A novel active learning reliability method combining adaptive Kriging and spherical decomposition-MCS (AK-SDMCS) for small failure probabilities

Abstract

Structural reliability analysis for small failure probabilities remains a challenging task, despite the significant progress made by the active learning reliability methods (ALRMs) represented by AK-MCS (ALRMs combining adaptive Kriging and Monte Carlo simulations). In order to address this issue, advanced ALRMs with improved computational efficiency than AK-MCS have been proposed, however at the expense of sacrificing the generality and simplicity of AK-MCS. Therefore, a novel ALRM combining adaptive Kriging and spherical decomposition-MCS (AK-SDMCS) was proposed to alleviate the computational cost and preserve the advantages of AK-MCS simultaneously. The key of AK-SDMCS lies in the spherical decomposition-MCS (SDMCS), which not only decomposes the computationally intensive active learning of AK-MCS into a series of easy-to-compute active learning in the divided subsets but also reduces the total number of candidate samples by focusing the sampling region on the most probable failure regions (MPFRs) and adaptively allocating samples in the divided subregions. As a result, AK-SDMCS significantly alleviates the computational cost of active learning of Kriging model. Since AK-SDMCS is built in the framework of AK-MCS, the advantages of AK-MCS can be preserved. Besides, the active learning strategy is modified to further increase the computational efficiency. Thus, AK-SDMCS provides an efficient, easy-to-implement and generalized option for reliability analysis of small failure probabilities. The application and efficiency of AK-SDMCS are demonstrated by three academic examples.