An efficient semi-analytical extreme value method for time-variant reliability analysis

• Published in: Structural and multidisciplinary optimization Vol. 64; no. 3; pp. 1469 - 1480
• Main Authors: Meng, Zeng, Zhao, Jingyu, Jiang, Chen
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021; Springer Nature B.V
• Subjects: Approximation; Computational efficiency; Computational Mathematics and Numerical Analysis; Computing costs; Cost analysis; Engineering; Engineering Design; Extreme values; Performance evaluation; Product reliability; Reliability analysis; Research Paper; Sampling; Series expansion; Stochastic processes; Taylor series; Theoretical and Applied Mechanics; Extreme value method; Taylor series expansion; Time-variant reliability analysis; Stochastic process discretization
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-021-02934-y

Time-variant reliability analysis plays a vital role in improving the validity and practicability of product reliability evaluation over a specific time interval. Sampling-based extreme value method is the most direct way to implement accurate reliability assessment. Its adoption for time-variant reliability analysis, however, is limited due to the computational burden caused by repeatedly evaluating performance function. This paper proposes a semi-analytical extreme value method to improve the computational efficiency of extreme value method. The time-variant performance function is transformed into dependent instantaneous performance functions in which the stochastic processes are discretized by the expansion optimal linear estimation method to simulate the dependence among different time instants. Each instantaneous function is separately approximated by Taylor series expansion at the most probable point through instantaneous reliability analysis. Based on the approximated performance functions, the computational cost of sampling-based extreme value method is significantly reduced. Results of three numerical examples demonstrate the efficacy of the proposed method.