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Semi-Bayesian active learning quadrature for estimating extremely low failure probabilities

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  • Dang, Chao
  • Beer, Michael

Abstract

The Bayesian failure probability inference (BFPI) framework provides a sound basis for developing new Bayesian active learning reliability analysis methods. However, it is still computationally challenging to make use of the posterior variance of the failure probability. This study presents a novel method called ‘semi-Bayesian active learning quadrature’ (SBALQ) for estimating extremely low failure probabilities, which builds upon the BFPI framework. The key idea lies in only leveraging the posterior mean of the failure probability to design two crucial components for active learning — the stopping criterion and learning function. In this context, a new stopping criterion is introduced through exploring the structure of the posterior mean. Besides, we also develop a numerical integration technique named ‘hyper-shell simulation’ to estimate the analytically intractable integrals inherent in the stopping criterion. Furthermore, a new learning function is derived from the stopping criterion and by maximizing it a single point can be identified in each iteration of the active learning phase. To enable multi-point selection and facilitate parallel computing, the proposed learning function is modified by incorporating an influence function. Through five numerical examples, it is demonstrated that the proposed method can assess extremely small failure probabilities with desired efficiency and accuracy.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:reensy:v:246:y:2024:i:c:s0951832024001273
    DOI: 10.1016/j.ress.2024.110052
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    References listed on IDEAS

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    1. Li, Guofa & Wang, Tianzhe & Chen, Zequan & He, Jialong & Wang, Xiaoye & Du, Xuejiao, 2023. "RBIK-SS: A parallel adaptive structural reliability analysis method for rare failure events," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    2. 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).
    3. Dang, Chao & Valdebenito, Marcos A. & Wei, Pengfei & Song, Jingwen & Beer, Michael, 2024. "Bayesian active learning line sampling with log-normal process for rare-event probability estimation," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    4. Razaaly, Nassim & Congedo, Pietro Marco, 2020. "Extension of AK-MCS for the efficient computation of very small failure probabilities," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    5. Dawei Zhan & Jiachang Qian & Yuansheng Cheng, 2017. "Pseudo expected improvement criterion for parallel EGO algorithm," Journal of Global Optimization, Springer, vol. 68(3), pages 641-662, July.
    6. Papaioannou, Iason & Geyer, Sebastian & Straub, Daniel, 2019. "Improved cross entropy-based importance sampling with a flexible mixture model," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
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