TY - GEN
T1 - Bayesian finite element model updating using a population markov chain monte carlo algorithm
AU - Sherri, M.
AU - Boulkaibet, I.
AU - Marwala, T.
AU - Friswell, M. I.
N1 - Publisher Copyright:
© 2021, The Society for Experimental Mechanics, Inc.
PY - 2021
Y1 - 2021
N2 - Bayesian methods have become very popular in the area of finite element model updating (FEMU) in the last decade, where these methods are considered as powerful tools in quantifying the uncertainties associated with the modelling and the experimental processes. Based on Bayes’ theorem, the posterior distribution function can be employed to describe the modelling and the experimental uncertainties while an improved version of the finite element model (FEM) is obtained by solving the posterior formulation. Unfortunately, an analytical solution of the posterior distribution function may not be available due to the complexity of the system as well as the size of the unknown parameters. Alternatively, Markov Chain Monte Carlo (MCMC) methods are very useful stochastic tools that can be employed to solve complex posterior functions and provide approximate solutions. The Metropolis-Hastings (M-H) method is the most common MCMC approach that has been frequently used to approximate distribution functions, where the M-H approach gained its simplicity from using random walk steps to define new candidates. Unfortunately, the performance of the M-H method decreases with the complexity of the modelled systems as well as the number of the uncertain parameters. Several techniques have been proposed to improve the performance of the M-H method such as introducing an adaptation procedure to improve the candidates. In this paper, an evolutionary approach, known as the Population Markov Chain Monte Carlo (Pop-MCMC) method, is adopted to improve the performance of the MCMC algorithms. In this approach, multiple chains are run in parallel and information exchange among these parallel chains are incorporated for the exploration of the search space, while a Metropolis-Hastings criterion is used to accept or reject the candidates for each chain. In this paper, the Pop-MCMC method is presented in detail while the performance of this method is investigated by updating two structural examples.
AB - Bayesian methods have become very popular in the area of finite element model updating (FEMU) in the last decade, where these methods are considered as powerful tools in quantifying the uncertainties associated with the modelling and the experimental processes. Based on Bayes’ theorem, the posterior distribution function can be employed to describe the modelling and the experimental uncertainties while an improved version of the finite element model (FEM) is obtained by solving the posterior formulation. Unfortunately, an analytical solution of the posterior distribution function may not be available due to the complexity of the system as well as the size of the unknown parameters. Alternatively, Markov Chain Monte Carlo (MCMC) methods are very useful stochastic tools that can be employed to solve complex posterior functions and provide approximate solutions. The Metropolis-Hastings (M-H) method is the most common MCMC approach that has been frequently used to approximate distribution functions, where the M-H approach gained its simplicity from using random walk steps to define new candidates. Unfortunately, the performance of the M-H method decreases with the complexity of the modelled systems as well as the number of the uncertain parameters. Several techniques have been proposed to improve the performance of the M-H method such as introducing an adaptation procedure to improve the candidates. In this paper, an evolutionary approach, known as the Population Markov Chain Monte Carlo (Pop-MCMC) method, is adopted to improve the performance of the MCMC algorithms. In this approach, multiple chains are run in parallel and information exchange among these parallel chains are incorporated for the exploration of the search space, while a Metropolis-Hastings criterion is used to accept or reject the candidates for each chain. In this paper, the Pop-MCMC method is presented in detail while the performance of this method is investigated by updating two structural examples.
KW - Bayesian method
KW - Evolutionary algorithm
KW - Finite element model updating
KW - Population Markov chain Monte Carlo
KW - Posterior distribution function
UR - http://www.scopus.com/inward/record.url?scp=85092255715&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-47709-7_24
DO - 10.1007/978-3-030-47709-7_24
M3 - Conference contribution
AN - SCOPUS:85092255715
SN - 9783030477080
T3 - Conference Proceedings of the Society for Experimental Mechanics Series
SP - 259
EP - 269
BT - Special Topics in Structural Dynamics and Experimental Techniques, Volume 5 - Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020
A2 - Epp, David S.
PB - Springer
T2 - 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020
Y2 - 10 February 2020 through 13 February 2020
ER -