Implementation of supervised principal component analysis for global sensitivity analysis of models with correlated inputs

Global Sensitivity Analysis (GSA) plays a significant role in quantifying the tangible impact of model inputs on the uncertainty of response variable. As GSA results are strongly affected by correlated inputs, several studies have considered this issue, but most of them are computationally expensive, labor-intensive, and difficult to implement. Accordingly, this paper puts forward a novel regression-based strategy based on the Supervised Principal Component Analysis (SPCA), benefiting from the Reproducing Kernel Hilbert Space. Indeed, by conducting one kind of variance-based sensitivity analysis, a renowned method exclusively customized for models with orthogonal inputs, on SPCA regression, the impact of the correlation structure of input variables is considered. The ability of the suggested technique is evaluated with five test cases as well as three hydrologic and hydraulic models, and the results are compared with those obtained from the correlation ratio method; Taken as a benchmark solution, which is a robust but quite complicated approach in terms of programming. It is found that the proposed method satisfactorily identifies the sensitivity ordering of model inputs. Furthermore, it is proved in this study that the performance of the proposed approach is also supported by the total contribution index in the derived covariance decomposition equation. Moreover, the proposed method compared with the correlation ratio method, is found to be computationally efficient and easy to implement. Overall, the proposed scheme is appropriate for high dimensional, quite strong nonlinear or expensive models with correlated inputs, whose coefficient of determination between the original model and regression-based SPCA model is larger than 0.33.