Intelligent Hysteresis Model and Its Distribution Function Considering the State Information of the Preisach Operator
Jing Ying1, Zhang Yanli1, Wang Zhen1, Zhang Dianhai1, Zhu Jianguo2
1. Key Laboratory of Special Motors and High Voltage Electrical Apparatus Ministry of Education Shenyang University of Technology Shenyang 110870 China; 2. School of Electrical and Information Engineering University of Sydney Sydney 2006 Australia
Abstract：With the increasing complexity of the operating conditions of electrical equipment such as transformers, accurately simulating the magnetic characteristics of soft magnetic materials under various conditions has become particularly important. The neural network hysteresis model has become one of the effective methods for predicting the magnetic properties of soft magnetic materials such as silicon steel. This paper proposes an Preisach operator intelligent hysteresis (POIH) model for predicting the magnetization and loss characteristics. This model embeds the Preisach theory into the neural network framework and can effectively capture and reproduce the hysteresis behavior of materials under different conditions. Meanwhile, the model maintains good adaptability to complex operating conditions while significantly reducing the number of input samples. In the POIH model, the Preisach diagram is non-uniformly discretized. 2N inversion points are selected to construct N(2N+1) grid nodes, each node corresponding to an Preisach operator and its state. The magnetization state matrix of the Preisach operator is constructed as the input of the back propagation (BP) neural network. In terms of the training strategy, the model only requires one limiting hysteresis loop and one basic magnetization loop to complete the training. To extend the model to dynamic conditions, the POIH model is coupled with the trapezoidal equivalent circuit, achieving the calculation of the iron loss components under sinusoidal and harmonic excitation. To establish the connection between the neural network parameters and physical meanings, the POIH model approximates the Sigmoid nonlinear function by Taylor expansion as a linear function, introduces the effective weight parameter with clear physical meaning, and thereby defines the discrete distribution function. To verify the performance of the POIH model, the magnetic properties of silicon steel under quasi-static, power frequency and harmonic magnetization were measured. Firstly, the static hysteresis loop prediction values of the POIH model, the limiting magnetic hysteresis loop method Preisach model and the BP neural network model under different magnetic intensities were compared. The comparison results showed that the POIH model had the best comprehensive performance in terms of data volume and prediction accuracy. Secondly, the distribution function characteristics were analyzed to reveal the intrinsic correspondence between them and the material magnetization process. Finally, the dynamic hysteresis loops under power frequency and harmonic magnetization were predicted using the POIH model, and the model showed good accuracy in both cases. The research results show: (1) The POIH model achieves an equivalent substitution for the integral operation of the Preisach model through the mapping of non-uniformly discretized Preisach diagram and neural network weights, while preserving the physical interpretability and avoiding the problem of easily getting stuck in local optima when traditional models rely on preset distribution functions and optimization algorithms. (2) By dynamically adjusting the weights using the backpropagation algorithm, a direct mapping between network weights and physical distribution functions is established, enabling adaptive identification and three-dimensional visualization of the distribution functions, providing a new means for the study of the correlation between microscopic magnetization mechanisms and macroscopic properties. (3) This model can accurately simulate the characteristics of direct current and sinusoidal alternating current magnetization, simultaneously can be extended to the case of harmonic excitation, demonstrating good generalization ability.
荆盈, 张艳丽, 王振, 张殿海, 朱建国. 计及Preisach算子状态信息的智能磁滞模型及其分布函数[J]. 电工技术学报, 2026, 41(1): 70-81.
Jing Ying, Zhang Yanli, Wang Zhen, Zhang Dianhai, Zhu Jianguo. Intelligent Hysteresis Model and Its Distribution Function Considering the State Information of the Preisach Operator. Transactions of China Electrotechnical Society, 2026, 41(1): 70-81.
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2026, Vol. 41 
