On the identification of a thermal expansion coefficient

Río, Juan Antonio Infante del; Molina–Rodríguez, M.; Ramos, Ángel

doi:10.1080/17415977.2015.1032274

Cited by 3 publications

(4 citation statements)

References 16 publications

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“…where we denoteû = (u 0 , u 1 , · · · , u n ) T . First, we define the indicator function (6), (8) and u i ≥ u 0 = log(k(0)), 0 otherwise. Next, we model the prior distribution of σ 2 using a Gamma distribution with probability density function…”

Section: Statistical Inversionmentioning

confidence: 99%

“…. , n and hypotheses (H1)-(H5) hold, i.e., u satisfies equations ( 6) and (8). In Subsection 2.3 we shall use the above notation to introduce a two tiered formulation of the inverse problem.…”

Section: Inverse Problemmentioning

confidence: 99%

“…Consequently, there are several research efforts to model the dynamics of food preservation processes which rely on high pressures away from thermal equilibrium [1,3,5,7,9,[13][14][15][16][17]. A related problem is to infer the thermal conductivity coefficient associated to food preservation processes given measurements of the temperature, see [8]. Of particular importance towards the solution of the inverse problem are results on the structural identifiability of the thermal conductivity coefficient, see [6].…”

Section: Introductionmentioning

confidence: 99%

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

Capistrán

Río

2019

Inverse Problems in Science and Engineering

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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. To address the known smoothing effect of the direct problem, 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. [6]. Furthermore, we propose a Single Variable Exchange Metropolis-Hastings algorithm 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 3 suffices to reliably retrieve the thermal conductivity coefficient.

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Section: Statistical Inversionmentioning

confidence: 99%

Section: Inverse Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Capistrán

Río

2019

Inverse Problems in Science and Engineering

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“…In order to validate the model and identify suitable parameters, it is often necessary to compare the solutions of the model with real-world data and minimize some error functional using suitable parameter identification techniques and minimization algorithms (see, e.g., [19,22,23]). Since internal properties of the battery such as the spatial distribution of Lithium ions cannot be measured during operation, it is standard to measure only the temperature T (on the outside of the battery, but it is a safe assumption that the temperature is spatially homogeneous) and the output voltage V (see, for example, [5,37]), which can be estimated by using (25).…”

Section: Model Validation and Identification Of Parametersmentioning

confidence: 99%

On the well-posedness of a multiscale mathematical model for Lithium-ion batteries

Díaz

Gómez-Castro

Ramos

2018

Advances in Nonlinear Analysis

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We consider the mathematical treatment of a system of nonlinear partial differential equations based on a model, proposed in 1972 by J. Newman, in which the coupling between the Lithium concentration, the phase potentials and temperature in the electrodes and the electrolyte of a Lithium battery cell is considered. After introducing some functional spaces well-adapted to our framework we obtain some rigorous results showing the well-posedness of the system, first for some short time and then, by considering some hypothesis on the nonlinearities, globally in time. As far as we know, this is the first result in the literature proving existence in time of the full Newman model, which follows previous results by the third author in 2016 regarding a simplified case. Keywords: Lithium-ion battery cell, multiscale mathematical model, Green operators, fixed point theory, Browder-Minty existence results, super and sub solutions 2010 MSC: 35M10, 35Q60, 35C15, 35B50, 35B60• The electric potential φ s = φ s (x, t) in the electrodes.• The electric potential measured by a reference Lithium electrode in the electrolyte, ϕ e = ϕ e (x, t).• The temperature T (t) in the cell.The system of equations is given by (5)-(9) below.

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An inverse meshfree thermoelastic analysis for identification of temperature-dependent thermal and mechanical material properties

Dadar

Hematiyan

Khosravifard

et al. 2020

Journal of Thermal Stresses

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On the identification of a thermal expansion coefficient

Cited by 3 publications

References 16 publications

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

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

On the well-posedness of a multiscale mathematical model for Lithium-ion batteries

An inverse meshfree thermoelastic analysis for identification of temperature-dependent thermal and mechanical material properties

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