A Novel Neural Network Cell Method for Solving Nonlinear Electromagnetic Problems

Abstract

AbstractEffective 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.