Kernel Parameter Optimization for Kriging Based on Structural Risk Minimization Principle

An improved kernel parameter optimization method based on Structural Risk Minimization (SRM) principle is proposed to enhance the generalization ability of traditional Kriging surrogate model. This article first analyses the importance of the generalization ability as an assessment criteria of surrogate model from the perspective of statistics and proves the applicability to Kriging. Kernel parameter optimization method is used to improve the fitting precision of Kriging model. With the smoothness measure of the generalization ability and the anisotropy kernel function, the modified Kriging surrogate model and its analysis process are established. Several benchmarks are tested to verify the effectiveness of the modified method under two different sampling states: uniform distribution and nonuniform distribution. The results show that the proposed Kriging has better generalization ability and adaptability, especially for nonuniform distribution sampling.