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基于LSTM-KF模型的高速列车群组追踪运行轨迹预测方法

张淼 何仪娟 杨博宇 罗正伟 卢万里 唐涛 李开成 吕继东

张淼, 何仪娟, 杨博宇, 罗正伟, 卢万里, 唐涛, 李开成, 吕继东. 基于LSTM-KF模型的高速列车群组追踪运行轨迹预测方法[J]. 交通运输工程学报, 2024, 24(3): 296-310. doi: 10.19818/j.cnki.1671-1637.2024.03.021
引用本文: 张淼, 何仪娟, 杨博宇, 罗正伟, 卢万里, 唐涛, 李开成, 吕继东. 基于LSTM-KF模型的高速列车群组追踪运行轨迹预测方法[J]. 交通运输工程学报, 2024, 24(3): 296-310. doi: 10.19818/j.cnki.1671-1637.2024.03.021
ZHANG Miao, HE Yi-juan, YANG Bo-yu, LUO Zheng-wei, LU Wan-li, TANG Tao, LI Kai-cheng, LYU Ji-dong. Trajectory prediction method for high-speed train group tracking operation based on LSTM-KF model[J]. Journal of Traffic and Transportation Engineering, 2024, 24(3): 296-310. doi: 10.19818/j.cnki.1671-1637.2024.03.021
Citation: ZHANG Miao, HE Yi-juan, YANG Bo-yu, LUO Zheng-wei, LU Wan-li, TANG Tao, LI Kai-cheng, LYU Ji-dong. Trajectory prediction method for high-speed train group tracking operation based on LSTM-KF model[J]. Journal of Traffic and Transportation Engineering, 2024, 24(3): 296-310. doi: 10.19818/j.cnki.1671-1637.2024.03.021

基于LSTM-KF模型的高速列车群组追踪运行轨迹预测方法

doi: 10.19818/j.cnki.1671-1637.2024.03.021
基金项目: 

中国国家铁路集团有限公司科技研究开发计划 L2021G003

国家自然科学基金项目 52272329

北京市自然科学基金项目 L211019

详细信息
    作者简介:

    张淼(1987-), 男, 陕西佳县人, 中国铁道科学研究院集团有限公司副研究员, 工学博士, 从事轨道交通列车运行控制研究

    通讯作者:

    吕继东(1981-), 男, 河北廊坊人, 北京交通大学教授, 工学博士

  • 中图分类号: U283.1

Trajectory prediction method for high-speed train group tracking operation based on LSTM-KF model

Funds: 

Science and Technology Research and Development Project of China State Railway Co., Ltd. L2021G003

National Natural Science Foundation of China 52272329

Natural Science Foundation of Beijing L211019

More Information
  • 摘要: 为进一步缩小列车追踪距离以提高运力,研究了高速列车群组追踪运行轨迹预测问题;考虑长短期记忆网络(LSTM)模型处理序列数据的优势和卡尔曼滤波(KF)模型噪声处理的能力,提出了一种新型列车轨迹预测LSTM-KF模型;使用列车运行的历史数据进行LSTM模型训练,生成了列车轨迹预测曲线;KF模型结合预测结果和动力学机理,更正了计算结果,使LSTM模型预测的列车轨迹变得平滑;依托于高铁列控系统仿真测试平台的标准线路数据进行了仿真验证。仿真结果表明:在巡航工况下,30个预测步长后,LSTM-KF、LSTM和循环神经网络(RNN)模型的位置预测误差分别为78、798和911 m,速度相对真实值的预测误差分别为1、22和1 m·s-1,LSTM-KF模型的位置均方根误差(RMSE)分别为LSTM和RNN的7%和15%,LSTM-KF模型的速度RMSE分别为LSTM和RNN的14%和30%;在加速工况下,3个模型的位置预测误差均值分别为94、294和2 691 m,速度预测误差均值分别为0.09、10.05和2.74 m·s-1;在减速工况下,3个模型的位置预测误差均值分别为1 181、4 135和4 079 m,速度预测误差均值分别为1.14、6.01和13.52 m·s-1。可见,LSTM-KF模型在不同运行工况下均能显著提升预测精度,能够有效生成长时域数据序列,为高速列车群组追踪运行提供决策。

     

  • 图  1  高速列车传统运行与群组运行方式

    Figure  1.  Traditional and group operation modes of high-speed train

    图  2  LSTM模型内存块

    Figure  2.  LSTM model memory block

    图  3  基于LSTM-KF模型的列车轨迹预测原理

    Figure  3.  Train track prediction principle based on LSTM-KF model

    图  4  LSTM-KF模型框架

    Figure  4.  LSTM-KF model framework

    图  5  基于LSTM-KF模型的算法流程

    Figure  5.  Algorithm flow of LSTM-KF model

    图  6  高速铁路列车群组追踪运行场景

    Figure  6.  High-speed railway train group tracking operation scenario

    图  7  速度预测评价指标

    Figure  7.  Evaluation indexes of speed prediction

    图  8  位置预测评价指标

    Figure  8.  Evaluation indexes of position prediction

    图  9  巡航工况下不同模型的速度预测结果

    Figure  9.  Speed prediction results of different models under cruising conditions

    图  10  巡航工况下不同模型的位置预测结果

    Figure  10.  Position prediction results of different models under cruising conditions

    图  11  巡航工况下不同模型的加速度预测结果

    Figure  11.  Acceleration prediction results of different models under cruising conditions

    图  12  巡航工况下不同模型的两车间距预测结果

    Figure  12.  Prediction results of distances between two trains under cruising conditions using different models

    图  13  巡航工况下不同模型的两车速度差预测结果

    Figure  13.  Prediction results of speed differences between two trains under cruising conditions using different models

    图  14  加速工况下不同模型的位置预测结果

    Figure  14.  Position prediction results of different models under acceleration conditions

    图  15  加速工况下不同模型的速度预测结果

    Figure  15.  Speed prediction results of different models under acceleration conditions

    图  16  减速工况下不同模型的位置预测结果

    Figure  16.  Position prediction results of different models under deceleration conditions

    图  17  减速工况下不同模型的速度预测结果

    Figure  17.  Speed prediction results of different models under deceleration conditions

    表  1  试验对比参数设置

    Table  1.   Experimental comparison parameter settings

    参数 取值
    LSTM网络结构 100×100
    预测时窗/s 6
    历史时间步长 12
    未来时间步长 30
    状态迁移矩阵 $\left[\begin{array}{cc}0 & 0.5 \\ 0 & 1\end{array}\right]$
    观测矩阵 $\left[\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right]$
    观测协方差矩阵 $\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]$
    过程误差协方差矩阵 $\left[\begin{array}{cc}0.1 & 0 \\ 0 & 0.1\end{array}\right]$
    下载: 导出CSV

    表  2  巡航工况下不同模型的位置预测结果评价

    Table  2.   Evaluation of position prediction results of different models under cruising conditions

    时间步 RMSE/m MAE/m MAPE/%
    RNN LSTM-KF LSTM RNN LSTM-KF LSTM RNN LSTM-KF LSTM
    1 1 456.41 78.95 2 799.74 1 456.41 78.95 2 799.74 0.08 0.00 0.14
    5 1 591.03 97.88 2 464.24 1 586.20 96.49 2 453.65 0.08 0.01 0.12
    10 1 904.61 132.90 2 234.40 1 870.70 127.31 2 211.47 0.10 0.01 0.11
    15 2 431.12 163.92 2 083.96 2 311.75 155.26 2 053.49 0.12 0.01 0.11
    20 3 345.82 185.87 1 961.03 3 011.15 176.17 1 921.79 0.14 0.01 0.10
    25 4 966.02 196.82 1 850.34 4 144.52 187.91 1 799.06 0.18 0.01 0.09
    下载: 导出CSV

    表  3  巡航工况下不同模型的速度预测结果评价

    Table  3.   Evaluation of speed prediction results of different models under cruising conditions

    时间步 RMSE/(m·s-1) MAE/(m·s-1) MAPE/%
    RNN LSTM-KF LSTM RNN LSTM-KF LSTM RNN LSTM-KF LSTM
    1 1.02 1.58 22.07 1.02 1.58 22.07 0.01 0.02 0.19
    5 1.16 0.85 19.28 1.15 0.77 19.17 0.01 0.01 0.16
    10 1.40 0.65 16.40 1.37 0.53 15.87 0.01 0.01 0.14
    15 1.76 0.55 14.08 1.68 0.40 12.93 0.02 0.00 0.12
    20 2.34 0.51 12.40 2.13 0.39 10.64 0.02 0.00 0.10
    25 3.31 0.51 11.16 2.83 0.42 8.87 0.03 0.00 0.08
    下载: 导出CSV

    表  4  不同工况下真实值和LSTM-KF模型预测值

    Table  4.   Real values and predicted values of LSTM-KF model under different conditions

    时间步 加速工况-位置/m 加速工况-速度/(m·s-1) 减速工况-位置/m 减速工况-速度/(m·s-1)
    真实值 LSTM-KF模型预测值 真实值 LSTM-KF模型预测值 真实值 LSTM-KF模型预测值 真实值 LSTM-KF模型预测值
    1 4 806.00 4 892.41 70.56 74.69 18 499.00 18 894.95 96.67 96.88
    2 4 806.00 4 892.41 71.11 74.89 18 519.00 18 983.17 96.11 96.03
    3 4 849.00 4 936.37 71.39 74.89 18 499.00 19 082.20 95.83 95.25
    4 4 877.00 4 964.85 71.67 74.87 18 519.00 19 189.04 95.00 94.16
    5 4 949.00 5 037.90 71.94 74.82 18 499.00 19 300.63 94.72 93.36
    6 4 992.00 5 081.46 72.50 74.97 18 517.00 19 414.51 94.44 92.60
    7 5 021.00 5 111.03 72.78 74.90 18 499.00 19 529.68 93.89 91.75
    8 5 065.00 5 155.61 73.06 74.84 18 517.00 19 644.79 93.33 90.96
    9 5 094.00 5 185.20 73.61 74.95 18 498.00 19 759.37 93.06 90.37
    10 5 138.00 5 229.78 73.89 74.89 18 517.00 19 872.41 92.50 89.69
    11 5 168.00 5 260.35 74.17 74.83 18 497.00 19 983.59 92.22 89.22
    12 5 212.00 5 304.92 74.72 74.98 18 517.00 20 092.02 91.39 88.53
    13 5 242.00 5 335.48 75.00 74.95 18 497.00 20 197.32 91.11 88.16
    14 5 287.00 5 381.00 75.28 74.99 18 515.00 20 294.13 90.56 87.74
    15 5 317.00 5 411.49 75.56 75.04 18 498.00 20 388.78 90.28 87.49
    16 5 363.00 5 457.98 76.11 75.30 18 515.00 20 480.60 89.72 87.10
    17 5 393.00 5 488.45 76.39 75.39 18 496.00 20 569.20 89.17 86.74
    18 5 439.00 5 534.91 76.94 75.69 18 515.00 20 654.33 88.89 86.53
    19 5 470.00 5 566.35 77.22 75.82 18 496.00 20 735.88 88.61 86.33
    20 5 516.00 5 612.77 77.50 75.98 18 514.00 20 813.79 87.78 85.86
    21 5 547.00 5 644.17 77.78 76.15 18 496.00 20 888.06 87.50 85.68
    22 5 594.00 5 691.55 78.33 76.54 18 513.00 20 958.73 86.94 85.37
    23 5 625.00 5 722.92 78.61 76.77 18 496.00 21 025.86 86.67 85.20
    24 5 672.00 5 770.26 78.89 77.03 18 512.00 21 089.52 86.11 84.90
    25 5 704.00 5 802.59 79.44 77.50 18 496.00 21 149.84 85.56 84.60
    26 5 751.00 5 849.89 79.72 77.81 18 512.00 21 206.93 85.00 84.31
    27 5 783.00 5 882.19 80.00 78.16 18 495.00 21 260.98 84.72 84.15
    28 5 832.00 5 931.46 80.56 78.74 18 511.00 21 312.05 84.17 83.86
    29 5 864.00 5 963.72 80.83 79.16 18 495.00 21 360.27 83.89 83.71
    30 5 912.00 6 011.96 81.11 79.64 18 511.00 21 405.73 83.33 83.42
    下载: 导出CSV
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出版历程
  • 收稿日期:  2024-01-20
  • 网络出版日期:  2024-07-18
  • 刊出日期:  2024-06-30

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