Phenomenological Modeling of Plasma Transport via Stochastic Filtering
C. Xu, Y. Ou, R. Arastoo, E. Schuster
Symposium on Fusion Engineering
San Diego, CA, May 31-June 5, 2009
Abstract
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The accuracy of first-principles predictive models for the evolution
of plasma profiles is sometimes limited by the lack of understanding
of the plasma transport phenomena. It is possible then to develop
approximate transport models for the prediction of the plasma dynamics
which are consistent with the available diagnostic data. This
data-driven approach, usually referred to as phenomenological modeling,
arises as an alternative to the more classical theory-driven approach.
In this work we propose a stochastic filtering approach based on an
extended Kalman filter to provide real-time estimates of poorly known
or totally unknown transport coefficients. We first assume that plasma
dynamics can be governed by tractable models obtained by first
principles. However, the transport parameters are considered unknown
and to-be-estimated. These estimates will be based solely on
input-output diagnostic data and limited understanding of the
transport physics. Numerical methods (e.g., finite differences) can be
used to discretize the PDE models both in space and time to obtain
finite-dimensional discrete-time state-space representations. The
system states and to-be-estimated parameters are then combined into an
augmented state vector. The resulting nonlinear state-space model is
used for the design of an extended Kalman filter that provides
real-time estimations not only of the system states but also of the
unknown transport coefficients. Simulation results demonstrate the
effectiveness of the proposed method for a benchmark transport model
in cylindrical coordinates.