An Adaptive Markov Chain Monte Carlo Method for Bayesian Finite Element Model Updating

摘要

In this paper, an adaptive Markov Chain Monte Carlo (MCMC) approach for Bayesian finite element model updating is presented. This approach is known as the Adaptive Hamiltonian Monte Carlo (AHMC) approach. The convergence rate of the Hamiltonian/Hybrid Monte Carlo (HMC) algorithm is high due to its trajectory which is guided by the derivative of the posterior probability distribution function. This can lead towards high probability areas in a reasonable period of time. However, the HMC performance decreases when sampling from posterior functions of high dimension and when there are strong correlations between the uncertain parameters. The AHMC approach, a locally adaptive version of the HMC approach, allows efficient sampling from complex posterior distribution functions and in high dimensions. The efficiency and accuracy of the AHMC method are investigated by updating a real structure.