Yuen Ka-Veng. Bayesian Methods for Structural Dynamics and Civil Engineering

John Wiley & Sons (Asia) Pte Ltd, 2010. — 294 p. — ISBN 978-0-470-82454-2Bayesian inference is a statistical process that quantifies the degree of belief of hypothesis, events or values of parameters. Many Bayesian methods have been developed in various areas of science and engineering, especially in statistical physics, medical sciences, electrical engineering, and information sciences, etc. This book presents various applications in civil engineering, including air quality prediction, finite-element model updating, hydraulic jump, seismic attenuation relationship, and structural health monitoring, etc.Thomas Bayes and Bayesian Methods in Engineering
Purpose of Model Updating
Source of Uncertainty and Bayesian Updating
Organization of the Book
Basic Concepts and Bayesian Probabilistic Framework
Conditional Probability and Basic Concepts
Bayesian Model Updating with Input–output Measurements
Deterministic versus Probabilistic Methods
Regression Problems
Numerical Representation of the Updated PDF
Application to Temperature Effects on Structural Behavior
Application to Noise Parameters Selection for the Kalman Filter
Application to Prediction of Particulate Matter Concentration
Bayesian Spectral Density Approach
Modal and Model Updating of Dynamical Systems
Random Vibration Analysis
Bayesian Spectral Density Approach
Numerical Verifications
Optimal Sensor Placement
Updating of a Nonlinear Oscillator
Application to Structural Behavior under Typhoons
Application to Hydraulic Jump
Bayesian Time-domain ApproachExact Bayesian Formulation and its Computational Difficulties
Random Vibration Analysis of Nonstationary Response
Bayesian Updating with Approximated PDF Expansion
Numerical Verification
Application to Model Updating with Unmeasured Earthquake Ground Motion
Concluding Remarks
Comparison of Spectral Density Approach and Time-domain Approach
Extended Readings
Model Updating Using Eigenvalue–Eigenvector MeasurementsFormulation
Linear Optimization Problems
Iterative Algorithm
Uncertainty Estimation
Applications to Structural Health Monitoring
Concluding Remarks
Bayesian Model Class SelectionBayesian Model Class Selection
Model Class Selection for Regression Problems
Application to Modal Updating
Application to Seismic Attenuation Empirical Relationship
Prior Distributions – Revisited
Final Remarks
Appendix A. Relationship between the Hessian and Covariance Matrix for Gaussian Random Variables
Appendix B. Contours of Marginal PDFs for Gaussian Random Variables
Appendix C. Conditional PDF for Prediction