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A Multilevel Simulation Method for Time-Variant Reliability Analysis

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

Crude Monte Carlo simulation (MCS) is the most robust and easily implemented method for performing time-variant reliability analysis (TRA). However, it is inefficient, especially for high reliability problems. This paper aims to present a random simulation method called the multilevel Monte Carlo (MLMC) method for TRA to enhance the computational efficiency of crude MCS while maintaining its accuracy and robustness. The proposed method first discretizes the time interval of interest using a geometric sequence of different timesteps. The cumulative probability of failure associated with the finest level can then be estimated by computing corrections using all levels. To assess the cumulative probability of failure in a way that minimizes the overall computational complexity, the number of random samples at each level is optimized. Moreover, the correction associated with each level is independently computed using crude MCS. Thereby, the proposed method can achieve the accuracy associated with the finest level at a much lower computational cost than that of crude MCS, and retains the robustness of crude MCS with respect to nonlinearity and dimensions. The effectiveness of the proposed method is validated by numerical examples.

Suggested Citation

  • Jian Wang & Xiang Gao & Zhili Sun, 2021. "A Multilevel Simulation Method for Time-Variant Reliability Analysis," Sustainability, MDPI, vol. 13(7), pages 1-16, March.
    • Handle: RePEc:gam:jsusta:v:13:y:2021:i:7:p:3646-:d:523968
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    References listed on IDEAS

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    1. Wang, Zhonglai & Liu, Jing & Yu, Shui, 2020. "Time-variant reliability prediction for dynamic systems using partial information," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    2. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    3. Breitung, Karl, 1988. "Asymptotic crossing rates for stationary Gaussian vector processes," Stochastic Processes and their Applications, Elsevier, vol. 29(2), pages 195-207, September.
    4. 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.
    5. Hao Tian & Yuanli Chen & Fangyuan Li, 2015. "A Novel Approach to Evaluate the Time-Variant System Reliability of Deteriorating Concrete Bridges," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-12, December.
    6. 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.
    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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    Cited by:

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    2. Jie Liu & Paul Schonfeld & Jinqu Chen & Yong Yin & Qiyuan Peng, 2021. "Perceived Trip Time Reliability and Its Cost in a Rail Transit Network," Sustainability, MDPI, vol. 13(13), pages 1-22, July.

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