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Observation strategies for mobile heating source tracking
L. Perez and A. Vergnaud

This study aims to present in a first part the resolution of an inverse problem based on the implementation of an iterative regularization method (conjugate gradient algorithm) in a thermal context. Two mobile heating sources – whose spatial supports are disks of constant radius while centre is mobile – are considered. It is assumed that their trajectories are unknown while their heating fluxes are given. In this work, some results are presented on the estimation of the source trajectories considering temperature measurements provided by several fixed punctual sensors. In a second time, the robustness of the proposed identification method is demonstrated considering temperature measurements and realistic disturbances. Then, in order to optimize the relevance of collected data or in order to reduce the computational time, different strategies of data acquisition are performed. At each iteration of the conjugate gradient algorithm from the iterative regularization method, the sensitivity functions to unknown parameters are calculated and provide information on the most relevant sensor versus time. Then, it becomes possible, at each iteration, to choose the amount of processed information and thus to reduce the number of used sensors. The influence of this strategy consisting in choosing the most informative sensor in order to reduce information only to the relevant one on the estimation results will be studied.

Keywords: Inverse problem, optimal observations, mobile heating sources

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