Probabilistic finite element model updating using Bayesian statistics : applications to aeronautical and mechanical engineering

✍ Scribed by Adhikari, Sondipon; Boulkaibet, Ilyes; Marwala, Tshilidzi

• Publisher: John Wiley & Sons
• Year: 2016
• Tongue: English
• Leaves: 241
• Category: Library

✦ Synopsis

Probabilistic Finite Element Model Updating Using Bayesian Statistics: Applications to aeronautical and Mechanical Engineering Tshilidzi Marwala and Ilyes Boulkaibet, University of Johannesburg, South Africa Sondipon Adhikari, Swansea University, UK Covers the probabilistic finite element model based on Bayesian statistics with applications to aeronautical and mechanical engineering Finite element models are used widely to model the dynamic behaviour of many systems including in electrical, aerospace and mechanical engineering. The book covers probabilistic finite element model updating, achieved using Bayesian statistics. The Bayesian framework is employed to estimate the probabilistic finite element models which take into account of the uncertainties in the measurements and the modelling procedure. The Bayesian formulation achieves this by formulating the finite element model as the posterior distribution of the model given the measured data within the context of computational statistics and applies these in aeronautical and mechanical engineering. Probabilistic Finite Element Model Updating Using Bayesian Statistics contains simple explanations of computational statistical techniques such as Metropolis-Hastings Algorithm, Slice sampling, Markov Chain Monte Carlo method, hybrid Monte Carlo as well as Shadow Hybrid Monte Carlo and their relevance in engineering. Key features: -Contains several contributions in the area of model updating using Bayesian techniques which are useful for graduate students. -Explains in detail the use of Bayesian techniques to quantify uncertainties in mechanical structures as well as the use of Markov Chain Monte Carlo techniques to evaluate the Bayesian formulations. The book is essential reading for researchers, practitioners and students in mechanical and aerospace engineering. Read more...

Abstract: Probabilistic Finite Element Model Updating Using Bayesian Statistics: Applications to aeronautical and Mechanical Engineering Tshilidzi Marwala and Ilyes Boulkaibet, University of Johannesburg, South Africa Sondipon Adhikari, Swansea University, UK Covers the probabilistic finite element model based on Bayesian statistics with applications to aeronautical and mechanical engineering Finite element models are used widely to model the dynamic behaviour of many systems including in electrical, aerospace and mechanical engineering. The book covers probabilistic finite element model updating, achieved using Bayesian statistics. The Bayesian framework is employed to estimate the probabilistic finite element models which take into account of the uncertainties in the measurements and the modelling procedure. The Bayesian formulation achieves this by formulating the finite element model as the posterior distribution of the model given the measured data within the context of computational statistics and applies these in aeronautical and mechanical engineering. Probabilistic Finite Element Model Updating Using Bayesian Statistics contains simple explanations of computational statistical techniques such as Metropolis-Hastings Algorithm, Slice sampling, Markov Chain Monte Carlo method, hybrid Monte Carlo as well as Shadow Hybrid Monte Carlo and their relevance in engineering. Key features: -Contains several contributions in the area of model updating using Bayesian techniques which are useful for graduate students. -Explains in detail the use of Bayesian techniques to quantify uncertainties in mechanical structures as well as the use of Markov Chain Monte Carlo techniques to evaluate the Bayesian formulations. The book is essential reading for researchers, practitioners and students in mechanical and aerospace engineering

✦ Table of Contents

Content: 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 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.

✦ Subjects

Finite element method;Bayesian statistical decision theory;Engineering;Mathematical models;TECHNOLOGY & ENGINEERING;Engineering (General);TECHNOLOGY & ENGINEERING;Reference