Application of Bayesian Inference Technique for the reconstruction of an isothermal hot spot inside a circular disc from peripheral temperature measurement - A critical assessment

In this communication an internal hot spot in a two dimensional circular domain has been reconstructed using Bayesian Inference Technique. A semi-analytical forward model based on boundary collocation method has been used for the determination of temperature distribution. The posterior mean and the maximum a posteriori estimates have been computed using the Markov Chain Monte Carlo sampling technique. Based on the problem definition the reconstruction of the hot spot requires the estimation of the location, size and boundary temperature of the spot. Estimation of each of these parameters has been done individually (single parameter estimation) as well as taking different combinations of them (multiple parameter estimation). Synthetic measurement data with and without uncertainty have been used first to critically examine the scheme of reconstruction and to judge the goodness of the scheme of estimation for each of the unknowns. An experimental scheme has also been devised to generate data for reconstruction. Estimation using data from both of these sources reveal that the uncertainty involved in the prediction of different parameters vary widely. It has been observed that the uncertainty involved in the prediction of eccentricity is much more compared to that for the prediction of the temperature or radius of the hot spot. The reason for this has been pinpointed through the sensitivity analysis. The sensitivity analysis further reveals that simultaneous estimation of all the attributes of the internal hotspot is difficult to make in the present scenario. Finally, the limitation of the present scheme has been discussed.