Using Cross-Validation to Design Trend Function in Kriging Surrogate Modeling

Abstract

The kriging method has been widely used in design optimization problems not only because it generates an accurate surrogate model but also because it provides a series of criteria to infill points to find the optimal design. With the purpose of improving the accuracy of surrogate models, a dynamic kriging method was proposed to obtain an optimal trend function instead of the fixed trend function in traditional kriging methods. However, the kriging process variance was set to be the objective function with a constant correlation parameter in the optimization problem of selecting the optimal basis functions in the original dynamic kriging method, which proved to be unsuccessful at finding the optimal basis functions. In this paper, a revised dynamic kriging method, including two branches which are different in the objective function of the optimization problem for trend function (named DK-XV1 and DK-XV2, respectively), is proposed to design the trend function using cross-validation. The results of numerical experiments show that DK-XV1 is the promising dynamic kriging method among the original and revised dynamic kriging methods through the comparisons of the root-mean-square error, error correlation coefficient, and consuming time. An engineering example of high-altitude airship conceptual design shows that the DK-XV1 method is effective in constructing accurate surrogate models in surrogate-based optimization.