Model Predictive Control-Based Speed Profile Optimization of a Freight Train Group With a Hierarchical Algorithm

Abstract

Once a freight train is delayed on a busy railway under a quasi-moving-block signaling system, the speed of its following trains may fluctuate, without proper adjustment. Updating the reference speed profile of the delayed freight train is an urgent task to improve the train operation performance and rail utilization ratio. To this end, this article proposes a speed profile optimization method for following delayed trains that is based on the idea of model predictive control (MPC). The state change time of the block section ahead is predicted for each following train according to the speed profile of its preceding train, based on which the distance between the following train and each speed protection curve (DTC) is predicted. The DTC is taken as a key optimization index for the speed profile optimization, and the other optimization indices are train delay and energy consumption. A two-step hierarchical optimization algorithm is proposed in this article. In the upper level, each prediction step is defined as the traveling time of the preceding train in each block section ahead, and the train target cruising speed sequence is calculated, with the dimension decided by the prediction horizon, using particle swarm optimization. In the lower level, the optimal speed profile is calculated based on the rolling optimization algorithm of the train speed curve in the prediction horizon. The proposed algorithm repeats the optimization process with updated train information after each control horizon. Three simulations are presented, which consider a downhill scenario, steep uphill scenario, and temporary speed limit, respectively. Then, the MPC parameters are analyzed and the optimized speed profiles are compared with the other algorithm.