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Asymptotic subset simulation: An efficient extrapolation tool for small probabilities approximation

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  • Rashki, Mohsen
  • Faes, Matthias G.R.
  • Wei, Pengfei
  • Song, Jingwen

Abstract

This study bridges the concepts of subset simulation with asymptotic approximation theory in multinormal integrals for the estimation of small probabilities. To meet this aim, for a sequence of scaled limit state functions (LSFs) with failure probabilities higher than the original LSF, it is found that the proposed asymptotic approximation and subset simulation can be applied within the same framework, and only a few steps of subset simulation could be sufficient to approximate small failure probabilities using extrapolation. The analogy of the formulation of the second-order reliability method (SORM) with the proposed concept is studied and, considering sequential sampling as a search algorithm, shown that the information obtained from a few steps of the design point search process could be enough to approximate the total failure probability of a problem. Solving intricate nonlinear and high-dimensional problems confirms the efficiency and robustness of the proposed framework for reliability analysis of real-world engineering problems with small probabilities.

Suggested Citation

  • Rashki, Mohsen & Faes, Matthias G.R. & Wei, Pengfei & Song, Jingwen, 2025. "Asymptotic subset simulation: An efficient extrapolation tool for small probabilities approximation," Reliability Engineering and System Safety, Elsevier, vol. 260(C).
    • Handle: RePEc:eee:reensy:v:260:y:2025:i:c:s0951832025002352
    DOI: 10.1016/j.ress.2025.111034
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    1. Yuan, Xiukai & Zheng, Weiming & Zhao, Chaofan & Valdebenito, Marcos A. & Faes, Matthias G.R. & Dong, Yiwei, 2024. "Line sampling for time-variant failure probability estimation using an adaptive combination approach," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    2. Chiron, Marie & Genest, Christian & Morio, Jérôme & Dubreuil, Sylvain, 2023. "Failure probability estimation through high-dimensional elliptical distribution modeling with multiple importance sampling," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    3. Shabanian-Poodeh, Mostafa & Hooshmand, Rahmat-Allah & Shafie-khah, Miadreza, 2025. "Reliability-constrained configuration optimization for integrated power and natural gas energy systems: A stochastic approach," Reliability Engineering and System Safety, Elsevier, vol. 254(PA).
    4. Beck, André T. & Rodrigues da Silva, Lucas A. & Miguel, Leandro F.F., 2023. "The latent failure probability: A conceptual basis for robust, reliability-based and risk-based design optimization," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    5. Breitung, Karl, 2024. "The return of the design points," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    6. Dang, Chao & Wei, Pengfei & Faes, Matthias G.R. & Valdebenito, Marcos A. & Beer, Michael, 2022. "Parallel adaptive Bayesian quadrature for rare event estimation," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    7. Zhou, Tong & Peng, Yongbo, 2022. "Reliability analysis using adaptive Polynomial-Chaos Kriging and probability density evolution method," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    8. Valdebenito, Marcos A. & Wei, Pengfei & Song, Jingwen & Beer, Michael & Broggi, Matteo, 2021. "Failure probability estimation of a class of series systems by multidomain Line Sampling," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    9. Breitung, Karl, 2019. "The geometry of limit state function graphs and subset simulation: Counterexamples," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 98-106.
    10. Li, Yan-Fu & Zhao, Wei & Zhang, Chen & Ye, Jiantao & He, Huiru, 2024. "A study on the prediction of service reliability of wireless telecommunication system via distribution regression," Reliability Engineering and System Safety, Elsevier, vol. 250(C).
    11. Wei, Pengfei & Zheng, Yu & Fu, Jiangfeng & Xu, Yuannan & Gao, Weikai, 2023. "An expected integrated error reduction function for accelerating Bayesian active learning of failure probability," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    12. Wang, Lei & Hu, Zhuo & Dang, Chao & Beer, Michael, 2024. "Refined parallel adaptive Bayesian quadrature for estimating small failure probabilities," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    13. Zheng, Weiming & Yuan, Xiukai & Bao, Xiya & Dong, Yiwei, 2025. "Adaptive support vector machine for time-variant failure probability function estimation," Reliability Engineering and System Safety, Elsevier, vol. 253(C).
    14. Dang, Chao & Beer, Michael, 2024. "Semi-Bayesian active learning quadrature for estimating extremely low failure probabilities," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    15. Han, Fucheng & Wang, Wenhua & Zheng, Xiao-Wei & Han, Xu & Shi, Wei & Li, Xin, 2025. "Investigation of essential parameters for the design of offshore wind turbine based on structural reliability," Reliability Engineering and System Safety, Elsevier, vol. 254(PA).
    16. Tang, Xueyang & Cai, Xiaopei & Wang, Yuqi & Wang, Pu & Yang, Fei, 2025. "Advanced VTSDREF for vehicle-turnout system dynamic reliability analysis: Integration of hybrid deep learning and adaptive probability density evolution method," Reliability Engineering and System Safety, Elsevier, vol. 256(C).
    17. Miele, S. & Karve, P. & Mahadevan, S., 2023. "Multi-fidelity physics-informed machine learning for probabilistic damage diagnosis," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    18. Surget, Charles & Dubreuil, Sylvain & Morio, Jérôme & Mattrand, Cécile & Bourinet, Jean-Marc & Gayton, Nicolas, 2025. "A sensitivity analysis based trade-off between probabilistic model identification and statistical estimation," Reliability Engineering and System Safety, Elsevier, vol. 254(PB).
    19. Lu, Yixin & Lu, Zhenzhou, 2025. "A novel cross-entropy-based importance sampling method for cumulative time-dependent failure probability function," Reliability Engineering and System Safety, Elsevier, vol. 253(C).
    20. Subramanian, Abhinav & Mahadevan, Sankaran, 2023. "Probabilistic physics-informed machine learning for dynamic systems," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
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