Abstract
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.
Highlights
Computer-intensive optimization problem becomes more and more as the increasing requirement for high-fidelity model in industry area, especially for aerospace engineering
The results show that the proposed Kriging has better generalization ability and adaptability, especially for nonuniform distribution sampling
More and more attention is paid to the improvement of fitting precision as the widely spread and applied surrogate model
Summary
Computer-intensive optimization problem becomes more and more as the increasing requirement for high-fidelity model in industry area, especially for aerospace engineering. It approximates the complicated and time-consuming physical model by building some analytical mathematical model, to reduce the analysis process and smooth the design space It becomes one of the most effective methods for computer-intensive problem and has been widely applied to high-fidelity design and optimization [3]. Kriging is an interpolation method based on statistical theory; the main idea is to evaluate the approximate function of the object based on the dynamic construction of design space to predict the information of unknown points [6, 7]. Chen [20] applied to SRM principle to RBF network study to improve the generalization ability These previous researches indicate that using SRM principle to optimize the parameters of the surrogate model really can improve the fitting precision of surrogate model. This paper proposes an anisotropic basis function parameter optimization method for Kriging based on SRM principle. The influence of the distribution pattern of sample points with uniform distribution and nonuniform distribution is studied
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