Abstract: An efficient method for constructing polynomial chaos expansion (PCE) is proposed. The polynomial coefficients are obtained by regression method using points of monomial cubature rules. The proposed method has two advantages over probabilistic collocation method (PCM) and stochastic response surface method (SRSM). Firstly, when PCE is constructed by using weighted residual method, sampling points of PCM and SRSM are these points of Gauss quadrature, which is exponential growth of the number of dimensions. Monomial cubature rules contrastively reduce integration points. Secondly, PCM and SRSM counts on the heuristic technique to select collocation point due to more points available when the number of dimension increases, at the end the point is selected randomly. Monomial cubature rules only need a few points, which can be sampled entirely. As compared with a mathematical example in which exact solution is available, this method can remarkably reduce the times of simulation and its accuracy is comparable to that of Monte Carlo method. The approach is applied to the tolerance prediction of the formability of a car deck-lid outer panel.

Key words: Monomial cubature rules, Numerical simulation, Polynomial chaos expansion, Probabilistic collocation method, Sheet metal forming, Stochastic response surface method, Tolerance prediction