Probabilistic finite element model updating using bayesian statistics: applications to aeronauticaland mechanical engineering

Physical dimension

Summary / review / table of contents

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.

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 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.

Copies