An Ensemble Learning-Based Predictive Parameterization Approach for Permanent Magnet Synchronous Machines

Permanent Magnet Synchronous Machines (PMSMs) are extensively utilized for their ability to deliver accurate position control, and the equivalent circuit characteristics of these machines are essential in several applications, particularly in formulating the control strategy. The study introduces an ensemble-based methodology for estimating the equivalent circuit parameters of PMSMs consisting of phase resistance (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i>), magnetizing reactance (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub>), and leakage reactance (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sub>) via manufacturer catalog data, which eliminates the necessity for experimental setups, high-quality real-time data, and operational disruptions. Six machine learning models—Multilayer Perceptron (MLP), Cascade Forward Neural Network (CFNN), Layer Recurrent Neural Network (LRNN), Transformer-like Network (TRF), Decision Tree (DT), and Support Vector Regression (SVR)—were evaluated in the first stage of the study. Among these, LRNN and TRF showed the best performance, with LRNN achieving the highest <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> (0.9212 ± 0.0973) for the (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i>) parameter, followed by TRF (<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>: 0.9163 ± 0.0561). An averaging voting ensemble model is developed by integrating the two highest-performing algorithms, LRNN and TRF, leveraging the strengths of both algorithms. The ensemble model combining TRF and LRNN further improved predictions, achieving an <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> of 0.9804 ± 0.0151 and TGF of 0.9827 ± 0.0173 for R, <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> of 0.9615 ± 0.0306 for (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub>), and TGF of 0.9236 ± 0.1177 for (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sub>). It also outperformed individual models in error metrics, with a MAPE of 7.66% for (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i>) compared to 23.06% (TRF) and 29.42% (LRNN). The visualization analysis confirmed the model’s strong predictive capability, as the error distribution is tightly clustered around zero, the estimated values align closely with the ideal line, and the real trends in efficiency and torque across various load conditions are accurately represented. Thus, the model’s capacity to accurately predict parameters and represent machine behavior has been revealed, and this method offers a feasible option for the effective use of resources, such as time and labor, in the estimation of PMSM parameters.