A Hybrid Electromagnetic Model of Tubular Permanent Magnet Linear Synchronous Motors Based on Transfer Learning

Accurate electromagnetic modeling and analysis are crucial for the design optimization of tubular permanent magnet linear synchronous motors (TPMLSMs). This article proposes a new electromagnetic modeling method for TPMLSMs based on transfer learning deep neural network (DNN). It integrates the electromagnetic mechanism into the data-driven model to achieve high-precision electromagnetic analysis with a small number of finite element analysis (FEA) samples. First, the electromagnetic analytical model of the slotted TPMLSM is derived from the motors’ structural parameters and relative permeability function. Second, a hybrid model based on transfer learning is developed. This model is pretrained by a large sample set generated from the analytical model in the mechanism analytical model. The trained model is then optimized in the target field using a few high-precision FEA sample sets to improve the prediction accuracy of the hybrid model. Appropriate combinations of training FEA samples are selected based on sensitivity analysis to further improve the model’s prediction accuracy and generalization ability. Third, experimental results demonstrate that the proposed method can significantly enhance the performance of the DNN model, especially when training sets are small. The key performance metrics 1−<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> decreased from 0.0607 to 0.0125, median absolute error (MEDAE) decreased from 3.535 to 1.311, RMSE decreased from 7.834 to 3.575, respectively, by DNN and the proposed method when the training set size is 5%.