吉林大学学报(工学版) ›› 2019, Vol. 49 ›› Issue (3): 749-756.doi: 10.13229/j.cnki.jdxbgxb20180120

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基于变间距动态规划的中高速磁悬浮列车 速度曲线优化

赖晴鹰1(),刘军1(),赵若愚1,骆泳吉2,孟令云1,徐亚之3   

  1. 1. 北京交通大学 交通运输学院,北京 100044
    2. 西南交通大学 交通运输与物流学院,成都 610031
    3. 中车唐山机车车辆有限公司,河北 唐山 064000
  • 收稿日期:2018-02-02 出版日期:2019-05-01 发布日期:2019-07-12
  • 通讯作者: 刘军 E-mail:15114243@bjtu.edu.cn;jliu@bjtu.edu.cn
  • 作者简介:赖晴鹰(1991?),男,博士研究生. 研究方向:交通运输规划与管理. E?mail:15114243@bjtu.edu.cn
  • 基金资助:
    国家重点研发计划项目(2016YFB1200601)

Optimal trajectory planning for middle⁃to⁃high speed maglev based on dynamic programming with mutative spacing

Qing⁃ying LAI1(),Jun LIU1(),Ruo⁃yu ZHAO1,Yong⁃ji LUO2,Ling⁃yun MENG1,Ya⁃zhi XU3   

  1. 1. School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China
    2. School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610031, China
    3. CRRC Tangshan Co. , Ltd. , Tangshan 064000, China
  • Received:2018-02-02 Online:2019-05-01 Published:2019-07-12
  • Contact: Jun LIU E-mail:15114243@bjtu.edu.cn;jliu@bjtu.edu.cn

摘要:

本文首先对中高速磁悬浮列车动力学模型进行分析,之后在考虑辅助停车区对列车运行影响的基础上提出了一种变间距的动态规划模型。该模型以双速度防护曲线临界点作为划分分区的依据,之后将分区再次划分为不同间距长度的子阶段,并构建阶段内能耗以及时间变化方程,最后在满足相关约束条件下采用逆推法求解变间距的动态规划模型。本文通过仿真案例,对比了变间距动态规划模型与等间距动态规划模型在列车速度曲线优化的异同,验证了本文提出的模型在时间效率以及能耗优化上的优势。

关键词: 铁路运输, 中高速磁悬浮, 速度曲线优化, 变间距动态规划, 辅助停车区

Abstract:

A significant approach to save energy of the middle?to?high speed maglev is to optimize the trajectory planning. This paper establishes a model based on dynamic programming with mutative spacing after analyzing the kinetic equations of the middle?to?high speed maglev and the effect of the assistant?stop area. The model firstly uses the crossover point of double protected curve as the foundation of partition. Then, model further divides the partition into small sub?stages with different spacing and formulates the equation of energy and time respectively. Finally, the model is solved by reversing push method under certain constraints. The established model is compared the conventional dynamic programming method through the numerical examples. The results indicate the advantage of the proposed model in energy saving and computational efficiency.

Key words: railway transportation, middle?to?high speed maglev, optimal trajectory planning, dynamic programming with mutative spacing, assistant?stop area

中图分类号: 

  • U293.1

图1

磁悬浮列车纵向受力分析图"

图2

速度转移情况示意图"

图3

双速度曲线防护临界点示意图"

图4

变间距动态规划算法流程图"

表1

辅助停车区位置坐标"

编号起始点/km终止点/km编号起始点/km终止点/km
10.000.821032.9733.38
21.612.041138.6839.10
33.373.771242.6843.11
45.776.201346.5947.01
58.819.231450.2150.63
612.3712.781553.0653.46
716.4116.841655.7256.14
821.0121.441757.9958.41
926.2326.631859.2060.43

表2

区段限速表"

区段/km限速/(km?h–1
0.0~3.6100
3.6~9.1163
9.1~15.0181
15.0~38.2200
38.2~45.5145
45.5~52.7167
52.7~60.0100

图5

不同模型优化后速度曲线对比分析(运行时间=50 min)"

图6

不同模型优化后速度曲线对比分析(运行时间为30 min)"

表3

不同模型参数对比分析(期望运行时间为30 min)"

情况方法间距/m阶段数能耗/(kW·h)时间误差/%计算时长/s
变间距动态规划-551196.40.67101.3
等间距动态规划601000186.70.42565.6
等间距动态规划100600245.20.33125.6

图7

能耗与运行时间关系图"

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