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An efficient evidence-based reliability analysis method via piecewise hyperplane approximation of limit state function

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Abstract

For evidence-based reliability analysis, whether a focal element belongs to the failure domain is commonly judged by the corresponding extreme values of a performance function in its response domain. In contrast, in this paper, an efficient method by which the ownership relationship between a focal element and the failure domain is directly determined in uncertain variable domain, is proposed via the piecewise hyperplane approximation of limit state function (LSF). The whole uncertainty domain is divided into several sub uncertainty domains on the defined reference direction. The approximate LSF is constructed by the piecewise hyperplane in each sub uncertainty domain, the belief measure and the plausibility measure of reliability analysis can be directly calculated in uncertainty domain through the approximate piecewise hyperplanes of LSF. The proposed evidence-based reliability analysis method is demonstrated by two numerical examples and two engineering applications.

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Acknowledgements

This work is supported by the National Science Foundation of China (11572115, 11402096) and independent research project of State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University (51475003), and the graduate student research innovation project of Hunan province (CX2016B090). The authors would like to thank the reviewers for their valuable suggestions.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, People’s Republic of China

    Lixiong Cao, Jie Liu, Xu Han, Chao Jiang & Qiming Liu

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  1. Lixiong Cao
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  2. Jie Liu
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  3. Xu Han
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  4. Chao Jiang
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  5. Qiming Liu
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Corresponding author

Correspondence to Jie Liu.

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Highlights

An efficient reliability analysis method is proposed by the piecewise hyperplane approximation of LSF.

The inclusion relationship between a focal element and the failure domain is directly determined in evidence variable domain.

The proposed method improves the accuracy of the Bel and Pl for evidence-based reliability analysis.

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Cao, L., Liu, J., Han, X. et al. An efficient evidence-based reliability analysis method via piecewise hyperplane approximation of limit state function. Struct Multidisc Optim 58, 201–213 (2018). https://doi.org/10.1007/s00158-017-1889-8

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  • DOI: https://doi.org/10.1007/s00158-017-1889-8

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