Scaling Laws From Statistical Data and Dimensional Analysis

[+] Author and Article Information
Patricio F. Mendez

Department of Metallurgical and Materials Engineering, Colorado School of Mines, Golden, CO 80401pmendez@mines.edu

Fernando Ordóñez

Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089fordon@usc.edu

J. Appl. Mech 72(5), 648-657 (Nov 26, 2004) (10 pages) doi:10.1115/1.1943434 History: Received November 14, 2003; Revised November 26, 2004

Scaling laws provide a simple yet meaningful representation of the dominant factors of complex engineering systems, and thus are well suited to guide engineering design. Current methods to obtain useful models of complex engineering systems are typically ad hoc, tedious, and time consuming. Here, we present an algorithm that obtains a scaling law in the form of a power law from experimental data (including simulated experiments). The proposed algorithm integrates dimensional analysis into the backward elimination procedure of multivariate linear regressions. In addition to the scaling laws, the algorithm returns a set of dimensionless groups ranked by relevance. We apply the algorithm to three examples, in each obtaining the scaling law that describes the system with minimal user input.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Geometry of the ceramic and metal parts to be joined

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Figure 2

Representation of a simple pendulum and its elements

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Figure 3

Theoretical and SLAW -generated scaling laws for the pendulum example

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Figure 4

SLAW -generated scaling laws for the ceramic-to-metal bonding example

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Figure 5

Geometry of the punch test

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Figure 6

SLAW -generated scaling laws for the punch test example



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