Multivariate Design of Experiments for Engineering Dimensional Analysis

TL;DR

This paper extends the Buckingham Pi-Theorem to multivariate responses, providing new criteria and guidelines for designing dimensional analysis experiments involving multiple responses, demonstrated through a heat exchanger example.

Contribution

It introduces a multivariate extension of the Buckingham Pi-Theorem and offers design construction guidelines for multivariate dimensional analysis experiments.

Findings

Extended the Buckingham Pi-Theorem to multivariate responses.

Developed criteria for multivariate design of experiments.

Provided a practical example with heat exchanger design.

Abstract

We consider the design of dimensional analysis experiments when there is more than a single response. We first give a brief overview of dimensional analysis experiments and the dimensional analysis (DA) procedure. The validity of the DA method for univariate responses was established by the Buckingham $\Pi$-Theorem in the early 20th century. We extend the theorem to the multivariate case, develop basic criteria for multivariate design of DA and give guidelines for design construction. Finally, we illustrate the construction of designs for DA experiments for an example involving the design of a heat exchanger.