A method is developed for the recursive identification of thermal convection system governed by the Boussinesq equation using an extended Kalman filter. A computationally feasible Kalman filter is constructed by reducing the Boussinesq equation to a small number of ordinary differential equations by means of the Karhunen-Loe`ve Galerkin procedure which is a type of Galerkin method employing the empirical eigenfunctions of the Karhunen-Loe`ve decomposition. Employing the Kalman filter constructed by using the reduced order model, the thermal convection induced by a spatially varying heat flux at the bottom is identified recursively by using either the Boussinesq equation or the reduced order model itself. The recursive identification technique developed in the present work is found to yield accurate results for thermal convection even with approximate covariance equation and noisy measurements. It is also shown that a reasonably accurate and computationally feasible method of recursive identification can be constructed even with a relatively inaccurate reduced order model.
Recursive Identification of Thermal Convection
Contributed by the Dynamic Systems and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division, January 2001; final revision, September 2002. Associate Editor: S. D. Fassois.
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Park, H. M., and Lee, W. J. (March 10, 2003). "Recursive Identification of Thermal Convection ." ASME. J. Dyn. Sys., Meas., Control. March 2003; 125(1): 1–10. https://doi.org/10.1115/1.1540116
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