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Generalized Reliability Importance Measure (GRIM) using Gaussian mixture

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  • Kim, Taeyong
  • Song, Junho

Abstract

In structural reliability analysis, it is often desirable to evaluate the relative contributions of random variables to the variability of the limit-state function in the failure domain. Based on the relative contributions, one can effectively reduce the dimension of the reliability problem or obtain useful insight and information. However, existing reliability importance measures, which are available as a by-product of reliability analysis by first-order reliability method (FORM), may not capture the contributions of random variables accurately when the limit-state surface shows a large curvature around the design point or multiple critical subdomains exist in the failure domain. To address the issue, this paper proposes a Generalized Reliability Importance Measure (GRIM) that can deal with multiple critical failure regions, large curvatures of limit-state surfaces and the correlation between the input random variables. By introducing Gaussian mixture and the regional participation factor, the failure domain is divided into several subdomains, and the relative contributions of random variables in each critical domain are evaluated. To facilitate the computations of GRIMs, the cross-entropy-based adaptive importance sampling technique (CE-AIS-GM) is employed to identify the locations of critical subdomains, their relative contributions and corresponding importance vectors. Eight numerical examples covering a variety of component and system reliability problems demonstrate the proposed method and its merits. The test results confirm robust performance against the number of important regions or the dimension. The proposed GRIMs and computational procedure are expected to provide more reliable measures for a wide range of component and system reliability problems. The supporting source code and data are available for download at https://github.com/TyongKim/GRIM.

Suggested Citation

  • Kim, Taeyong & Song, Junho, 2018. "Generalized Reliability Importance Measure (GRIM) using Gaussian mixture," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 105-115.
    • Handle: RePEc:eee:reensy:v:173:y:2018:i:c:p:105-115
    DOI: 10.1016/j.ress.2018.01.005
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    References listed on IDEAS

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    Cited by:

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    3. Papaioannou, Iason & Straub, Daniel, 2021. "Variance-based reliability sensitivity analysis and the FORM α-factors," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    4. Ye, Zhenggeng & Yang, Hui & Cai, Zhiqiang & Si, Shubin & Zhou, Fuli, 2021. "Performance evaluation of serial-parallel manufacturing systems based on the impact of heterogeneous feedstocks on machine degradation," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    5. Lyu, Dong & Si, Shubin, 2020. "Dynamic importance measure for the K-out-of-n: G system under repeated random load," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    6. Yadong Zhang & Chao Zhang & Shaoping Wang & Rentong Chen & Mileta M. Tomovic, 2022. "Performance Degradation Based on Importance Change and Application in Dissimilar Redundancy Actuation System," Mathematics, MDPI, vol. 10(5), pages 1-15, March.
    7. Lyu, Dong & Si, Shubin, 2021. "Importance measure for K-out-of-n: G systems under dynamic random load considering strength degradation," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    8. Ehre, Max & Papaioannou, Iason & Straub, Daniel, 2020. "A framework for global reliability sensitivity analysis in the presence of multi-uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    9. Zhao, Jiangbin & Si, Shubin & Cai, Zhiqiang & Guo, Peng & Zhu, Wenjin, 2020. "Mission success probability optimization for phased-mission systems with repairable component modules," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    10. Cheng, Jin & Wang, Jian & Wu, Xuezhou & Wang, Shuo, 2019. "An improved polynomial-based nonlinear variable importance measure and its application to degradation assessment for high-voltage transformer under imbalance data," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 175-191.

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