Adaptive hybrid modeling method based on CV-Hypercube

Abstract

As common surrogate models, Kriging and RBF models have been widely used in various fields. Although the Kriging model and the RBF model have their own advantages, when the problems are complex and diverse, a single Kriging or RBF model usually cannot meet the requirements of global approximation. Luckily, the Kriging and the RBF model have good complementarity in performance. In view of this, an adaptive hybrid modeling method (AHM-CVH) based on cross-validation hypercube of Kriging and RBF is proposed in this paper. The CVH adaptive sampling strategy first generates a hypercube centered on the sample point with the largest cross-validation error, then candidate points are randomly sampled in the hypercube, and finally get a new sample point which is farthest from the center and surrounding samples. Eight benchmark functions ranging from 2 to 6 dimensions and an engineering example are validated, and the results show that the AHM-CVH method is superior to the single Kriging or RBF models in performance, and has the characteristics of high accuracy and strong stability.