Building efficient response surfaces of aerodynamic functions with kriging and cokriging

In this paper, we compare the global accuracy of different strategies to build response surfaces by varying sampling methods and modeling techniques. The aerodynamic test functions are obtained by deforming the shape of a transonic airfoil. For comparisons, a robust strategy for model fit using a new efficient initialization technique followed by a gradient optimization was applied. First, a study of different sampling methods proves that including a posteriori information on the function to sample distribution can improve accuracy over classical space-filling methods such as Latin hypercube sampling. Second, comparing kriging and gradient-enhanced kriging on two- to six-dimensional test cases shows that interpolating gradient vectors drastically improves response-surface accuracy. Although direct and indirect cokriging have equivalent formulations, the indirect cokriging outperforms the direct approach. The slow linear phase of error convergence when increasing sample size is not avoided by cokriging. Thus, the number of samples needed to have a globally accurate surface stays generally out of reach for problems considering more than four design variables.