A Particle-Filtering Approach for Real-Time Estimation of Thermal Conductivity and Temperature Tracking in Homogeneous Masses

Abstract

Knowledge of the thermal conductivity is a key factor for several applications, which benefits from easy and cheap estimation procedures. We consider an existing experimental layout, and we propose a Rao-Blackwellized particle filter that jointly approximates the posterior distribution of the temperatures and analytically estimates the unknown thermal conductivity of a homogeneous mass. Its main advantage is the sequential estimation of the conductivity. In contrast, in other approaches, all of the temperatures need to be stored before processing the data. The results obtained with a polymethylmethacrylate specimen provide good estimates and demonstrate the real-time applicability of the approach.

Bayesian inference for solving a class of heat conduction problems

“…Various methods for solving the thermal conductivity of materials have been proposed, such as the spirit sensitivity method, the least squares method, the regularization method, and the conjugate gradient method. Martí n-Ferná ndez and Lanzarone used the Monte Carlo method to solve the heat conduction problem [11]. Tifkitsis Tifkitsis and Skordos [12] developed a modified scheme based on the Markov Chain Monte Carlo for the estimation of unknown stochastic input parameters, such as the heat transfer coefficient.…”