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Bayesian Inverse Problems: Fundamentals and Engineering Applications [Kõva köide]

Edited by (University of Nottingham, UK), Edited by (University of Nottingham, UK), Edited by (NASA Ames Research Center, Moffett Field, CA, USA)
  • Formaat: Hardback, 232 pages, kõrgus x laius: 254x178 mm, kaal: 680 g, 15 Tables, black and white; 2 Illustrations, color; 56 Illustrations, black and white
  • Ilmumisaeg: 11-Nov-2021
  • Kirjastus: CRC Press
  • ISBN-10: 1138035858
  • ISBN-13: 9781138035850
Teised raamatud teemal:
Bayesian Inverse Problems: Fundamentals and Engineering ApplicationsSuurem pilt
  • Formaat: Hardback, 232 pages, kõrgus x laius: 254x178 mm, kaal: 680 g, 15 Tables, black and white; 2 Illustrations, color; 56 Illustrations, black and white
  • Ilmumisaeg: 11-Nov-2021
  • Kirjastus: CRC Press
  • ISBN-10: 1138035858
  • ISBN-13: 9781138035850
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781138035850.html
Märksõnad:
This book is devoted to a special class of engineering problems called Bayesian inverse problems. These problems comprise not only the probabilistic Bayesian formulation of engineering problems, but also the associated stochastic simulation methods needed to solve them. Through this book, the reader will learn how this class of methods can be useful to rigorously address a range of engineering problems where empirical data and fundamental knowledge come into play. The book is written for a non-expert audience and it is contributed to by many of the most renowned academic experts in this field.
Preface v
List of Figures
xii
List of Tables
xiv
Contributors xv
Part I Fundamentals
1(76)
1 Introduction to Bayesian Inverse Problems
3(22)
Juan Chiachio-Ruano
Manuel Chiachio-Ruano
Shankar Sankararaman
1.1 Introduction
3(1)
1.2 Sources of uncertainty
4(1)
1.3 Formal definition of probability
5(1)
1.4 Interpretations of probability
6(2)
1.4.1 Physical probability
7(1)
1.4.2 Subjective probability
7(1)
1.5 Probability fundamentals
8(2)
1.5.1 Bayes' Theorem
8(1)
1.5.2 Total probability theorem
9(1)
1.6 The Bayesian approach to inverse problems
10(4)
1.6.1 The forward problem
11(2)
1.6.2 The inverse problem
13(1)
1.7 Bayesian inference of model parameters
14(5)
1.7.1 Markov Chain Monte Carlo methods
18(1)
1.7.1.1 Metropolis-Hasting algorithm
18(1)
1.8 Bayesian model class selection
19(5)
1.8.1 Computation of the evidence of a model class
21(2)
1.8.2 Information-theory approach to model-class selection
23(1)
1.9 Concluding remarks
24(1)
2 Solving Inverse Problems by Approximate Bayesian Computation
25(14)
Manuel Chiachio-Ruano
Juan Chiachio-Ruano
Maria L. Jalon
2.1 Introduction to the ABC method
25(5)
2.2 Basis of ABC using Subset Simulation
30(4)
2.2.1 Introduction to Subset Simulation
30(3)
2.2.2 Subset Simulation for ABC
33(1)
2.3 The ABC-SubSim algorithm
34(2)
2.4 Summary
36(3)
3 Fundamentals of Sequential System Monitoring and Prognostics Methods
39(22)
David E. Acuha-Ureta
Juan Chiachio-Ruano
Manuel Chiachio-Ruano
Marcos E. Orchard
3.1 Fundamentals
39(4)
3.1.1 Prognostics and SHM
40(1)
3.1.2 Damage response modelling
40(1)
3.1.3 Interpreting uncertainty for prognostics
41(1)
3.1.4 Prognostic performance metrics
41(2)
3.2 Bayesian tracking methods
43(9)
3.2.1 Linear Bayesian Processor: The Kalman Filter
44(2)
3.2.2 Unscented Transformation and Sigma Points: The Unscented Kalman Filter
46(3)
3.2.3 Sequential Monte Carlo methods: Particle Filters
49(1)
3.2.3.1 Sequential importance sampling
50(1)
3.2.3.2 Resampling
51(1)
3.3 Calculation of EOL and RUL
52(8)
3.3.1 The failure prognosis problem
53(2)
3.3.2 Future state prediction
55(5)
3.4 Summary
60(1)
4 Parameter Identification Based on Conditional Expectation
61(16)
Elmar Zander
Noemi Friedman
Hermann G. Matthies
4.1 Introduction
61(5)
4.1.1 Preliminaries---basics of probability and information
63(1)
4.1.1.1 Random variables
63(1)
4.1.2 Bayes' theorem
64(1)
4.1.3 Conditional expectation
65(1)
4.2 The Mean Square Error Estimator
66(4)
4.2.1 Numerical approximation of the MMSE
67(1)
4.2.2 Numerical examples
68(2)
4.3 Parameter identification using the MMSE
70(6)
4.3.1 The MMSE filter
70(2)
4.3.2 The Kalman filter
72(1)
4.3.3 Numerical examples
73(3)
4.4 Conclusion
76(1)
Part II Engineering Applications
77(30)
5 Sparse Bayesian Learning and its Application in Bayesian System Identification
79(28)
Yong Huang
James L. Beck
5.1 Introduction
79(2)
5.2 Sparse Bayesian learning
81(3)
5.2.1 General formulation of sparse Bayesian learning with the ARD prior
81(2)
5.2.2 Bayesian Ockham's razor implementation in sparse Bayesian learning
83(1)
5.3 Applying sparse Bayesian learning to system identification
84(11)
5.3.1 Hierarchical Bayesian model class for system identification
84(4)
5.3.2 Fast sparse Bayesian learning algorithm
88(1)
5.3.2.1 Formulation
88(5)
5.3.2.2 Proposed fast SBL algorithm for stiffness inversion
93(1)
5.3.2.3 Damage assessment
94(1)
5.4 Case studies
95(10)
5.5 Concluding remarks
105(2)
Appendices
107(98)
Appendix A Derivation of MAP estimation equations for a and ft
109(4)
6 Ultrasonic Guided-waves Based Bayesian Damage Localisation and Optimal Sensor Configuration
113(20)
Sergio Cantero-Chinchilla
Juan Chiachio
Manuel Chiachio
Dimitrios Chronopoulos
6.1 Introduction
113(1)
6.2 Damage localisation
114(11)
6.2.1 Time-frequency model selection
115(1)
6.2.1.1 Stochastic embedding of TF models
115(1)
6.2.1.2 Model parameters estimation
116(1)
6.2.1.3 Model class assessment
117(5)
6.2.2 Bayesian damage localisation
122(1)
6.2.2.1 Probabilistic description of ToF model
122(1)
6.2.2.2 Model parameter estimation
123(2)
6.3 Optimal sensor configuration
125(6)
6.3.1 Value of information for optimal design
126(1)
6.3.2 Expected value of information
127(1)
6.3.2.1 Algorithmic implementation
127(4)
6.4 Summary
131(2)
7 Fast Bayesian Approach for Stochastic Model Updating using Modal Information from Multiple Setups
133(22)
Wang-Ji Yan
Lambros Katafygiotis
Costas Papadimitriou
7.1 Introduction
133(1)
7.2 Probabilistic consideration of frequency-domain responses
134(2)
7.2.1 PDF of multivariate FFT coefficients
134(1)
7.2.2 PDF of PSD matrix
135(1)
7.2.3 PDF of the trace of the PSD matrix
135(1)
7.3 A two-stage fast Bayesian operational modal analysis
136(3)
7.3.1 Prediction error model connecting modal responses and measurements
136(1)
7.3.2 Spectrum variables identification using FBSTA
137(1)
7.3.3 Mode shape identification using FBSDA
138(1)
7.3.4 Statistical modal information for model updating
139(1)
7.4 Bayesian model updating with modal data from multiple setups
139(5)
7.4.1 Structural model class
139(1)
7.4.2 Formulation of Bayesian model updating
140(1)
7.4.2.1 The introduction of instrumental variables system mode shapes
140(1)
7.4.2.2 Probability model connecting `system mode shapes' and measured local mode shape
140(1)
7.4.2.3 Probability model for the eigenvalue equation errors
141(1)
7.4.2.4 Negative log-likelihood function for model updating
142(1)
7.4.3 Solution strategy
142(2)
7.5 Numerical example
144(3)
7.5.1 Robustness test of the probabilistic model of trace of PSD matrix
144(1)
7.5.2 Bayesian operational modal analysis
145(1)
7.5.3 Bayesian model updating
146(1)
7.6 Experimental study
147(5)
7.6.1 Bayesian operational modal analysis
149(1)
7.6.2 Bayesian model updating
150(2)
7.7 Concluding remarks
152(3)
8 A Worked-out Example of Surrogate-based Bayesian Parameter and Field Identification Methods
155(50)
Noemi Friedman
Claudia Zoccarato
Elmar Zander
Hermann G. Matthies
8.1 Introduction
155(2)
8.2 Numerical modelling of seabed displacement
157(7)
8.2.1 The deterministic computation of seabed displacements
157(2)
8.2.2 Modified probabilistic formulation
159(5)
8.3 Surrogate modelling
164(7)
8.3.1 Computation of the surrogate by orthogonal projection
165(4)
8.3.2 Computation of statistics
169(1)
8.3.3 Validating surrogate models
170(1)
8.4 Efficient representation of random fields
171(8)
8.4.1 Karhunen-Loeve Expansion (KLE)
171(2)
8.4.2 Proper Orthogonal Decomposition (POD)
173(6)
8.5 Identification of the compressibility field
179(23)
8.5.1 Bayes' Theorem
179(1)
8.5.2 Sampling-based procedures---the MCMC method
180(5)
8.5.3 The Kalman filter and its modified versions
185(1)
8.5.3.1 The Kalman filter
185(1)
8.5.3.2 The ensemble Kalman filter
186(2)
8.5.3.3 The PCE-based Kalman filter
188(5)
8.5.4 Non-linear filters
193(9)
8.6 Summary, conclusion, and outlook
202(3)
Appendices
205(12)
Appendix A FEM computation of seabed displacements
207(2)
Appendix B Hermite polynomials
209(3)
B.1 Generation of Hermite Polynomials
209(2)
B.2 Calculation of the norms
211(1)
B.3 Quadrature points and weights
211(1)
Appendix C Galerkin solution of the Karhunen Loeve eigenfunction problem
212(4)
Appendix D Computation of the PCE Coefficients by Orthogonal projection
216(1)
Bibliography 217(14)
Index 231
Juan Chiachío-Ruano is an Associate Professor of Structural Engineering at University of Granada (Spain), and a researcher at the Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI). He has devoted his research career to the study and development of Bayesian methods in application to a wide range of Mechanical and Structural Engineering problems. Prior to joining University of Granada, he has developed a significant international research career working at top academic institutions in the UK and the USA.

Manuel Chiachío-Ruano holds a PhD in Structural Engineering (2014) by the University of Granada (Spain). Currently, he is Associate Professor and Head of the Intelligent Prognostics and Cyber-physical Structural Systems Laboratory (iPHMLab) at the University of Granada. He has developed a significant part of his research in collaboration with the California Institute of Technology (USA), the University of Nottingham (UK) and NASA Ames Research Center (USA), during his stays at these institutions.

Shankar Sankararaman received his PhD in Civil Engineering from Vanderbilt University, Nashville, TN, USA, in 2012. Soon after, he joined NASA Ames Research Center, where he developed Machine Learning algorithms and Bayesian methods for system health monitoring, prognostics, decision-making, and uncertainty management. Dr Sankararaman has co-authored a book on prognostics and published over 100 technical articles in international journals and conferences. Presently, Shankar is a scientist at Intuit AI, where he focuses on implementing cutting edge research in products and solutions for Intuits customers.