Sparse polynomial chaos expansions for global sensitivity analysis with partial least squares and distance correlation

摘要

Polynomial chaos expansion (PCE) has been proven to be a powerful tool for developing surrogate models in the field of uncertainty and global sensitivity analysis. The computational cost of classical PCE is unaffordable since the number of terms grows exponentially with the dimensionality of inputs. This considerably restricts the practical use of PCE. An efficient approach to address this problem is to build a sparse PCE. Since some basis polynomials in representation are highly correlated and the number of available training samples is small, the sparse PCE obtained by the original least square (LS) regression using these samples may not be accurate. Meanwhile, correlation between the non-influential basis polynomial and the important basis polynomials may disturb the correct selection of the important terms. To overcome the influence of correlation in the construction of sparse PCE, a full PCE of model response is first developed based on partial least squares technique in the paper. And an adaptive algorithm based on distance correlation is proposed to select influential basis polynomials, where the distance correlation is used to quantify effectively the impact of basis polynomials on model response. The accuracy of the surrogate model is assessed by leave-one-out cross validation. The proposed method is validated by several examples and global sensitivity analysis is performed. The results show that it maintains a balance between model accuracy and complexity.