Design search and optimisation using radial basis functions with regression capabilities

Abstract

Modern design search and optimisation (DSO) processes that involve the use of expensive computer simulations commonly use surrogate modelling techniques, where data is collected from planned experiments on the expensive codes and then used to build meta-models. Such models (often termed response surface models or RSMs) can be built using many methods that have a variety of capabilities. For example, simple polynomial (often linear or quadratic) regression curves have been used in this way for many years. These lack the ability to model complex shapes and so are not very useful in constructing global RSM’s for non-linear codes such as the Navier Stokes solvers used in CFD - they are, however, easy to build. By contrast Kriging and Gaussian Process models can be much more sophisticated but are often difficult and time consuming to set up and tune. At an intermediate level radial basis function (RBF) models using simple spline functions offer rapid modelling capabilities with some ability to fit complex data. However, as normally used such RBF RSM’s strictly interpolate the available computational data and while acceptable in some cases, when used with codes that are iteratively converged, they find it difficult to deal with the numerical noise inevitably present. This paper describes a modification to the basic RBF scheme that allows a systematic variation of the degree of regression from a pure linear regression line to a fully interpolating cubic radial basis function model. The ideas presented are illustrated with data from the field of aerospace design.