A novel approach for multi‐output structural system reliability problem with small failure probability

• Published in: International journal for numerical methods in engineering 2022-12, Vol.123 (23), p.5986-5999
• Main Authors: Qian, Hua‐Ming, Huang, Hong‐Zhong, Li, Yan‐Feng, Wei, Jing
• Format: Article
• Language: English
• Subjects: Correlation analysis; Failure; Finite element method; Gaussian process; Importance sampling; Learning; multiple response Gaussian process; multi‐output structural system; Reliability analysis; Reliability engineering; small failure probability; Structural reliability; System reliability
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.7097

The multi‐output structural system with implicit function widely exists in actual engineering, which refers that the multiple output responses of structural system can be obtained by one experiment or finite element simulation. Considering the correlation of multiple output responses and the small failure probability involved in multi‐output structural system, this article proposes a novel active learning Kriging (ALK) based reliability method for multi‐output structural system by combining multiple response Gaussian process (MRGP) and importance sampling (IS). First, due to the Kriging model can only construct the surrogate model under the single‐output variable, the MRGP model is introduced to substitute the Kriging model and thus the correlation in multiple output responses can be efficiently described by a correlation matrix in MRGP model. Second, for the case that the distance information of new iterated sample point is not considered by the commonly used learning functions (U‐function, EFF‐function and H‐function) in ALK, three improved learning functions are correspondingly proposed. Finally, aiming at the problem that the small failure probability leads to the increasing of candidate sample pool and further results in low computational efficiency, the IS method is combined with the MRGP model to efficiently accomplish the reliability analysis for multi‐output structural system. Several examples are also provided to demonstrate the effectiveness of the proposed method.