A Taylor series approach to the robust parameter design of computer simulations using kriging and radial basis function neural networks

Abstract

Robust parameter design is used to identify a system's control settings that offer a compromise between obtaining desired mean responses and minimising the variability about those responses. Two popular combined-array strategies - the response surface model (RSM) approach and the emulator approach - are limited when applied to simulations. In the former case, the mean and variance models can be inadequate due to the high level of nonlinearity within many simulations. In the latter case, precise mean and variance approximations are developed at the expense of extensive Monte Carlo sampling. This paper extends the RSM approach to include nonlinear metamodels, namely kriging and radial basis function neural networks. The mean and variance of second-order Taylor series approximations of these metamodels are generated via the multivariate delta method and subsequent optimisation problems employing these approximations are solved. Results show that improved mean and variance prediction models, relative to the RSM approach, can be attained at a fraction of the emulator approach's cost.