留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于GM(1, 1)模型与相关向量机的轨道不平顺区间预测

王英杰 楚杭 陈云峰 时瑾

王英杰, 楚杭, 陈云峰, 时瑾. 基于GM(1, 1)模型与相关向量机的轨道不平顺区间预测[J]. 交通运输工程学报, 2023, 23(6): 135-145. doi: 10.19818/j.cnki.1671-1637.2023.06.007
引用本文: 王英杰, 楚杭, 陈云峰, 时瑾. 基于GM(1, 1)模型与相关向量机的轨道不平顺区间预测[J]. 交通运输工程学报, 2023, 23(6): 135-145. doi: 10.19818/j.cnki.1671-1637.2023.06.007
WANG Ying-jie, CHU Hang, CHEN Yun-feng, SHI Jin. Interval prediction of track irregularity based on GM(1, 1) model and relevance vector machine[J]. Journal of Traffic and Transportation Engineering, 2023, 23(6): 135-145. doi: 10.19818/j.cnki.1671-1637.2023.06.007
Citation: WANG Ying-jie, CHU Hang, CHEN Yun-feng, SHI Jin. Interval prediction of track irregularity based on GM(1, 1) model and relevance vector machine[J]. Journal of Traffic and Transportation Engineering, 2023, 23(6): 135-145. doi: 10.19818/j.cnki.1671-1637.2023.06.007

基于GM(1, 1)模型与相关向量机的轨道不平顺区间预测

doi: 10.19818/j.cnki.1671-1637.2023.06.007
基金项目: 

中央高校基本科研业务费专项资金项目 2022JBMC041

国家自然科学基金项目 52178406

国家自然科学基金项目 52078035

详细信息
    作者简介:

    王英杰(1982-),男,河北元氏人,北京交通大学副教授,工学博士,从事铁路线路养护维修技术研究

  • 中图分类号: U213.2

Interval prediction of track irregularity based on GM(1, 1) model and relevance vector machine

Funds: 

Fundamental Research Funds for the Central Universities 2022JBMC041

National Natural Science Foundation of China 52178406

National Natural Science Foundation of China 52078035

More Information
  • 摘要: 为开展以预防修为主的养护维修作业,联合GM(1, 1)灰色模型与相关向量机(RVM)算法,提出一种预测轨道不平顺演化区间的GM(1, 1)-RVM组合模型;结合轨道质量指数(TQI)的振荡演变特性,通过二次-对数复合函数平滑优化和序列权重优化改进了GM(1, 1)模型,通过粒子群优化(PSO)算法对待优化参数进行搜索确定,并在此基础上计算点的预测值;构造以点预测值为输入,以TQI实测值为输出的样本特征映射模式,引入5折交叉验证环节优化与训练了RVM模型的组合核函数;通过GM(1, 1)模型与RVM模型间的输入-输出衔接机制集成了组合预测模型,并以某有砟线路中的2个区段为实例检验了轨道不平顺区间的预测效果。研究结果表明:与既有预测模型相比,改进GM(1, 1)-RVM组合模型可得到预测区间的均值和方差,从而将预测结果从单点数值扩充到预测区间;2个区段实例在外推区间上的点预测结果与TQI真实值相比,平均百分比误差分别为1.53%和4.67%,较支持向量回归(SVR)模型分别降低了0.58%和0.61%,较GM(1, 1)-反向传播神经网络(BPNN)模型分别降低了0.15%和1.87%;改进GM(1, 1)-RVM组合模型在90%、95%和99%三种置信度下的最大平均预测区间宽度分别为0.324 5、0.387 9和0.510 5 mm,最低预测区间覆盖率分别为91.67%、95.83%和95.83%,预测区间基本涵盖了外推区间内的TQI演化数据。可见,利用预测的均值和方差构造区间边界可有效把控轨道不平顺演变过程中的随机波动,为轨道不平顺预测提供了一种新思路。

     

  • 图  1  改进GM(1, 1)-RVM组合模型求解流程

    Figure  1.  Solving process of improved GM(1, 1)-RVM combination model

    图  2  K210+800~K211+000区段迭代结果

    Figure  2.  Iteration results of K210+800-K211+000 section

    图  3  K210+800~K211+000区段预测结果

    Figure  3.  Prediction results of K210+800-K211+000 section

    图  4  K441+200~K441+400区段迭代结果

    Figure  4.  Iteration results of K441+200-K441+400 section

    图  5  K441+200~K441+400区段预测结果

    Figure  5.  Prediction results of K441+200-K441+400 section

    表  1  TQI检测数据

    Table  1.   Detection data of TQI

    动检日期 相对时间/d 实测值/mm 动检日期 相对时间/d 实测值/mm 动检日期 相对时间/d 实测值/mm
    TQI1 TQI2 TQI1 TQI2 TQI1 TQI2
    2021-01-07 0 2.65 2.47 2021-05-07 120 2.96 2.56 2021-09-07 243 3.06 3.08
    2021-01-21 14 2.55 2.25 2021-05-20 133 2.91 2.54 2021-09-24 260 3.04 3.07
    2021-02-01 25 2.63 2.31 2021-06-07 151 2.94 2.54 2021-10-09 275 3.08 3.33
    2021-02-21 45 2.55 2.17 2021-06-20 164 2.74 2.5 2021-10-23 289 3.13 3.27
    2021-03-01 53 2.37 2.59 2021-07-05 179 2.74 2.81 2021-11-08 305 3.17 3.37
    2021-03-15 67 2.51 2.44 2021-07-21 195 2.83 2.87 2021-11-15 312 3.04 3.16
    2021-04-06 89 2.84 2.73 2021-08-03 208 2.74 3.13 2021-11-22 319 3.12 3.64
    2021-04-18 101 2.99 2.65 2021-08-15 220 3.02 3.15 2021-12-08 335 3.06 3.47
    下载: 导出CSV

    表  2  K210+800~K211+000区段预测精度

    Table  2.   Prediction accuracies of K210+800-K211+000 section

    模型 MPE/% MPIW/mm PICP/%
    SVR模型[18] 2.11
    GM(1, 1)-BPNN模型[19] 1.68
    改进GM(1,1)-RVM组合模型(90%置信度) 1.53 0.324 5 100
    改进GM(1,1)-RVM组合模型(95%置信度) 0.387 9 100
    改进GM(1,1)-RVM组合模型(99%置信度) 0.510 5 100
    下载: 导出CSV

    表  3  K441+200~K441+400区段预测精度

    Table  3.   Prediction accuracies of K441+200-K441+400 section

    模型 MPE/% MPIW/mm PICP/%
    SVR模型[18] 5.28
    GM(1, 1)-BPNN模型[19] 6.54
    改进GM(1,1)-RVM组合模型(90%置信度) 4.67 0.275 3 91.67
    改进GM(1,1)-RVM组合模型(95%置信度) 0.329 0 95.83
    改进GM(1,1)-RVM组合模型(99%置信度) 0.433 0 95.83
    下载: 导出CSV
  • [1] 李再帏, 雷晓燕, 高亮. 轨道短波不平顺数值模拟新方法[J]. 交通运输工程学报, 2016, 16(1): 37-45. doi: 10.19818/j.cnki.1671-1637.2016.01.005

    LI Zai-wei, LEI Xiao-yan, GAO Liang. New numerical simulation method of shortwave track irregularity[J]. Journal of Traffic and Transportation Engineering, 2016, 16(1): 37-45. (in Chinese) doi: 10.19818/j.cnki.1671-1637.2016.01.005
    [2] 肖乾, 王丹红, 陈道云, 等. 高速列车轮轨激励作用机理及其影响综述[J]. 交通运输工程学报, 2021, 21(3): 93-109. doi: 10.19818/j.cnki.1671-1637.2021.03.005

    XIAO Qian, WANG Dan-hong, CHEN Dao-yun, et al. Review on mechanism and influence of wheel-rail excitation of high-speed train[J]. Journal of Traffic and Transportation Engineering, 2021, 21(3): 93-109. (in Chinese) doi: 10.19818/j.cnki.1671-1637.2021.03.005
    [3] GONZALO A P, HORRIDGE R, STEELE H, et al. Review of data analytics for condition monitoring of railway track geometry[J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(12): 22737-22754. doi: 10.1109/TITS.2022.3214121
    [4] LASISI A, ATTOH-OKINE N. An unsupervised learning framework for track quality index and safety[J]. Transportation Infrastructure Geotechnology, 2020, 7(1): 1-12. doi: 10.1007/s40515-019-00087-6
    [5] ANDRADE A R, TEIXEIRA P F. Uncertainty in rail-track geometry degradation: Lisbon-Oporto Line case study[J]. Journal of Transportation Engineering, 2011, 137(3): 193-200. doi: 10.1061/(ASCE)TE.1943-5436.0000206
    [6] CAETANO L F, TEIXEIRA P F. Availability approach to optimizing railway track renewal operations[J]. Journal of Transportation Engineering, 2013, 139(9): 941-948. doi: 10.1061/(ASCE)TE.1943-5436.0000575
    [7] KHOUZANI A H E, GOLROO A, BAGHERI M. Railway maintenance management using a stochastic geometrical degradation model[J]. Journal of Transportation Engineering, Part A: Systems, 2017, 143(1): 4016002. doi: 10.1061/JTEPBS.0000002
    [8] FAMUREWA S M, JUNTTI U, NISSEN A, et al. Augmented utilisation of possession time: analysis for track geometry maintenance[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2016, 230(4): 1118-1130. doi: 10.1177/0954409715583890
    [9] LIU Reng-kui, XU Peng, WANG Fu-tian. Research on a short-range prediction model for track irregularity over small track lengths[J]. Journal of Transportation Engineering, 2010, 136(12): 1085-1091. doi: 10.1061/(ASCE)TE.1943-5436.0000192
    [10] XU P, SUN Q, LIU R, et al. A short-range prediction model for track quality index[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2011, 225(3): 277-285. doi: 10.1177/2041301710392477
    [11] 常艳艳, 刘仍奎, 王福田, 等. 兰新线铁路轨道几何状态劣化短期预测模型研究[J]. 铁道学报, 2020, 42(11): 124-129.

    CHANG Yan-yan, LIU Reng-kui, WANG Fu-tian, et al. Short-term prediction model for track geometry degradation on Lanzhou-Xinjiang Railway[J]. Journal of the China Railway Society, 2020, 42(11): 124-129. (in Chinese)
    [12] LASISI A, ATTOH-OKINE N. Principal components analysis and track quality index: a machine learning approach[J]. Transportation Research Part C: Emerging Technologies, 2018, 91: 230-248. doi: 10.1016/j.trc.2018.04.001
    [13] SRESAKOOLCHAI J, KAEWUNRUEN S. Railway defect detection based on track geometry using supervised and unsupervised machine learning[J]. Structural Health Monitoring, 2022, 21(4): 1757-1767. doi: 10.1177/14759217211044492
    [14] KHAJEHEI H, AHMADI A, SOLEIMANMEIGOUNI I, et al. Prediction of track geometry degradation using artificial neural network: a case study[J]. International Journal of Rail Transportation, 2022, 10(1): 24-43. doi: 10.1080/23248378.2021.1875065
    [15] GULER H. Prediction of railway track geometry deterioration using artificial neural networks: a case study for Turkish state railways[J]. Structure and Infrastructure Engineering, 2014, 10(5): 614-626. doi: 10.1080/15732479.2012.757791
    [16] LEE J S, HWANG S H, CHOI I Y, et al. Prediction of track deterioration using maintenance data and machine learning schemes[J]. Journal of Transportation Engineering, Part A: Systems, 2018, 144(9): 04018045. doi: 10.1061/JTEPBS.0000173
    [17] 彭丽宇, 张进川, 苟娟琼, 等. 基于BP神经网络的铁路轨道几何不平顺预测方法[J]. 铁道学报, 2018, 40(9): 154-158.

    PENG Li-yu, ZHANG Jin-chuan, GOU Juan-qiong, et al. Prediction method of railway track geometric irregularity based on BP neural network[J]. Journal of the China Railway Society, 2018, 40(9): 154-158. (in Chinese)
    [18] 于瑶, 刘仍奎, 王福田. 基于支持向量机的轨道不平顺预测研究[J]. 铁道科学与工程学报, 2018, 15(7): 1671-1677.

    YU Yao, LIU Reng-kui, WANG Fu-tian. Prediction for track irregularity based on support vector machine[J]. Journal of Railway Science and Engineering, 2018, 15(7): 1671-1677. (in Chinese)
    [19] 韩晋, 杨岳, 陈峰, 等. 基于非等时距加权灰色模型与神经网络的轨道不平顺预测[J]. 铁道学报, 2014, 36(1): 81-87.

    HAN Jin, YANG Yue, CHEN Feng, et al. Prediction of track irregularity based on non-equal interval weighted grey model and neural network[J]. Journal of the China Railway Society, 2014, 36(1): 81-87. (in Chinese)
    [20] 马子骥, 郭帅锋, 李元良. 基于改进非等间距灰色模型和PSVM的轨道质量指数预测[J]. 铁道学报, 2018, 40(6): 154-160.

    MA Zi-ji, GUO Shuai-feng, LI Yuan-liang. Forecasting of track irregularity based on improved non-equal interval grey model and PSVM[J]. Journal of the China Railway Society, 2018, 40(6): 154-160. (in Chinese)
    [21] TIPPING M E. Sparse Bayesian learning and the relevance vector machine[J]. Journal of Machine Learning Research, 2001, 1(3): 211-244.
    [22] 明祖涛, 刘军, 夏力, 等. 改进的灰色模型在高铁沉降预测中的应用[J]. 测绘科学, 2015, 40(4): 137-140.

    MING Zu-tao, LIU Jun, XIA Li, et al. Study of the implementation of improved grey model in high-speed railway settlement prediction[J]. Science of Surveying and Mapping, 2015, 40(4): 137-140. (in Chinese)
    [23] NABAEI A, HAMIAN M, PARSAEI M R, et al. Topologies and performance of intelligent algorithms: a comprehensive review[J]. Artificial Intelligence Review, 2018, 49(1): 79-103. doi: 10.1007/s10462-016-9517-3
    [24] 杨维, 李歧强. 粒子群优化算法综述[J]. 中国工程科学, 2004, 6(5): 87-94.

    YANG Wei, LI Qi-qiang. Survey on particle swarm optimization algorithm[J]. Engineering Science, 2004, 6(5): 87-94. (in Chinese)
    [25] 王春雷, 赵琦, 秦孝丽, 等. 基于改进相关向量机的锂电池寿命预测方法[J]. 北京航空航天大学学报, 2018, 44(9): 1998-2003.

    WANG Chun-lei, ZHAO Qi, QIN Xiao-li, et al. Life prediction method of lithium battery based on improved relevance vector machine[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(9): 1998-2003. (in Chinese)
    [26] 雷亚国, 陈吴, 李乃鹏, 等. 自适应多核组合相关向量机预测方法及其在机械设备剩余寿命预测中的应用[J]. 机械工程学报, 2016, 52(1): 87-93.

    LEI Ya-guo, CHEN Wu, LI Nai-peng, et al. A relevance vector machine prediction method based on adaptive multi-kernel combination and its application to remaining useful life prediction of machinery[J]. Journal of Mechanical Engineering, 2016, 52(1): 87-93. (in Chinese)
    [27] FALAMARZI A, MORIDPOUR S, NAZEM M, et al. Prediction of tram track gauge deviation using artificial neural network and support vector regression[J]. Australian Journal of Civil Engineering, 2019, 17(1): 63-71. doi: 10.1080/14488353.2019.1616357
    [28] 李麟玮, 吴益平, 苗发盛, 等. 基于不同Bootstrap方法和KELM-BPNN模型的滑坡位移区间预测[J]. 岩石力学与工程学报, 2019, 38(5): 912-926.

    LI Lin-wei, WU Yi-ping, MIAO Fa-sheng, et al. Landslide displacement interval prediction based on different Bootstrap methods and KELM-BPNN model[J]. Chinese Journal of Rock Mechanics and Engineering, 2019, 38(5): 912-926. (in Chinese)
    [29] 惠阳, 王永岗, 彭辉, 等. 基于优化PSO-BP算法的耦合时空特征下地铁客流预测[J]. 交通运输工程学报, 2021, 21(4): 210-222. doi: 10.19818/j.cnki.1671-1637.2021.04.016

    HUI Yang, WANG Yong-gang, PENG Hui, et al. Subway passenger flow prediction based on optimized PSO-BP algorithm with coupled spatial-temporal characteristics[J]. Journal of Traffic and Transportation Engineering, 2021, 21(4): 210-222. (in Chinese) doi: 10.19818/j.cnki.1671-1637.2021.04.016
    [30] 刘刚, 孙佳琦, 董伟星. 改进粒子群优化算法在建筑能耗优化中的参数设置[J]. 天津大学学报(自然科学与工程技术版), 2021, 54(1): 82-90.

    LIU Gang, SUN Jia-qi, DONG Wei-xing. Parameter settings of improved particle swarm optimization algorithm in building energy consumption optimization[J]. Journal of Tianjin University (Science and Technology), 2021, 54(1): 82-90. (in Chinese)
  • 加载中
图(5) / 表(3)
计量
  • 文章访问数:  202
  • HTML全文浏览量:  62
  • PDF下载量:  85
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-06-05
  • 刊出日期:  2023-12-25

目录

    /

    返回文章
    返回