Guaranteed characterization of thermal conductivity and diffusivity in presence of model uncertainty

A crucial problem that occurs when estimating physical parameters from experimental data is the computation of reliable uncertainty bounds for the estimated parameters, while accounting for uncertainty in the model and data. We introduce a new numerical method that contributes to the solution of this problem. We show how to deal with uncertain nuisance parameters located within prior intervals. The method advocated in this article makes it possible to detect the absence of solution when the model hypotheses are inconsistent with the data. An analysis of the sensitivity of estimated uncertainty bounds to the nuisance parameters is also conducted. These features are illustrated with actual data collected on a thermal device used to estimate simultaneously the conductivity and diffusivity of materials.