A GRU-KAN Surrogate Model with Genetic Algorithm Uniform Sampling for Active Magnetic Bearings-Rotor Critical Speed Prediction.

Abstract

With the development of active magnetic bearings (AMBs) toward higher speeds, understanding high-speed rotor dynamics has become a crucial focus in AMB research. Traditional finite element modeling (FEM) methods, however, are unable to rapidly and comprehensively uncover the complex interplay between controller parameters and dynamic behavior. To address this limitation, a surrogate modeling approach based on a hybrid gated recurrent unit-Kolmogorov-Arnold network (GRU-KAN) is introduced to mathematically capture the effects of coupled control gains on rotor dynamics. To enhance model generalization, a genetic algorithm-driven uniform design sampling strategy is also implemented. Comparative studies against support vector regression and Kriging surrogates indicate a higher coefficient of determination (R2=0.9887) and lower residuals for the proposed approach. Experimental validation across multiple controller parameter combinations shows that the resulting machine learning surrogate predicts the critical speed with a mean absolute error of only 38.51 rpm and a mean absolute percentage error of 1.56×10-1%, while requiring merely 1.14×10-4 s per evaluation-compared to 201 s for traditional FEM. These findings demonstrate the surrogate's efficiency, accuracy, and comprehensive predictive capabilities, offering an effective method for rapid critical speed estimation in AMB-rotor systems.