Structural and Multidisciplinary Optimization

, Volume 60, Issue 6, pp 2325–2341 | Cite as

A coupled subset simulation and active learning kriging reliability analysis method for rare failure events

  • Chunyan Ling
  • Zhenzhou LuEmail author
  • Kaixuan Feng
  • Xiaobo Zhang
Research Paper


It is widely recognized that the active learning kriging (AK) combined with Monte Carlo simulation (AK-MCS) is a very efficient strategy for failure probability estimation. However, for the rare failure event, the AK-MCS would be time-consuming due to the large size of the sample pool. Therefore, an efficient method coupling the subset simulation (SS) with AK is proposed to overcome the time-consuming character of AK-MCS in case of estimating the small failure probability. The SS strategy is firstly employed by the proposed method to transform the small failure probability into the product of a series of larger conditional failure probabilities of the introduced intermediate failure events. Then, a kriging model is iteratively updated for each intermediate failure event until all the conditional failure probabilities are obtained by the well-trained kriging model, on which the failure probability will be estimated by the product of these conditional failure probabilities. The proposed method significantly reduces the number of evaluating the actual complicated limit state function compared with AK-MCS, and it overcomes the time-consuming character of AK-MCS since the sample pool size of SS is significantly smaller than that of MCS. The presented examples demonstrate the efficiency and accuracy of the proposed method.


Kriging Failure probability Subset simulation Intermediate failure event 


Funding information

This work was supported by the National Natural Science Foundation of China (Grant no. NSFC 51775439). This manuscript is approved by all authors for publication. We would like to declare that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of AeronauticsNorthwestern Polytechnical UniversityXi’anChina

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