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A novel learning function of adaptively updating Kriging model for reliability analysis under fuzzy uncertainty

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Abstract

In the existing method combining adaptive Kriging and fuzzy simulation (AK–FS) for estimating the failure possibility, the AK is required to correctly identify the state of each sample point in the candidate sample pool of FS. However, the states of some sample points have no contributions to the accuracy of estimating the failure possibility, and identifying their states by the existing AK–FS only results in a loss of efficiency. Therefore, this paper proposes a new probability learning strategy to improve the efficiency of the existing AK–FS. According to the theory of failure possibility, when taking the product of the failure domain indicator function and the joint membership function as the failure pointer of the point, failure possibility is the maximum, and the corresponding point is called fuzzy design point. Based on the probabilistic prediction property of Kriging, the proposed strategy establishes a global strategy. The probability of the failure indicator at arbitrary candidate point greater than the predicted maximum failure pointer is analytically derived for the single and multiple failure modes, respectively, and this probability represents the degree of the point to be fuzzy design point, thus it can be used to measure the contribution of the point to improve the accuracy. By adaptively adding the points with the largest contribution to the training sample set, the real failure possibility can be approximated gradually. The efficiency and accuracy of the proposed strategy are verified by several examples.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. NSFC 12272300).

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Authors and Affiliations

  1. School of Aeronautics, Northwestern Polytechnical University, **’an, 710072, Shaanxi, China

    Zhuangbo Chen & Zhenzhou Lu

  2. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Kaixuan Feng

Authors
  1. Zhuangbo Chen
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  2. Zhenzhou Lu
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  3. Kaixuan Feng
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Contributions

ZC: Conceptualization, Methodology, Validation, Writing—original draft, and Writing—review and editing. ZL: Conceptualization, Methodology, Validation, Writing—review and editing, and Funding acquisition. KF: Validation.

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Correspondence to Zhenzhou Lu.

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Replication of results

The original code of Example 5.1 is available in the Supplementary Materials.

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Responsible Editor: Hongyi Xu

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Appendix: Common membership function

Appendix: Common membership function

See Table 14.

Table 14 Common membership function
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Chen, Z., Lu, Z. & Feng, K. A novel learning function of adaptively updating Kriging model for reliability analysis under fuzzy uncertainty. Struct Multidisc Optim 66, 135 (2023). https://doi.org/10.1007/s00158-023-03576-y

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