Time-variant reliability analysis using phase-type distribution-based methods

• Published in: Advances in engineering software (1992) 2024-12, Vol.198, p.103792, Article 103792
• Main Authors: Li, Junxiang, Guo, Xiwei, Cao, Longchao, Zhang, Xinxin
• Format: Article
• Language: English
• Subjects: Extreme value; Phase-type distribution; Stochastic process; Time-invariant reliability methods; Time-variant reliability
• ISSN: 0965-9978
• DOI: 10.1016/j.advengsoft.2024.103792

•The phase-type (PH) distribution-based methods are developed for efficient time-variant reliability analysis.•The extreme value of the stochastic process is approximated as a PH distributed random variable, and the time parameter is treated as a uniformly distributed variable.•The time-variant reliability analysis is transformed into a time-invariant one.•The PH distribution-based approximation strategy is combined with three different time-invariant reliability methods.•The proposed methods show excellent computational efficiency and accuracy in evaluating time-variant reliability. The performance of engineering structures often varies over time due to the randomness and time variability of material properties, environmental conditions and load effects. This paper proposes phase-type (PH) distribution-based methods for efficient time-variant reliability analysis. The core of the proposed methods is to approximate the extreme value of a stochastic process as a PH distributed random variable, and treat the time parameter as a uniformly distributed variable. Consequently, the time-variant reliability problem is transformed into a time-invariant one. Three representative time-invariant reliability methods, first-order reliability method (FORM), importance sampling (IS) and adaptive Kriging (AK) surrogate model-based IS method (AK-IS), are integrated with the PH distribution-based approximation strategy to form the proposed methods, namely PH-FORM, PH-IS and PH-AKIS. The efficiency and accuracy of these methods are demonstrated through three examples. All codes in the study are implemented in MATLAB and provided as supplementary materials.