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Importance analysis for models with correlated variables and its sparse grid solution

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  • Li, Luyi
  • Lu, Zhenzhou

Abstract

For structural models involving correlated input variables, a novel interpretation for variance-based importance measures is proposed based on the contribution of the correlated input variables to the variance of the model output. After the novel interpretation of the variance-based importance measures is compared with the existing ones, two solutions of the variance-based importance measures of the correlated input variables are built on the sparse grid numerical integration (SGI): double-loop nested sparse grid integration (DSGI) method and single loop sparse grid integration (SSGI) method. The DSGI method solves the importance measure by decreasing the dimensionality of the input variables procedurally, while SSGI method performs importance analysis through extending the dimensionality of the inputs. Both of them can make full use of the advantages of the SGI, and are well tailored for different situations. By analyzing the results of several numerical and engineering examples, it is found that the novel proposed interpretation about the importance measures of the correlated input variables is reasonable, and the proposed methods for solving importance measures are efficient and accurate.

Suggested Citation

  • Li, Luyi & Lu, Zhenzhou, 2013. "Importance analysis for models with correlated variables and its sparse grid solution," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 207-217.
    • Handle: RePEc:eee:reensy:v:119:y:2013:i:c:p:207-217
    DOI: 10.1016/j.ress.2013.06.036
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    References listed on IDEAS

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    1. Borgonovo, E., 2007. "A new uncertainty importance measure," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 771-784.
    2. Castillo, Enrique & Mínguez, Roberto & Castillo, Carmen, 2008. "Sensitivity analysis in optimization and reliability problems," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1788-1800.
    3. Xu, Chonggang & Gertner, George Zdzislaw, 2008. "Uncertainty and sensitivity analysis for models with correlated parameters," Reliability Engineering and System Safety, Elsevier, vol. 93(10), pages 1563-1573.
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    2. Wang, Pan & Lu, Zhenzhou & Zhang, Kaichao & Xiao, Sinan & Yue, Zhufeng, 2018. "Copula-based decomposition approach for the derivative-based sensitivity of variance contributions with dependent variables," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 437-450.

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