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                <term xml:lang="en">fractional derivative</term>
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                <term xml:lang="en">Barkhausen noise</term>
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              <p>The characterization of the stress state in a material is important in the aeronautical and spatial sector, because the fatigue strength is intimately bounded to their internal stress distribution. The purpose of our work is to present and to develop a magnetic model of the Barkhausen noise to identify the stress profiles of the contact zones of the bearing raceways and rolling elements. By means of a post-processing technique, we succeeded in plotting magnetic Barkhausen noise energy hysteresis cycles MBNenergy(H). These cycles were compared to the usual hysteresis cycles, displaying the evolution of the magnetic induction field B versus the magnetic excitation H. The divergence between these comparisons as the excitation frequency was increased gave rise to the conclusion that there was a difference in the dynamics of the induction field and of the MBNenergy related to the domain wall movements. Indeed, for the MBNenergy hysteresis cycle, merely the domain wall movements were involved. On the other hand, for the usual B(H) cycle, two dynamic contributions were observed: domain wall movements and diffusion of the magnetic field excitation. From a simulation point of view, it was demonstrated that over a large frequency bandwidth a correct dynamic behavior of the domain wall movement MBNenergy(H) cycle could be taken into account using first-order derivation whereas fractional orders were required for the B(H) cycles. The present article also gives a detailed description of how to use the developed process to obtain the MBNenergy(H) hysteresis cycle as well as its evolution as the frequency increases. Moreover, this article provides an interesting explanation of the separation of magnetic loss contributions through a magnetic sample: a wall movement contribution varying according to first-order dynamics and a diffusion contribution which in a lump model can be taken into account using fractional order dynamics.</p>
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