计及Preisach算子状态信息的智能磁滞模型及其分布函数

doi:10.19595/j.cnki.1000-6753.tces.251074

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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.

Key words： Preisach operator neural network effective weight parameter distribution function

Received: 18 June 2025

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TM275

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	Jing Ying
	Zhang Yanli
	Wang Zhen
	Zhang Dianhai
	Zhu Jianguo

Cite this article:

Jing Ying,Zhang Yanli,Wang Zhen等. Intelligent Hysteresis Model and Its Distribution Function Considering the State Information of the Preisach Operator[J]. Transactions of China Electrotechnical Society, 2026, 41(1): 70-81.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.251074 OR https://dgjsxb.ces-transaction.com/EN/Y2026/V41/I1/70

[1] 陈彬, 王川源, 刘洋, 等. 基于磁导-电容类比法和解析Preisach模型的铁心动态磁滞建模方法[J]. 电工技术学报, 2024, 39(18): 5576-5587.
Chen Bin, Wang Chuanyuan, Liu Yang, et al.Dynamic hysteresis modeling method for iron core based on permeance-capacitance analogy and analytic Preisach model[J]. Transactions of China Electrotechnical Society, 2024, 39(18): 5576-5587.
[2] 刘任, 杜莹雪, 李琳, 等. 解析逆Preisach磁滞模型[J]. 电工技术学报, 2023, 38(10): 2567-2576.
Liu Ren, Du Yingxue, Li Lin, et al.Analytical inverse Preisach hysteresis model[J]. Transactions of China Electrotechnical Society, 2023, 38(10): 2567-2576.
[3] Stoner E C, Wohlfarth E P.A mechanism of magnetic hysteresis in heterogeneous alloys[J]. IEEE Transactions on Magnetics, 1991, 27(4): 3475-3518.
[4] ElBidweihy H. Rotational magnetization lag-angle plots using the anisotropic stoner-wohlfarth model[J]. IEEE Transactions on Magnetics, 2017, 53(11): 7300906.
[5] 李永建, 李宗明, 利雅婷, 等. 考虑磁-力耦合效应的混合磁滞模型研究[J]. 电工技术学报, 2024, 39(22): 6941-6951.
Li Yongjian, Li Zongming, Li Yating, et al.Study of hybrid hysteresis model considering magnetic-force coupling effect[J]. Transactions of China Electro-technical Society, 2024, 39(22): 6941-6951.
[6] 朱育莹, 李琳. 考虑各向异性和模型参数应力依赖关系的改进Sablik-Jiles-Atherton磁滞模型[J]. 电工技术学报, 2023, 38(17): 4586-4596.
Zhu Yuying, Li Lin.An improved Sablik-Jiles-Atherton hysteresis model considering anisotropy and stress dependence of model parameters[J]. Transactions of China Electrotechnical Society, 2023, 38(17): 4586-4596.
[7] Alejos O, Della Torre E.Improving numerical simulations of Preisach models for accuracy and speed[J]. IEEE Transactions on Magnetics, 2000, 36(5): 3102-3104.
[8] Preisach F.Über die magnetische nachwirkung[J]. Zeitschrift Für Physik, 1935, 94(5): 277-302.
[9] 刘任, 杜莹雪, 李琳, 等. 解析正Preisach磁滞模型的推导与修正[J]. 中国电机工程学报, 2023, 43(5): 2070-2079.
Liu Ren, Du Yingxue, Li Lin, et al.Derivation and modification of analytical forward Preisach hysteresis model[J]. Proceedings of the CSEE, 2023, 43(5): 2070-2079.
[10] De Biasi E.Faster modified protocol for first order reversal curve measurements[J]. Journal of Magnetism and Magnetic Materials, 2017, 439: 259-268.
[11] Szabó Z, Füzi J.Implementation and identification of Preisach type hysteresis models with Everett Function in closed form[J]. Journal of Magnetism and Magnetic Materials, 2016, 406: 251-258.
[12] 赵小军, 仪卓, 武欣怡, 等. 基于同心磁滞回环的Preisach磁滞模型参数辨识及其应用[J/OL]. 西安理工大学学报, 2024: 1-12. (2024-03-30). https://kns. cnki.net/KCMS/detail/detail.aspx?filename=XALD20240327003&dbname=CJFD&dbcode=CJFQ.
Zhao Xiaojun, Yi Zhuo, Wu Xinyi, et al. Parameter identification of Preisach hysteresis model based on concentric hysteresis loop and its application[J/OL]. Journal of Xi’an University of Technology, 2024: 1-12. (2024-03-30). https://kns.cnki.net/KCMS/detail/ detail.aspx?filename=XALD20240327003&dbname=CJFD&dbcode=CJFQ.
[13] Bernard Y, Mendes E, Ren Z.Determination of the distribution function of Preisach’s model using centred cycles[J]. COMPEL - the International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2000, 19(4): 997-1006.
[14] 李伊玲, 李琳, 刘任, 等. 基于非均匀单元离散法的静态逆Preisach模型分布函数辨识[J]. 中国电机工程学报, 2021, 41(15): 5340-5351.
Li Yiling, Li Lin, Liu Ren, et al.The non-uniform element discretization method for identifying distribution function of static inverse Preisach model[J]. Proceedings of the CSEE, 2021, 41(15): 5340-5351.
[15] Peng Daixiao, Sima Wenxia, Yang Ming, et al.An improved centered cycle method for identifying the Preisach distribution function[J]. IEEE Transactions on Magnetics, 2018, 54(11): 7301405.
[16] Zhao Zhigang, Liu Fugui, Ho S L, et al.Modeling magnetic hysteresis under DC-biased magnetization using the neural network[J]. IEEE Transactions on Magnetics, 2009, 45(10): 3958-3961.
[17] Riganti Fulginei F, Salvini A.Neural network approach for modelling hysteretic magnetic materials under distorted excitations[J]. IEEE Transactions on Magnetics, 2012, 48(2): 307-310.
[18] Saliah H H, Lowther D A.The use of neural networks in magnetic hysteresis identification[J]. Physica B: Condensed Matter, 1997, 233(4): 318-323.
[19] Wang Zhen, Zhang Yanli, Ren Ziyan, et al.Modeling of anisotropic magnetostriction under DC bias based on an optimized BP neural network[J]. IEEE Transactions on Magnetics, 2020, 56(3): 7512204.
[20] Wang Yifan, Xu Rui, Zhou Miaolei.Prandtl-ishlinskii modeling for giant magnetostrictive actuator based on internal time-delay recurrent neural network[J]. IEEE Transactions on Magnetics, 2018, 54(11): 7301004.
[21] 马阳阳, 李永建, 孙鹤, 等. 基于深度置信网络算法的面向铁磁材料旋转磁滞损耗的矢量磁滞模型[J]. 电工技术学报, 2023, 38(15): 4063-4075.
Ma Yangyang, Li Yongjian, Sun He, et al.Vector hysteresis model for rotational hysteresis loss of ferromagnetic materials based on deep belief network algorithm[J]. Transactions of China Electrotechnical Society, 2023, 38(15): 4063-4075.
[22] 黄雷, 包广清, 陈俊全. 基于Levenberg-Marquardt算法的改进Preisach模型磁特性模拟与验证[J]. 中国电机工程学报, 2020, 40(18): 6006-6015.
Huang Lei, Bao Guangqing, Chen Junquan.Magnetic property simulation and verification with improved Preisach hysteresis model based on Levenberg-Marquardt algorithm[J]. Proceedings of the CSEE, 2020, 40(18): 6006-6015.
[23] 陈龙, 易琼洋, 贲彤, 等. 全局优化算法在Preisach磁滞模型参数辨识问题中的应用与性能对比[J]. 电工技术学报, 2021, 36(12): 2585-2593, 2606.
Chen Long, Yi Qiongyang, Ben Tong, et al.Application and performance comparison of global optimization algorithms in the parameter identification problems of the Preisach hysteresis model[J]. Transactions of China Electrotechnical Society, 2021, 36(12): 2585-2593, 2606.
[24] 段娜娜, 徐伟杰, 李永建, 等. 基于极限磁滞回线法的软磁复合材料磁特性模拟[J]. 电工技术学报, 2018, 33(20): 4739-4745.
Duan Nana, Xu Weijie, Li Yongjian, et al.Electromagnetic property modeling of the soft magnetic composite material based on the limiting loop method[J]. Transactions of China Electrotechnical Society, 2018, 33(20): 4739-4745.
[25] Hui S Y R, Zhu J. Numerical modelling and simulation of hysteresis effects in magnetic cores using transmission-line modelling and the Preisach theory[J]. IEE Proceedings-Electric Power Applications, 1995, 142(1): 57-62.
[26] Novak M, Eichler J, Kosek M.Difficulty in identification of Preisach hysteresis model weighting function using first order reversal curves method in soft magnetic materials[J]. Applied Mathematics and Computation, 2018, 319: 469-485.
[27] Miyazaki T, Mifune T, Matsuo T, et al. Equivalent circuit modeling of dynamic hysteretic property of silicon steel under pulse width modulation excitation[J]. Journal of Applied Physics, 2015, 117(17): 17D110.
[28] 荆盈, 张艳丽, 王振, 等. 高频激励下软磁复合材料动态磁滞模型及实验验证[J]. 中国电机工程学报, 2025, 45(7): 2845-2855.
Jing Ying, Zhang Yanli, Wang Zhen, et al.Dynamic hysteresis model and experimental verification of soft magnetic composites under high frequency excitation[J]. Proceedings of the CSEE, 2025, 45(7): 2845-2855.