Surface temperature estimation in determined multi-wavelength pyrometry systems.

Abstract

A multi-wavelength pyrometry model was derived using Wien's law. The surface spectral emissivity was modeled as the exponential of a polynomial in wavelength with one free parameter less than the number of pyrometer wavelength channels, resulting in a determined system of linear equations. Multi-wavelength temperature outputs were simulated using values generated by different emissivity functions. Surface temperature estimates were computed using a simple linear model based on polynomial interpolation. Although the accuracy of temperature estimates was reasonably high for some emissivity-generating functions, for other functions, the accuracy of the estimates was unacceptably low. As an alternative, ridge regression, a statistical technique to solve ill-posed problems, was applied to determined multi-wavelength systems, resulting in a substantial increase in the accuracy of temperature estimates, especially for higher-order pyrometry systems: the estimation errors were observed to decrease about 52% when the number of channels increased from 3 to 20; the estimation errors were observed to decrease more than 65% when the number of channels increased from 2, using the simple linear model, to 20, using the ridge regression model. These results demonstrate the potential of using ridge regression to improve the accuracy of temperature estimation in multi-wavelength pyrometry systems.