Sensitivity Coefficients Utilized in Nonlinear Estimation With Small Parameters in a Heat Transfer Problem

[+] Author and Article Information
J. V. Beck

Department of Mechanical Engineering and Division of Engineering Research, Michigan State University, East Lansing, Mich.

J. Basic Eng 92(2), 215-221 (Jun 01, 1970) (7 pages) doi:10.1115/1.3424973 History: Received July 29, 1969; Online October 27, 2010


The method of nonlinear estimation for determining parameters in differential equations is extended to treat more efficiently the problem of determining dominant and small parameters. Using the sensitivity coefficients, it is shown how to determine the dominant parameters first using nonlinear estimation and then using linear least squares to find the small parameters. This procedure can save a considerable amount of computer time. Even more important is the application to model-building (identification). The residuals for the difference of the temperatures calculated, assuming the small parameters are zero, and the measured temperatures are shown to yield information for discriminating between alternate mathematical models. A transient heat-conduction example is given to illustrate some of the concepts developed.

Copyright © 1970 by ASME
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