Dual sampling method for evaluating uncertainty when updating a Bayesian estimation model of a high-speed railway bridge

Abstract

In Bayesian model updating, the parameters and uncertainties of a numerical model are updated with measured values to reproduce the conditions of an existing structure. However, the correlation of updated model parameters makes distortion of the tail space of the joint posterior distribution and uncertainty assessment difficult. To overcome this, a new uncertainty estimation methodology, dual Markov chain Monte Carlo (MCMC) method, is proposed in this study. First, the approximate shape of the joint posterior distribution is estimated and an empirical distribution of the likelihood is obtained by using the MCMC method. Second, the likelihood is transformed by using the obtained empirical distribution, and the tail space is estimated by using the replica exchange Monte Carlo method (REMC). The effectiveness of the proposed methodology is verified in updating a Bayesian structural model of a high-speed railway bridge using bridge acceleration during train passages. The joint posterior distribution of the estimated bridge frequency, modal damping ratio, and support stiffness had a large tail space distortion due to the correlation between each parameter. In general MCMC method, the number of MCMC samples corresponding to tail space is small, making it difficult to estimate the uncertainty. In addition, the model using the lower 5% confidence interval of the posterior distribution, which assumes each parameter to be independent, deviates significantly from the measurement results. On the other hand, the parameter sets expressing the tail space of posterior distribution obtained by proposed dual MCMC are efficiently estimated because the first step information is reflected in the second step sampling process. In addition, experimental results showed that the model updated by the proposed methodology could accurately estimate the resonance speed and evaluate the safety of the measured values while the model updated only by the MCMC method could not accurately estimate.