Fractional Universal Kriging Metamodel

Abstract

In this study, a Kriging-based metamodel is proposed that can be used instead of the simulation model for complex problems where data generation with a simulation model may be costly. In this new model structure, which is proposed for cases where the drift function structure of the Universal Kriging meta-model is not known. A power function of the variables that can also take fractional values is used instead of the first and second order regression models used as the drift function in the Universal Kriging metamodel. The predictive power of this metamodel, which is called Fractional Universal Kriging metamodel, has been investigated by experimentally computational analysis. Validation analysis reveals that the Fractional Universal Kriging metamodels have superior predictive power with respect to Mean Squared Error and Maximum Squared Error performance measures. Thus, in the case that the input-output relationship of the simulation model can be expressed with a power function that includes the effects of higher order and different from the quadratic polynomial case, Fractional Universal Kriging metamodels are proposed as a new metamodel approach.