Metamodeling with Radial Basis Functions

Abstract

In this paper, we study the accuracy of global metamodels created with radial basis functions (RBF) for both low- and high -order nonlinear responses. The commonly used response surface methodology (RSM), which typically uses linear or quadratic polynomials, is inappropriate for creating global models for highly nonlinear responses. The RBF, on the other hand, has been shown to be fairly accurate for highly nonlinear responses with large sample size typically in the order of tens of thousand or even millions of design points. However, for most complex engineering applications only a limited number of samples can be afford ed. Since the RBF is less accurate for linear and/or quadratic responses, the augmented RBF has to be adopted with an imposed orthogonality constraint, which may affect the accuracy of RBF models for small sample sizes. Because the types of true responses are usually unknown, it is essential to determine which RBF or RBFs are generally appropriate for various responses including linear, quadratic, and higher-order nonlinear responses. We show in this paper that the augmented RBF models created with Wu’s compactly supported functions are the most accurate for the various test functions used in this study.