An efficient Kriging-based subset simulation method for hybrid reliability analysis under random and interval variables with small failure probability

  • Mi Xiao
  • Jinhao ZhangEmail author
  • Liang Gao
  • Soobum Lee
  • Amin Toghi Eshghi
Research Paper


This paper proposes an efficient Kriging-based subset simulation (KSS) method for hybrid reliability analysis under random and interval variables (HRA-RI) with small failure probability. In this method, Kriging metamodel is employed to replace the true performance function, and it is smartly updated based on the samples in the first and last levels of subset simulation (SS). To achieve the smart update, a new update strategy is developed to search out samples located around the projection outlines on the limit-state surface. Meanwhile, the number of samples in each level of SS is adaptively adjusted according to the coefficients of variation of estimated failure probabilities. Besides, to quantify the Kriging metamodel uncertainty in the estimation of the upper and lower bounds of the small failure probability, two uncertainty functions are defined and the corresponding termination conditions are developed to control Kriging update. The performance of KSS is tested by four examples. Results indicate that KSS is accurate and efficient for HRA-RI with small failure probability.


Hybrid reliability analysis under random and interval variables Small failure probability Subset simulation Kriging metamodel Uncertainty 


Funding information

This research was financially supported by the National Natural Science Foundation of China [grant numbers 51675196 and 51721092] and the Program for HUST Academic Frontier Youth Team.


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Copyright information

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

Authors and Affiliations

  1. 1.State Key Laboratory of Digital Manufacturing Equipment and TechnologyHuazhong University of Science and TechnologyWuhanChina
  2. 2.Department of Mechanical EngineeringUniversity of Maryland, Baltimore CountyBaltimoreUSA

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