Generalized Radial Basis Function-Based High-Dimensional Model Representation Handling Existing Random Data

Abstract

The radial basis function-based high-dimensional model representation (RBF–HDMR) is very promising as a metamodel for high dimensional costly simulation-based functions. But in the modeling procedure, it requires well-structured regular points sampled on cut lines and planes. In practice, we usually have some existing random points that do not lie on cut lines or planes. For this case, RBF–HDMR cannot utilize the information of these random points because of its inner regular sampling process. To utilize the existing random points, this article presents two strategies to build a generalized RBF–HDMR (GRBF–HDMR) model. The GRBF–HDMR model using the error model (EM) strategy, called GRBF–HDMREM, constructs an error RBF model based on the prediction errors at all the sampled points to improve the RBF–HDMR predictions. While the GRBF–HDMR model using the error allocation (EA) strategy, called GRBF–HDMREA, employs the virtual regular points projected from the random points and the estimated virtual responses to update the component RBF predictions, which thereafter improves the overall RBF–HDMR predictions. Numerical experiments on eight functions and an engineering example reveal that the error allocation strategy is more effective in utilizing the random data to improve the RBF–HDMR predictions, since it creates the virtual points that follow the sampling rule in RBF–HDMR and estimates the virtual responses accurately for most cases.