Uncertainty-aware adaptive Bayesian inference method for structural time-dependent reliability analysis

Time-dependent reliability analysis is critical for assessing the safety of structures throughout their full life cycle. Bayesian active learning methods have recently gained attention in reliability analysis, demonstrating more attractive features than existing active learning methods, e.g., the capability of providing and utilizing the probabilistic uncertainty measures over the failure probability. However, they are only investigated in the context of time-invariant reliability analysis. This study proposes a novel Bayesian active learning method termed ‘Uncertainty-aware Adaptive Bayesian Inference’ (UABI) for time-dependent reliability analysis with small failure probabilities. The time-dependent failure probability integral is first interpreted from a Bayesian inference perspective to quantify the uncertainty arising from the discretization error. The posterior mean and upper-bound posterior standard deviation of time-dependent failure probability are then derived to facilitate the construction of adaptive strategies. Besides, a new hyper-ring decomposition importance sampling technique is developed to numerically approximate the posterior statistics, which can greatly reduce the required sample size. Furthermore, a learning function and two stopping criteria are proposed based on the concept of reducing and judging the numerical uncertainty of the time-dependent failure probability, thereby enabling active learning. The performance of the proposed method is verified by five examples. The proposed method is shown to be able to accurately estimate the time-dependent failure probability, while requiring fewer limit state function calls and less computational time than other state-of-art active learning methods.