Bayesian Estimation of Thermal Conductivity and Temperature Profile in a Homogeneous Mass

Abstract

International standards propose several methods for measuring thermal conductivity; however, they often require expensive experimental layouts and marginally consider the uncertainty in the estimation procedure. In this article, we propose a temperature transient method and a Bayesian procedure to estimate the thermal conductivity of a homogeneous mass, and to reproduce the entire temperature profile evolution over time by means of latent temperature data. To validate the approach, experiments are conducted giving heating and cooling cycles to a polymethyl methacrylate (PMMA) specimen. Results show the applicability of the proposed approach and good estimations.

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

“…As in our previous study [5], here we deal with a temperature-transient method. Generally, in these methods, the temperature changes over time, and it is measured by one or more sensors.…”

“…This study was motivated by the fact that the Bayesian approach proposed in [5], which was based on a Markov Chain Monte Carlo (MCMC) method, required the acquisition and storage of all of the temperatures before processing the data, thus making any real-time estimation while an experiment is ongoing impossible. In particular, we propose here a Rao-Blackwellized particle filter (RBPF) [6,7] that jointly approximates the posterior distribution of the temperatures and analytically estimates the unknown conductivity.…”

“…In this context, in [5] we proposed an alternative transient method for the estimation of the thermal conductivity of a homogeneous mass, with the twofold aim of simplifying the experimental layout and explicitly considering quantification of the uncertainty. This method was based on a Bayesian estimation procedure, to jointly estimate the thermal conductivity of a homogeneous specimen and reproduce the entire temperature profile evolution over time, with the generation of latent temperature data where measurements were not acquired.…”

A Bayesian approach for the identification of patient-specific parameters in a dialysis kinetic model

“…V is t ð Þ is taken every hour; . M While HFO analyzes the approach in the presence of a high number of observations, as commonly in the literature, 23,25,26 LFO considers a realistic clinical setting. The goal is to quantify possible detriments of the estimates under commonly adopted acquisition frequencies.…”

“…22 Indeed, once the stochastic characterization of model parameters has been conducted, SDEs and SPDEs can be solved, and the result is another stochastic process. 20,21 For example, they have been applied to estimate the inertance in a hydraulic simulator of the human circulation, 23 the parameters in a stochastic predator-prey system, 24 the thermal conductivity and the temperature profile in polymers, 25 and the aortic stiffness from non-invasive measurements. 26 More recently, Bayesian approaches have been considered for estimating the parameters that characterize the dynamics of aquatic communities, 27 and for the estimation of the mortality terms in a stage-structured demographic model.…”