基于方差的相关输入变量重要性测度分析新方法

A Novel Method for Analyzing Variance Based Importance Measure of Correlated Input Variables

为了清晰地掌握相关输入变量情况下响应量方差的来源,非常有必要将基于方差的重要性测度(VBIM)分离为相关部分和独立部分。为此,在二阶非线性回归的基础上,提出了一种适用于非线性响应量的相关变量重要性分析的新方法。一个输入变量对响应量方差的相关贡献由该变量与每一个剩余变量两两相关的贡献分量组成,所以又进一步提出了一种概念简单有效的求解相关贡献分量的方法,并在此基础上定义了重要性矩阵,以便清晰地表达相关变量对响应量方差贡献的各个分量。数值算例和工程应用算例中,各相关输入变量的重要性测度分析的结果表明:本文方法可以在二次非线性响应量情况下合理分解相关变量的相关贡献和独立贡献;对于更复杂的非线性响应量情况,通过将所提方法中的二次非线性回归扩展为更合理的近似模型,可以得到重要性分析的高精度结果。

To explore the origin of the variance of the output response in cases where the correlated input variables are in- volved, it is necessary to divide the variance based importance measure （VBIM） into correlated and uncorrelated contributions. For this purpose, a novel method adaptable for the nonlinear output responses is proposed based on second order nonlinear regression. The correlated contribution is composed of the components of the individual input variable correlated with each of the other input variables. An effective method simple in concept is further proposed to decompose the correlated contribution into its components, based on which an importance matrix is defined for explicitly exposing the contribution com- ponents of the correlated input variable to the variance of the output response. The VBIMs of the numerical and engineering examples show that the proposed novel method can accurately decompose the contribution of the correlated input variables to the variance of the second order nonlinear output response. For output models more complicated than the second order nonlinear output response, the VBIM decomposition with high precision can be obtained by extending the second order nonlinear regression to a more reasonable approximation of the response.