An adaptive method fusing the kriging model and multimodal importance sampling for profust reliability analysis

Abstract

Profust reliability analysis is investigated in this article. The main aim is to address problems with very small failure probabilities. First, a single-layer multimodal importance sampling (MMIS) method based on the most probable points (MPPs) in the fuzzy failure region is proposed. Secondly, to reduce function calls, an adaptive method fusing kriging model and MMIS is developed. In this method, a surrogate fuzzy failure region (SFFR) based on the kriging prediction information is defined. The MPPs in the SFFR are explored, the important samples are generated, the optimal training point is chosen, and the kriging model and the SFFR are updated. The learning process is executed iteratively until the SFFR converges to the true one. To find all MPPs and maintain unbiasedness, an intelligent multimodal optimization method based on multi-objective optimization is introduced. Four case studies are used to verify the advantages of the proposed method.

KEYWORDS:

• Adaptive kriging model
• profust reliability analysis
• multimodal optimization
• multimodal importance sampling

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 51705433]; Sichuan Science and Technology Program [grant number 2021YFG0178].