Active Learning of Small Failure Probabilities of Highly Nonstationary Geotechnical Systems by Adaptive Bayesian Compressive Sensing and Subset Simulation

Estimating small failure probabilities in complex geotechnical systems with highly nonstationary responses and time-consuming models is a significant challenge. The nonparametric adaptive Bayesian compressive sensing Monte Carlo simulation (ABCS-MCS) has proven to be an effective active learning reliability method for highly nonstationary geotechnical systems. However, when applied to complex geotechnical systems with small failure probabilities, the computational time required for reliability analysis using ABCS-MCS remains prohibitively high. This study develops a novel active learning reliability method using ABCS and subset simulation (SS), termed ABCS-SS, to specifically address this challenge in highly nonstationary geotechnical systems. In ABCS-SS, Bayesian compressive sensing (BCS) is used to construct a response surface for performing SS and is integrated with a learning function that sequentially selects additional sampling points in subsets to improve the accuracy of the reliability analysis until the target accuracy is achieved. Since the candidate sample set generated by SS is much smaller than that by MCS, and samples are more proximate to the failure domain, ABCS-SS significantly enhances the active learning efficiency for small failure probabilities. Moreover, ABCS-SS is directly applicable to geotechnical systems with highly nonstationary responses. Investigations using three highly nonstationary examples demonstrate that ABCS-SS substantially reduces the computational time for reliability analysis of small failure probabilities compared to ABCS-MCS.