基于深度算子网络的电磁轨道发射速度趋肤效应的快速计算方法

doi:10.19595/j.cnki.1000-6753.tces.240431

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摘要

速度趋肤效应是影响电磁轨道发射性能的重要因素,数值计算是研究该效应的重要手段。然而,基于有限差分、有限元和有限体积法的传统数值算法,难以满足电磁轨道发射实时模拟和数字孪生场景下对速度趋肤效应的快速计算需求。为此,该文提出一种基于深度算子网络（DeepONet）的电磁轨道发射速度趋肤效应快速计算方法。首先,基于传统有限元法求解获得不同速度和电流条件下轨道区域内的磁感应强度,构建训练数据集;其次,构建非堆叠型深度算子网络,包含分支网络和主干网络,分别用于对变化参数和时空坐标进行编码,并将电枢和导轨的磁感应强度数据输入网络中进行训练;最后,通过对比不同速度和电流条件下有限元法和深度算子网络获得的结果,验证深度算子网络方法的有效性。算例实验结果表明,以有限元法的结果为基准,基于深度算子网络的电磁轨道发射模型在训练条件区间内的相对L2误差为0.43%,在训练条件区间外的相对L2误差为0.74%,平均预测时长为0.865 s,验证了所提方法的准确性和实时性。

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关键词 ：电磁轨道发射, 速度趋肤效应, 深度算子网络, 数据驱动

Abstract：

Electromagnetic rail launch is a technology that uses precisely controlled magnetic forces to accelerate the armature to a very high speed. The distribution characteristics of magnetic fields are closely related to the launch performance, and one of the physical effects that have an important impact on the magnetic field distribution is the velocity skin effect. However, the traditional numerical algorithms based on finite difference, finite element and finite volume methods are difficult to perform fast calculation of velocity skin effect in real-time simulation and digital twin scenarios of electromagnetic rail launch. Therefore, a fast calculation method based on deep operator network (DeepONet) is proposed in this paper, which can accurately and efficiently solve the velocity skin effect of electromagnetic rail launch.
DeepONet, as a powerful deep learning model that can learn nonlinear operators based on the general approximation theorem of operators, has been proven to have better generalization ability in solving calculus problems than other neural network architectures. DeepONet consists of two subnetworks, one with functions as inputs in the form of discrete points for encoding input functions on a fixed number of sensors, called Branch Net, and another for encoding domains of output functions, called Trunk Net.
In order to verify the performance of DeepONet-based method, this paper solves the magnetic field distribution of electromagnetic rail launch under different velocity and current conditions. Firstly, the magnetic induction intensity in the rail region is obtained based on the traditional finite element method, and the training data set is constructed accordingly. Then, a non-stacked DeepONet is constructed, including branch network and trunk network, which are used to encode the variable parameters and space-time coordinates, respectively. The magnetic induction intensity data of armature and rail are then fed into DeepONet for training. Finally, the results obtained by finite element method and DeepONet are compared under different conditions of velocity and current to verify the effectiveness of DeepONet-based method. The experimental results show that, the relative L2 error between the DeepONet-based method and the finite element method is 0.43% within the training conditions, and 0.74% outside the training conditions, and the average prediction time reaches 0.865s.
The following conclusions can be drawn: (1) Compared with the finite element method, the proposed DeepONet-based method introduces branch and trunk networks to decouple the electromagnetic launch parameters and the space-time computational domain, which can obtain the magnetic field distribution in the electromagnetic rail launch with higher computational efficiency. It does not need to redo finite element calculation for each electromagnetic launch condition. (2) In the transient calculation, the DeepONet-based method realizes the effective simulation of electromagnetic rail launch by introducing time variable into the branch network. The average prediction time in the transient model is 0.87 seconds, which is equivalent to the steady-state model, indicating that even with an increase in problem complexity, the inference efficiency of the DeepONet-based method is still relatively high. (3) The sensitivity analysis shows that network size has a significant impact on the performance of the DeepONet-based method, and the optimal network size for branch and trunk networks may not be the same. Although increasing the network size within a certain range can improve the learning ability of the model and reduce learning errors, overfitting is also prone to occur. Therefore, a reasonable selection of network structure and scale is crucial for the practical application of the DeepONet-based method.

Key words： Electromagnetic rail launch velocity skin effect deep operator network (DeepONet) data driven

收稿日期: 2024-03-18

PACS:

TMl53+.1

基金资助:

国家自然科学基金（92066106）、江苏省基础研究计划自然科学基金（BK20231427）、东南大学“至善青年学者”支持计划（中央高校基本科研业务费）（2242022R40022）、国家级大学生创新创业训练计划（202210286099Z）资助项目

通讯作者: 仲林林男,1990年生,副研究员,博士生导师,研究方向为高电压技术、放电等离子体技术、人工智能技术。E-mail：linlin@seu.edu.cn

作者简介: 魏蓉女,2002年生,本科生,研究方向为人工智能技术在电气工程领域的应用。E-mail：rongw.56@qq.com

引用本文:

魏蓉, 陈锦培, 仲林林. 基于深度算子网络的电磁轨道发射速度趋肤效应的快速计算方法[J]. 电工技术学报, 0, (): 2492927-2492927. Wei Rong, Chen Jinpei, Zhong Linlin. A Fast Computational Method for Velocity Skin Effect of Electromagnetic Rail Launch Based on Deep Operator Network. Transactions of China Electrotechnical Society, 0, (): 2492927-2492927.

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