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A stratified beta-sphere sampling method combined with important sampling and active learning for rare event analysis.

Authors :
Hong, Fangqi
Song, Jingwen
Wei, Pengfei
Huang, Ziteng
Beer, Michael
Source :
Structural Safety. Jan2025, Vol. 112, pN.PAG-N.PAG. 1p.
Publication Year :
2025

Abstract

Accurate and efficient estimation of small failure probability subjected to high-dimensional and multiple failure domains is still a challenging task in structural reliability engineering. In this paper, we propose a stratified beta-spheres sampling method (SBSS) to tackle this task. Initially, the whole support space of random input variables is divided into a series of subdomains by using multiple specified beta-spheres, which is a hypersphere centered in the origin in standard normal space, then, the corresponding samples truncated by beta-spheres are generated explicitly and efficiently. Based on the truncated samples, the real failure probability can be estimated by the sum of failure probabilities of these subdomains. Next, we discuss and demonstrate the unbiasedness of the estimation of failure probability. The proposed method stands out for inheriting the advantages of Monte Carlo simulation (MCS) for highly nonlinear, high-dimensional problems, and problems with multiple failure domains, while overcoming the disadvantages of MCS for rare event. Furthermore, the SBSS method equipped with importance sampling technique (SBSS-IS) is also proposed to improve the robustness of estimation. Additionally, we combine the proposed SBSS and SBSS-IS methods with GPR model and active learning strategy so as to further substantially reduce the computational cost under the desired requirement of estimated accuracy. Finally, the superiorities of the proposed methods are demonstrated by six examples with different problem settings. • A stratified beta-sphere sampling method (SBSS) is first proposed for reliability analysis. • SBSS works well for rare event analysis with high nonlinearity and high dimension. • An important sampling technique is developed to improve the estimated robustness. • Active learning strategy is introduced to further reduce the computational cost. • The superiorities of the developed methods are proved by extensive examples. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
01674730
Volume :
112
Database :
Academic Search Index
Journal :
Structural Safety
Publication Type :
Academic Journal
Accession number :
181410556
Full Text :
https://doi.org/10.1016/j.strusafe.2024.102546