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Probabilistic Finite Element Model Updating Using Bayesian Statistics : Applications to Aeronautical and Mechanical Engineering.

By: Contributor(s): Material type: TextTextPublisher: Newark : John Wiley & Sons, Incorporated, 2016Copyright date: ©2017Edition: 1st edDescription: 1 online resource (245 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781119153009
Subject(s): Genre/Form: Additional physical formats: Print version:: Probabilistic Finite Element Model Updating Using Bayesian StatisticsDDC classification:
  • 620.00151825
LOC classification:
  • TA347.F5.M379 2017
Online resources:
Contents:
Intro -- 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 -- References -- Chapter 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 Laplace´s 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 Method -- 3.8.3 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 -- 6.3 Application 1: Cantilevered Beam -- 6.4 Application 2: Asymmetrical H-Shaped Beam -- 6.5 Application 3: Aircraft GARTEUR Structure -- 6.6 Conclusion -- References -- Chapter 7 Hybrid Monte Carlo Technique for Finite Element Model Updating -- 7.1 Introduction -- 7.2 Hybrid Monte Carlo Method -- 7.3 Properties of the HMC Method -- 7.3.1 Time Reversibility -- 7.3.2 Volume Preservation -- 7.3.3 Energy Conservation -- 7.4 The Molecular Dynamics Algorithm -- 7.5 Improving the HMC -- 7.5.1 Choosing an Efficient Time Step -- 7.5.2 Suppressing the Random Walk in the Momentum -- 7.5.3 Gradient Computation -- 7.6 Application 1: Cantilever Beam.
7.7 Application 2: Asymmetrical H-Shaped Structure -- 7.8 Conclusion -- References -- Chapter 8 Shadow Hybrid Monte Carlo Technique for Finite Element Model Updating -- 8.1 Introduction -- 8.2 Effect of Time Step in the Hybrid Monte Carlo Method -- 8.3 The Shadow Hybrid Monte Carlo Method -- 8.4 The Shadow Hamiltonian -- 8.5 Application: GARTEUR SM-AG19 Structure -- 8.6 Conclusion -- References -- Chapter 9 Separable Shadow Hybrid Monte Carlo in Finite Element Updating -- 9.1 Introduction -- 9.2 Separable Shadow Hybrid Monte Carlo -- 9.3 Theoretical Justifications of the S2HMC Method -- 9.4 Application 1: Asymmetrical H-Shaped Structure -- 9.5 Application 2: GARTEUR SM-AG19 Structure -- 9.6 Conclusions -- References -- Chapter 10 Evolutionary Approach to Finite Element Model Updating -- 10.1 Introduction -- 10.2 The Bayesian Formulation -- 10.3 The Evolutionary MCMC Algorithm -- 10.3.1 Mutation -- 10.3.2 Crossover -- 10.3.3 Exchange -- 10.4 Metropolis-Hastings Method -- 10.5 Application: Asymmetrical H-Shaped Structure -- 10.6 Conclusion -- References -- Chapter 11 Adaptive Markov Chain Monte Carlo Method for Finite Element Model Updating -- 11.1 Introduction -- 11.2 Bayesian Theory -- 11.3 Adaptive Hybrid Monte Carlo -- 11.4 Application 1: A Linear System with Three Degrees of Freedom -- 11.4.1 Updating the Stiffness Parameters -- 11.5 Application 2: Asymmetrical H-Shaped Structure -- 11.5.1 H-Shaped Structure Simulation -- 11.6 Conclusion -- References -- Chapter 12 Conclusions and Further Work -- 12.1 Introduction -- 12.2 Further Work -- 12.2.1 Reversible Jump Monte Carlo -- 12.2.2 Multiple-Try Metropolis-Hastings -- 12.2.3 Dynamic Programming -- 12.2.4 Sequential Monte Carlo -- References -- Appendix A: Experimental Examples -- A.1 Cantilevered Beam -- A.2 H-Shaped Structure Simulation -- A.3 GARTEUR SM-AG19 Structure -- References.
Appendix B: Markov Chain Monte Carlo -- B.1 Introduction -- B.2 Basic Definition of the Markov Chain -- B.3 Invariant Distribution -- B.4 Reversibility and Ergodicity -- References -- Appendix C: Gaussian Distribution -- C.1 Introduction -- C.2 Gaussian Distribution -- C.3 Properties of the Gaussian Distribution -- References -- Index -- EULA.
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Intro -- 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 -- References -- Chapter 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 Laplace´s 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 Method -- 3.8.3 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 -- 6.3 Application 1: Cantilevered Beam -- 6.4 Application 2: Asymmetrical H-Shaped Beam -- 6.5 Application 3: Aircraft GARTEUR Structure -- 6.6 Conclusion -- References -- Chapter 7 Hybrid Monte Carlo Technique for Finite Element Model Updating -- 7.1 Introduction -- 7.2 Hybrid Monte Carlo Method -- 7.3 Properties of the HMC Method -- 7.3.1 Time Reversibility -- 7.3.2 Volume Preservation -- 7.3.3 Energy Conservation -- 7.4 The Molecular Dynamics Algorithm -- 7.5 Improving the HMC -- 7.5.1 Choosing an Efficient Time Step -- 7.5.2 Suppressing the Random Walk in the Momentum -- 7.5.3 Gradient Computation -- 7.6 Application 1: Cantilever Beam.

7.7 Application 2: Asymmetrical H-Shaped Structure -- 7.8 Conclusion -- References -- Chapter 8 Shadow Hybrid Monte Carlo Technique for Finite Element Model Updating -- 8.1 Introduction -- 8.2 Effect of Time Step in the Hybrid Monte Carlo Method -- 8.3 The Shadow Hybrid Monte Carlo Method -- 8.4 The Shadow Hamiltonian -- 8.5 Application: GARTEUR SM-AG19 Structure -- 8.6 Conclusion -- References -- Chapter 9 Separable Shadow Hybrid Monte Carlo in Finite Element Updating -- 9.1 Introduction -- 9.2 Separable Shadow Hybrid Monte Carlo -- 9.3 Theoretical Justifications of the S2HMC Method -- 9.4 Application 1: Asymmetrical H-Shaped Structure -- 9.5 Application 2: GARTEUR SM-AG19 Structure -- 9.6 Conclusions -- References -- Chapter 10 Evolutionary Approach to Finite Element Model Updating -- 10.1 Introduction -- 10.2 The Bayesian Formulation -- 10.3 The Evolutionary MCMC Algorithm -- 10.3.1 Mutation -- 10.3.2 Crossover -- 10.3.3 Exchange -- 10.4 Metropolis-Hastings Method -- 10.5 Application: Asymmetrical H-Shaped Structure -- 10.6 Conclusion -- References -- Chapter 11 Adaptive Markov Chain Monte Carlo Method for Finite Element Model Updating -- 11.1 Introduction -- 11.2 Bayesian Theory -- 11.3 Adaptive Hybrid Monte Carlo -- 11.4 Application 1: A Linear System with Three Degrees of Freedom -- 11.4.1 Updating the Stiffness Parameters -- 11.5 Application 2: Asymmetrical H-Shaped Structure -- 11.5.1 H-Shaped Structure Simulation -- 11.6 Conclusion -- References -- Chapter 12 Conclusions and Further Work -- 12.1 Introduction -- 12.2 Further Work -- 12.2.1 Reversible Jump Monte Carlo -- 12.2.2 Multiple-Try Metropolis-Hastings -- 12.2.3 Dynamic Programming -- 12.2.4 Sequential Monte Carlo -- References -- Appendix A: Experimental Examples -- A.1 Cantilevered Beam -- A.2 H-Shaped Structure Simulation -- A.3 GARTEUR SM-AG19 Structure -- References.

Appendix B: Markov Chain Monte Carlo -- B.1 Introduction -- B.2 Basic Definition of the Markov Chain -- B.3 Invariant Distribution -- B.4 Reversibility and Ergodicity -- References -- Appendix C: Gaussian Distribution -- C.1 Introduction -- C.2 Gaussian Distribution -- C.3 Properties of the Gaussian Distribution -- References -- Index -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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