TY - JOUR

T1 - Reliability and reliability sensitivity analysis of structure by combining adaptive linked importance sampling and Kriging reliability method

AU - Liu, Fuchao

AU - Wei, Pengfei

AU - Zhou, Changcong

AU - Yue, Zhufeng

N1 - Funding information: This work is supported by National Natural Science Foundation of China (Nos. 51905430 , 51608446 ). Also, the Fundamental Research Fund for Central Universities (No. 3102018zy011 ) is gratefully acknowledged. The second author would also like to acknowledge the supports of Alexander von Humboldt Foundation of Germany and the Top International University Visiting Program for Outstanding Young scholars of Northwestern Polytechnical University.

PY - 2020/4

Y1 - 2020/4

N2 - The application of reliability analysis and reliability sensitivity analysis methods to complicated structures faces two main challenges: small failure probability (typical less than 10−5) and time-demanding mechanical models. This paper proposes an improved active learning surrogate model method, which combines the advantages of the classical Active Kriging – Monte Carlo Simulation (AK-MCS) procedure and the Adaptive Linked Importance Sampling (ALIS) procedure. The proposed procedure can, on the one hand, adaptively produce a series of intermediate sampling density approaching the quasi-optimal Importance Sampling (IS) density, on the other hand, adaptively generate a set of intermediate surrogate models approaching the true failure surface of the rare failure event. Then, the small failure probability and the corresponding reliability sensitivity indices are efficiently estimated by their IS estimators based on the quasi-optimal IS density and the surrogate models. Compared with the classical AK-MCS and Active Kriging – Importance Sampling (AK-IS) procedure, the proposed method neither need to build very large sample pool even when the failure probability is extremely small, nor need to estimate the Most Probable Points (MPPs), thus it is computationally more efficient and more applicable especially for problems with multiple MPPs. The effectiveness and engineering applicability of the proposed method are demonstrated by one numerical test example and two engineering applications.

AB - The application of reliability analysis and reliability sensitivity analysis methods to complicated structures faces two main challenges: small failure probability (typical less than 10−5) and time-demanding mechanical models. This paper proposes an improved active learning surrogate model method, which combines the advantages of the classical Active Kriging – Monte Carlo Simulation (AK-MCS) procedure and the Adaptive Linked Importance Sampling (ALIS) procedure. The proposed procedure can, on the one hand, adaptively produce a series of intermediate sampling density approaching the quasi-optimal Importance Sampling (IS) density, on the other hand, adaptively generate a set of intermediate surrogate models approaching the true failure surface of the rare failure event. Then, the small failure probability and the corresponding reliability sensitivity indices are efficiently estimated by their IS estimators based on the quasi-optimal IS density and the surrogate models. Compared with the classical AK-MCS and Active Kriging – Importance Sampling (AK-IS) procedure, the proposed method neither need to build very large sample pool even when the failure probability is extremely small, nor need to estimate the Most Probable Points (MPPs), thus it is computationally more efficient and more applicable especially for problems with multiple MPPs. The effectiveness and engineering applicability of the proposed method are demonstrated by one numerical test example and two engineering applications.

KW - Active learning Kriging model

KW - Adaptive linked importance sampling

KW - Reliability analysis

KW - Sensitivity analysis

KW - Small failure probability

UR - http://www.scopus.com/inward/record.url?scp=85083308393&partnerID=8YFLogxK

U2 - 10.1016/j.cja.2019.12.032

DO - 10.1016/j.cja.2019.12.032

M3 - Article

AN - SCOPUS:85083308393

VL - 33

SP - 1218

EP - 1227

JO - Chinese journal of aeronautics

JF - Chinese journal of aeronautics

SN - 1000-9361

IS - 4

ER -