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.
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e-mail: pmendez@mines.edu
e-mail: fordon@usc.edu
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September 2005
Technical Papers
Scaling Laws From Statistical Data and Dimensional Analysis
Patricio F. Mendez,
Patricio F. Mendez
Department of Metallurgical and Materials Engineering,
e-mail: pmendez@mines.edu
Colorado School of Mines
, Golden, CO 80401
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Fernando Ordóñez
Fernando Ordóñez
Industrial and Systems Engineering,
e-mail: fordon@usc.edu
University of Southern California
, Los Angeles, CA 90089
Search for other works by this author on:
Patricio F. Mendez
Department of Metallurgical and Materials Engineering,
Colorado School of Mines
, Golden, CO 80401e-mail: pmendez@mines.edu
Fernando Ordóñez
Industrial and Systems Engineering,
University of Southern California
, Los Angeles, CA 90089e-mail: fordon@usc.edu
J. Appl. Mech. Sep 2005, 72(5): 648-657 (10 pages)
Published Online: November 26, 2004
Article history
Received:
November 14, 2003
Revised:
November 26, 2004
Citation
Mendez, P. F., and Ordóñez, F. (November 26, 2004). "Scaling Laws From Statistical Data and Dimensional Analysis." ASME. J. Appl. Mech. September 2005; 72(5): 648–657. https://doi.org/10.1115/1.1943434
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