An efficient parallelized adaptive learning framework for small failure probability analysis

In this study, an efficient parallelized adaptive learning framework is developed for estimating small failure probabilities. The method introduces a parallelized infilling criterion in which pseudo-learning functions, augmented by an influence factor, approximate the impact of newly selected samples on the learning-function values without requiring prior evaluations of the true performance function. An adaptive strategy is further employed to determine the optimal batch size in each iteration. Following the principle of maximizing uncertainty reduction in failure-probability estimation, an error-based learning-function allocation strategy is proposed to dynamically choose the most suitable function from a predefined library. For rare-failure scenarios, a Markov chain Monte Carlo-based importance sampling (MCMC-IS) scheme is adopted, in which a kernel density function is used to construct the IS density from the final failure population generated by MCMC. The effectiveness and robustness of the proposed framework are demonstrated through three numerical benchmarks and a suspension bridge subjected to wind and lane actions, with failure probabilities ranging from 10–5 to 10–9.