A new phase-type distribution-based method for time-dependent system reliability analysis

ABSTRACT

It remains a grand challenge to handle time-dependent system reliability with stochastic process due to the complexity and the high computational cost. In this work, a new phase-type (PH) distribution-based method is proposed for time-dependent system reliability analysis. The PH distribution-based strategy is incorporated with the adaptive Kriging (AK) surrogate model to make up the new PH-AK method. In the PH stage, the main concern of the method is to obtain the extreme value distribution of the stochastic process, which is approximated as a random variable with PH distribution. Moreover, the time parameter is treated as a uniform random variable. Therefore, the time-dependent system reliability analysis is transformed into a time-independent one. In the AK stage, the AK surrogate model is then employed for efficient reliability analysis. And the Metropolis-Hastings algorithm is adopted for generating samples of the extreme value based on the probability density function of the PH distribution. Four examples are utilized to illustrate the effectiveness of the PH-AK method, and results show that the proposed method can efficiently and accurately analyze the time-dependent system reliability.

KEYWORDS:

• Time-dependent system reliability
• stochastic process
• phase-type distribution
• adaptive Kriging surrogate model
• extreme value distribution

Acknowledgements

The authors sincerely thank the editor and anonymous reviewers for their constructive comments on this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Replication of results

We state that the results presented in this paper can be reproduced by the codes provided by the authors upon reasonable request.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [nos. 11832013 and 11572134], Natural Science Foundation of Hubei Province [no. 2024AFB235], Hubei Provincial Department of Education Science and Technology Research Project [no. Q20221714], and the Opening Foundation of Hubei Key Laboratory of Digital Textile Equipment [nos. DTL2023019 and DTL2022012].

Notes on contributors

Junxiang Li

Junxiang Li received Ph.D. degrees from the Department of Mechanics at Huazhong University of Science and Technology, Wuhan, China. He is currently a lecturer with School of Mechanical Engineering and Automation, Wuhan Textile University. His research interests mainly focus on time-dependent reliability analysis.

Jianqiao Chen

Jianqiao Chen received his B.A. degree in 1982 from Huazhong University of Science and Technology, Wuhan, China, and his M.A. and Ph.D. degrees in mechanical engineering, respectively, from Nagoya University, Japan, in 1985 and 1988. He is a professor in Department of Mechanics at Huazhong University of Science and Technology, Wuhan, China. His research area is optimum design of composite structures, structural reliability analysis and optimization algorithm.

Xinxin Zhang

Xinxin Zhang received Ph.D. degrees from China University of Geosciences in Wuhan. He is currently a lecturer in School of Mechanical Engineering and Automation at Wuhan Textile University, Wuhan, China. His research interests are reliability analysis and robot control system.

Zijun Wu

Zijun Wu was born in China in 1985. He is an associate professor in School of Mechanical Engineering and Automation at Wuhan Textile University, Wuhan, China. His research area is topology optimization and numerical methods.

Lianqing Yu

Lianqing Yu received the Ph.D. degree in School of Mechanical Science and Engineering from Huazhong University of Science and Technology, Wuhan, China, in 2007. He is currently working with Wuhan Textile University. His primary research interests include mechatronics technology and modern textile equipment.