IMPROVED WEIGHTED GRADIENT-ENHANCED KRIGING MODEL FOR HIGH-DIMENSIONAL AERODYNAMIC MODELING PROBLEMS

Weighted gradient-enhanced kriging has been demonstrated to be superior to conventional gradient-enhanced kriging when applied to high-dimensional aerodynamic modeling and optimization problems, through the core idea of summing up a series of submodels with much smaller coloration matrices by appropriate weight coefficients. It avoids the prohibit computational cost associated with directly decomposing the large correlation matrix of a gradient-enhanced kriging, and provides a probable way to ameliorate the “curse of dimensionality”. However, with the increase of model training data, the number of required submodels grows rapidly, resulting in another dilemma that the total computation cost of decomposing all the small matrices could become prohibitive. In the paper, an improved formulation of weighted gradient-enhanced kriging is proposed and provides a method to adaptively determine the best suitable number of gradients to be interpolated for each submodel, saving the computation budget for matrix decomposition as much as possible and reaching a win-win situation for both model accuracy and modeling efficiency. Numerical examples are employed to compare the proposed method with other gradient-enhanced modeling approaches. Results demonstrate the advantage of the proposed method in both prediction accuracy and efficiency. It is also applied to the aerodynamic modeling of an RAE2822 airfoil in transonic regime, to further illustrate its capability to support engineering design problems driven by expensive numerical simulations.