Time-dependent structural reliability analysis: A single-loop approximate Bayesian active learning quadrature approach

Time-dependent reliability analysis allows for assessing the performance and safety of an engineering structure over its entire lifespan, accounting for inherent randomness and time-varying factors in both structural properties and external loads. However, incorporating the time dimension dramatically increases the computational complexity. To address this challenge, we propose a novel method for computationally expensive time-dependent reliability analysis, which is called ‘single-loop approximate Bayesian active learning quadrature’ (SL-ABALQ). First of all, estimation of the time-dependent failure probability is treated as a Bayesian inference problem with the help of Gaussian process regression. To avoid the intractability of exact Bayesian inference, an approximate Bayesian inference approach is instead developed. In this context, the mean of an approximate posterior failure probability is given, which can serve as a failure probability estimator. Moreover, we also derive an upper bound on the mean absolute deviation of the approximate posterior failure probability, which provides a measure of uncertainty for the failure probability estimator. Second, leveraging the estimator and its associated uncertainty measure, a novel stopping criterion is proposed to determine when the iterative learning process should terminate. Third, two new learning functions are introduced to identity the next best time instant and the sample point given the time instant. The performance of the proposed method is demonstrated by five numerical examples, with comparison to several existing methods. It is shown that our method can reduce the number of performance function evaluations without compromising accuracy.