A multi-thermogram-based Bayesian model for the determination of the thermal diffusivity of a material

The determination of thermal diffusivity is at the heart of modern materials characterisation. The evaluation of the associated uncertainty is difficult because the determination is performed in an indirect way, in the sense that the thermal diffusivity cannot be measured directly. The well-known GUM uncertainty framework does not provide a reliable evaluation of measurement uncertainty for such inverse problems, because in that framework the underlying measurement model is supposed to be a direct relationship between the measurand (the quantity intended to be measured) and the input quantities on which the measurand depends. This paper is concerned with the development of a Bayesian approach to evaluate the measurement uncertainty associated with thermal diffusivity. A Bayesian model is first developed for a single thermogram and is then extended to the case of several thermograms obtained under repeatability and reproducibility conditions. This multi-thermogram based model is able to take into consideration a large set of influencing quantities that occur during the measurements and yields a more reliable uncertainty evaluation than the one obtained from a single thermogram. Different aspects of the Bayesian model are discussed, including the sensitivity to the choice of the prior distribution, the Metropolis–Hastings algorithm used for the inference and the convergence of the Markov chains.