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.

Notes

¹We use p to denote probability functions, including densities and masses. This notation is argument-wise, common in Bayesian analysis and in particle-filtering literature. For example, if x are continuous random variables, then p(x) is their probability density function; if x is a discrete random variable, then p(x) is its probability mass function. Conditional densities and masses are indicated as p(x|y).

²We use the approximate measure built with the particles before resampling to approximate the posterior mean and variance of λ₀. This avoids the introduction of additional Monte Carlo variance due to the resampling step [7].