A physics-informed LSTM framework with lag compensation for coupled vibration signal modeling

Investigating vibration signals in complex electromechanical systems is essential for improving system stability and control performance. This study proposes a data–physics dual-driven framework to model the dynamic coupling between suspension current and levitation gap in maglev systems. A joint time–frequency analysis is first conducted using Fourier transform, ripple coefficient evaluation, and hysteresis correlation to quantify nonlinear coupling strength and identify a positively lagged relationship between current and gap. To capture this effect, we develop a physics-informed neural network (PINN) that integrates a lag compensation module, embeds electromagnetic equations as physical constraints, and employs an LSTM architecture for end-to-end vibration signal prediction. Unlike conventional approaches that design neural controllers from a control perspective, our method focuses on learning intrinsic coupling patterns directly from real-world operational data. This data-informed modeling approach, enhanced with time-delay compensation and physical consistency, enables accurate prediction of dynamic responses under realistic disturbances. Experiments on data from the Changsha medium-low-speed maglev train show that our model achieves the lowest MAE and RMSE compared to standard PINNs and purely data-driven baselines. It also responds rapidly to gap changes, with a response time of 0.167 ms, making it suitable for real-time maglev control applications. The implementation code is available at: https://github.com/sunning2024/RPinn .