Efficient Sampling Approaches for Stochastic Response Surface Method

Stochastic response surface methods (SRSM) based on polynomial chaos expansion (PCE) has been widely used for uncertainty propagation. It is necessary to select efficient sampling technique to estimate the PCE coefficients in SRSM. In this paper, the three advanced sampling approaches, namely, Gaussian Quadrature point (GQ), Monomial Cubature Rule (MCR), and Latin Hypercube Design (LID) are introduced and investigated, whose performances are tested through several examples. It is shown that the results of UP for the three sampling approaches show great agreements to those of Monte Carlo simulation. Specifically, GQ yields the most accurate result of UP, followed by MCR and LHD, while MCR shows the best efficiency for lower PCE order.