Global sensitivity analysis through advanced ANCOVA decomposition for correlated inputs

Sensitivity analysis methods have been shown to provide useful information on the influence of the variance of model inputs on the variance of the model response. Several methodologies have been devised to effectively capture these influences, particularly in the context of uncorrelated inputs. However, many real-world applications are hindered by the fact that inputs are correlated, a challenge that traditional methods often fail to address effectively. Consequently, a new methodology is proposed that can differentiate between structural and correlated influences for systems with quadratic main and interaction effects, using an advanced ANCOVA (analysis of covariance) approach. This approach is defined by a detailed analytical decomposition of the covariance matrix provided by the approximated model by means of a high dimensional model representation. This decomposition of the variance- and covariance-equations enables a novel allocation of all the derived terms, thus formulating new sensitivity measures. The validity of the proposed methodology is substantiated by means of a comprehensive numerical investigation, which involves the analysis of multiple test functions.