Thermal properties are generally determined through solving inverse problems. Because the temperature is a non-linear function of the properties, the solutions are usually effected by linearizing the equations. The statistics of these linearized estimates are based upon the assumptions that the measurement noise has zero mean and is normally distributed, yielding unbiased and normally distributed parameter estimates. In fact, even for this type of noise, nonlinear functions can lead to bias and nonnormal distributions of estimated properties. We examine these effects and show that for typical thermal systems that while the estimates are unbiased and normal, the confidence limits may be inaccurately defined and the residuals of the fits may not be zero mean and uncorrelated. Characterizing the estimated parameters is critical when nonlinear models are to be used for extrapolation.
Parameter Estimation for Highly Nonlinear Models With Noisy Data
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Emery, AF, & Bardot, D. "Parameter Estimation for Highly Nonlinear Models With Noisy Data." Proceedings of the ASME 2003 Heat Transfer Summer Conference. Heat Transfer: Volume 3. Las Vegas, Nevada, USA. July 21–23, 2003. pp. 739-748. ASME. https://doi.org/10.1115/HT2003-47193
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