Abstract：During the engineering case design session, Finite Element Method (FEM) analysis is essential to address the physical fields of the study object. However, the significant number of degrees of freedom often results in lengthy computation times for FEM, particularly when solving 3D problems involving coupled multi-physical fields. In design-oriented problems like battery structure optimization, finding the optimal solution typically requires thousands of iterations. If the FEM method is employed, this process could take months to complete, significantly delaying project schedules. Furthermore, it is crucial to assess equipment status based on sensor data such as motor digital twin modeling and transformer hot spot temperature real-time calculation. Utilizing the time-consuming finite element method in these scenarios may lead to delayed identification and resolution of failures, potentially causing further harm. A deep learning-based fast computation method for physical fields is proposed by combining FEM with the U-net convolutional neural network (U-net CNN), studying the effectiveness of this approach in electromagnetic fields. Firstly, we employ the finite element method to model and simulate the research object based on the actual physical model. Secondly, we export the obtained simulation results and transform the model by dividing, rasterizing, and converting it into a point cloud. These modifications are based on the geometric parameters, boundary conditions, and physical field solution results. Thirdly, we train the U-net CNN by optimizing its network parameters and utilize the trained model for swift physical field calculations of the research object. The trained model allows for rapid computation of the physical field. To assess the practicality of our method, we select a two-dimensional insulator uniform pressure ring model and a three-dimensional transformer model to calculate the electrostatic and magnetic fields. In the two-dimensional model, we employ both single-channel and multi-channel inputs. The single-channel input solely consists of the geometric model parameters, while the multi-channel input includes additional data including the radius and uplift of the size equalizing ring. To minimize memory space, we merge the multi-channel inputs using a Gaussian distribution. The results demonstrate that the single-channel U-net CNN achieves the accuracy of 99.88% for potential and 99.52% for electric field strength. Meanwhile, the FCNs-16 model achieves a potential accuracy of 99.15% and an electric field strength of 98.33%. The potential accuracy attained with the multi-channel input is 99.93%, with an electric field strength of 99.52%. The potential accuracy achieved with the FCNs-16 model is 99.80%, along with an electric field strength of 99.24%. Additionally, the computation time for the U-net CNN is 0.017 s for the single-channel input and 0.016 s for the multi-channel input both significantly faster than the finite element method. Finally, by reducing the size of the dataset, the network's prediction accuracy remains above 90% with 306 groups of data, and even with just 203 groups, it maintains an accuracy of over 85%. In the three-dimensional model, we address the magnetic field of the transformer at t=0.05 s through field-path coupling. The inputs for this model consist of Sampling pointcoordinates and voltage. The results reveal that the U-net CNN achieves the highest accuracy for magnetic induction intensity at 99.26%, while the FCNs-16 model achieves an accuracy of 98.91%. By reducing the dataset size, the model can still maintain a high prediction accuracy, even with only 193 groups of data. The method possesses the capability to be employed in real-time calculations for equipment condition assessment, as well as in design sessions necessitating multiple iterations.
张宇娇, 赵志涛, 徐斌, 孙宏达, 黄雄峰. 基于U-net卷积神经网络的电磁场快速计算方法[J]. 电工技术学报, 2024, 39(9): 2730-2742.
Zhang Yujiao, Zhao Zhitao, Xu Bin, Sun Hongda, Huang Xiongfeng. Fast Calculation Method of Electromagnetic Field Based on U-Net Convolutional Neural Network. Transactions of China Electrotechnical Society, 2024, 39(9): 2730-2742.
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