Data-driven long-term response prediction method for maglev train suspension systems

To overcome the error accumulation problem in long-term prediction of dynamic responses of high-speed maglev train suspension systems, a data-driven response prediction method was proposed without requiring explicit dynamic differential equations. Two improvements are proposed on the basis of the deep unknown equations (DUE) flow map learning framework. First, a state-disturbance decoupling strategy was adopted. Track irregularity was treated as a known external input and concatenated with state variables at the network input, while state variables were predicted alone at the network output. Error propagation through the disturbance channel was thus fundamentally eliminated. Second, an initial-state anchoring mechanism was introduced. Real observations from the initial segment of the trajectory were used as fixed anchor points and continuously injected into the network input. A global reference baseline free from prediction error contamination was thereby provided for the recursive chain. The single-point suspension system of an electromagnetic suspension type high-speed maglev train was taken as the study object. Validation was conducted under two excitation scenarios, namely, ideal track irregularity and measured track irregularity. The results show that the prediction curves of the DUE baseline model exhibit obvious drift and divergence as the number of recursive steps increases. After the introduction of state-disturbance decoupling and initial-state anchoring, the improved scheme achieves a reduction of over 80% in all error metrics compared with the baseline under the ideal track irregularity scenario. Ablation experiments demonstrate that state-disturbance decoupling serves as the fundamental safeguard against recursive divergence, while initial-state anchoring effectively suppresses the cumulative error caused by the decay of initial information. The two strategies exhibit clear functional complementarity. Under the measured track irregularity scenario, the mean relative error of prediction is still kept within 4%. Good statistical consistency is also demonstrated under different initial conditions and disturbance sequences. The proposed method can provide a new approach for rapid dynamic response prediction of high-speed maglev suspension systems without relying on explicit dynamic equations.