Fractional modelling and identification of thermal systems

Heat transfer in homogeneous media obeys to diffusion phenomenon which can be modelled with the help of fractional systems. In this paper, we use a parsimonious black box model based on an original fractional integrator whose order 12 acts only over a limited spectral band. We carried out simulations of front face thermal experimentations which consist in measuring the temperature at the surface of a material where a random heat flux is applied. We consider the characterization of the thermal behaviour of a wall or a sphere. These simulations show the ability of the fractional model, thanks to an output error identification technique, to obtain accurate estimation of diffusion interface temperature evolution as well as frequency response using time data series for the two considered geometries. Experimental results are given in the case of the sphere.

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