AK-PDEMi: a failure-informed enrichment algorithm for improving the AK-PDEM in reliability analysis

Authors

T. Zhou, S. Marelli, B. Sudret, Y. Peng

Abstract

A failure-informed enrichment algorithm is devised to improve the performance of the existing adaptive Kriging-probability density evolution method (AK-PDEM) for reliability analysis. This improved method is named the AK-PDEMi.

Contrary to empirically prescribing the sample size of representative points in the existing AK-PDEM, the representative point set in the AK-PDEMi is sequentially enriched by new sets of representative points generated by a failure-informed enrichment scheme, which aims to sequentially making fine partitions of the key sub-regions where the representative points make critical contributions to the failure probability. In this regard, a double-loop configuration is devised: the inner loop adaptively refines the accuracy of Kriging model to reduce the Kriging-induced error, and the outer loop involves the failure-informed enrichment process to alleviate the PDEM-associated discretization error.
The outer and inner loops are complementary and proceed sequentially until both of their convergence criteria are satisfied.

Three numerical examples are studied and comprehensive comparisons are made between the proposed AK-PDEMi and other conventional reliability algorithms. Results show that the AK-PDEMi shows remarkable advantage over the existing AK-PDEM.