Global response approximation with radial basis functions

Abstract

In this article, a study is performed on the accuracy of radial basis functions (RBFs) in creating global metamodels for both low- and high-order nonlinear responses. The 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 accurate for highly nonlinear responses when the sample size is large. However, for most complex engineering applications only limited numbers of samples can be afforded; it is desirable to know whether the RBF is appropriate in this situation, especially when the augmented RBF has to be used. Because the types of true responses are typically unknown a priori, it is essential for high-fidelity metamodeling to have an RBF or RBFs that are appropriate for linear, quadratic, and higher-order responses. To this end, this study compares a variety of existing basis functions in both non-augmented and augmented forms with various types of responses and limited numbers of samples. This article shows that the augmented RBF models created by Wu’s compactly supported functions are the most accurate for the various test functions used in this study.