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The demand for fast magnetic field approximation for the optimal design of electromagnetic devices is urgent nowadays. However, due to the lack of a publicly available dataset and the unclear definition of each parameter in the magnetic field dataset, the expansion of data-driven magnetic field approximation is severely limited. This study presents a physics-informed generative adversarial network (PIGAN), as well as a permanent magnet linear synchronous motor (PMLSM)-based magnetic field dataset, for fast magnetic field approximation. It includes the current density, material distribution, electromagnetic material properties, and other parameters of the electric machine. Physics-informed loss functions are utilized in the training process, making the output governed by Maxwell's equation. Different slot-pole combinations of the PMLSM are involved in the dataset to extend the generalization of PIGAN. Some indicators for the further evaluation of magnetic approximation performance, including image-based metrics and calculation methods for the performance of electric motors, are presented in this study. Some challenges of magnetic field approximation using PIGAN are also discussed. The effectiveness of the physics-informed method is verified by comparing the magnetic field approximation results and the performance analysis results of the PMLSM with FEM, and the speed of PIGAN is approximately 40 times faster than that of FEM, while the accuracy is similar. [ABSTRACT FROM AUTHOR]

In this article, a novel pre-processing method is proposed for magnetic field approximation based on neural networks. The process of calculating magnetic fields based on neural networks is presented first. In order to save the training time and reduce the estimation error, an excitation distance function, which is inspired by an analytical formula of magnetic potential, is proposed to integrate the input data, such as the geometry, excitations, and boundaries. This pre-processing or roughly reduces the dimension of the input layer by three quarters, while the training process is accelerated by a more integrated input layer. Preliminary experiments show that the predicted results by the proposed pre-processing method are close to the ground truth, with a significant reduction of computation time compared with the traditional finite element method (FEM). [ABSTRACT FROM AUTHOR]

In this article, an adaptive degrees-of-freedom (DoFs) finite-element method (FEM) is presented to solve the 3-D transient magnetic problems. For time-dependent problems, the error distribution changes over time, and hence mesh coarsening is needed in some regions to keep the number of DoFs small. In this novel h-type adaptive FEM, real mesh coarsening is replaced by an implicit elimination of DoFs, which avoids the following operations after mesh coarsening and the interpolation errors from fine mesh to coarse mesh. The DoFs to be eliminated are constrained by interpolation functions, which are formulated by the master DoFs. To adapt to the 3-D field, a constraint with a variable number of master DoFs and rational coefficients is adopted. The constraints are then integrated into the finite-element (FE) equation in the element level using the slave–master technique, which is followed by a global assembly process. After solving the global FE equation, the solution of constrained DoFs can be recovered from the solution of master DoFs. Several transient problems are computed to showcase the effectiveness of this proposed method. [ABSTRACT FROM AUTHOR]

An adaptive degrees-of-freedom finite element method (FEM) for 3-dimensional nonlinear magneto-thermal fields is proposed in this article. Both magnetic field and thermal field are discretized using a single FEM mesh, and their degrees of freedom (DoFs) are individually controlled based on the field characteristics. Before solving the algebraic equations, the constrained DoFs are removed using the slave-master technique. The computing time and the storage resources of the second set of FEM mesh are saved while meeting the different requirements on discretization. Data transfer between the thermal and magnetic fields are easily implemented, and mapping errors between different meshes are avoided. To showcase the feasibility and the effectiveness of this method, several numerical examples are tested. [ABSTRACT FROM AUTHOR]