Double Loop Trajectory Planning for Virtually Coupled Trains Considering Line Condition Disturbances

The emergence of virtual coupling (VC) technology has the potential to substantially enhance the capacity of existing railway infrastructure. However, the complexity of line conditions introduces considerable disturbances to convoy operations, negatively affecting both energy consumption and operational efficiency. To address this issue, this study proposes a double loop trajectory optimization method for high-speed trains in a convoy, incorporating line condition disturbances and train dynamic characteristics. The proposed approach begins with an analysis of operating sequences under varying line conditions, leading to the development of a multi-resolution sequence optimization model for the leading train (LT). Subsequently, a train-following model is introduced to define the acceleration adjustment rules for the following train (FT) in different operating state. On this basis, a cooperative optimization framework is established to integrate the above models and define the detailed optimization procedure. Finally, a double loop seeker optimization algorithm is developed to obtain the optimal solution for the proposed model. Numerical experiments using field data from the Wuhan-Guangzhou high-speed railway line demonstrate the effectiveness of the proposed method. The experimental result proves that our method can generate trajectories with superior energy-saving and time-efficient performance while consistently maintaining safe and stable separation between virtually coupled trains.