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 引用本文: 宋静文, 吕震宙. 输入变量相关情况下重要性测度指标关系[J]. 力学学报, 2014, 46(4): 601-610.
Song Jingwen, Lü Zhenzhou. INVESTIGATION OF THE RELATION OF IMPORTANCE ANALYSIS INDICES FOR MODEL WITH CORRELATED INPUTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(4): 601-610.
 Citation: Song Jingwen, Lü Zhenzhou. INVESTIGATION OF THE RELATION OF IMPORTANCE ANALYSIS INDICES FOR MODEL WITH CORRELATED INPUTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(4): 601-610.

## INVESTIGATION OF THE RELATION OF IMPORTANCE ANALYSIS INDICES FOR MODEL WITH CORRELATED INPUTS

• 摘要: 为了根据不同需求找到输入变量相关情况下最优重要性测度分析方法，非常有必要对现有重要性测度方法之间的关系进行探究比较. 分别以不含交叉项和包含交叉项的二次多项式输出模型为例，解析推导了相关正态输入变量情况下基于协方差分解的重要性测度指标，包括总贡献、结构贡献和相关贡献. 进一步以所推导的解析结论为基础，理论推导了传统基于方差的重要性测度指标与基于协方差分解的重要性测度指标之间的关系.并从特殊二次多项式模型的研究结果对一般模型做出推断，然后从高维模型分解的角度验证所推断的结论，并详细阐述了不同重要性测度指标的优缺点. 最后结合具体算例深入地分析了各指标之间的关系，为输入变量相关情况下结构性能对输入特性的重要性分析与工程设计提供指导.

Abstract: Nowadays, several importance analysis methods have been developed for model with correlated inputs. For choosing the most appropriate analysis methods to meet different requirements, it is necessary to make differences among these existing methods. In this paper, the importance indices, including the total, the structural and the correlative contributions, derived from the covariance decomposition, are firstly derived for the quadratic polynomial without interaction terms and the one with interaction terms. Then, based on these derived analytical solutions, the relation between the traditional variance based method and the newly covariance based method is explored. The results derived from the quadratic polynomials are then extended to general cases, and validated from the point of high dimensional model representation. Three examples are introduced for investigating the relation between the two groups of importance indices, and relative merits of each. The conclusions are instructive and meaningful to importance analysis and engineering design when the model inputs are correlated.

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