ESTIMATING RAPID FLOW TRANSIENTS USING EXTENDED KALMAN FILTER
Journal Title: Silesian Journal of Pure and Applied Mathematics - Year 2016, Vol 6, Issue 1
Abstract
Theoretical and numerical modeling of flow transients in pipelines is a challenging field of research. The governing flow equations constitute a system of nonlinear hyperbolic partial differential equations enforcing the conservation laws for mass, momentum and energy. The application of these mathematical models might be limited due to the absence of complete knowledge about the physical phenomena and uncertainties. Information about the initial and boundary conditions is usually obtained from measurements. The presence of noise and inaccuracies, as well as inexactness of the flow model and numerical approximations for solving the full model can lead to predictions that differ from reality. In this paper, we deal with the problem of extracting information about states of the system in real time given noisy measurements. We solved the isothermal flow model during a hydraulic shock while using the extended Kalman filter to estimate the hidden state variables. To avoid spurious oscillations in the solution, the flow model in conservative form was solved using Roe’s flux limiter within the finite volume framework to ensure the total variation diminishing property. Numerical approximation of the Jacobian was done with an adaptive routine and showed that most entries in the matrix are zero and therefore sparse. The robustness of the extended Kalman filter was examined by varying the noise statistics. In most of the situations, we can conclude that the extended Kalman filter was successful in estimating the rapid transients of natural gas.
Authors and Affiliations
Ferdinand Evert UILHOORN
Keywords
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