Kriging/RBF-hybrid response surface method for highly nonlinear functions

Abstract

In order to construct a response surface of an unknown function robustly, a hybrid method between the Kriging model and the radial basis function (RBF) networks is proposed in this paper. In the hybrid method, RBF approximates the macro trend of the function and the Kriging model estimates the micro trend. Then, hybrid methods using two types of model selection criteria (MSC): leave-one-out cross-validation and generalized cross-validation for RBF and the ordinary Kriging (OK) model for comparison are applied to three types of one dimensional test problems, in which the accuracy of each response surface is compared by shapes and root mean square errors. As a result, the hybrid models are more accurate than the OK model for highly nonlinear functions because the hybrid models can capture the macro trend of the function properly by RBF, but the OK model cannot. However, because the accuracy of the hybrid method turns down significantly when RBF causes overfitting, stable MSC is required. In addition, the hybrid models can find out the global optimum with a few sample points by using the Kriging model's approximation errors effectively.