Importance ranking of correlated variables in one analysis

This paper addresses the problem of ranking correlated random variables according to relative importance. The importance of a variable derives from its influence on the variability of the response from a model. Applications include any input–output model for which response derivatives are available from each response analysis. Structural analysis models, i.e., finite element models, represent the specific motivation for this paper. The response derivatives are collected in a vector and transformed into a standardized parameter space. Points along that vector are transformed back to the original parameter space and utilized for the purpose of model insights and parameter ranking. Comparisons are made with the first-order Sobol sensitivity index, which requires sampling instead of the proposed single-analysis approach. Results suggest that the proposed importance measure matches the first-order Sobol index in many situations. However, for pure multiplicative “interaction” models, the first-order Sobol index tends to be anchored at the zero-correlation case. In contrast, the proposed measures are sensitive to correlation and the effect of correlation can be significant.