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Preface | p. xi |
Acknowledgements | p. xiii |
Nomenclature | p. xv |
Introduction | p. 1 |
Thomas Bayes and Bayesian Methods in Engineering | p. 1 |
Purpose of Model Updating | p. 3 |
Source of Uncertainty and Bayesian Updating | p. 5 |
Organization of the Book | p. 8 |
Basic Concepts and Bayesian Probabilistic Framework | p. 11 |
Conditional Probability and Basic Concepts | p. 12 |
Bayes' Theorem for Discrete Events | p. 13 |
Bayes' Theorem for Continuous-valued Parameters by Discrete Events | p. 15 |
Bayes' Theorem for Discrete Events by Continuous-valued Parameters | p. 17 |
Bayes' Theorem between Continuous-valued Parameters | p. 18 |
Bayesian Inference | p. 20 |
Examples of Bayesian Inference | p. 24 |
Bayesian Model Updating with Input-output Measurements | p. 33 |
Input-output Measurements | p. 33 |
Bayesian Parametric Identification | p. 34 |
Model Identifiability | p. 35 |
Deterministic versus Probabilistic Methods | p. 40 |
Regression Problems | p. 43 |
Linear Regression Problems | p. 43 |
Nonlinear Regression Problems | p. 47 |
Numerical Representation of the Updated PDF | p. 48 |
General Form of Reliability Integrals | p. 48 |
Monte Carlo Simulation | p. 49 |
Adaptive Markov Chain Monte Carlo Simulation | p. 50 |
Illustrative Example | p. 54 |
Application to Temperature Effects on Structural Behavior | p. 61 |
Problem Description | p. 61 |
Thermal Effects on Modal Frequencies of Buildings | p. 61 |
Bayesian Regression Analysis | p. 64 |
Analysis of the Measurements | p. 66 |
Concluding Remarks | p. 68 |
Application to Noise Parameters Selection for the Kalman Filter | p. 68 |
Problem Description | p. 68 |
Kalman Filter | p. 68 |
Illustrative Examples | p. 71 |
Application to Prediction of Particulate Matter Concentration | p. 77 |
Introduction | p. 77 |
Extended-Kalman-filter based Time-varying Statistical Models | p. 80 |
Analysis with Monitoring Data | p. 87 |
Conclusion | p. 98 |
Bayesian Spectral Density Approach | p. 99 |
Modal and Model Updating of Dynamical Systems | p. 99 |
Random Vibration Analysis | p. 101 |
Single-degree-of-freedom Systems | p. 101 |
Multi-degree-of-freedom Systems | p. 102 |
Bayesian Spectral Density Approach | p. 104 |
Formulation for Single-channel Output Measurements | p. 105 |
Formulation for Multiple-channel Output Measurements | p. 110 |
Selection of the Frequency Index Set | p. 115 |
Nonlinear Systems | p. 116 |
Numerical Verifications | p. 116 |
Aliasing and Leakage | p. 117 |
Identification with the Spectral Density Approach | p. 122 |
Identification with Small Amount of Data | p. 126 |
Concluding Remarks | p. 127 |
Optimal Sensor Placement | p. 127 |
Information Entropy with Globally Identifiable Case | p. 128 |
Optimal Sensor Configuration | p. 129 |
Robust Information Entropy | p. 130 |
Discrete Optimization Algorithm for Suboptimal Solution | p. 131 |
Updating of a Nonlinear Oscillator | p. 132 |
Application to Structural Behavior under Typhoons | p. 138 |
Problem Description | p. 138 |
Meteorological Information of the Two Typhoons | p. 140 |
Analysis of Monitoring Data | p. 142 |
Concluding Remarks | p. 152 |
Application to Hydraulic Jump | p. 152 |
Problem Description | p. 152 |
Fundamentals of Hydraulic Jump | p. 153 |
Roller Formation-advection Model | p. 153 |
Statistical Modeling of the Surface Fluctuation | p. 154 |
Experimental Setup and Results | p. 155 |
Concluding Remarks | p. 159 |
Bayesian Time-domain Approach | p. 161 |
Introduction | p. 161 |
Exact Bayesian Formulation and its Computational Difficulties | p. 162 |
Random Vibration Analysis of Nonstationary Response | p. 164 |
Bayesian Updating with Approximated PDF Expansion | p. 167 |
Reduced-order Likelihood Function | p. 172 |
Conditional PDFs | p. 172 |
Numerical Verification | p. 174 |
Application to Model Updating with Unmeasured Earthquake Ground Motion | p. 179 |
Transient Response of a Linear Oscillator | p. 179 |
Building Subjected to Nonstationary Ground Excitation | p. 182 |
Concluding Remarks | p. 186 |
Comparison of Spectral Density Approach and Time-domain Approach | p. 187 |
Extended Readings | p. 189 |
Model Updating Using Eigenvalue-Eigenvector Measurements | p. 193 |
Introduction | p. 193 |
Formulation | p. 196 |
Linear Optimization Problems | p. 198 |
Optimization for Mode Shapes | p. 199 |
Optimization for Modal Frequencies | p. 199 |
Optimization for Model Parameters | p. 200 |
Iterative Algorithm | p. 200 |
Uncertainty Estimation | p. 201 |
Applications to Structural Health Monitoring | p. 202 |
Twelve-story Shear Building | p. 202 |
Three-dimensional Six-story Braced Frame | p. 205 |
Concluding Remarks | p. 210 |
Bayesian Model Class Selection | p. 213 |
Introduction | p. 213 |
Sensitivity, Data Fitness and Parametric Uncertainty | p. 216 |
Bayesian Model Class Selection | p. 219 |
Globally Identifiable Case | p. 221 |
General Case | p. 225 |
Computational Issues: Transitional Markov Chain Monte Carlo Method | p. 228 |
Model Class Selection for Regression Problems | p. 229 |
Linear Regression Problems | p. 229 |
Nonlinear Regression Problems | p. 234 |
Application to Modal Updating | p. 235 |
Application to Seismic Attenuation Empirical Relationship | p. 238 |
Problem Description | p. 238 |
Selection of the Predictive Model Class | p. 239 |
Analysis with Strong Ground Motion Measurements | p. 241 |
Concluding Remarks | p. 249 |
Prior Distributions - Revisited | p. 250 |
Final Remarks | p. 252 |
Relationship between the Hessian and Covariance Matrix for Gaussian Random Variables | p. 257 |
Contours of Marginal PDFs for Gaussian Random Variables | p. 263 |
Conditional PDF for Prediction | p. 269 |
Two Random Variables | p. 269 |
General Cases | p. 273 |
References | p. 279 |
Index | p. 291 |
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