Closure to “Discussion of ‘Sensitivity Coefficients Utilized in Nonlinear Estimation With Small Parameters in a Heat Transfer Problem’” (1970, ASME J. Basic Eng., 92, pp. 221–222)

1970 ◽  
Vol 92 (2) ◽  
pp. 222-222
Author(s):  
J. V. Beck
Keyword(s):  
Heat Transfer ◽  
Transfer Problem ◽  
Nonlinear Estimation ◽  
Heat Transfer Problem ◽  
Sensitivity Coefficients ◽  
Small Parameters

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

1970 ◽  
Vol 92 (2) ◽  
pp. 215-221 ◽  
Author(s):  
J. V. Beck
Keyword(s):  
Model Building ◽  
Transfer Problem ◽  
Nonlinear Estimation ◽  
Transient Heat Conduction ◽  
Computer Time ◽  
Sensitivity Coefficients ◽  
Yield Information ◽  
Small Parameters ◽  
The Difference ◽  
Building Identification

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.

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