Bayesian Statistics in Structural Dynamics

This chapter introduces the concept of Bayesian statistics within the context of structural mechanics. Bayesian statistics basically states that the probability of event A happening, given that event B has happened (also known as the posterior probability), is equal to the product of the probability...

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Bibliographic Details
Published inProbabilistic Finite Element Model Updating Using Bayesian Statistics pp. 42 - 64
Format Book Chapter
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 10.11.2016
Subjects
Bayesian methods
Bayes’ rule
finite element model updating
Gaussian approximation
Gibbs sampling
Laplace approximation method
Markov chain Monte Carlo methods
maximum a posteriori parameter estimate
maximum likelihood method
Monte Carlo methods
quasi‐Newton Broyden–Fletcher–Goldfarb–Shanno method
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ISBN9781119153030
1119153034
DOI10.1002/9781119153023.ch3

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Summary:This chapter introduces the concept of Bayesian statistics within the context of structural mechanics. Bayesian statistics basically states that the probability of event A happening, given that event B has happened (also known as the posterior probability), is equal to the product of the probability of event B happening, given that event A has happened (the likelihood function), and the probability of event A happening (the prior), divided by the probability of event B happening (the evidence). In this chapter mass and spring system with a single degree of freedom is studied. The distributions of the measured natural frequency and the mass are known, and the Bayesian technique is formulated to estimate the distribution of the stiffness.
ISBN:9781119153030
1119153034
DOI:10.1002/9781119153023.ch3