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A hybrid Kriging-based reliability method for small failure probabilities

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  • Chen, Weidong
  • Xu, Chunlong
  • Shi, Yaqin
  • Ma, Jingxin
  • Lu, Shengzhuo

Abstract

The main goal of structural reliability is to determine the failure probability of a structure by considering the randomness of the inputs. When the failure probability is small, the simulation methods may have high computational costs, especially for complicated and time-consuming numerical models. In this paper, a modified algorithm based on Monte Carlo simulations and the Kriging metamodel (AK-MCS) is proposed. The strategy is to replace the initial population with two or more populations. The next best point is identified by the iterative approach based on a point not in the original populations. There are enough candidate points near the performance function, which is important for refining the Kriging model. The modification can deal with multiple failure regions that are characterized by complex, high non-linear limit states. Five examples are provided to illustrate the efficiency of methodology. With reference to five case studies in the literature, satisfactory results and efficiency are obtained by the proposed algorithm.

Suggested Citation

  • Chen, Weidong & Xu, Chunlong & Shi, Yaqin & Ma, Jingxin & Lu, Shengzhuo, 2019. "A hybrid Kriging-based reliability method for small failure probabilities," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 31-41.
    • Handle: RePEc:eee:reensy:v:189:y:2019:i:c:p:31-41
    DOI: 10.1016/j.ress.2019.04.003
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    2. Zhang, Yu & Dong, You & Frangopol, Dan M., 2024. "An error-based stopping criterion for spherical decomposition-based adaptive Kriging model and rare event estimation," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
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    4. Wang, Zeyu & Shafieezadeh, Abdollah, 2020. "On confidence intervals for failure probability estimates in Kriging-based reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
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    6. Wang, Zeyu & Shafieezadeh, Abdollah, 2020. "Real-time high-fidelity reliability updating with equality information using adaptive Kriging," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    7. Shi, Yan & Lu, Zhenzhou & He, Ruyang & Zhou, Yicheng & Chen, Siyu, 2020. "A novel learning function based on Kriging for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    8. Zhang, Yu & Dong, You & Xu, Jun, 2023. "An accelerated active learning Kriging model with the distance-based subdomain and a new stopping criterion for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    9. Li, Guosheng & Ma, Shuaichao & Zhang, Dequan & Yang, Leping & Zhang, Weihua & Wu, Zeping, 2024. "An efficient sequential anisotropic RBF reliability analysis method with fast cross-validation and parallelizability," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    10. Xiao, Mi & Zhang, Jinhao & Gao, Liang, 2020. "A system active learning Kriging method for system reliability-based design optimization with a multiple response model," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    11. Wang, Jinsheng & Xu, Guoji & Li, Yongle & Kareem, Ahsan, 2022. "AKSE: A novel adaptive Kriging method combining sampling region scheme and error-based stopping criterion for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    12. Xiong, Yifang & Sampath, Suresh, 2021. "A fast-convergence algorithm for reliability analysis based on the AK-MCS," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    13. Ling, Chunyan & Lu, Zhenzhou & Zhang, Xiaobo, 2020. "An efficient method based on AK-MCS for estimating failure probability function," Reliability Engineering and System Safety, Elsevier, vol. 201(C).

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