Engineering Response Surface Metamodeling Using Fractional Brownian Fields (and other Kriging Fixes)

Kriging has emerged as the method of choice for metamodeling engineering response surfaces generated via computer simulation. Although Kriging has many desirable characteristics, it also has some undesirable ones. When implemented with a stationary spatial random field (SRF) model, the response prediction reverts to the mean as the predicted location strays from the simulated locations. Moreover, SRF models that give a reasonable predicted surface often give unreasonably narrow prediction intervals. In this talk, we discuss two fixes for these problems. The first uses fractional Brownian fields (FBFs) as the SRF model, and the second (which we call dual-model Kriging) uses two separate SRF models – one to fit the predicted surface and the other to fit the prediction error variance. We argue that FBFs, although not nearly as widely used as stationary SRF models, are very attractive choices for engineering response surface modeling. We also argue that there is little reason to fit the predicted surface and the prediction error variance using a single model, if the response surface is not truly an SRP, and that dual-model Kriging often provides more reasonable quantification of the prediction uncertainty.