Probabilistic finite element model updating using Bayesian statistics / / Tshilidzi Marwala and Ilyes Boulkaibet, Sondipon Adhikari

• Record Nr.: UNINA9910166635403321
• Autore: Marwala Tshilidzi <1971->
• Pubbl/distr/stampa: Chichester, [England] : , : Wiley, , 2017; ©2017
• ISBN: 1-119-15301-8; 1-119-15300-X; 1-119-15302-6
• Descrizione fisica: 1 online resource (245 p.)
• Disciplina: 620.001/51825
• Soggetti: Finite element method; Bayesian statistical decision theory; Engineering - Mathematical models
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
• Nota di contenuto: Title Page ; Copyright; Contents; Acknowledgements; Nomenclature ; Chapter 1 Introduction to Finite Element Model Updating ; 1.1 Introduction; 1.2 Finite Element Modelling; 1.3 Vibration Analysis; 1.3.1 Modal Domain Data; 1.3.2 Frequency Domain Data; 1.4 Finite Element Model Updating; 1.5 Finite Element Model Updating and Bounded Rationality; 1.6 Finite Element Model Updating Methods; 1.6.1 Direct Methods; 1.6.2 Iterative Methods; 1.6.3 Artificial Intelligence Methods; 1.6.4 Uncertainty Quantification Methods; 1.7 Bayesian Approach versus Maximum Likelihood Method; 1.8 Outline of the Book; ReferencesChapter 2 Model Selection in Finite Element Model Updating ; 2.1 Introduction; 2.2 Model Selection in Finite Element Modelling; 2.2.1 Akaike Information Criterion; 2.2.2 Bayesian Information Criterion; 2.2.3 Bayes Factor; 2.2.4 Deviance Information Criterion; 2.2.5 Particle Swarm Optimisation for Model Selection; 2.2.6 Regularisation; 2.2.7 Cross-Validation; 2.2.8 Nested Sampling for Model Selection; 2.3 Simulated Annealing; 2.4 Asymmetrical H-Shaped Structure; 2.4.1 Regularisation; 2.4.2 Cross-Validation; 2.4.3 Bayes ; Factor and Nested Sampling; 2.5 Conclusion; References; Chapter 3 Bayesian Statistics in Structural Dynamics 3.1 Introduction; 3.2 Bayes ́Rule; 3.3 Maximum Likelihood Method; 3.4 Maximum a Posteriori Parameter Estimates; 3.5 Laplaceś Method; 3.6 Prior, Likelihood and Posterior Function of a Simple Dynamic Example; 3.6.1 Likelihood Function; 3.6.2 Prior Function; 3.6.3 Posterior Function; 3.6.4 Gaussian Approximation; 3.7 The Posterior Approximation; 3.7.1 Objective Function; 3.7.2 Optimisation Approach; 3.7.3 Case Example; 3.8 Sampling Approaches for Estimating Posterior Distribution; 3.8.1 Monte Carlo Method; 3.8.2 Markov Chain Monte Carlo Method3.8.3 Simulated Annealing; 3.8.4 Gibbs Sampling; 3.9 Comparison between Approaches; 3.9.1 Numerical Example; 3.10 Conclusions; References; Chapter 4 Metropolis-Hastings and Slice Sampling for Finite Element Updating ; 4.1 Introduction; 4.2 Likelihood, Prior and the Posterior Functions; 4.3 The Metropolis-Hastings Algorithm; 4.4 The Slice Sampling Algorithm; 4.5 Statistical Measures; 4.6 Application 1: Cantilevered Beam; 4.7 Application 2: Asymmetrical H-Shaped Structure; 4.8 Conclusions; References; Chapter 5 Dynamically Weighted Importance Sampling for Finite Element Updating 5.1 Introduction; 5.2 Bayesian Modelling Approach; 5.3 Metropolis-Hastings (M-H) Algorithm; 5.4 Importance Sampling; 5.5 Dynamically Weighted Importance Sampling; 5.5.1 Markov Chain; 5.5.2 Adaptive Pruned-Enriched Population Control Scheme; 5.5.3 Monte Carlo Dynamically Weighted Importance Sampling; 5.6 Application 1: Cantilevered Beam; 5.7 Application 2: H-Shaped Structure; 5.8 Conclusions; References; Chapter 6 Adaptive Metropolis-Hastings for Finite Element Updating ; 6.1 Introduction; 6.2 Adaptive Metropolis-Hastings Algorithm