An Improved PC-Kriging Method for Efficient Robust Design Optimization

Abstract

The polynomial-chaos-kriging (PC-Kriging) method has been derived as a new uncertainty propagation approach and widely used for robust design optimization in a straightforward manner, of which the statistical moments would be estimated through directly conducting Monte Carlo simulation (MCS) on the PC-Kriging model. However, the computational cost still cannot be negligible because thousands of statistical moment estimations might be performed during robust optimization, especially for highly nonlinear and complicated engineering problems. An analytical statistical moment estimation method is derived for PC-Kriging in this work to reduce the computational cost rather than referring to MCS. Meanwhile, a sequential sampling strategy is applied for PC-Kriging model construction, in which the sample points are not generated all at once, but sequentially allocated in the region with the largest prediction uncertainty to improve the accuracy of PC-Kriging model as much as possible. Through testing on three mathematical examples and an airfoil robust optimization design problem, it is noticed that the improved PC-Kriging method with analytical statistical moment estimation and sequential sampling strategy is more efficient than the traditional ones, demonstrating its effectiveness and advantage.