Given the considerable length and weight of freight trains, their operation can be quite challenging. Improper operation may lead to train decoupling and derailment. Driver Advisory Systems (DASs) are used in some countries to assist train drivers by providing the speed curves, which are desired to be easy to track. Multi-mass train model is a good choice to depict the in-train forces in train speed curve generating, but its application is often hindered by the computation time. A single mass train model is considered as another choice to simplify the computation. To exploit the advantages of the multi-mass and single-mass models, this paper proposes a Two-step Optimization Method to generate the optimal speed curves for the freight trains. In the first step, the Rolling Optimization Algorithm (ROA) is proposed to optimize the speed curve on the basis of the single-mass model, taking the train energy consumption and punctuality as the optimization objectives. In order to assist the driver in operating the train smoothly, the speed curve generated by the ROA was tested on DAS, but it could not be followed accurately in the actual operation. To solve this problem, a Model Predictive Control (MPC) algorithm based on a multi-mass model is adopted as the second optimization step, which takes the output speed curve of the ROA as the reference speed curve. The MPC algorithm will generate a new speed curve, taking in-train forces, energy consumption and punctuality as the optimization indices. Simulations are carried out using the data from the Dalailong railway in China to evaluate the proposed method. The simulation results show that the speed curves generated by the Two-step Optimization Method are smoother than that of the ROA, and the throttle sequences are more conducive for the driver to follow in practical operation. The simulation results show that the energy consumption is reduced by 17.1% compared to that of the ROA simulation. The speed curve also can be integrated into the onboard DAS or the Automatic Train Operation (ATO) system, aiming to obtain a smooth and energy-efficient train operation.

Given the considerable length and weight of freight trains, their operation can be quite challenging. Improper operation may lead to train decoupling and derailment. Driver Advisory Systems (DASs) are used in some countries to assist the train drivers by providing the speed curves, which are desired to be easy to track. Multi-mass train model is a good choice to depict the in-train forces in train speed curve generating, but its application is often hindered by the computation time. Single mass train model is considered as another choice to simplify the computation. To exploit the advantages of the multi-mass and single mass models, this paper proposes a Two-step Optimization Method to generate the optimal speed curves for the freight trains. In the first step, the Rolling Optimization Algorithm (ROA) is proposed to optimize the speed curve on the basis of single mass model, taking the train energy consumption and punctuality as the optimization objectives. In order to assist the driver to operate the train smoothly, the speed curve generated by the ROA was tested on DAS, but it could not be followed accurately in actual operation. To solve this problem, a Model Predictive Control (MPC) algorithm based on multi-mass model is adopted as the second optimization step, which takes the output speed curve of the ROA as the reference speed curve. The MPC algorithm will generate a new speed curve, taking in-train forces, energy consumption and punctuality as the optimization indices. Simulations are carried out using the data of Dalailong railway in China to evaluate the proposed method. The simulation results show that the speed curves generated by Two-step Optimization Method are smoother than that of the ROA, and the throttle sequences are more conducive for the driver to follow in practical operation. The simulation results show that the energy consumption is reduced by 17.1% compared to that of ROA simulation. The speed curve also can be integrated into the onboard DAS or the Automatic Train Operation (ATO) system, aiming to obtain a smooth and energy-efficient train operation.