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Activity Number: 628 - Statistical Applications in the Physical Sciences
Type: Contributed
Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
Sponsor: Section on Physical and Engineering Sciences
Abstract #323650
Title: Selecting Basis Quantities for Dimensional Analysis: a Data-Driven Approach
Author(s): Ching-Chi Yang* and Dennis K.J. Lin
Companies: Penn State and Penn State University
Keywords: Bias Correction ; Dimension Reduction ; Minimum-Variance Unbiased Estimator
Abstract:

Dimensional analysis (DA) is a widely used methodology in engineering and physical sciences. The importance of DA in statistics has been recognized only recently. One of the fundamental rules in DA is to maintain dimensional homogeneity in model building. The Buckingham pi theorem is the key theorem in DA which provides a method of computing the dimensionless variables. However, the choice of the basis quantities is not unique.

This paper proposes a guideline based on data to obtain an optimal selection of the basis quantities. From the statistics point of view, this optimal selection can guarantee less confounding pattern among dimensionless variables. One of the data-driven criteria is based on the variance of the basis quantities and their observed value. It is shown that considering variables with a smaller proposed criterion as basis quantities results in smaller correlations among dimensionless variables. Theoretical result is provided and a real-life case study is used to illustrate the benefit of using the optimal choice.


Authors who are presenting talks have a * after their name.

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