多输出性能下的重要性测度指标及其求解方法

针对基于马氏距离的重要性测度存在的问题,提出了基于谱分解加权摩尔彭罗斯马氏距离的重要性测度指标,通过构造多输出协方差阵的广义逆矩阵以及谱分解的策略,有效解决了协方差阵求逆奇异情况以及由于未能充分考虑多输出之间的相互关系而导致的错误识别重要变量的问题,克服了基于马氏距离指标的局限性。数值算例与工程算例结果表明:所提重要性测度可以更加准确地获得输入变量对结构系统多输出性能随机取值特征贡献的排序,从而为可靠性设计提供充分的信息。

Global sensitivity analysis for multiple outputs and their solutions

Aiming at solving the existing drawbacks of indices of the Mahalanobis distance, an importance measure based on the Moore-Penrose Mahalanobis distance weighted by spectral decomposition was proposed. Through building the generalized matrix inversion of covariance matrix of multi-output and the spectral decomposition, the problems that the covariance matrix was be inversed and misidentification for lacking the adequate consideration about the relation among the multiple outputs were solved. Thus, the limitations of indices of Mahalanobis distance were overcome. The results of numerical examples and engineer instance show that the proposed importance measurement can accurately get the effects of input variables on the integrated performance of multi-output structure system, thus providing effective information for reliability design.