Quasi-online method for the identification of heat flux densities and trajectories of two mobile heating sources

This paper deals with a complex inverse ill-posed problem related to the identification of numerous unknown parameters of a system described by partial differential equations. A quasi-online identification method of heat flux densities and trajectories of two mobile heating sources is proposed. This approach is based on a modification of the conjugate gradient method with automatically adaptive sliding window size in order to ensure online identification. A set of fixed sensors is located on the domain in order to measure temperature evolution. Observations are disturbed according to a realistic Gaussian noise. The effectiveness of the proposed method will be illustrated considering numerical results of several simulations.

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