Online Optimization Method for Virtually Coupled Train Operation Deviation from Reference Curve

Virtually coupled train set (VCTS) has become a popular research topic in the railway industry in recent years. It is considered one of the solutions to the uneven spatial and temporal distribution of passenger flow in urban rail transit. A VCTS consists of multiple train units (TUs). The overall operation of the VCTS relies on the coordinated efforts of each TU. A feasible approach involves pre-planning reference curves for the TUs, with the Automatic Train Operation (ATO) system tracking these curves. However, as the TUs operate at close intervals, the control strategy needs to ensure safety and precise control. Consequently, the reference curve of the TU is characterized by frequent changes in acceleration. As a result, the ATO system is prone to deviating from the curve. This paper builds a time-varying vehicle dynamics model and a controller performance model based on data learning. Using these models, we predict deviations and construct an online optimization model. A mesh adaptive direct search (MASD) algorithm is designed to solve for online adjustment curves, promptly correcting any deviations. Simulation experiments demonstrate the effectiveness of the proposed online optimization method when combined with PID and MPC alzorithms.