Bayesian Methods for Structural Dynamics and Civil Engineering

BAYESIAN METHODS FOR STRUCTURAL DYNAMICS AND CIVIL ENGINEERING......Page 5
Contents......Page 9
Preface......Page 13
Acknowledgements......Page 15
Nomenclature......Page 17
1.1 Thomas Bayes and Bayesian Methods in Engineering......Page 19
1.2 Purpose of Model Updating......Page 21
1.3 Source of Uncertainty and Bayesian Updating......Page 23
1.4 Organization of the Book......Page 26
2 Basic Concepts and Bayesian Probabilistic Framework......Page 29
2.1 Conditional Probability and Basic Concepts......Page 30
2.1.1 Bayes’ Theorem for Discrete Events......Page 31
2.1.2 Bayes’ Theorem for Continuous-valued Parameters by Discrete Events......Page 33
2.1.3 Bayes’ Theorem for Discrete Events by Continuous-valued Parameters......Page 35
2.1.4 Bayes’ Theorem between Continuous-valued Parameters......Page 36
2.1.5 Bayesian Inference......Page 38
2.1.6 Examples of Bayesian Inference......Page 42
2.2.1 Input–output Measurements......Page 51
2.2.2 Bayesian Parametric Identification......Page 52
2.2.3 Model Identifiability......Page 53
2.3 Deterministic versus Probabilistic Methods......Page 58
2.4.1 Linear Regression Problems......Page 61
2.4.2 Nonlinear Regression Problems......Page 65
2.5.1 General Form of Reliability Integrals......Page 66
2.5.2 Monte Carlo Simulation......Page 67
2.5.3 Adaptive Markov Chain Monte Carlo Simulation......Page 68
2.5.4 Illustrative Example......Page 72
2.6.2 Thermal Effects on Modal Frequencies of Buildings......Page 79
2.6.3 Bayesian Regression Analysis......Page 82
2.6.4 Analysis of the Measurements......Page 84
2.7.2 Kalman Filter......Page 86
2.7.3 Illustrative Examples......Page 89
2.8.1 Introduction......Page 95
2.8.2 Extended-Kalman-filter based Time-varying Statistical Models......Page 98
2.8.3 Analysis with Monitoring Data......Page 105
2.8.4 Conclusion......Page 116
3.1 Modal and Model Updating of Dynamical Systems......Page 117
3.2.1 Single-degree-of-freedom Systems......Page 119
3.2.2 Multi-degree-of-freedom Systems......Page 120
3.3 Bayesian Spectral Density Approach......Page 122
3.3.1 Formulation for Single-channel Output Measurements......Page 123
3.3.2 Formulation for Multiple-channel Output Measurements......Page 128
3.3.3 Selection of the Frequency Index Set......Page 133
3.4 Numerical Verifications......Page 134
3.4.1 Aliasing and Leakage......Page 135
3.4.2 Identification with the Spectral Density Approach......Page 140
3.4.3 Identification with Small Amount of Data......Page 144
3.5 Optimal Sensor Placement......Page 145
3.5.1 Information Entropy with Globally Identifiable Case......Page 146
3.5.2 Optimal Sensor Configuration......Page 147
3.5.3 Robust Information Entropy......Page 148
3.5.4 Discrete Optimization Algorithm for Suboptimal Solution......Page 149
3.6 Updating of a Nonlinear Oscillator......Page 150
3.7.1 Problem Description......Page 156
3.7.2 Meteorological Information of the Two Typhoons......Page 158
3.7.3 Analysis of Monitoring Data......Page 160
3.8.1 Problem Description......Page 170
3.8.3 Roller Formation-advection Model......Page 171
3.8.4 Statistical Modeling of the Surface Fluctuation......Page 172
3.8.5 Experimental Setup and Results......Page 173
3.8.6 Concluding Remarks......Page 177
4.1 Introduction......Page 179
4.2 Exact Bayesian Formulation and its Computational Difficulties......Page 180
4.3 Random Vibration Analysis of Nonstationary Response......Page 182
4.4 Bayesian Updating with Approximated PDF Expansion......Page 185
4.4.2 Conditional PDFs......Page 190
4.5 Numerical Verification......Page 192
4.6.1 Transient Response of a Linear Oscillator......Page 197
4.6.2 Building Subjected to Nonstationary Ground Excitation......Page 200
4.7 Concluding Remarks......Page 204
4.8 Comparison of Spectral Density Approach and Time-domain Approach......Page 205
4.9 Extended Readings......Page 207
5.1 Introduction......Page 211
5.2 Formulation......Page 214
5.3 Linear Optimization Problems......Page 216
5.3.2 Optimization for Modal Frequencies......Page 217
5.4 Iterative Algorithm......Page 218
5.5 Uncertainty Estimation......Page 219
5.6.1 Twelve-story Shear Building......Page 220
5.6.2 Three-dimensional Six-story Braced Frame......Page 223
5.7 Concluding Remarks......Page 228
6.1 Introduction......Page 231
6.1.1 Sensitivity, Data Fitness and Parametric Uncertainty......Page 234
6.2 Bayesian Model Class Selection......Page 237
6.2.1 Globally Identifiable Case......Page 239
6.2.2 General Case......Page 243
6.2.3 Computational Issues: Transitional Markov Chain Monte Carlo Method......Page 246
6.3.1 Linear Regression Problems......Page 247
6.3.2 Nonlinear Regression Problems......Page 252
6.4 Application to Modal Updating......Page 253
6.5.1 Problem Description......Page 256
6.5.2 Selection of the Predictive Model Class......Page 257
6.5.3 Analysis with Strong Ground Motion Measurements......Page 259
6.5.4 Concluding Remarks......Page 267
6.6 Prior Distributions – Revisited......Page 268
6.7 Final Remarks......Page 270
Appendix A: Relationship between the Hessian and Covariance Matrix for Gaussian Random Variables......Page 275
Appendix B: Contours of Marginal PDFs for Gaussian Random Variables......Page 281
C.1 Two Random Variables......Page 287
C.2 General Cases......Page 291
References......Page 297
Index......Page 309