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Bayesian inverse problems: fundamentals and engineering applications
Publisher
CRC Press
Publication Date
2021.
Language
English
Description
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Contributors
Chiachío-Ruano, Juan,1983- editor
ISBN
9781351869652
9781351869645
9781351869669
9781315232973
9781351869645
9781351869669
9781315232973
Table of Contents
From the eBook - First edition.
Cover
Title Page
Copyright Page
Dedication
Preface
Table of Contents
List of Figures
List of Tables
Contributors
Part I Fundamentals
1. Introduction to Bayesian Inverse Problems
1.1 Introduction
1.2 Sources of uncertainty
1.3 Formal definition of probability
1.4 Interpretations of probability
1.4.1 Physical probability
1.4.2 Subjective probability
1.5 Probability fundamentals
1.5.1 Bayes' Theorem
1.5.2 Total probability theorem
1.6 The Bayesian approach to inverse problems
1.6.1 The forward problem
1.6.2 The inverse problem
1.7 Bayesian inference of model parameters
1.7.1 Markov Chain Monte Carlo methods
1.7.1.1 Metropolis-Hasting algorithm
1.8 Bayesian model class selection
1.8.1 Computation of the evidence of a model class
1.8.2 Information-theory approach to model-class selection
1.9 Concluding remarks
2. Solving Inverse Problems by Approximate Bayesian Computation
2.1 Introduction to the ABC method
2.2 Basis of ABC using Subset Simulation
2.2.1 Introduction to Subset Simulation
2.2.2 Subset Simulation for ABC
2.3 The ABC-SubSim algorithm
2.4 Summary
3. Fundamentals of Sequential System Monitoring and Prognostics Methods
3.1 Fundamentals
3.1.1 Prognostics and SHM
3.1.2 Damage response modelling
3.1.3 Interpreting uncertainty for prognostics
3.1.4 Prognostic performance metrics
3.2 Bayesian tracking methods
3.2.1 Linear Bayesian Processor: The Kalman Filter
3.2.2 Unscented Transformation and Sigma Points: The Unscented Kalman Filter
3.2.3 Sequential Monte Carlo methods: Particle Filters
3.2.3.1 Sequential importance sampling
3.2.3.2 Resampling
3.3 Calculation of EOL and RUL
3.3.1 The failure prognosis problem
3.3.2 Future state prediction
3.4 Summary.
7. Fast Bayesian Approach for Stochastic Model Updating using Modal Information from Multiple Setups
7.1 Introduction
7.2 Probabilistic consideration of frequency-domain responses
7.2.1 PDF of multivariate FFT coefficients
7.2.2 PDF of PSD matrix
7.2.3 PDF of the trace of the PSD matrix
7.3 A two-stage fast Bayesian operational modal analysis
7.3.1 Prediction error model connecting modal responses and measurements
7.3.2 Spectrum variables identification using FBSTA
7.3.3 Mode shape identification using FBSDA
7.3.4 Statistical modal information for model updating
7.4 Bayesian model updating with modal data from multiple setups
7.4.1 Structural model class
7.4.2 Formulation of Bayesian model updating
7.4.2.1 The introduction of instrumental variables system mode shapes
7.4.2.2 Probability model connecting 'system mode shapes' and measured local mode shape
7.4.2.3 Probability model for the eigenvalue equation errors
7.4.2.4 Negative log-likelihood function for model updating
7.4.3 Solution strategy
7.5 Numerical example
7.5.1 Robustness test of the probabilistic model of trace of PSD matrix
7.5.2 Bayesian operational modal analysis
7.5.3 Bayesian model updating
7.6 Experimental study
7.6.1 Bayesian operational modal analysis
7.6.2 Bayesian model updating
7.7 Concluding remarks
8. A Worked-out Example of Surrogate-based Bayesian Parameter and Field Identification Methods
8.1 Introduction
8.2 Numerical modelling of seabed displacement
8.2.1 The deterministic computation of seabed displacements
8.2.2 Modified probabilistic formulation
8.3 Surrogate modelling
8.3.1 Computation of the surrogate by orthogonal projection
8.3.2 Computation of statistics
8.3.3 Validating surrogate models
8.4 Efficient representation of random fields.
8.4.1 Karhunen-Loève Expansion (KLE)
8.4.2 Proper Orthogonal Decomposition (POD)
8.5 Identification of the compressibility field
8.5.1 Bayes' Theorem
8.5.2 Sampling-based procedures-the MCMC method
8.5.3 The Kalman filter and its modified versions
8.5.3.1 The Kalman filter
8.5.3.2 The ensemble Kalman filter
8.5.3.3 The PCE-based Kalman filter
8.5.4 Non-linear filters
8.6 Summary, conclusion, and outlook
Appendices
Appendix A: FEM computation of seabed displacements
Appendix B: Hermite polynomials
B.1 Generation of Hermite Polynomials
B.2 Calculation of the norms
B.3 Quadrature points and weights
Appendix C: Galerkin solution of the Karhunen Loève eigenfunction problem
Appendix D: Computation of the PCE Coefficients by Orthogonal projection
Bibliography
Index.
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