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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摘要随着变压器等电气设备运行工况复杂程度的提高,神经网络磁滞模型已成为预估硅钢等软磁材料磁特性的有效方法之一。为了减少传统神经网络模型对磁特性测量数据样本的依赖性,提高模型对不同磁化方式模拟的适用程度,该文将材料磁化特征融入神经网络模型,提出一种计及Preisach算子状态信息的智能磁滞模型。首先,利用非均匀离散策略构建具有Preisach算子位置信息和状态信息的磁化状态矩阵,并作为反向传播（BP）神经网络的输入;其次,定义一个可以直接反映每个Preisach算子离散点的磁滞特性对整体磁化过程贡献度的有效权重参数,通过提取权重生成具有可视化效果的分布函数,并尝试从图形中寻找材料磁化的某些特征;最后,在测量直流、工频及谐波磁化下硅钢特性的基础上,通过与实测数据对比验证了不同磁化条件下所提模型的计算精度。结果表明,将Preisach算子与神经网络相结合,可以有效地捕捉并反映材料的磁滞特性,同时在减少输入样本的情况下提高模型复杂工况的适用性。

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关键词 ： Preisach算子, 神经网络, 有效权重参数, 分布函数

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

收稿日期: 2025-06-18

PACS:

TM275

基金资助:国家自然科学基金面上项目资助（52277015）

通讯作者: 张艳丽女,1975年生,教授,博士生导师,研究方向为工程电磁与磁性材料复杂电磁特性模拟。E-mail：zhangyanli_sy@hotmail.com

作者简介: 荆盈女,1994年生,博士研究生,研究方向为工程电磁与磁性材料复杂电磁特性模拟。E-mail：jingying@smail.sut.edu.cn

引用本文:

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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