Thermal system identification for large temperature variations using fractional Volterra series

Linear fractional differentiation models have proven their efficacy in modeling thermal diffusive phenomena for small temperature variations with constant thermal parameters (thermal diffusivity and conductivity). However for large temperature variations, the thermal parameters are no longer constant but vary along with the temperature itself. Consequently, the thermal system is no longer linear and could be modeled by non linear fractional differentiation models. The extension of Volterra series to fractional systems is first recalled. Fractional orthogonal generating functions are used as kernels. As compared to a previous work, non linear parameters, such as s -poles of the orthogonal functions and commensurate differentiation order, are estimated along with linear coefficient of Volterra series. Then, Volterra series are applied to model an ARMCO iron sample for large temperature variations in simulation with data generated using finite elements method and in a real life experiment using real data.

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