Adaptive sparse polynomial chaos expansions for global sensitivity analysis based on support vector regression

In the context of uncertainty analysis, Polynomial chaos expansion (PCE) has been proven to be a powerful tool for developing meta-models in a wide range of applications, especially for sensitivity analysis. But the computational cost of classic PCE grows exponentially with the size of the input variables. An efficient approach to address this problem is to build a sparse PCE. In this paper, a full PCE meta-model is first developed based on support vector regression (SVR) technique using an orthogonal polynomials kernel function. Then an adaptive algorithm is proposed to select the significant basis functions from the kernel function. The selection criterion is based on the variance contribution of each term to the model output. In the adaptive algorithm, an elimination procedure is used to delete the non-significant bases, and a selection procedure is used to select the important bases. Due to the structural risk minimization principle employing by SVR model, the proposed method provides better generalization ability compared to the common least square regression algorithm. The proposed method is examined by several examples and the global sensitivity analysis is performed. The results show that the proposed method establishes accurate meta-model for global sensitivity analysis of complex models.