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Abstract
In practical applications, a response surface may have a shape that is too complicated to be adequately described by a low-order polynomial over the region where predictions are required. The use of polynomial spline regression models in which the effects of one or more factors are modeled using B-spline basis functions allows greater model flexibility and can lead to more accurate predictions than traditional polynomial models. Multifactor B-spline regression models are described that have useful properties for designing experiments, including the advantage that linear model theory applies. An application of the models is discussed in a case study from the automotive industry on modeling torque in engine mapping using a two-stage hierarchical model. A B-spline model with known knots is used at the second stage to represent each of the response features of engineering interest that are carried forward from the first-stage modeling. The model is fitted over a constrained design region using data obtained from an experiment that employs a V-optimal design generated by a standard search algorithm using a tailored candidate list. Validation runs are used to assess the accuracy of predictions and to show that the approach is effective.
Additional information
Notes on contributors
Daniel M. Grove
Dr. Grove is an Independent Consultant and Associate Member of the Southampton Statistical Sciences Research Institute. His email address is D.Grove@soton.ac.uk.
David C. Woods
Dr. Woods is a Lecturer in Statistics in the Southampton Statistical Sciences Research Institute. His email address is D.C.Woods@maths.soton.ac.uk.
Susan M. Lewis
Dr. Lewis is a Professor of Statistics in the Southampton Statistical Sciences Research Institute. Her email address is S.M.Lewis@maths.soton.ac.uk.