Gradient-Enhanced Hierarchical Kriging Model for Aerodynamic Design Optimization

A cokriging model incorporating gradient information and the function value of sample points can reduce the computational cost with a given level of accuracy. In this paper, the hierarchical kriging, a recently proposed cokriging method is employed, and a new method called gradient-enhanced hierarchical kriging (GEHK) is developed. First of all, a low-fidelity kriging model is built using derived samples, which are obtained by Taylor approximation using gradients and selected step sizes. Then a high-fidelity model is built by adjusting the low-fidelity kriging model with initial sample points. The GEHK model is more efficient than the traditional gradient-based cokriging model in the aerodynamic optimization, and could get a better optimum value. Taking the advantage of the modeling strategy, the global accuracy of the GEHK is not sensitive to step sizes, and the accuracy of prediction is enhanced evidently. The GEHK method is able to overcome limitations of traditional gradient-based cokriging models, and the prediction accuracy of the model is improved globally.