Bayesian finite element model updating based on Markov chain population competition

The traditional Markov chain Monte Carlo(MCMC） simulation method is inefficient and difficult to converge in high dimensional problems and complicated posterior probability density.In order to overcome these shortcomings, a Bayesian finite element model updating algorithm based on Markov chain population competition was proposed. First, the differential evolution algorithm was introduced in the traditional method of Metropolis-Hastings (MH) random walk algorithm.Based on the interaction of different information carried by Markov chains in the population，optimization suggestions were obtained to approach the objective function quickly. It solves the defect of sampling retention in the updating process of high-dimensional parameter model. Then, the competition algorithm was introduced, which has constant competitive incentives and a built-in mechanism for losers to learn from winners. Higher precision was obtained by using fewer Markov chains, which improves the efficiency and precision of model updating. Finally, a numerical example of finite element model updating of a truss structure was used to verify the proposed algorithm.Compared with the results of standard MH algorithm, the proposed algorithm can quickly update the high-dimensional parameter model with high accuracy and good robustness to random noise. It provides a stable and effective method for finite element model updating of large-scale structure considering uncertainty.