张宇娇, 赵志涛, 赵常威, 钱宇骋, 黄雄峰. 基于深度算子网络的电磁场快速计算方法[J]. 高电压技术, 2025, 51(3): 1484-1494. DOI: 10.13336/j.1003-6520.hve.20241627
引用本文: 张宇娇, 赵志涛, 赵常威, 钱宇骋, 黄雄峰. 基于深度算子网络的电磁场快速计算方法[J]. 高电压技术, 2025, 51(3): 1484-1494. DOI: 10.13336/j.1003-6520.hve.20241627
ZHANG Yujiao, ZHAO Zhitao, ZHAO Changwei, QIAN Yucheng, HUANG Xiongfeng. Rapid Calculation Method for Electromagnetic Fields Based on Deep Operator Network[J]. High Voltage Engineering, 2025, 51(3): 1484-1494. DOI: 10.13336/j.1003-6520.hve.20241627
Citation: ZHANG Yujiao, ZHAO Zhitao, ZHAO Changwei, QIAN Yucheng, HUANG Xiongfeng. Rapid Calculation Method for Electromagnetic Fields Based on Deep Operator Network[J]. High Voltage Engineering, 2025, 51(3): 1484-1494. DOI: 10.13336/j.1003-6520.hve.20241627

基于深度算子网络的电磁场快速计算方法

Rapid Calculation Method for Electromagnetic Fields Based on Deep Operator Network

  • 摘要: 为了提升电力设备的设计制造与运行可靠性,有限元法常被用于分析不同工况下的电磁场分布,但因其参数化计算耗时较长,深度学习代理模型在工程分析中变得愈发重要。然而,传统的基于卷积的模型,例如U-net卷积神经网络,在池化操作中可能会丢失高频信息,且没有考虑到位置坐标。该文介绍了一种基于深度算子网络(deep operator network, DeepONet)的电磁场快速计算方法。首先通过仿真或实验得到数据集,采用统一补点的方式解决不同边界条件下网格点数量不一致的问题。然后将输入数据进行傅里叶变换,以增强神经网络的高频特征提取能力。之后基于DeepONet框架,将多个可变参数和位置坐标作为输入,将磁矢势或电势作为输出,进而通过自动微分计算磁感应强度、电场强度等物理量。以简单2维算例分析不同微分约束对网络性能的影响,并最终推广到3维案例的计算。结果表明,采用所提方法计算磁感应强度和电场强度等物理量的相对误差都在3%以内,计算时间均远小于有限元法,能够实现秒级计算,相较于U-net方法具有更高的计算准确率,且易于后处理。该方法可用于需要多组参数计算的设计阶段以及满足设备状态评估或数字孪生的实时性要求。

     

    Abstract: To enhance the design, manufacturing, and operational reliability of power equipment, the finite element method (FEM) is widely employed to analyze electromagnetic field distributions under varying operating conditions. However, the computational expense associated with FEM-based parametric analyses has led to an increasing reliance on deep learning models in engineering applications. Traditional convolution-based models, such as U-net convolutional neural networks, often suffer from the loss of high-frequency information during pooling operations and fail to incorporate positional coordinates effectively. This paper introduces a rapid computational approach for electromagnetic field analysis based on the deep operator network (DeepONet). The dataset is initially generated through simulations or experiments, and the problem of inconsistency in grid point numbers under varying boundary conditions is solved by employing uniform complementary points. Fourier transformations are applied to the input data to enhance the neural network's capability for extracting high-frequency features. Within the DeepONet framework, multiple variable parameters and positional coordinates serve as inputs, while outputs include magnetic vector potential or electric potential, with derived physical quantities such as magnetic induction strength and electric field strength calculated via automatic differentiation. A simplified two-dimensional arithmetic example is presented to evaluate the impact of different differential constraints on network performance, followed by an extension to three-dimensional cases. The results demonstrate that the proposed method achieves computational errors below 3% while significantly reducing computation time compared to FEM, enabling second-level computations. Additionally, higher accuracy and greater ease of post-processingcan be obtained compared to the U-net method. This approach is particularly suitable for applications requiring extensive parametric computations during the design phase and for real-time applications such as equipment condition monitoring and digital twin implementations.

     

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