常导高速磁浮列车节能速度曲线鲁棒优化研究

Robust optimization of energy-efficient speed profile for normal high-speed maglev

列车速度曲线的优化是轨道交通节省运营成本的重要途径之一,鲁棒优化方法有助于克服速度曲线节能优化中的不确定因素。针对常导高速磁浮列车节能速度曲线优化,首先将区间划分为若干区段,进而将列车运行控制的停车点步进机制、列车悬浮运行的阻力特性、区间限速、运行时分与乘坐舒适性要求以及列车总重的不确定性纳入鲁棒优化模型,并结合三项引理将其重构为带二次项和区间数的混合整数规划(MIP)问题。联合Gurobi求解器以及基于可接受目标函数值波动范围的鲁棒优化方法讨论求解算法。借助仿真算例检验模型与算法的有效性,分析列车总重、运行时分以及区段划分对运行能耗的影响。研究结果显示:列车总重取最大值时所得悲观速度曲线与列车总重取最小时所得乐观速度曲线存在差异,优化速度曲线时有必要考虑列车总重的不确定性;列车总重取最小与最大时,鲁棒速度曲线分别较悲观速度曲线和乐观速度曲线节能2.222%和7.087%;在大多数情况下,鲁棒速度曲线能够克服悲观速度曲线的保守特性;放松对运行时分的要求有助于降低列车运行能耗;选择合适的区段划分间隔有助于获取更优的节能速度曲线。所提出方法可为常导高速磁浮列车节能速度曲线的获取提供有效手段,对其他制式轨道交通列车速度曲线的优化也有参考价值。

The optimization of train speed profiles is one of the important ways to save operating costs for rail transit.The robust optimization method is helpful to overcome the uncertainties in the process of energy-efficient speed profile acquisition.Aiming at the optimization of the energy-efficient speed profile for normal high-speed maglev trains,firstly,the section was divided into several segments.Then the stopping point stepping mechanism of train operation control,the resistance characteristics of train running process,maximum speed limit,requirements of ride comfort and running time at an interval.The uncertainty of train weight was included into the robust optimization model.The combining with three lemmas,the model was reconstructed as a mixed integer programming(MIP)problem with quadratic terms and an interval number.An algorithm was designed by combining the Gurobi solver and the robust optimization method based on the acceptable objective variation range.The effectiveness of the model and the algorithm was verified by a simulation study,and the influence of the train weight,running time and segment division on the energy consumption was analyzed.The results suggest that there is a difference between the pessimistic speed profile with the maximum train weight and the optimistic speed profile with the minimum train weight.It is necessary to consider the uncertainty of the train weight when optimizing train speed profiles.When the train weight is minimum and maximum,the energy consumption of the robust speed profile is 2.222%and 7.087%less than that of the pessimistic and optimistic speed profile,respectively.In most cases,the robust speed profile can overcome the conservative characteristics of pessimistic speed profile.Relaxing the requirement on running time will reduce the energy consumption.The proposed method can provide an effective way to obtain the energy-efficient speed profile for normal high-speed maglev,and also has a useful guideline to the optimization of train speed profile for rail transit systems with other types.