A screening-based gradient-enhanced Kriging modeling method for high-dimensional problems

Abstract

• A novel gradient-enhanced Kriging modeling method which benefits from the merits of feature selection is proposed. • An empirical evaluation rule is presented to balance the model accuracy and modeling efficiency. • The proposed method is demonstrated and validated by five numerical benchmarks and an airfoil optimal shape design. • Results show that the proposed method can provide an alternative way for approximating high-dimensional problems. By exploring the auxiliary information from gradients, the accuracy of Kriging model can be improved. However, the dramatically increased time for model training tends to be unaffordable. Therefore, a novel gradient-enhanced Kriging modeling method which utilizes only a partial set of gradients, is developed in this article. Within the framework of this method, a balance between model accuracy and modeling efficiency can be achieved. More specifically, the influence of each input variable on output is estimated and ranked by feature selection technique. Then an empirical evaluation rule is proposed to facilitate the selection of gradients. Five representative numerical benchmarks from 10-D to 30-D and an airfoil optimal shape design with 18 variables are used for validation. Results show that when compared with the conventional Gradient-enhanced Kriging, the modeling time of the proposed method is significantly reduced, while the loss of accuracy is negligible. As a consequence, the proposed surrogate modeling method can provide an alternative way for approximating high-dimensional problems.