Estimation of Heat Source Term and Thermal Diffusion in Tokamak Plasmas Using a Kalman Filtering Method in the Early Lumping Approach
Résumé
— In this paper, early lumping estimation of space-time varying diffusion coefficient and source term for a non-homogeneous linear parabolic partial differential equation (PDE) describing Tokamak plasma heat transport is considered. The analysis of this PDE is achieved in a finite dimensional framework using the cubic b-splines finite element method with the Galerkin formulation. This leads to a finite dimensional linear time-varying state-space model with unknown parameters and inputs. The Extended Kalman Filter with Unknown Inputs Without Direct Feed-through (EKF-UI-WDF) is applied to estimate simultaneously the unknown parameters and inputs and an adaptive fading memory coefficient is introduced in the EKF-UI-WDF, to deal with time varying parameters. Conditions under which the direct problem is well posed and the reduced order model converges to the initial one are established. Insilico and real data simulations are provided to evaluate the performances of the proposed technique.
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