基于残差U-Net和自注意力Transformer编码器的磁场预测方法

doi:10.19595/j.cnki.1000-6753.tces.230265

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摘要

利用有限元方法对几何结构复杂的电机和变压器进行磁场分析,存在仿真时间长且无法复用的问题。因此,本文提出一种基于残差U-Net和自注意力Transformer编码器的磁场预测方法。首先建立永磁同步电机（PMSM）和非晶合金变压器（AMT）有限元模型,得到深度学习训练所需的数据集,然后将Transformer模块与U-Net模型结合,并引入短残差机制建立ResUnet-Transformer模型,通过预测图像的像素实现磁场预测。进一步,通过Targeted Dropout算法和动态学习率调整策略对模型进行优化,解决过拟合问题并提高预测精度。计算实例证明,ResUnet-Transformer模型在PMSM和AMT数据集上测试集的平均绝对百分比误差（MAPE）均小于1%,仅需500组样本。本文提出的磁场预测方法能减少实际工况和多工况下精细模拟和拓扑优化的时间和资源消耗,亦是虚拟传感器乃至数字孪生的关键实现方法之一。

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	金亮
	尹振豪
	刘璐
	宋居恒
	刘元凯

关键词 ：有限元方法, 电磁场, 深度学习, U-Net, Transformer

Abstract：

Fine simulation of electromagnetic characteristics analysis of electrical equipment relies on the finite element method. Due to the increasing complexity of large electrical machines and transformers, it may take dozens or even hundreds of hours to simulate structurally complex large electrical machines and transformers for improving computational accuracy, resulting in significant consumption of computational resources. At the same time, the finite element method cannot establish a priori model, when design parameters, structures, and operating conditions undergo slight changes, it is necessary to reestablish the model for calculation, which makes it difficult to meet the requirements of practical engineering and digital twins in terms of speed and adaptability. Considering the powerful feature extraction ability of deep learning, it can extract useful information from massive data, this paper proposes a magnetic field prediction method based on residual U-Net and self-attention Transformer encoder. The finite element method is used to obtain the dataset required for deep learning training. The successful deep learning model which can be trained once and used for multiple predictions, is fully utilized for magnetic field prediction problems, to solve the problem of the non-reusability of the finite element method and reduce the computational time and resource consumption.
Firstly, this paper leveraged the inherent advantages of Convolutional Neural Network (CNN) in image processing, particularly the U-shaped CNN known as U-Net based on encoder and decoder structure, which exhibits stronger capability in capturing fine details and learning from limited samples compared to traditional CNN. To mitigate network degradation and address the limitations of convolutional operations, the paper introduced short residual connections and Transformer modules to the U-Net architecture, creating the ResUnet-Transformer model. The short residual connections accelerate network training, while the self-attention mechanism from the Transformer network enables effective interaction of global features. Secondly, this paper introduced the Targeted Dropout algorithm and adaptive learning rate to suppress overfitting and enhance magnetic field prediction accuracy. The Targeted Dropout algorithm incorporates post-pruning strategies into the training process of neural networks, effectively mitigating overfitting and improving model generalization. Additionally, an adaptive learning rate is implemented using the cosine annealing algorithm based on the Adam optimization algorithm. This adaptive adjustment gradually reduces the learning rate as the objective function converges to the vicinity of the optimal value, avoiding oscillations or non-convergence. Finally, the ResUnet-Transformer model was validated through engineering cases involving Permanent Magnet Synchronous Motor (PMSM) and Amorphous Metal Transformer (AMT).
The experimental results show that on the PMSM dataset, training the ResUnet-Transformer model with 250 samples and testing it with 100 samples, the mean square error (MSE) and mean absolute percentage error (MAPE) are used as performance evaluation metrics. Compared to CNN, U-Net, and Linknet models, the ResUnet-Transformer model achieves the highest prediction accuracy, with an MSE of 0.07×10^-3 and MAPE of 1.4%. The prediction efficiency of the 100 test samples using the ResUnet-Transformer model is 66.1% higher than that of the finite element method. By keeping the other structural and parameter settings, as well as data preprocessing, consistent with the ResUnet-Transformer model, the introduction of the Targeted Dropout algorithm and cosine annealing algorithm improves the prediction accuracy by 36.4% and 26.3%, respectively. To assess the model's generalization ability, the number of training samples for PMSM and AMT datasets is varied, and the model is tested using 100 samples. In the validation on the test set, when the number of training samples is small, the magnetic field prediction performance is poor and does not meet the accuracy requirements. When the training dataset size increases to 300, the prediction error does not decrease but slightly rises. However, with further increases in the training dataset size, the error significantly decreases, and the MAPE on the PMSM and AMT datasets can reach 0.7% and 0.5%, respectively, with just 500 training samples.

Key words： Finite element method electromagnetic field deep learning u-net transformer

收稿日期: 2023-03-08

PACS:

TM153

基金资助:

国家自然科学基金面上项目（51977148）,国家自然科学基金重大研究计划（92066206）和中央引导地方科技发展专项自由探索项目（226Z4503G）

通讯作者: 金亮, 男,1982年生,博士,教授,研究方向为工程电磁场与磁技术、电磁场云计算和电磁无损检测等。E-mail：jinliang_email@163.com

作者简介: 尹振豪, 男,2000年生,硕士研究生,研究方向为深度学习在电工装备中的应用。E-mail：1691150589@qq.com

引用本文:

金亮, 尹振豪, 刘璐, 宋居恒, 刘元凯. 基于残差U-Net和自注意力Transformer编码器的磁场预测方法[J]. 电工技术学报, 0, (): 9021-21. Jin Liang, Yin Zhenhao, Liu Lu, Song Jvheng, Liu Yuankai. Magnetic Field Prediction Method Based on Residual U-Net and Self-Attention Transformer Encoder. Transactions of China Electrotechnical Society, 0, (): 9021-21.

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