AK-MSS: An adaptation of the AK-MCS method for small failure probabilities

Structural reliability analysis aims to estimate the failure probability of a structure with respect to the performance function. This estimation may be a difficult task when the computation of a structural response requires large computational efforts. Although simulation-based methods can be used directly, they may require a large number of calls to the performance function for small failure probabilities. Metamodels (such as Kriging) that can replace the original performance function can be applied to address the computational costs. Among these methods, the active learning reliability method combining Kriging and Monte Carlo simulation (AK-MCS) is efficient, except for small failure probabilities and system reliability analysis. In this paper, a modified algorithm that combines the AK-MCS and the modified subset simulation (MSS) is proposed to estimate small failure probabilities. The strategy replaces the initial population with a large population that is generated by the MSS. No prior knowledge about the probability level is needed, and the sample size will adaptively change according to the estimation that is obtained in the last iteration and the target coefficient of variation. Therefore, the limit state can be covered by the new population, which is important for refining the Kriging model. The efficiency and accuracy of the proposed algorithm are illustrated using several examples.