基于相关变量分解的重要性测度分析新方法

为了清晰地掌握相关输入变量情况下响应量方差的来源,有必要将重要性测度分离为相关部分和独立部分。通过将相关变量构造为独立变量的线性组合,相关输入变量对功能响应的方差贡献可被分离为相关部分和非相关部分,提出线性响应量情况下基于相关变量分解的重要性测度分析方法。所提方法不仅能将某一相关变量对响应的方差贡献分解为独立部分和相关部分,还可将其相关贡献分离为其与每一相关变量间的相关贡献分量。在此基础上针对非线性响应量的情况建立了基于迭代一阶泰勒展开的重要性求解方法,该方法可在响应的一阶泰勒展开式的方差与原响应方差基本一致的情况下对相关变量进行重要性测度求解。采用所提方法,对文中数值算例和工程应用算例中各相关输入变量的相关部分和独立部分的重要性测度指标进行了求解,证明了文中提出的基于相关变量分解的重要性测度方法是合理、可行的。

A Novel and Rational Method Based on Decomposition of Correlated Variables for Analyzing Importance Measure

Sections 1 and 2 of the full paper explain the method mentioned in the title,which we believe is novel and rational.Their core consists of."For exploring the origin of the variance of the output response in the case that correlated input variables are involved,it is necessary to divide the variance based importance measure(VBIM) into the correlated part and the uncorrelated one.Correlated variables are constructed by the linear combination of independent factors to divide the contributions by correlated input variables into correlated ones and uncorrelated ones,by which the novel method based on the decomposition of correlated variables for analyzing importance measure is proposed.The novel method not only can divide the contribution by an individual input variable into uncorrelated one and correlated one,but also can separate the latter into components of the individual input variable correlated with each of other input variables.For nonlinear responses,an iterative first-order Taylor expansion based method is established,which aims at analyzing the importance measure of correlated variables when the variance of response is consistent with its first-order Taylor expansion." The proposed novel method is employed to obtain respectively the VBIMs of two examples.The calculated results,presented in Tables 1 and 3,and their analysis demonstrate preliminarily that the novel method based on the decomposition of correlated variables for analyzing importance measure is indeed rational.