巡航模式下地铁纵断面节能坡优化研究

地铁列车运行常采用巡航模式来保证运营的安全、舒适和准点，而人工纵断面线形设计较难契合列车的巡航状态、不适应设计条件的多变，无法做到有效节能。以变坡点里程和高程为变量，以列车双向运行牵引能耗为目标建立纵断面线形节能优化模型，采用差分进化算法进行模型求解。优化策略包括初始方案搜索和整正两个阶段，初始方案搜索阶段依据区间长度假定适当多的变坡点进行优化，方案整正阶段将删除初始方案上坡度代数差极小的变坡点得到优化方案。优化结果表明：巡航模式下，节能坡坡度值越大，中间坡度越缓，列车双向能耗越小。灵敏性分析表明：惰行距离较长时，宜设置较长的节能坡；车站高差增大时，宜缩小低位车站节能坡的长度和坡度值，增长高位车站节能坡的长度。

Energy-saving Slop Optimization of Metro Profile in Cruising Mode

The cruising mode is commonly used by metro trains for safety, comfort, and punctual operation. However, the manual design of vertical alignment is difficult to fit with the cruising state and variation in design conditions, which results in ineffective energy saving. This study defines the mileages and elevations of the gradient change points, sets up a vertical alignment optimization model based on the objective of minimizing the traction energy consumption in both directions, and utilizes a differential evolution algorithm to solve the optimization model. The optimization strategy includes two stages: initial alignment search and adjustment. In the initial alignment search stage, the appropriate number of gradient change points is set according to the interval length. The gradient change points with small gradient differences in the initial alignment are deleted to obtain the final optimal alignment. The optimization results reveal that the energy savings in both directions can be small, while the energy-saving slopes are steep, and the middle slopes are gentle. Sensitivity analysis shows that the length of the energy-saving slope should be large if the coasting length is large. If there is a significant elevation difference between the stations, the gradient and length of the energy-saving slope adjacent to the lower station should be small, and the length of the energy-saving slope adjacent to the higher station should be larger.