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APPLICATIONS OF ERROR PROPAGATION ANALYSIS TO THE UNCERTAINTIES OF REGRESSION MODELS IN EXPERIMENTAL THERMAL AND FLUIDS ENGINEERING

Sheldon M. Jeter

Georgia Institute of Technology

Introduction

Regression models are common in experimental thermal and fluids engineering. Typical applications are calibration of instruments, correlation of thermodynamic properties, and development of transport models. For the models to be used confidently and competently, students and practitioners must understand both the development of the models and the evaluation of the uncertainty of the models. The latter understanding is apparently not adequately developed in typical undergraduate statistics courses. Engineering students usually have adequate familiarity with the development of simple regression models. An example of such a model is a linear or a polynomial calibration curve. A specific example is a fitting the data for the thermoelectric potential of a thermocouple to a polynomial of temperature over the range of calibration. Students are somewhat familiar with the uncertainty of the data with respect to such a model, but even in such a simple case, students are usually unfamiliar with evaluating the uncertainty of model itself.

A further interesting complication is introduced when the model is developed not in terms of the variables directly measured but instead in terms of transformed variables calculated from the measured variables. An example of such a model is the widely applied Clausius- Clapeyron expression for the logarithm of the vapor pressure as a polynomial function of the inverse absolute temperature. In the literature of experimental uncertainty, such as the report by Taylor and Mohr 3, the result of reading a graduated instrument is called a direct measurement; and the result of a calculation using direct measurements is called an indirect measurement. For consistently in the absence of obvious distinguishing terms in the literature, this paper will refer to models based on direct measurements as “direct models”, and models involving indirect measurements will be called “indirect models”.

The well understood theory and practice of developing simple direct models are easily expanded to include the development of indirect models so long as they are still linear in their parameters. In the case of even a relatively simple indirect model, however, most students are unable to evaluate even the uncertainty of the data and are certainly unable to evaluate the uncertainty of the model. The students are, of course, even less familiar with the development

Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright Ó 2002, American Society for Engineering Education Main Menu

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Jeter, S. (2002, June), Applications Of Error Propagation Analysis To The Uncertainties Of Regression Models Paper presented at 2002 Annual Conference, Montreal, Canada. 10.18260/1-2--10443