Piecewise Kriging Model Under Spline Basis

Experimental design is an important branch of mathematical statistics, and its appli-cation field is very extensive. With the rapid development of computer technology, many experiments can be simulated using the computer, which can not only save time and cost,also can overcome the limitations of traditional physical experiments in some areas. The research of computer experiments mainly includes two parts, modeling and constructing design. Among them, in terms of modeling, kriging model is a far-reaching modeling method. The researchers improved the traditional kriging model,and got many more ac-curate prediction methods, which makes the building of the model can adapt to a wider range of response surfaces.This paper firstly introduces some modeling methods of computer experiments in recent years. Then based on the idea of using piecewise function to approximate the true response, this paper constructs the piecewise kriging model under spline basis. The model describes the global trend using a linear combination of a set of selected spline basis functions. Then by the unique piecewise feature of the spline basis, in each piece,a different variance of the Gaussian process is used to describe the error. It can produce more accurate prediction to fit the surfaces with different fluctuations. In addition, for the given data, this paper also gave and proved the best linear unbiased prediction of the true response. The related properties and the estimation of unknown parameters of the model are also discussed. Finally,three examples are given to illustrate the advantages of the proposed model, with respect to the ordinary kriging model. In addition, it can also give a good prediction in different kinds of designs.