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An Importance Sampling Framework for Time-Variant Reliability Analysis Involving Stochastic Processes

Author

Listed:
  • Jian Wang

    (School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China)

  • Xiang Gao

    (School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China)

  • Zhili Sun

    (School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China)

Abstract

In recent years, methods were proposed so as to efficiently perform time-variant reliability analysis. However, importance sampling (IS) for time-variant reliability analysis is barely studied in the literature. In this paper, an IS framework is proposed. A multi-dimensional integral is first derived to define the time-variant cumulative probability of failure, which has the similar expression to the classical definition of time-invariant failure probability. An IS framework is then developed according to the fact that time-invariant random variables are commonly involved in time-variant reliability analysis. The basic idea of the proposed framework is to simultaneously apply time-invariant IS and crude Monte Carlo simulation on time-invariant random variables and stochastic processes, respectively. Thus, the probability of acquiring failure trajectories of time-variant performance function is increased. Two auxiliary probability density functions are proposed to implement the IS framework. However, auxiliary PDFs available for the framework are not limited to the proposed two. Three examples are studied in order to validate the effectiveness of the proposed IS framework.

Suggested Citation

  • Jian Wang & Xiang Gao & Zhili Sun, 2021. "An Importance Sampling Framework for Time-Variant Reliability Analysis Involving Stochastic Processes," Sustainability, MDPI, vol. 13(14), pages 1-16, July.
    • Handle: RePEc:gam:jsusta:v:13:y:2021:i:14:p:7776-:d:592867
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    References listed on IDEAS

    as
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    2. Yan Shi & Zhenzhou Lu & Ruyang He, 2020. "Advanced time-dependent reliability analysis based on adaptive sampling region with Kriging model," Journal of Risk and Reliability, , vol. 234(4), pages 588-600, August.
    3. Hawchar, Lara & El Soueidy, Charbel-Pierre & Schoefs, Franck, 2017. "Principal component analysis and polynomial chaos expansion for time-variant reliability problems," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 406-416.
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    5. Sonal, S.D. & Ammanagi, S & Kanjilal, O & Manohar, C.S., 2018. "Experimental estimation of time variant system reliability of vibrating structures based on subset simulation with Markov chain splitting," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 55-68.
    6. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
    7. Du, Weiqi & Luo, Yuanxin & Wang, Yongqin, 2019. "Time-variant reliability analysis using the parallel subset simulation," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 250-257.
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