Efficient aerodynamic optimization using hierarchical kriging combined with gradient

The gradient information could improve the design efficiency of the original kriging model. A new method combined gradients with Hierarchical Kriging (HK) model is developed in this paper. The model is built in two steps. At first, initial sample points and the gradient with respect to design variables are computed by high-fidelity solvers. Gradient information and a selected step size are used for Taylor approximation to obtain derived sample points. Then these sample point are used for building a low-fidelity kriging model. At last, a high-fidelity model can be obtained by adjusting the low-fidelity using the initial samples. An analytical function test case demonstrates that the gradient enhanced Hierarchical Kriging (GEHK) model has overcome limitations of traditional gradient-based kriging model, and the prediction accuracy of the model can be improved evidently. In the airfoil drag reduction case, the GEHK model improves the optimization efficiency, and could get a better result compared with the ordinary kriging model.