 Random Vibration Analysis	p. 101
3.2.1 Single-degree-of-freedom Systems	p. 101
3.2.2 Multi-degree-of-freedom Systems	p. 102
3.3 Bayesian Spectral Density Approach	p. 104
3.3.1 Formulation for Single-channel Output Measurements	p. 105
3.3.2 Formulation for Multiple-channel Output Measurements	p. 110
3.3.3 Selection of the Frequency Index Set	p. 115
3.3.4 Nonlinear Systems	p. 116
3.4 Numerical Verifications	p. 116
3.4.1 Aliasing and Leakage	p. 117
3.4.2 Identification with the Spectral Density Approach	p. 122
3.4.3 Identification with Small Amount of Data	p. 126
3.4.4 Concluding Remarks	p. 127
3.5 Optimal Sensor Placement	p. 127
3.5.1 Information Entropy with Globally Identifiable Case	p. 128
3.5.2 Optimal Sensor Configuration	p. 129
3.5.3 Robust Information Entropy	p. 130
3.5.4 Discrete Optimization Algorithm for Suboptimal Solution	p. 131
3.6 Updating of a Nonlinear Oscillator	p. 132
3.7 Application to Structural Behavior under Typhoons	p. 138
3.7.1 Problem Description	p. 138
3.7.2 Meteorological Information of the Two Typhoons	p. 140
3.7.3 Analysis of Monitoring Data	p. 142
3.7.4 Concluding Remarks	p. 152
3.8 Application to Hydraulic Jump	p. 152
3.8.1 Problem Description	p. 152
3.8.2 Fundamentals of Hydraulic Jump	p. 153
3.8.3 Roller Formation-advection Model	p. 153
3.8.4 Statistical Modeling of the Surface Fluctuation	p. 154
3.8.5 Experimental Setup and Results	p. 155
3.8.6 Concluding Remarks	p. 159
4 Bayesian Time-domain Approach	p. 161
4.1 Introduction	p. 161
4.2 Exact Bayesian Formulation and its Computational Difficulties	p. 162
4.3 Random Vibration Analysis of Nonstationary Response	p. 164
4.4 Bayesian Updating with Approximated PDF Expansion	p. 167
4.4.1 Reduced-order Likelihood Function	p. 172
4.4.2 Conditional PDFs	p. 172
4.5 Numerical Verification	p. 174
4.6 Application to Model Updating with Unmeasured Earthquake Ground Motion	p. 179
4.6.1 Transient Response of a Linear Oscillator	p. 179
4.6.2 Building Subjected to Nonstationary Ground Excitation	p. 182
4.7 Concluding Remarks	p. 186
4.8 Comparison of Spectral Density Approach and Time-domain Approach	p. 187
4.9 Extended Readings	p. 189
5 Model Updating Using Eigenvalue-Eigenvector Measurements	p. 193
5.1 Introduction	p. 193
5.2 Formulation	p. 196
5.3 Linear Optimization Problems	p. 198
5.3.1 Optimization for Mode Shapes	p. 199
5.3.2 Optimization for Modal Frequencies	p. 199
5.3.3 Optimization for Model Parameters	p. 200
5.4 Iterative Algorithm	p. 200
5.5 Uncertainty Estimation	p. 201
5.6 Applications to Structural Health Monitoring	p. 202
5.6.1 Twelve-story Shear Building	p. 202
5.6.2 Three-dimensional Six-story Braced Frame	p. 205
5.7 Concluding Remarks	p. 210
6 Bayesian Model Class Selection	p. 213
6.1 Introduction	p. 213
6.1.1 Sensitivity, Data Fitness and Parametric Uncertainty	p. 216
6.2 Bayesian Model Class Selection	p. 219
6.2.1 Globally Identifiable Case	p. 221
6.2.2 General Case	p. 225
6.2.3 Computational Issues: Transitional Markov Chain Monte Carlo Method	p. 228
6.3 Model Class Selection for Regression Problems	p. 229
6.3.1 Linear Regression Problems	p. 229
6.3.2 Nonlinear Regression Problems	p. 234
6.4 Application to Modal Updating	p. 235
6.5 Application to Seismic Attenuation Empirical Relationship	p. 238
6.5.1 Problem Description	p. 238
6.5.2 Selection of the Predictive Model Class	p. 239
6.5.3 Analysis with Strong Ground Motion Measurements	p. 241
6.5.4 Concluding Remarks	p. 249
6.6 Prior Distributions - Revisited	p. 250
6.7 Final Remarks	p. 252
Appendix A Relationship between the Hessian and Covariance Matrix for Gaussian Random Variables	p. 257
Appendix B Contours of Marginal PDFs for Gaussian Random Variables	p. 263
Appendix C Conditional PDF for Prediction	p. 269
C.l Two Random Variables	p. 269
C.2 General Cases	p. 273
References	p. 279
Index	p. 291

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents