| Description |
1 online resource (249 p.) |
| Contents |
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 |
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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 |
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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 |
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3.3.1 The failure prognosis problem -- 3.3.2 Future state prediction -- 3.4 Summary -- 4. Parameter Identification Based on Conditional Expectation -- 4.1 Introduction -- 4.1.1 Preliminaries-basics of probability and information -- 4.1.1.1 Random variables -- 4.1.2 Bayes' theorem -- 4.1.3 Conditional expectation -- 4.2 The Mean Square Error Estimator -- 4.2.1 Numerical approximation of the MMSE -- 4.2.2 Numerical examples -- 4.3 Parameter identification using the MMSE -- 4.3.1 The MMSE filter -- 4.3.2 The Kalman filter -- 4.3.3 Numerical examples -- 4.4 Conclusion |
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Part II Engineering Applications -- 5. Sparse Bayesian Learning and its Application in Bayesian System Identification -- 5.1 Introduction -- 5.2 Sparse Bayesian learning -- 5.2.1 General formulation of sparse Bayesian learning with the ARD prior -- 5.2.2 Bayesian Ockham's razor implementation in sparse Bayesian learning -- 5.3 Applying sparse Bayesian learning to system identification -- 5.3.1 Hierarchical Bayesian model class for system identification -- 5.3.2 Fast sparse Bayesian learning algorithm -- 5.3.2.1 Formulation -- 5.3.2.2 Proposed fast SBL algorithm for stiffness inversion |
| Notes |
Description based upon print version of record |
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5.3.2.3 Damage assessment |
| Form |
Electronic book
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| Author |
Sankararaman, Shankar
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|
Chiachio-Ruano, Manuel
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| ISBN |
9781351869652 |
|
1351869655 |
|
