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3.2.6 Statistical Modeling for Polymer Temperature Measurement

Mark G. Vangel

Stefan D. Leigh

Statistical Engineering Division, CAML

Anthony J. Bur

Polymers Division, MSEL

The objective of this project is to develop a method for indirectly measuring the temperature of a polymer during fabrication. A compound is added to the polymer which fluoresces when excited by a laser. Empirically, it has been shown that the ratio of the intensities of the resulting spectrum at two wavelengths is, for a practically useful range of temperature, nearly linearly related to the temperature within the material. Thus, a calibration curve can be determined which relates this ratio to temperature. By measuring the intensity at two wavelengths, a user can then use this curve to estimate temperature.

Statistical models have been developed for experimental spectra in an attempt to explain this empirically-based calibration curve. A mixture of four Gaussians where the mixture proportions are allowed to vary with temperature was fit to data, with good results. From the figure, it is clear that the proportions vary linearly with temperature. Some hysteresis is also apparent, probably because of a change in the additive when it is heated. This model will hopefully provide insights leading eventually to a physical explanation of the phenomenon.


Figure 18: Proportions of Components of a Gaussian Mixture as Functions of Temperature

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Date created: 7/20/2001
Last updated: 7/20/2001
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