A system reliability analysis method combining active learning Kriging model with adaptive size of candidate points

  • Xufeng YangEmail author
  • Caiying Mi
  • Dingyuan Deng
  • Yongshou Liu
Research Paper


This paper investigates the improvement of system reliability analysis (SRA) methods which combine active learning Kriging (ALK) model with Monte Carlo simulation. In this kind of methods, a number of Monte Carlo samples are treated as the candidate points of the ALK models, and the size (or the number) of candidate points vitally affects the efficiency. However, the existing strategies fail to build the Kriging model with the optimal size of candidate points. Therefore, a certain quantity of training points was wasted. To circumvent this drawback, a strategy with an adaptive size of candidate points (ASCP) is exploited and seamlessly integrated into one of the recently proposed ALK model-based SRA method. In this strategy, the optimal size is iteratively predicted and updated according to the predicted information of component Kriging models. After several iterations, the optimal size can be approximately obtained, and the learning process can be executed with an optimal size of candidate points hereafter. Three numerical examples are investigated to demonstrate the efficiency and accuracy of the proposed method.


System reliability analysis Multiple failure modes Active learning Kriging model Adaptive size of candidate points 



active learning Kriging,


adaptive size of candidate points,


system reliability analysis,


component reliability analysis,


First order reliability method,


second order reliability method,


Monte Carlo simulation,


coefficient of variation,


ALK model with truncated candidate region,


component performance function,


design of experiments,


Truncated candidate region.


Funding information

This work is supported by the National Natural Science Foundation of China (Grant No. 51705433, 51475386), the Fundamental Research Funds for the Central Universities (Grant No. 2682017CX028), the Open Project Program of The State Key Laboratory of Heavy Duty AC Drive Electric Locomotive Systems Integration (Grant No. 2017ZJKF04, 2017ZJKF02), and the scholarship of China Scholarship Council.


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Copyright information

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

Authors and Affiliations

  • Xufeng Yang
    • 1
    Email author
  • Caiying Mi
    • 1
  • Dingyuan Deng
    • 2
  • Yongshou Liu
    • 3
  1. 1.School of Mechanical EngineeringSouthwest Jiaotong UniversityChengduPeople’s Republic of China
  2. 2.Shanghai Satellite Engineering InstituteShanghaiPeople’s Republic of China
  3. 3.Department of Engineering MechanicsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China

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