Finite Element Model Updating Using a Shuffled Complex Evolution Markov Chain Algorithm

Abstract

AbstractIn this paper, a probabilistic-based evolution Markov chain algorithm is used for updating finite element models. The Bayesian approaches are well-known algorithms used for quantifying uncertainties associated with structural systems and several other engineering domains. In this approach, the unknown parameters and their associated uncertainties are obtained by solving the posterior distribution function, which is difficult to attain analytically due to the complexity of the structural system as well as the size of the updating parameters. Alternatively, Markov chain Monte Carlo (MCMC) algorithms are very popular numerical algorithms used to solve the Bayesian updating problem. These algorithms can approximate the posterior distribution function and obtain the unknown parameters vector and its associated uncertainty. The Metropolis-Hastings (M-H) algorithm, which is the most common MCMC algorithms, is used to obtain a sequence of random samples from a posterior probability distribution. Different approaches are proposed to enhance the performance of the Metropolis-Hastings where M-H depends on a single-chain and random-walk step to propose new samples. The evolutionary-based algorithms are extensively used for complex optimization problems where these algorithms can evolve a population of solutions and keep the fittest solution to the last. In this paper, a population-based Markov chain algorithm is used to approximate the posterior distribution function by drawing new samples using a multi-chain procedure for the Bayesian finite element model updating (FEMU) problem. In this algorithm, the M-H method is combined with the Scuffled Complex Evolution (SCE) strategy to propose new samples where a proposed sample is established through a stochastic move, survival for the fittest procedure, and the complex shuffling process. The proposed SCE-MC algorithm is used for FEMU problems where a real structural system is investigated and the obtained results are compared with other MCMC samplers.KeywordsBayesian model updatingMarkov chain Monte CarloScuffled complex evolutionFinite element modelEvolutionary algorithm