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Abstract: 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 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. [ABSTRACT FROM AUTHOR]

The present study addresses the initialisation problem of output-error (OE) identification methods. The challenge is to find a suitable initialization, which brings about a convergence towards the global optimum. A common way to initialise OE methods is to use the ARX model, but it must be used cautiously. The purpose of this study is to describe an alternative method based on the reinitialised partial moment (the RPM model) and to compare this approach with the ARX model by analysing the bias. The RPM model property is an implicit embedded filter that substitutes the explicit data filter required by the ARX model. [ABSTRACT FROM AUTHOR]