Combined distributed parameters and source estimation in tokamak plasma heat transport

Mechhoud, Sarah; Witrant, Emmanuel; Dugard, Luc; Moreau, D.

doi:10.23919/ecc.2013.6669180

Cited by 8 publications

(8 citation statements)

References 15 publications

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“…., t m }. As a sample of these fields, we note applications in meteorology (Talagrand and Courtier, 1987;Evensen, 2009;Lorenc and Payne, 2007), geochemistry (Eibern and Schmidt, 1999), fluid dynamics (Zadeh, 2008) and plasma physics (Mechhoud et al , 2013), among many others.…”

Section: Introductionmentioning

confidence: 99%

Improved variational methods in statistical data assimilation

Kadakia

Rozdeba

et al. 2015

Nonlin. Processes Geophys.

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Abstract. Data assimilation transfers information from an observed system to a physically based model system with state variables x(t). The observations are typically noisy, the model has errors, and the initial state x(t 0 ) is uncertain: the data assimilation is statistical. One can ask about expected values of functions G(X) on the path X = {x(t 0 ), . . ., x(t m )} of the model state through the observation window t n = {t 0 , . . ., t m }. The conditional (on the measurements) probability distribution P (X) = exp[−A 0 (X)] determines these expected values. Variational methods using saddle points of the "action" A 0 (X), known as 4DVar (Talagrand and Courtier, 1987;Evensen, 2009), are utilized for estimating G(X) . In a path integral formulation of statistical data assimilation, we consider variational approximations in a realization of the action where measurement errors and model errors are Gaussian. We (a) discuss an annealing method for locating the path X 0 giving a consistent minimum of the action A 0 (X 0 ), (b) consider the explicit role of the number of measurements at each t n in determining A 0 (X 0 ), and (c) identify a parameter regime for the scale of model errors, which allows X 0 to give a precise estimate of G(X 0 ) with computable, small higher-order corrections.

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Section: Introductionmentioning

confidence: 99%

Improved variational methods in statistical data assimilation

Kadakia

Rozdeba

et al. 2015

Nonlin. Processes Geophys.

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“…Simulations are performed using MATLAB/Simulink. Since the identifier is infinite-dimensional, the bspline-cubic Galerkin method is used in order to implement it ( [3], [1]). The simulated data is generated by using:…”

Section: Simulation Resultsmentioning

confidence: 99%

“…In this work, we consider one-dimensional heat transport governed by a diffusionreaction PDE with mixed Dirichlet-Neumann boundary conditions and where the source term (the input power adsorbed by the process) is distributed and poorly known. In our previous works ( [1], [2]), we attempted to solve this problem for thermonuclear heat transport in an early lumping estimation approach. First the problem was discretized using the Galerkin formulation and then a modified Kalman filter was applied to estimate both the diffusion coefficient and the unknown input.…”

Section: Introductionmentioning

confidence: 99%

Adaptive space-time distributed parameter and input estimation in heat transport with unknown bounds

Mechhoud

Witrant

Dugard

2013

3rd International Conference on Systems and Control

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Abstract-: In this paper, we discuss on-line adaptive estimation of distributed diffusion and source term coefficients for a non-homogeneous linear parabolic partial differential equation describing heat transport. An estimator is defined in the infinite-dimensional framework having the system state and the parameters' estimate as its states. Our scheme allows to estimate spatially distributed and space-time distributed parameters. While the parameters convergence depends on the plant signal richness assumption, the state convergence is established using the Lyapunov approach. Since the estimator is infinitedimensional, the b-splines Galerkin finite element method is used to implement it. In silico simulations are provided to illustrate the performance of the proposed approach.

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“…As an illustration, let us mention, e.g., the identification of a thermal characteristic of a plasma in a nuclear fusion reactor (Mechhoud et al, 2013), the identification of boundary conditions (a temperature dependent heat transfer coefficient) in a plasma assisted chemical vapor deposition process (Rouquette et al, 2007a), the localization of weak heat sources in electronic devices (Rakotoniaina et al, 2002) or the electron beam welding process (Rouquette et al, 2007b). Among industrial applications, several usual objectives can be mentioned: predictive model validation, identification of systems dynamic behavior, estimation of thermo-physical properties, or diagnosis of processes or materials.…”

Section: Introductionmentioning

confidence: 99%

Heating source localization in a reduced time

Beddiaf

Autrique

Perez

et al. 2016

International Journal of Applied Mathematics and Computer Science

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Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced. To this end, several configurations are detailed and effects of noisy observations are investigated.

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Combined distributed parameters and source estimation in tokamak plasma heat transport

Cited by 8 publications

References 15 publications

Improved variational methods in statistical data assimilation

Improved variational methods in statistical data assimilation

Adaptive space-time distributed parameter and input estimation in heat transport with unknown bounds

Heating source localization in a reduced time

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