二维气动问题中Kriging代理模型精度影响因素

Factors influencing the accuracy of Kriging surrogate model in two-dimensional aerodynamic problem

以二维跨声速临界翼型的阻力特性为对象,探讨样本点数目、Kriging代理模型参数及其类型等对模型精度的影响.阻力系数采用计算流体力学（CFD）方法得到.模型精度的验证采用交叉验证方法,采用平均误差、最大误差和标准交叉验证残差来衡量Kriging代理模型的精度.研究结果表明：1Kriging代理模型预测气动阻力效果较好.2模型精度随样本点的增多而提高,剔除与样本点响应趋势不相符的＂奇异点＂后,模型精度显著提高,平均误差减小5%-38%,最大误差减小13%-77%.3核函数类型对模型精度的影响最大,相关参数次之,回归模型的影响最小.采用高斯相关函数、2阶多项式回归模型,以及合适的相关参数值时,Kriging代理模型的精度最高.

The factors influencing the accuracy of Kriging surrogate model including the number of sample points, the parameters of model and their types, were researched. The drag property of two-dimensional transonic airfoil was used to construct the surrogate model. The computational fluid dynamics （CFD） was employed to compute the drag coefficient. Three kinds of errors , i.e. average error, maximal error and standardized cross-validated residual were employed to measure the accuracy of the Kriging surrogate model while the cross validation was applied as the accuracy validation method. The results obtained are summarized as follows. First, the Kriging surrogate model performs well when predicting the aerodynamic drag of the two-dimensional transonic airfoil. Second, the accuracy of model improves with the increase of sample number, and when the ‘bizarre airfoil’ whose responses based on Kriging surrogate model are opposite with the normal ones are deleted, the accuracy of the model is improved obviously, and the average error and maximal error decrease 5 %-38% and 13%-77% respectively. Third, the model accuracy is mainly affected by type of kernal function, followed by the correlation parameter, while the regression model has little influences. The Kriging surrogate model with Gauss correlation function, second order regression model and optimal correlation parameter has the best accuracy.