Efficient aerodynamic optimization method using hierarchical Kriging model combined with gradient

It is well-known that the accuracy of Kriging model can be improved when the gradients of objective function are involved in the model. But ordinary methods have some defects. A new method combining gradients with hierarchical Kriging (Gradient Enhanced Hierarchical Kriging, GEHK) model is developed in this paper. New samples are derived by Taylor approximation using gradients and selected steps. Then a low-fidelity Kriging model is built using derived samples. Finally, a high-fidelity model is obtained by adjusting the low-fidelity Kriging with initial samples. Optimization cases of airfoils have proved that the gradient-based GEHK is not sensitive to derived steps and the accuracy of prediction is enhanced. Taking this advantage, GEHK is more efficient than indirect Kriging and performs better in aerodynamic optimization and gets a better result. Compared with standard hierarchical Kriging model, using Euler solutions as low-fidelity data, derived samples provide a better global prediction for building Kriging model and thus GEHK obtains better results. GEHK model has been successfully used in a multipoint drag reduction case, which indicates its ability in complicated design cases. The new method has overcome limitations of traditional gradient-based Kriging model and the prediction accuracy of the model can be improved globally. The optimization is more efficient employing the proposed model.