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