Global sensitivity analysis using orthogonal augmented radial basis function

Global sensitivity analysis (GSA) plays an important role in determining how the output behavior is related to the changes in the inputs, which can be utilized to quantify the influence of the inputs and their interactions or eliminate the unessential input parameters. When the computationally expensive analysis model is utilized, the computation of sampling-based GSA is rather a challenging task, and the metamodel based GSA is a promising alternative. This paper proposes an orthogonal augment radial basis function (OA-RBF) method, for estimating a general class of Sobol' indices. To this end, the orthogonal condition of augment RBF is derived first to decouple the impact of polynomial and RBF items. Then analytical formulas for Sobol' indices are obtained based on the proposed OA-RBF metamodel. Five examples are presented to demonstrate the performance of the proposed approach. For all the problems, the proposed approach yields satisfactory results with a significantly reduced computational effort. The results obtained, to some extent, indicate that the approach proposed here can be utilized for GSA of industrial-scale engineering problems.