Fast Calculation Method of 3D Nonlinear Magnetic Field Based on Adaptive Model Order Reduction
Liu Yutong, Ren Ziyan, Chi Lianqiang, Zhang Dianhai, Zhang Yanli
Key Laboratory of Special Motors and High-voltage Electrical Apparatus, Ministry of Education （Shenyang University of Technology） Shenyang 110870 China
Abstract：Digital twins, as a key technology to achieve real-time monitoring and full life-cycle management of industrial products, are required to reflect the physical characteristics of in-service electrical equipment in real time through simulation. The finite element method (FEM) is commonly used for analyzing electromagnetic properties of low-frequency electrical equipment. For complex three-dimensional problems, the high spatial freedom of geometric model and many time steps result in a large amount of computational time required for finite element analysis. In addition, if the nonlinear behavior of the equipment medium is considered, the stiffness matrix has to contain the parameter information of the previous calculation, and the matrix has to be reassembled for each iteration, which greatly reduces the efficiency of the finite element calculation. The expensive computational cost limits the application of digital twin technology for the optimal design of electrical equipment and for real-time performance analysis. The greedy strategy and improved sparrow search algorithm (ISSA) are combined with the proper orthogonal decomposition (POD) method to propose an adaptive model reduction method applicable for three-dimensional nonlinear magnetic field problems. Firstly, the full-order FEM was used to model and simulate the research object, and the FEM solutions corresponding to different sample points were calculated as the sample library. Secondly, the POD was combined with radial basis function (RBF) interpolation, while the ISSA-POD-RBF reduced-order model considering optimal combination of RBF width parameters was constructed based on the ISSA; Finally, the iterative computation of snapshot matrix and optimal width parameter combination was carried out by the greedy strategy to construct a fast computational model that more closely matches the original full-order model. To verify the effectiveness of the proposed model reduction method, the TEAM24 problem and a traction transformer are taken as the research objects.The speed and accuracy of the reduction model are investigated by comparing computational results and computation time of the reduction model with the FEM full-order model. In the TEAM24 problem, a sample library containing 100 samples corresponding to the FEM solutions is prepared in advance, and the iteration termination condition of the greedy strategy is set to the maximum relative error e2max<0.5%. The final size of the snapshot matrix is determined to be (118 831×3)×13, and the POD basis retains the order of 2nd order.The results show thatthe relative errors of the samples computed by the reduced-order model constructed with the optimal combination of width parameters were overall smaller than the computational errors of the reduced-order model constructed with the same width parameters. The single-point error of flux density comparison at local nodes does not exceed 0.01%. The computational times of the proposed reduced-order model and the FEM full-order model are 205 s and 0.56 s, respectively, and the acceleration ratio is 366.07. In the three-dimensional model, the size of the finalized snapshot matrix is (125 403×3)×40, and the POD basis retains the order of 11th order. The results show that the computational errors of the model are in the same order of magnitude as those introduced during simulation due to uncertainties in material properties, dimensions, and simulation operations. The computational times of the proposed reduced-order model and the FEM full-order model are 386.4 s and 3.9 s, respectively, with an acceleration ratio of 99.08. The proposed fast solution method for the nonlinear magnetic field problem of electrical equipment provides a real-time simulation solution for the construction of digital twin models of electromagnetic performance of electrical equipment.
刘禹彤, 任自艳, 迟连强, 张殿海, 张艳丽. 基于自适应模型降阶的三维非线性磁场快速计算方法[J]. 电工技术学报, 2025, 40(1): 1-12.
Liu Yutong, Ren Ziyan, Chi Lianqiang, Zhang Dianhai, Zhang Yanli. Fast Calculation Method of 3D Nonlinear Magnetic Field Based on Adaptive Model Order Reduction. Transactions of China Electrotechnical Society, 2025, 40(1): 1-12.
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2025, Vol. 40 
