Model Accuracy Evaluation of Compactly Supported RBFs

Abstract

In this study, the effectiveness of assessing the accuracy of radial basis functions (RBFs) at design points is evaluated. The RBF, particularly in the augmented form, has been shown to be appropriate for creating approximation functions for linear, quadratic, and higher- order nonlinear responses even with relatively small size of design samples. Since an RBF model passes exactly through design points, it has no fitting error at design points. Therefore, commonly used statistical parameters in polynomial-regression such as the F- statistics, R 2 , and RMSE cannot be used to assess its model accuracy. Since obtaining additional samples for many complex engineering applications is expensive, it is desirable to have some knowledge of the model accuracy based on evaluations on design points to select the best RBF model(s). In this paper, the effectiveness of using statistical parameter R 2 for prediction (R 2 prediction) is evaluated for two RBFs that are identified from a previous study to be highly accurate models. Mathematical functions and real engineering applications are used to generate different types of responses. The results show that the R 2 prediction does not generally work well and should be used with caution especially when the number of design points is small and/or the number of design variables is large.