A Conjugate Model for Dimensional Analysis

Weijie Shen, Dennis K.J. Lin

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Dimensional analysis (DA) is a methodology widely used in physics and engineering. The main idea is to extract key variables based on physical dimensions. Its overlooked importance in statistics has been recognized recently. However, most literature treats DA as merely a preprocessing tool, leading to multiple statistical issues. In particular, there are three critical aspects: (a) the nonunique choice of basis quantities and dimensionless variables; (b) the statistical representation and testing of DA constraints; (c) the spurious correlations between post-DA variables. There is an immediate need for an appropriate statistical methodology that integrates DA and the quantitative modeling. In this article, we propose a power-law type of “DA conjugate” model that is useful for incorporating dimensional information and analyzing post-DA variables. Adapting the similar idea of “conjugacy” in Bayesian analysis, we show that the proposed modeling technique not only produces flexible and effective results, but also provides good solutions to the above three issues. A modified projection pursuit regression analysis is implemented to fit the additive power-law model. A numerical study on ocean wave speed is discussed in detail to illustrate and evaluate the advantages of the proposed procedure. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)79-89
Number of pages11
JournalTechnometrics
Volume60
Issue number1
DOIs
StatePublished - Jan 2 2018

Fingerprint

Dimensional Analysis
Water waves
Regression analysis
Physics
Statistics
Testing
Model
Power Law
Projection Pursuit Regression
Methodology
Wave Speed
Conjugacy
Bayesian Analysis
Modeling
Regression Analysis
Dimensionless
Ocean
Preprocessing
Numerical Study
Integrate

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Cite this

Shen, Weijie ; Lin, Dennis K.J. / A Conjugate Model for Dimensional Analysis. In: Technometrics. 2018 ; Vol. 60, No. 1. pp. 79-89.
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A Conjugate Model for Dimensional Analysis. / Shen, Weijie; Lin, Dennis K.J.

In: Technometrics, Vol. 60, No. 1, 02.01.2018, p. 79-89.

Research output: Contribution to journalArticle

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