基于物理信息神经网络的短间隙流注放电模拟  

Short⁃gap Streamer Discharge Simulation Based on Physics⁃informed Neural Network

作　　者：彭长志 董旭柱 阮江军[1,2,3] 裴学凯 张琛 邓永清 PENG Changzhi;DONG Xuzhu;RUAN Jiangjun;PEI Xuekai;ZHANG Chen;DENG Yongqing(State Key Laboratory of Power Grid Environmental Protection,Wuhan University,Wuhan 430072,China;School of Electrical Engineering and Automation,Wuhan University,Wuhan 430072,China;Hubei Engineering and Technology Research Center for AC/DC Intelligent Distribution Network,School of Electrical Engineering and Automation,Wuhan University,Wuhan 430072,China)

机构地区：[1]武汉大学电网环境保护全国重点实验室,武汉430072 [2]武汉大学电气与自动化学院,武汉430072 [3]交直流智能配电网湖北省工程中心,武汉430072

出　　处：《高压电器》2023年第9期90-97,共8页High Voltage Apparatus

基　　金：国家自然科学基金智能电网联合基金(U2066217);广西电网公司科技项目资助(GXKJXM20220072)。

摘　　要：流注放电物理过程可由相互耦合的泊松方程和对流扩散方程描述,是涉及电磁学和流体动力学的多物理场问题。针对瞬态流注放电计算量大的问题,本研究提出了一种基于物理信息融合神经网络的流注放电高效求解模型,该模型相对传统的数值求解算法可大幅提高模型的求解效率。首先,基于二维泊松方程的解析解形式,获取了大量二维随机分布空间电荷的电场分布。利用电荷分布与电场分布的对应关系,作为泊松算子物理神经网络的训练集,得到预训练的泊松方程神经网络求解算子。随后,基于二维有限元求解器获取了不同边界条件下考虑等离子体化学反应的粒子对流—扩散的求解结果,将其作为用于预训练对流扩散物理信息神经网络的训练集。最后,将预训练的泊松算子和流体算子进行连接,得到流注放电求解模型。本研究中用于生成预训练模型的神经网络结构为DeepONet,该网络能够良好的学习偏微分方程。它包含两层子网络,其中分枝网络用于输入物理场,主网络用于输入几何的空间位置。模拟结果表明,该神经网络在两类方程的学习中精度较高,相对误差小于5%。通过将两个预训练的神经网络算子迭代求解,可以复现流注放电的电子动态演变过程,且相对误差小于10%。The streamer discharge physical process can be described by the mutual coupled Poisson equation and the convection-diffusion equation,which involves the issue of multi physical field of electromagnetic and fluid dynamics.In view of large calculation of transient streamer discharge,a kind of high efficient solution model of streamer discharge based on physics-informed neutral network is proposed in this study,which,compared to the traditional numerical solution algorithm,can greatly improve the solution efficiency of the model.Firstly,the electric field distribution of a large number of two-dimensional random distribution charge is obtained based on the analytical solution of two-dimensional Poisson equation.The corresponding relation of charge and the electric field distribution is used as the training set of the Poisson operator physical neutral grid to obtain the the solution operator of the pre-trained Poisson equation neutral grid.Then,the solution result of ion convection-diffusion with consideration of the chemical reaction of plasma is obtained under different boundary conditions and on the basis of two-dimensional finite element solver,which is used as the train set of the pre-trained convection diffusion physics-informed neutral grid.Finally,the pre-trained Poisson and the fluid operator are connected to obtain the stream discharge solution model.The neural network structure used for generating the pre-trained model in this study is the DeepONet,which can learn partial differential equation very well.It contains two sub-networks,of which the branch network is used to input the physical field,and the trunk network is used to input the geometric space position.The simulation result shows that the neural network has high accuracy in the learning of the two types of equations and the relative error is less than 5%.The iterative solution of two pre-trained neutral network operator can reproduce electronic dynamic evolution of streamer discharge and the relative error is less than 10%.

关 键 词：流注放电 物理信息神经网络 DeepONet算子 深度学习 

分 类 号：TM855[电气工程—高电压与绝缘技术] TP183[自动化与计算机技术—控制理论与控制工程]