A Novel Neural Network Cell Method for Solving Nonlinear Electromagnetic Problems,Advanced Theory and Simulations

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A Novel Neural Network Cell Method for Solving Nonlinear Electromagnetic Problems
Advanced Theory and Simulations ( IF 2.9 ) Pub Date : 2021-10-13 , DOI: 10.1002/adts.202100216
Gaojia Zhu ₁ , Longnv Li ₁ , Weinong Fu _{2,

3} , Ming Xue ₁ , Tao Liu ₁ , Jianguo Zhu ₄

Affiliation

Effective analysis of nonlinear electromagnetic fields is essential for the accurate modeling of electromagnetic devices, such as transformers, generators, and motors. This paper proposes a novel approach of coupled neural network (NN) and cell method (CM) or NNCM for solving nonlinear electromagnetic problems with ferromagnetic domains. While the topologically linear relations of the cell complexes are mathematically assembled through a transformation in the Tonti diagram by the CM, and the constitutive nonlinear magnetic relations are dealt with by partially connected NN for the fast prediction of the permeability distribution inside the ferromagnetic domain. Since the construction of NN is directly related to the grid connections, a partially connected NN structure with a small number of neurons can reduce the computational cost of the training process. By using a compact NN, the proposed NNCM can effectively eliminate the time consuming iterations for determining the nonlinear permeability distribution, and improve the computational efficiency significantly. The NNCM is employed to analyze the transient electromagnetic field distribution inside a cylindrical ferromagnetic core. The results are compared with those obtained by the traditional iterative CM, which determines the nonlinear permeability distribution by lengthy numerical iterations, to verify the feasibility and effectiveness of the proposed NNCM.

中文翻译：

一种求解非线性电磁问题的新型神经网络元胞方法

非线性电磁场的有效分析对于电磁设备（例如变压器、发电机和电动机）的精确建模至关重要。本文提出了一种耦合神经网络 (NN) 和单元法 (CM) 或 NNCM 的新方法，用于解决具有铁磁域的非线性电磁问题。而单元复合体的拓扑线性关系通过CM通过Tonti图中的变换在数学上组装，并且本构非线性磁关系由部分连接的NN处理，以快速预测铁磁域内的磁导率分布。由于NN的构建与网格连接直接相关，具有少量神经元的部分连接的 NN 结构可以降低训练过程的计算成本。通过使用紧凑的 NN，所提出的 NNCM 可以有效地消除确定非线性渗透率分布的耗时迭代，并显着提高计算效率。NNCM 用于分析圆柱形铁磁芯内部的瞬态电磁场分布。将结果与传统迭代CM获得的结果进行比较，传统迭代CM通过长时间的数值迭代确定非线性渗透率分布，以验证所提出的NNCM的可行性和有效性。并显着提高计算效率。NNCM 用于分析圆柱形铁磁芯内部的瞬态电磁场分布。将结果与传统迭代CM获得的结果进行比较，传统迭代CM通过长时间的数值迭代确定非线性渗透率分布，以验证所提出的NNCM的可行性和有效性。并显着提高计算效率。NNCM 用于分析圆柱形铁磁芯内部的瞬态电磁场分布。将结果与传统迭代CM获得的结果进行比较，传统迭代CM通过长时间的数值迭代确定非线性渗透率分布，以验证所提出的NNCM的可行性和有效性。

更新日期：2021-12-07

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