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Efficient methods by active learning Kriging coupled with variance reduction based sampling methods for time-dependent failure probability

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  • Ling, Chunyan
  • Lu, Zhenzhou
  • Zhu, Xianming

Abstract

For efficiently estimating the time-dependent failure probability, two new methods named as the active learning Kriging (AK) coupled with importance sampling (AK-co-IS) and AK coupled with subset simulation (AK-co-SS) are proposed. The proposed methods are based on the fact that the AK coupled with Monte Carlo simulation (AK-MCS) method has been proved to be a very efficient method. However, for problem with small time-dependent failure probability or long service time, the size of candidate sample pool generated by MCS would be so large that the efficiency of AK-MCS is reduced. Therefore, the AK-co-IS and AK-co-SS are proposed to highly enhance the computational efficiency by greatly reducing the candidate sample pool size. And these two methods reduce the candidate sample pool size respectively by searching the optimal time-dependent design point to increase the ratio of failure samples and converting a rare event simulation problem into sequence of more frequent event ones. Through iteratively constructing the AK model to be convergent by the U-learning function in the IS and SS sample pools, respectively, the computational cost of estimating the time-dependent failure probability would reduce drastically compared with AK-MCS. Several examples are used to illustrate the efficiency and accuracy of the proposed methods.

Suggested Citation

  • Ling, Chunyan & Lu, Zhenzhou & Zhu, Xianming, 2019. "Efficient methods by active learning Kriging coupled with variance reduction based sampling methods for time-dependent failure probability," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 23-35.
    • Handle: RePEc:eee:reensy:v:188:y:2019:i:c:p:23-35
    DOI: 10.1016/j.ress.2019.03.004
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    References listed on IDEAS

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    Cited by:

    1. Cao, Runan & Sun, Zhili & Wang, Jian & Guo, Fanyi, 2022. "A single-loop reliability analysis strategy for time-dependent problems with small failure probability," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    2. Shi, Yan & Lu, Zhenzhou & He, Ruyang & Zhou, Yicheng & Chen, Siyu, 2020. "A novel learning function based on Kriging for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    3. Jiang, Chen & Yan, Yifang & Wang, Dapeng & Qiu, Haobo & Gao, Liang, 2021. "Global and local Kriging limit state approximation for time-dependent reliability-based design optimization through wrong-classification probability," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    4. Qian, Hua-Ming & Li, Yan-Feng & Huang, Hong-Zhong, 2021. "Time-variant system reliability analysis method for a small failure probability problem," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    5. Carlon, André Gustavo & Kroetz, Henrique Machado & Torii, André Jacomel & Lopez, Rafael Holdorf & Miguel, Leandro Fleck Fadel, 2022. "Risk optimization using the Chernoff bound and stochastic gradient descent," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    6. Ni, Pinghe & Li, Jun & Hao, Hong & Yan, Weimin & Du, Xiuli & Zhou, Hongyuan, 2020. "Reliability analysis and design optimization of nonlinear structures," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    7. Ameryan, Ala & Ghalehnovi, Mansour & Rashki, Mohsen, 2022. "AK-SESC: a novel reliability procedure based on the integration of active learning kriging and sequential space conversion method," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    8. Wang, Dapeng & Qiu, Haobo & Gao, Liang & Jiang, Chen, 2021. "A single-loop Kriging coupled with subset simulation for time-dependent reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    9. Jiang, Chen & Qiu, Haobo & Gao, Liang & Wang, Dapeng & Yang, Zan & Chen, Liming, 2020. "EEK-SYS: System reliability analysis through estimation error-guided adaptive Kriging approximation of multiple limit state surfaces," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    10. Xu, Zhaoyi & Saleh, Joseph Homer, 2021. "Machine learning for reliability engineering and safety applications: Review of current status and future opportunities," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    11. Saraygord Afshari, Sajad & Enayatollahi, Fatemeh & Xu, Xiangyang & Liang, Xihui, 2022. "Machine learning-based methods in structural reliability analysis: A review," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    12. Zhao, Zhao & Lu, Zhao-Hui & Zhang, Xuan-Yi & Zhao, Yan-Gang, 2022. "A nested single-loop Kriging model coupled with subset simulation for time-dependent system reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    13. Hao, Peng & Yang, Hao & Wang, Yutian & Liu, Xuanxiu & Wang, Bo & Li, Gang, 2021. "Efficient reliability-based design optimization of composite structures via isogeometric analysis," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    14. Ling, Chunyan & Lu, Zhenzhou & Zhang, Xiaobo, 2020. "An efficient method based on AK-MCS for estimating failure probability function," Reliability Engineering and System Safety, Elsevier, vol. 201(C).

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