Bayesian filtering for thermal conductivity estimation given temperature observations

International standards often require complex experimental layouts to estimate the thermal conductivity of materials, and they marginally take into account the uncertainty in the estimation procedure. In this paper, we propose a particle filtering approach coupled with a simple experimental layout for the real-time estimation of the thermal conductivity in homogeneous materials. Indeed, based on the heat equation, we define a state-space model for the temperature evaluation based on the unknown conductivity, and we apply a Rao-Blackwellized particle filter. Finally, the approach is validated considering heating and cooling cycles given to a specimen made up of polymethylmethacrylate (PMMA) in forced convection. Results show good estimates in accordance with the PMMA conductivity range, and computational times confirm the possibility of a real-time estimation.