Dimensional Analysis in Experimental Design
Seminar Room 1, Newton Institute
In this talk, and since we are in the Isaac Newton Institute, I will focus on using the physics of the problem being tackled to determine a strategy to design an experiment to fit a model for prediction. At the heart of the approach is an application of Edgar Buckingham’s 1914 “Pi” theorem. Buckingham’s result, which is based on dimensional analysis, has been seemingly neglected by statisticians, but it provides a “bridge” between a purely theoretical approach to model building, and an empirical one based on e.g. polynomial approximations such as 2nd order response surfaces.
I will illustrate the ideas with a few examples, in the hope that I can show that dimensional analysis should take its place at the heart of experimental design in engineering applications.