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| Magnetic Field Prediction Method Based on Residual U-Net and Self-Attention Transformer Encoder |
| Jin Liang1,2, Yin Zhenhao1,2, Liu Lu1, Song Juheng1, Liu Yuankai1 |
1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment Hebei University of Technology Tianjin 300401 China;
2. Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province Hebei University of Technology Tianjin 300401 China |
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Abstract Accurate simulation of electromagnetic characteristics in electrical equipment relies on the finite element method. However, the increasing complexity of large electrical machines and transformers poses challenges, leading to prolonged simulation time and significant computational resource consumption. At the same time, the finite element method cannot establish a priori model. When design parameters, structures, or operating conditions change, it is necessary to reestablish the model. Considering the powerful feature extraction ability of deep learning, this paper proposes a magnetic field prediction method based on a residual U-Net and a self-attention Transformer encoder. The finite element method is used to obtain the dataset for deep learning training. The deep learning model can be trained once and used for multiple predictions, addressing the limitations of the finite element method and reducing computational time and resource consumption.
Firstly, this paper leverages the inherent advantages of the convolutional neural network (CNN) in image processing, particularly the U-shaped CNN, known as U-Net, based on the encoder and decoder structure. This architecture exhibits a stronger ability to capture fine details and learn from limited samples than the traditional CNN. To mitigate network degradation and address convolutional operation limitations, short residual connections and Transformer modules are introduced 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 facilitates the effective interaction of global features. Secondly, this paper introduces the Targeted Dropout algorithm and adaptive learning rate to suppress overfitting and enhance the accuracy of magnetic field predictions. The Targeted Dropout algorithm incorporates post-pruning strategies into the training process of neural networks, effectively mitigating overfitting and improving the model’s generalization. Additionally, an adaptive learning rate is implemented using the cosine annealing algorithm based on the Adam optimization algorithm, gradually reducing the learning rate as the objective function converges to the optimal value and avoiding oscillations or non-convergence. Finally, the ResUnet-Transformer model is validated through engineering cases involving permanent magnet synchronous motors (PMSM) and amorphous metal transformers (AMT).
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 a MAPE of 1.4%. The prediction efficiency of the 100 test samples using the ResUnet-Transformer model surpasses the finite element method by 66.1%. Maintaining consistency in structural and parameter settings, introducing the Targeted Dropout algorithm and cosine annealing algorithm improves the prediction accuracy by 36.4% and 26.3%, respectively. To evaluate the model's generalization capability, the number of training samples for PMSM and AMT datasets is varied, and the model is tested using 100 samples. Inadequate training samples result in poor magnetic field prediction performance. When the training dataset size increases to 300, the prediction error does not decrease but shows a slight rise. However, with further increases in the training dataset size, the error significantly decreases, and the MAPE for the PMSM and AMT datasets reaches 0.7% and 0.5%, respectively, with just 500 training samples.
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Received: 08 March 2023
Published: 07 June 2024
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2024, Vol. 39 
