Enhanced Single-Point Mass Dynamic Model of Urban Trains for Automatic Train Operation (ATO) Systems

Accurate prediction of train acceleration is an essential requirement for Automatic Train Operation (ATO) in urban railways. While traditional single-point mass models fail to capture the distributed dynamics of coupled vehicles, multi-point models are rarely practical due to their computational cost. In this paper, we propose an enhanced single-point mass model based on Long Short-Term Memory (LSTM) networks. The model is trained on Train Control and Monitoring System (TCMS) data from Busan Metro Line 3. By averaging the coupled dynamics of sequence-cars, we obtain a realistic single-point representation. The input data undergoes kinematic preprocessing and feature engineering, including lagging, cross, and statistical measurements. The key innovation of this paper is the physics-based feedback loop mechanism, which is built into the LSTM. This mechanism uses the predicted train acceleration at each time step to update systematically the acceleration-dependent features and make new predictions. This maintains physical consistency and causal relationships without requiring future measurements, reflecting the real-world ATO operational limits. Results demonstrate very high accuracy (R² = 0.9993, MAE = 0.0083 km/h²) without error accumulation, suggesting benefits for both ATO control accuracy and energy efficiency.