Accelerating subset simulation with surrogate model ensuring unbiased failure probability estimation

Yuanzhuo Ma; Chuang Li; Binbin Li

doi:10.1088/3050-2454/ae202a

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Accelerating subset simulation with surrogate model ensuring unbiased failure probability estimation

Papers | 更新时间：2026-02-13

- Accelerating subset simulation with surrogate model ensuring unbiased failure probability estimation
- 一种确保无偏失效概率估计的代理模型加速子集模拟
- Journal of Reliability Science and Engineering Issue 4, Pages: 1-19(2025)
- 作者机构：
  
  School of Renewable Energy, Hohai University, Changzhou, People’s Republic of China
  School of Electrical and Power Engineering, Hohai University, Nanjing, People’s Republic of China
  State Key Laboratory of Biobased Transportation Fuel Technology, ZJU-UIUC Institute, Zhejiang University, Haining, People’s Republic of China
- 作者简介：
  
  [ "Yuanzhuo Ma is an associate professor at the School of Renewable Energy, Hohai University. He is engaged in research in the fields of uncertainty quantification, structural reliability, and robust design optimization, the research results of which have been applied to the reliability, robustness design, evaluation, and ensurance of large-scale wind turbines, thermal protection systems for aerospace aircraft, aviation turbine engines, multi-body systems for weapons, and electronic devices such as mobile phones. He has presided over 7 projects including the National Natural Science Foundation of China, the Rapid Support Project for Equipment Development, the Natural Science Foundation of Jiangsu Province, and the Postdoctoral Foundation. More than 40 academic papers have been published in well-known domestic and international journal, and one Chinese academic monograph has been published in the field of structural reliability and optimization. Previously worked as a reliability engineer at Shanghai Huawei Technologies Co., LTD Youth editorial board member of JRSE, reviewer for RESS and other journals." ]
  [ "Chuang Li is a postgraduate student at the School of Electrical and Power Engineering, Hohai University. He specializes in structural optimization of fluid machinery, with core research focusing on the development of novel subset simulation optimization methods and their practical application in fluid machinery structures. His research objects mainly include wind turbine blades and gear structures. He has published one SCI paper in the related research field, and remains dedicated to advancing efficient and reliable optimization methodologies for fluid machinery structural design." ]
  [ "Binbin Li is a tenured associate professor (2025-) in the Zhejiang University/University of Illinois at Urbana-Champaign Institute (ZJUI) at the Zhejiang University, International Campus. He obtained his PhD in Civil Engineering from the University of California-Berkeley in 2016. Before joining ZJU, he worked as a research associate at the University of Liverpool from 2016–2018. Dr Li’s research focuses on developing innovative statistical methods to address safety, sustainability and resilience issues of the built civil infrastructure systems including bridges, buildings, and road/rail networks. His specific interests include Bayesian system identification, operational modal analysis, infrastructural network modeling and field test, for structure and infrastructure health management and resilience assessment." ]
- 基金信息：
- DOI：10.1088/3050-2454/ae202a
  CLC：
- Received：23 July 2025，
  
  Revised：2025-10-17，
  
  Accepted：17 November 2025，
  
  Online First：08 December 2025，
  
  Published：2025
- 稿件说明：
移动端阅览
Yuanzhuo Ma, Chuang Li, Binbin Li. Accelerating subset simulation with surrogate model ensuring unbiased failure probability estimation[J]. Journal of Reliability Science and Engineering, 2025, (4): 1-19.
DOI：

Yuanzhuo Ma, Chuang Li, Binbin Li. Accelerating subset simulation with surrogate model ensuring unbiased failure probability estimation[J]. Journal of Reliability Science and Engineering, 2025, (4): 1-19. DOI： 10.1088/3050-2454/ae202a.

摘要

代理模型可有效加速失效概率的估计过程，但当代理模型未能准确刻画真实失效面时，往往会引入估计偏差，这在高维度和/或强非线性的实际工程问题中尤为常见。借鉴马尔可夫链蒙特卡罗（MCMC）方法中的延迟接受（delayed acceptance，DA）思想，本文提出了一种将子集模拟（subset simulation，SuS）与代理模型相结合的新策略，称为 DA-SuS 方法。该方法将 MCMC 中的接受过程分解为三个阶段，其中候选样本首先由代理模型进行判别；若在该阶段被拒绝，则不再进入后续计算。该延迟接受机制不会破坏 MCMC 的详细平衡条件，即无论代理模型精度如何，其平稳分布始终保持为目标分布，从而保证了 MCMC 估计量的渐近无偏性。尽管该策略在一定程度上会降低统计效率，但由于仅对具有较高失效域概率的候选样本调用真实模型进行评估，从而显著减少了计算开销，整体计算效率得到提升。进一步地，本文引入了三种改进策略，包括 Kriging 代理模型的自适应训练、基于误判误差引导的接受准则以及链级更新方案。通过三个基准算例对 DA-SuS 算法的性能进行了验证，并与传统 SuS 及其结合代理模型的改进方法进行了对比。结果表明，所提出的 DA-SuS 方法即使在高维和强非线性问题中，仍能够实现失效概率的无偏估计，但其统计效率和计算效率在一定程度上依赖于代理模型的质量。

Abstract

Surrogate models can accelerate the failure probability estimation

but at the risk of biasedness when the surrogate does not capture the real failure surface

which is typical for real engineering problems with high dimensionality and/or high nonlinearity. Following the idea of delayed acceptance (DA) in Markov Chain Monte Carlo (MCMC)

a new strategy of combining subset simulation (SuS) and surrogate model is developed in this paper

named as DA-SuS. It decomposes the acceptance process in MCMC into three steps

in which the candidate samples are first checked by the surrogate model. If rejected by the surrogate model

the sample is no more considered. This DA does not destroy the detailed balance of MCMC

i.e.

the stationary distribution will always be the targeted one

no matter how bad the surrogate model is. Consequently

the asymptotic unbiasedness of MCMC estimator is preserved. Although the statistical efficiency deteriorates slightly

the DA brings computational savings because only those candidates with high probability in the failure domain are eventually evaluated by the true model

thus increasing the overall computational efficiency. Three improvement strategies are further introduced

including adaptive training of Kriging model

misjudgment error-guided acceptance and chain-wise updating scheme. The performance of DA-SuS algorithm is demonstrated via three benchmark examples

and compared with conventional SuS and its variants equipped with surrogate models. The proposed DA-SuS algorithm yields an unbiased estimation of the failure probability

even in the case with high dimensionality and nonlinearity

although its statistical and computational efficiency depend on the quality of the surrogate.

关键词

Keywords

references

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