A Bayesian bridge model update with complex uncertainty under high-speed train passages

Bayesian structural model updating is an important technique to achieve digital twin with uncertainty. However, complexly distorted tails of the joint posterior probability density function (PDF) are not easy to estimate when a correlation exists between model parameters. Estimating the lower confidence bound of the joint posterior PDF requires several samples at the tails of the PDF. However, this task is difficult to achieve because the Markov chain Monte Carlo (MCMC) method concentrates on the samples near the expected value. Thus, to estimate the distorted tails of the joint posterior, the authors develop a new methodology called dual sampling, comprising two-step MCMCs. The second step sampling complements the samples around the tail of the joint posterior PDF, which are insufficient in the first step conventional MCMC method. The proposed method is applied to the maximum acceleration data of an Italian high-speed railway bridge.