A unified double-bridging TMCMC method for posterior reliability analysis of structures with monitoring data

To overcome the separation between model updating and reliability evaluation in conventional two-stage posterior reliability analysis, this study proposes an integrated double-bridging transitional Markov chain Monte Carlo (DB-TMCMC) method. Rather than treating Bayesian model updating and reliability estimation as two independent procedures, the proposed method starts from the integral-ratio form of posterior failure probability and constructs a unified sequence of intermediate distributions in the joint prior space of structural parameters and basic random variables. The innovation of the method lies primarily in the unified bridging framework and the associated sequential sampling path, through which likelihood information from monitoring data and failure-event information are introduced in a coupled and adaptive manner within a single TMCMC procedure. Within this framework, a monitoring-data likelihood bridge and a failure-event bridge are incorporated simultaneously, and an effective-sample-size-based adaptive alternating strategy is employed to advance the two bridging processes. A smooth failure-bridging function is further introduced to improve numerical stability and alleviate weight degeneracy during the progressive enforcement of the failure constraint. The method is validated using a five-story shear-type structure, a two-dimensional simply supported truss bridge, and a field case study of the Wangjiabai steel truss bridge. The results show that Bayesian updating based on natural frequencies and mode shapes effectively reduces parameter uncertainty and improves modal prediction accuracy. Monitoring data have a significant influence on structural reliability assessment, and the proposed DB-TMCMC method provides posterior failure probability estimates consistent with benchmark posterior Monte Carlo and sequential TMCMC-Subset Simulation results. In addition, repeated-run statistics and computational-cost comparisons demonstrate that the method enables structural model updating, posterior failure-sample generation, and failure-probability estimation within a single sequential sampling procedure, showing strong applicability to monitoring-data-informed reliability assessment of complex bridge structures.