Abstract
In this paper, a method based on Bayesian inference is proposed to conjointly estimate the following two fields of thermophysical parameters. The first is a thermal characteristic time directly linked to the thermal diffusivity and the thickness, whereas the second is the Biot number, which is directly linked to the heat loss and thermal conductivity. This method is robust to noise and leads to very good estimations of the parameters with an algorithm that is very fast and less time consuming than a classical minimization method. At the end of the study, a setup and a methodology are also presented to estimate the average value of the thermal conductivity of an unknown material.
Highlights
Thermal diffusivity is one of the main parameters in the thermal characterization of materials
Other works proposed estimating the thermal diffusivity with whole thermograms using least-squares methods by minimizing the residual composed of the norm of the difference between the measured data and the theoretical model
The high difference between the two methods is the computation time: the complete estimation of the couple (τ, Bi) on each pixel of the sample took 2 h 35 min for the LM algorithm, whereas it was only 20 min with the Bayesian methodology, with similar precision. This difference is explained by the type of the algorithm. Minimization methods such as the LM algorithm require the inversion of matrices, which is of high complexity, whereas Bayesian methodology is based on the subtraction of thermograms, which is of minimal complexity
Summary
Thermal diffusivity is one of the main parameters in the thermal characterization of materials. A method based on Bayesian inference is proposed to locally and conjointly estimate the two parameters on each point of the material with whole thermograms without using the MCMC methods but with the generation of a base that represents the physical model. This method is compared to the classical minimization method using least squares, and the performances are compared, on the estimation precision and the time computation of the algorithm. METHODOLOGY FOR THE SIMULTANEOUS ESTIMATION OF THE HEAT LOSS AND THE DIFFUSIVITY
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