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A numerical issue arises when we extend the convolutional neural network (CNN) U-net to the anisotropic magnetostatic field computation. The output magnetic field has a significant gradient with respect to the input geometry parameter, which introduces inevitable errors in the training process to degrade the performance of deep learning (DL). To address this issue, the subset selection approach is utilized to divide the whole database into several subsets, where the samples are assigned according to the gradient between the input and output. Then these subsets with different sample densities are combined into a global one. Taking the uniform dataset with the same sample size as a comparison, the influence of subset selection on DL is investigated by comparing the performance of CNN on different datasets. Numerical experiments illustrate that the adaptive subset selection can be employed to improve the accuracy and efficiency of the CNN network. [ABSTRACT FROM AUTHOR]

Convolutional neural networks (CNN) have shown great potentials and have been proven to be an effective tool for some image‐based deep learning tasks in the field of computational electromagnetism (CEM). In this work, an energy‐based physics‐informed neural network (EPINN) is proposed for low‐frequency electromagnetic computation. Two different physics‐informed loss functions are designed. To help the network focus on the region of interest instead of computing the whole domain on average, the magnetic energy norm error loss function is proposed. Besides, the methodology of energy minimization is integrated into the CNN by introducing the magnetic energy error loss function. It is observed that the introduction of the physics‐informed loss functions improved the accuracy of the network with the same architecture and database. Meanwhile, these changes also cause the network to be more sensitive to some hyperparameters and makes the training process oscillate or even diverge. To address this issue, the sensitivity of the network hyperparameters for both physics‐informed loss functions are further investigated. Numerical experiments demonstrate that the proposed approaches have good accuracy and efficiency with fine‐tuned hyperparameters. Furthermore, the post‐test illustrates that the EPINN has excellent interpolation performance and can obtain good extrapolation results under certain restrictions. [ABSTRACT FROM AUTHOR]

Deep learning (DL) has attracted more and more attention in computational electromagnetism. Particularly, the convolutional neural network (CNN) is one of the most popular learning models in DL due to its excellent capacity for feature extraction and convergence. The efficiency of CNN mainly depends on how many training samples are needed to effectively converge the network. The sample preparation process often involves a lot of numerical computations, which can be very expensive and time-consuming. In this article, based on the traditional DL network training procedure, two different approaches, namely adding smart training samples and reference samples, are proposed to help the DL network converge. The smart sample selection is based on a greedy algorithm, which can be applied for both training and reference samples. The influences of these two approaches on the CNN training process are investigated by an example of the coupled magneto-thermal computation applied to a transformer. Numerical results show that the two proposed approaches can significantly help the network to converge and improve the efficiency of the DL model. [ABSTRACT FROM AUTHOR]

Transformer winding hot‐spot temperature (HST) is one of the important factors affecting transformer oil–paper insulation deterioration. This study presents a three‐dimensional coupled electromagnetic‐fluid‐thermal analysis method for HST calculation in a 10 kV oil‐immersed distribution transformer, the influence of the transformer internal metal structure parts on the HST of the winding is considered in the simulation. Combining electromagnetic‐field calculation with no‐load test and load test of the transformer provides a more accurate method to determine internal losses of the transformer. Taking those power losses as heat sources, the transformer fluid‐thermal field analysis is conducted with the finite volume method. The variation of physical parameters of transformer oil with temperature is considered in the simulation. On the basis of the equivalent thermal resistance theory, the equivalent thermal conductivities of transformer windings are obtained. The simulation results deduced from the proposed method agree well with the experimental ones, which are obtained with fibre optic temperature sensors during the transformer temperature rise test, the maximum temperature difference is <3°C. The results validated the validity and accuracy of the proposed transformer HST calculation method. [ABSTRACT FROM AUTHOR]

A quasi‐3D coupled‐field method is introduced and applied on a ventilated dry‐type transformer to study temperature rise of windings in this study. A simplified 3D model was first established to calculate energy loss of core and velocity distribution in a plane above the lower yoke. Then two accurate 2D models were built up to figure out energy losses in the windings. With a combination of indirect and sequential coupling, energy losses of both windings and core were used as heat source, and velocities for both 2D models were applied as boundary condition for analysing fluid‐thermal field. Final results of temperature rise were calculated with temperature rise of two 2D models. In the end, numerical results were compared with experimental data to prove the effectiveness of this method. [ABSTRACT FROM AUTHOR]