An improved first order approximate reliability analysis method for uncertain structures based on evidence theory

Abstract

In this paper, an improved first order approximate reliability analysis method based on evidence theory is developed to evaluate the uncertain structures reliability. Firstly, the uncertain variables are described by using frame of discernment (FD) and the basic probability assignment (BPA). Secondly, the improved HL-RF (iHL-RF) method and Newton method are used to solve the most possible point(MPP) and the bound points, respectively. Thirdly, the limit-state functions are approximated by first order Taylor series at all key points obtained by most possible point and bound points. Then, based on the above approximate limit-state functions, the extremum analysis of all focal element is performed to solve the reliability measure indexes: the belief measure (Bel) and plausibility measure (Pl). Finally, two numerical examples and two engineering applications are discussed to verify the effectivity of the presented method.

Keywords:

• Structural reliability analysis
• Evidence theory
• First order Taylor series
• Reliability evaluate
• Extremum analysis

Acknowledgments

The authors would also like to thank anonymous reviewers for their valuable comments.

Replication of results

The results presented in this article can be replicated by implementing the data structures and algorithms presented in this article. Because the codes of algorithms are not open source, the authors wish to withhold the code for commercialization purposes.

The conflict of interest statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Grant No.51775057), the Research Foundation of Education Department of Hunan Province (No.20K008), the Hunan Provincial Natural Science Foundation of China (No.2018JJ3279) and Open Fund of Engineering Research Center of Catastrophic Prophylaxis and Treatment of Road & Traffic Safety of Ministry of Education (kfj170401).