耦合梯度与分级Kriging模型的高效气动优化方法

Kriging代理模型中引入梯度信息能够提高模型的预测精度，但常规耦合梯度的方法都有不足之处。本文结合分级Kriging模型，提出了一种变可信度分级Kriging模型耦合梯度（GEHK）信息的新方法。首先利用梯度信息，选取扰动步长得到初始样本点附近的派生点，以派生点拟合出能够预测目标函数趋势的低精度Kriging模型。然后以初始样本点修正该模型得到高精度的Kriging模型。翼型减阻优化设计算例表明，与常规耦合梯度的Kriging模型相比，基于分级Kriging的梯度耦合方法对于扰动步长引入的误差不敏感，明显提高了模型预测精度，优化效率因此提升并使得目标函数值下降得更加迅速。相比Euler解作为低精度数据的常规分级Kriging模型，由梯度信息得到的派生点为模型提供了更准确的全局趋势预测，取得了更好的优化结果。本文方法成功应用于翼型多点减阻优化问题，说明该方法对复杂设计问题有很好的适应性。基于分级Kriging模型的耦合梯度方法克服了常规方法的缺点，提高了模型全局拟合精度，是一种优化效率更高的Kriging方法。

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.