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Nonlinear filtering for the inverse estimation of nonhomogeneous thermal disturbances applied to energy systems

The application of the optimal filtering in the energy engineering field has emerged as an efficient method to solve inverse problems. In the present paper, an approach of the extended Kalman filter (EKF) based on the augmented state concept is adopted for the reconstruction of a surface thermal disturbance, variable in time and space. The history of a laser heating flux of Gaussian space variation, applied to the boundary of a heat conducting cylinder, is successfully recovered using multiple measurement sensors. A parametric study is performed in order to provide a guide for a judicious adjustment of the identification parameters. These parameters include the position of the sensors, the measurement noise, the time step of measurements and the model error. The EKF augmented state approach allows to estimate the temperature field, simultaneously with the heat flux and to recover with a good accuracy other disturbance profiles with a periodic time variation.