Estimating a pressure dependent thermal conductivity coefficient with applications in food technology

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Capistrán, Marcos A. and Infante del Río, Juan Antonio (2019) Estimating a pressure dependent thermal conductivity coefficient with applications in food technology. Inverse Problems in Science and Engineering, 28 (2). pp. 277-293. ISSN 1741-5977

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Official URL: https://doi.org/10.1080/17415977.2019.1632841




Abstract

In this paper we introduce a method to estimate a pressure dependent thermal conductivity coefficient arising in a heat diffusion model with applications in food technology. The strong smoothing effect of the corresponding direct problem renders the inverse problem under consideration severely ill-posed. Thus specially tailored methods are necessary in order to obtain a stable solution. Consequently, we model the uncertainty of the conductivity coefficient as a hierarchical Gaussian Markov random field (GMRF) restricted to uniqueness conditions for the solution of the inverse problem established in Fraguela et al. [1]. Furthermore, we propose a Single Variable Exchange Metropolis-Hastings algorithm (SVEMH) to sample the corresponding conditional probability distribution of the conductivity coefficient given observations of the temperature. Sensitivity analysis of the direct problem suggests that large integration times are necessary to identify the thermal conductivity coefficient. Numerical evidence indicates that a signal to noise ratio of roughly 10 cubed suffices to reliably retrieve the thermal conductivity coefficient.


Item Type:Article
Additional Information:

“This is an Accepted Manuscript of an article published by Taylor & Francis in Inverse Problems in Science and Engineering on 26-jun-2019, available online: https://www.tandfonline.com/doi/full/10.1080/17415977.2019.1632841.”

Uncontrolled Keywords:Metropolis-Hastings, Food technology, Thermal conductivity coefficient, Gaussian Markov Random Field, Hierarchical model
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Mathematics > Operations research
Sciences > Mathematics > Probabilities
Sciences > Mathematics > Stochastic processes
Medical sciences > Pharmacy > Food technology
ID Code:63108
Deposited On:20 Jan 2021 16:51
Last Modified:21 Jan 2021 08:07

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