A trended Kriging model with R-2 indicator and application to design optimization

Abstract

A trended Kriging model is known to improve the overall accuracy and efficiency of surrogate modeling; however, most studies have focused on a non-trended Kriging model because of the difficulty in the identification of a trend from an unknown data set. In the present study, an R-2 indicator for a Kriging surrogate model has been developed to identify the trend from a training data set. Both linear and nonlinear trends are identified with the R-2 indicator using the function analytic values and the function derivatives of the Kriging predictor. The trends identified by the indicator are used to determine the order of the drift function in the trended Kriging model. A trend identification of the Kriging model was validated with various analytic test functions. Subsequently, more practical uses of the R-2 indicator applied to actual responses from the Computational Fluid Dynamics (CFD) analysis of transonic airfoil. In Conclusion, the trended Kriging model can improve overall accuracy of responses if the maximum order of drift function is properly adjusted to the trend of sample space identified by the R-2 indicator.