Experimental design for engineering dimensional analysis

Dimensional analysis (DA) is a fundamental method in the engineering and physical sciences for analytically reducing the number of experimental variables affecting a given phenomenon prior to experimentation. Two powerful advantages associated with the method relative to standard design of experiment (DOE) approaches are (a) a priori dimension reduction and (b) scalability of results. The latter advantage permits the experimenter to effectively extrapolate results to similar experimental systems of differing scale. Unfortunately, DA experiments are underused because very few statisticians are familiar with them. In this article, we first provide an overview of DA and give basic recommendations for designing DA experiments. Next, we consider various risks associated with the DA approach, the foremost among them is the possibility that the analyst might omit a key explanatory variable, leading to an incorrect DA model. When this happens, the DA model will fail and experimentation will be largely wasted. To protect against this possibility, we develop a robust-DA design approach that combines the best of the standard empirical DOE approach with our suggested design strategy. Results are illustrated with some straightforward applications of DA. A Matlab code for computing robust-DA designs is available as supplementary material online.