Non-intrusive uncertainty quantification by combination of reduced basis method and regression-based polynomial chaos expansion

Abstract

In this study, an efficient non-intrusive model reduction scheme is developed for uncertainty quantification using proper orthogonal decomposition and the regression-based non-intrusive polynomial chaos approach. The key idea is to retrieve the optimal orthogonal basis via inexpensive calculations on a coarse mesh and then use them for the fine-scale analysis. The reduced basis approach was applied to a highly nonlinear analytical test function, the 2D RAE2822 airfoil with geometrical uncertainties and the NASA rotor 37 with combined geometrical and operational uncertainties. The numerical results show that the developed model is able to produce acceptable results for the statistical quantities of interest. The computation time of the reduced basis method was found to be much lower than that of the classical polynomial chaos expansion method.