In this paper, we propose a method for identifying the measure of the stochastic Preisach operator using machine learning techniques. The classical Preisach operator model is widely used to describe hysteresis phenomena in various fields such as physics, chemistry, economics, and biology. However, it does not account for uncontrolled fluctuations in the parameters of elementary hysteresis carriers — hysterons, which limits its applicability in real systems where these parameters can be stochastic variables. The proposed method is based on sequential reconstruction of the operator's measure on the plane of hysteron threshold parameters $ (\alpha, \beta) $. The identification is carried out through specially constructed input signals that trigger switching of only specific hysterons in given local regions of this plane. Multiple repetitions of such input actions and application of the law of large numbers allow for estimating the mathematical expectations of hysteron state changes. These estimates are used in the algorithm to minimize a loss functional, leading to the reconstruction of the operator's measure from experimental data. The results open new possibilities for modeling and analyzing complex systems with hysteretic properties, taking into account the stochastic nature of parameters.
Citation: Aleksandr I. Proshunin, Sergei V. Borzunov, Nikolay I. Sel'vesyuk. Identification of the parameters of the stochastic Preisach operator[J]. Mathematics in Engineering, 2025, 7(5): 586-609. doi: 10.3934/mine.2025024
In this paper, we propose a method for identifying the measure of the stochastic Preisach operator using machine learning techniques. The classical Preisach operator model is widely used to describe hysteresis phenomena in various fields such as physics, chemistry, economics, and biology. However, it does not account for uncontrolled fluctuations in the parameters of elementary hysteresis carriers — hysterons, which limits its applicability in real systems where these parameters can be stochastic variables. The proposed method is based on sequential reconstruction of the operator's measure on the plane of hysteron threshold parameters $ (\alpha, \beta) $. The identification is carried out through specially constructed input signals that trigger switching of only specific hysterons in given local regions of this plane. Multiple repetitions of such input actions and application of the law of large numbers allow for estimating the mathematical expectations of hysteron state changes. These estimates are used in the algorithm to minimize a loss functional, leading to the reconstruction of the operator's measure from experimental data. The results open new possibilities for modeling and analyzing complex systems with hysteretic properties, taking into account the stochastic nature of parameters.
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Aleksandr I. Proshunin, Sergei V. Borzunov, Nikolay I. Sel'vesyuk. Identification of the parameters of the stochastic Preisach operator[J]. Mathematics in Engineering, 2025, 7(5): 586-609. doi: 10.3934/mine.2025024
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