Recursive Identification of Thermal Convection

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.