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Sliced inverse regression-based sparse polynomial chaos expansions for reliability analysis in high dimensions

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  • Pan, Qiujing
  • Dias, Daniel

Abstract

Reliability analysis requires a large number of original model evaluations, especially for high-nonlinear and high-dimensional problems. This could be computationally expensive when a single evaluation is time-consuming, finite element models for example. Metamodeling techniques have been developed for reliability assessments in order to enhance computational efficiency. Polynomial chaos expansions are widely used for metamodel buildings, but suffering from the “curse of dimensionality†. This work proposes an efficient reliability method which combines the sliced inverse regression (SIR) with sparse polynomial chaos expansions (SPCE). The SIR technique is firstly adopted to achieve a dimension reduction by finding a new input vector which reduces the dimension of the original input vector without losing the essential information of model responses. Then a SPCE metamodel is built with respect to the reduced dimensionality by means of the stepwise regression technique. An iteration algorithm is employed to select the optimal metamodel for a given size of design of experiments. Three representative examples with random variables ranging from 6 to 300 are provided for validation, which show great effectiveness and efficiency of the proposed approach, particularly for high-dimensional problems.

Suggested Citation

  • Pan, Qiujing & Dias, Daniel, 2017. "Sliced inverse regression-based sparse polynomial chaos expansions for reliability analysis in high dimensions," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 484-493.
    • Handle: RePEc:eee:reensy:v:167:y:2017:i:c:p:484-493
    DOI: 10.1016/j.ress.2017.06.026
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    References listed on IDEAS

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    1. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    2. Gannoun, Ali & Girard, Stephane & Guinot, Christiane & Saracco, Jerome, 2004. "Sliced inverse regression in reference curves estimation," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 103-122, May.
    3. Song, Shufang & Lu, Zhenzhou & Qiao, Hongwei, 2009. "Subset simulation for structural reliability sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 658-665.
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    5. Xu, Jun & Wang, Ding, 2019. "Structural reliability analysis based on polynomial chaos, Voronoi cells and dimension reduction technique," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 329-340.
    6. Zhou, Yicheng & Lu, Zhenzhou & Yun, Wanying, 2020. "Active sparse polynomial chaos expansion for system reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    7. Yao, Wen & Zheng, Xiaohu & Zhang, Jun & Wang, Ning & Tang, Guijian, 2023. "Deep adaptive arbitrary polynomial chaos expansion: A mini-data-driven semi-supervised method for uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
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    9. Wang, Tianzhe & Chen, Zequan & Li, Guofa & He, Jialong & Liu, Chao & Du, Xuejiao, 2024. "A novel method for high-dimensional reliability analysis based on activity score and adaptive Kriging," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    10. Ding, Jiayi & Zhou, Jianfang & Cai, Wei, 2023. "An efficient variable selection-based Kriging model method for the reliability analysis of slopes with spatially variable soils," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
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    13. 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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