Application of generalised equivalent extreme-value event in structural system reliability analysis

Abstract

To alleviate the difficulty of combination explosion, in this work, a generalised equivalent extreme-value event is presented to the problem of multi-component simultaneous failure in system reliability analysis, where m components in total l components are failed simultaneously. Firstly, the generalised equivalent extreme-value event is formulated with rigorous mathematical derivation for single boundary problem. Secondly, based on a mathematical transformation, the generalised equivalent extreme-value event is extended to double boundaries problem. Thirdly, by introducing the point estimation method (PEM) and the principle of maximum entropy to calculate the first four-order statistical moments and the failure probability of the equivalent performance function, an easy-to-implement method is proposed, which is capable of solving the multi-component simultaneous failure problem of static and dynamic systems. Finally, the feasibility of the proposed method is verified through a mathematical example and two engineering examples. The comparison to the Monte Carlo simulation shows that the proposed method is of high precision and high efficiency.

Keywords:

• Structural system reliability
• equivalent extreme-value event
• generalised equivalent extreme-value event
• multi-component simultaneous failure
• principle of maximum entropy
• point estimation method
• double boundaries problem

Acknowledgements

The authors also would like to appreciate Professor Yiannis Tsompanakis from the Technical University of Crete and two anonymous reviewers for their vital and insightful suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Grant No. 51678092) and NSFC-JSPS China-Japan Scientific Cooperation Project (No. 51611140123).