An improved AK-MCS for reliability analysis by an efficient and simple reduction strategy of candidate sample pool

• Published in: Structures (Oxford) 2022-01, Vol.35, p.373-387
• Main Authors: Liu, Ziyi, Lu, Zhenzhou, Ling, Chunyan, Feng, Kaixuan, Hu, Yingshi
• Format: Article
• Language: English
• Subjects: Candidate sample pool reduction; Failure probability; Kriging; MCS; U-learning function
• ISSN: 2352-0124; 2352-0124
• DOI: 10.1016/j.istruc.2021.10.090

Adaptive Kriging combined with Monte Carlo simulation (AK-MCS) is popularly used to estimate the failure probability, but its candidate sample pool (CSP) size should be large enough to guarantee the accuracy of failure probability estimation, especially for small failure probability. To select training point for updating the Kriging model, AK-MCS needs to traverse the CSP to calculate the U-learning function of every point, which is time-demanding. Thus, an enhanced AK-MCS (shorten as EAK-MCS Ⅰ) is proposed by use of an efficient CSP reduction strategy. In EAK-MCS Ⅰ, the candidate samples are classified into two types, i.e., the samples with accurately judged states and the other samples. Obviously, removing the first type samples from CSP does not need extra computational cost, which has no effect on the precision of estimating failure probability and can improve the efficiency of training Kriging model. Hence, EAK-MCS Ⅰ is more efficient than AK-MCS in estimating failure probability. Additionally, for the risk of misjudging the states of the samples by the Kriging model trained in the reduced CSP for complicated problem, another version of EAK-MCS Ⅰ (shorten as EAK-MCS Ⅱ) is proposed by nesting an adaptive strategy to calibrate the Kriging model. The proposed methods improve the efficiency of AK-MCS and inherit all advantages of AK-MCS.