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Article(id=1244336754346537920, tenantId=1146029695717560320, journalId=1244311425741537314, issueId=1244336743298740932, articleNumber=null, orderNo=null, doi=10.16450/j.cnki.issn.1004-6801.2025.05.023, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1675958400000, receivedDateStr=2023-02-10, revisedDate=1689782400000, revisedDateStr=2023-07-20, acceptedDate=null, acceptedDateStr=null, onlineDate=1774602600895, onlineDateStr=2026-03-27, pubDate=1759248000000, pubDateStr=2025-10-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774602600895, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774602600895, creator=13701087609, updateTime=1774602600895, updator=13701087609, issue=Issue{id=1244336743298740932, tenantId=1146029695717560320, journalId=1244311425741537314, year='2025', volume='45', issue='5', pageStart='855', pageEnd='1056', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774602598261, creator=13701087609, updateTime=1774603435030, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244340253042000577, tenantId=1146029695717560320, journalId=1244311425741537314, issueId=1244336743298740932, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244340253042000578, tenantId=1146029695717560320, journalId=1244311425741537314, issueId=1244336743298740932, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1028, endPage=1036, ext={EN=ArticleExt(id=1244336756091368397, articleId=1244336754346537920, tenantId=1146029695717560320, journalId=1244311425741537314, language=EN, title=Rapid Detection Method for Metro Rail Corrugation Based on Vibration Energy Ratio, columnId=1244336744728998604, journalTitle=Journal of Vibration,Measurement and Diagnosis, columnName=PAPER, runingTitle=null, highlight=null, articleAbstract=

To investigate the data-driven evolution of rail corrugation in subways，a spatio-temporally dense measurement method is proposed for rapid detection. First，high-precision sensors are used to measure car-body vibration，collecting triaxial acceleration data. Second，vehicle speed and mileage position are estimated by fusing triaxial vibration acceleration from different car bodies. Then，the vertical vibration acceleration of the car body is decomposed via wavelet packet analysis，and a vibration energy ratio index is defined as the ratio of the energy in the characteristic frequency band excited by rail corrugation wavelength to the total vibration energy. The vibration energy ratio threshold is set to automatically identify rail corrugation and output mileage information. Finally，the corrugation wavelength is derived from the ratio of vehicle speed to characteristic frequency，and the relationship between vibration energy ratio and corrugation amplitude is analyzed. Results show that using a vibration energy ratio threshold of 0.2 yields corrugation mileage distribution consistent with that from noise-based identification，and the calculated corrugation wavelength matches the measured value of 175 mm from a corrugation analyzer. Statistical clustering reveals that the relationship between rail corrugation amplitude and vibration energy ratio is not purely linear. Line-wide rapid detection shows that non-corrugated sections account for 76.56% of the track，while corrugation sections account for 23.44%. Among the corrugated sections，those with wavelengths below 60 mm dominate （77.88%），whereas those above 60 mm account for 22.12%.

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为研究数据驱动的地铁钢轨波磨状态演变规律，针对地铁钢轨波磨的快速检测问题，提出了一种时空密集型的地铁钢轨波磨快速测量方式。首先，采用高精度传感器检测列车编组车体振动，收集车体三向振动加速度数据；其次，融合不同车体三向振动加速度估计车速和里程位置；然后，采用小波包分解车体垂向振动加速度，定义振动能量比指标，即钢轨波磨波长激发的车体振动特征频带能量与振动总能量的比值，确定振动能量比阈值自动识别钢轨波磨，并输出里程信息；最后，通过车速与特征频率的比值得到钢轨波磨波长信息，并分析振动能量比和钢轨波磨幅值的映射关系。结果表明：振动能量比阈值取为0.2时识别的钢轨波磨里程分布与车厢噪声识别结果一致，计算的钢轨波磨波长与波磨仪实测波长均为175 mm；统计聚类发现钢轨波磨幅值与振动能量比不是单一线性映射关系；基于振动能量比快速检测全线钢轨波磨分布，发现无波磨区段占比为76.56%，波磨区段占比为23.44%，其中钢轨波磨波长以60 mm以下为主，占比为77.88%，波长60 mm以上的波磨占比为22.12%。

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陈嵘，男，1981年9月生，博士、教授、博士生导师。主要研究方向为轨道动力学及轨道平顺性。曾发表《高速道岔尖轨弹性波频散特性研究》（《铁道学报》2022年第44卷第4期）等论文。E-mail：

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陈嵘，男，1981年9月生，博士、教授、博士生导师。主要研究方向为轨道动力学及轨道平顺性。曾发表《高速道岔尖轨弹性波频散特性研究》（《铁道学报》2022年第44卷第4期）等论文。E-mail：

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陈嵘，男，1981年9月生，博士、教授、博士生导师。主要研究方向为轨道动力学及轨道平顺性。曾发表《高速道岔尖轨弹性波频散特性研究》（《铁道学报》2022年第44卷第4期）等论文。E-mail：

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Journal of Naval Aeronautical and Astronautical University， 2020， 35（3）： 265-270， 284.（in Chinese）, articleTitle=Rolling bearing condition vibration monitoring based on wavelet packet and principal component analysis, refAbstract=null)], funds=[Fund(id=1244351852167409844, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336754346537920, awardId=2024NSFTD0010, language=CN, fundingSource=四川省科技计划资助项目(2024NSFTD0010), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1244351842797335508, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336754346537920, xref=1., ext=[AuthorCompanyExt(id=1244351842801529813, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336754346537920, companyId=1244351842797335508, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.School of Civil Engineering，Southwest Jiaotong University　Chengdu，610031，China), 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基于振动能量比的地铁钢轨波磨快速检测方法
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陈嵘 1, 2 , 徐舟 1, 2 , 从建力 1, 2 , 薛旻 1, 2 , 安博洋 1, 2 , 王平 1, 2
振动、测试与诊断 | 论文 2025,45(5): 1028-1036
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振动、测试与诊断 | 论文 2025, 45(5): 1028-1036
基于振动能量比的地铁钢轨波磨快速检测方法
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陈嵘1, 2 , 徐舟1, 2, 从建力1, 2, 薛旻1, 2, 安博洋1, 2, 王平1, 2
作者信息
  • 1西南交通大学土木工程学院　成都，610031
  • 2西南交通大学高速铁路线路工程教育部重点实验室　成都，610031

    • 陈嵘，男，1981年9月生，博士、教授、博士生导师。主要研究方向为轨道动力学及轨道平顺性。曾发表《高速道岔尖轨弹性波频散特性研究》（《铁道学报》2022年第44卷第4期）等论文。E-mail：

Rapid Detection Method for Metro Rail Corrugation Based on Vibration Energy Ratio
Rong CHEN1, 2 , Zhou XU1, 2, Jianli CONG1, 2, Min XUE1, 2, Boyang AN1, 2, Ping WANG1, 2
Affiliations
  • 1.School of Civil Engineering，Southwest Jiaotong University　Chengdu，610031，China
  • 2.Key Laboratory of High-Speed Railway Engineering，Ministry of Education，Southwest Jiaotong University　Chengdu，610031，China
出版时间: 2025-10-01 doi: 10.16450/j.cnki.issn.1004-6801.2025.05.023
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摘要
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为研究数据驱动的地铁钢轨波磨状态演变规律，针对地铁钢轨波磨的快速检测问题，提出了一种时空密集型的地铁钢轨波磨快速测量方式。首先，采用高精度传感器检测列车编组车体振动，收集车体三向振动加速度数据；其次，融合不同车体三向振动加速度估计车速和里程位置；然后，采用小波包分解车体垂向振动加速度，定义振动能量比指标，即钢轨波磨波长激发的车体振动特征频带能量与振动总能量的比值，确定振动能量比阈值自动识别钢轨波磨，并输出里程信息；最后，通过车速与特征频率的比值得到钢轨波磨波长信息，并分析振动能量比和钢轨波磨幅值的映射关系。结果表明：振动能量比阈值取为0.2时识别的钢轨波磨里程分布与车厢噪声识别结果一致，计算的钢轨波磨波长与波磨仪实测波长均为175 mm；统计聚类发现钢轨波磨幅值与振动能量比不是单一线性映射关系；基于振动能量比快速检测全线钢轨波磨分布，发现无波磨区段占比为76.56%，波磨区段占比为23.44%，其中钢轨波磨波长以60 mm以下为主，占比为77.88%，波长60 mm以上的波磨占比为22.12%。

钢轨波磨  /  车体振动加速度  /  小波包分析  /  振动能量比  /  特征频带

To investigate the data-driven evolution of rail corrugation in subways，a spatio-temporally dense measurement method is proposed for rapid detection. First，high-precision sensors are used to measure car-body vibration，collecting triaxial acceleration data. Second，vehicle speed and mileage position are estimated by fusing triaxial vibration acceleration from different car bodies. Then，the vertical vibration acceleration of the car body is decomposed via wavelet packet analysis，and a vibration energy ratio index is defined as the ratio of the energy in the characteristic frequency band excited by rail corrugation wavelength to the total vibration energy. The vibration energy ratio threshold is set to automatically identify rail corrugation and output mileage information. Finally，the corrugation wavelength is derived from the ratio of vehicle speed to characteristic frequency，and the relationship between vibration energy ratio and corrugation amplitude is analyzed. Results show that using a vibration energy ratio threshold of 0.2 yields corrugation mileage distribution consistent with that from noise-based identification，and the calculated corrugation wavelength matches the measured value of 175 mm from a corrugation analyzer. Statistical clustering reveals that the relationship between rail corrugation amplitude and vibration energy ratio is not purely linear. Line-wide rapid detection shows that non-corrugated sections account for 76.56% of the track，while corrugation sections account for 23.44%. Among the corrugated sections，those with wavelengths below 60 mm dominate （77.88%），whereas those above 60 mm account for 22.12%.

rail corrugation  /  car-body vibration acceleration  /  wavelet packet analysis  /  vibration energy ratio  /  characteristic frequency band
陈嵘, 徐舟, 从建力, 薛旻, 安博洋, 王平. 基于振动能量比的地铁钢轨波磨快速检测方法. 振动、测试与诊断, 2025 , 45 (5) : 1028 -1036 . DOI: 10.16450/j.cnki.issn.1004-6801.2025.05.023
Rong CHEN, Zhou XU, Jianli CONG, Min XUE, Boyang AN, Ping WANG. Rapid Detection Method for Metro Rail Corrugation Based on Vibration Energy Ratio[J]. Journal of Vibration,Measurement and Diagnosis, 2025 , 45 (5) : 1028 -1036 . DOI: 10.16450/j.cnki.issn.1004-6801.2025.05.023
正文
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引言
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城市轨道交通具有运量大、密度大、速度快等特点［1］，为保障地铁运行安全性和乘客乘坐舒适性，目前平均每月2次的轨道检测周期已不能满足需求。钢轨波磨［1⁃2］不仅会恶化轮轨接触关系，引起车辆构件及轨道结构高频振动，还会产生疲劳伤损和噪声，影响行车安全和乘坐舒适性［3］。因此，需要快速检测地铁钢轨波磨特征，为钢轨打磨管理的科学决策提供数据支撑。
国内外通常采用直接测量法作为评价钢轨波磨和制定打磨策略的测量依据［4］。直接测量法［5］可以直接测量钢轨波磨的几何特征，结果精确直观，但是测量速度慢。为快速检测钢轨波磨并及时打磨维修，间接测量法以车辆轴箱加速度等轮轨接触响应作为测量指标对钢轨波磨进行检测。王林栋［6］对我国高速铁路钢轨波磨进行多次测试，通过分析轴箱振动特征提出了振动响应快速检测方法。Salvador等［7］对西班牙铁路网进行了测试，以不同方式收集和分析了轴箱振动加速度，研究结果表明，轴箱加速度可以有效识别钢轨波磨。谢清林等［8］结合深度学习，利用轴箱加速度构建了一种基于一维卷积神经网络的地铁钢轨波磨智能识别方法。Pieringer等［9］提出了一种改进的根据轴箱加速度识别钢轨波磨的方法，在时域信息中能够分离出车轮多边形和钢轨波磨特征。文献［10‑12］利用车载设备，通过监测轴箱加速度识别和管理钢轨波磨，该方法可实现钢轨波磨里程覆盖式的周期性测量，但在运营的地铁列车轴箱位置加装振动加速度监测装置，运维成本高且存在安全隐患。
为满足数据驱动的钢轨波磨状态评估，国内外学者研究发现，车厢噪声与钢轨波磨诱发的轮轨噪声映射关系显著，车体振动含有钢轨波磨激发的频率成分。Wei等［13］将车厢噪声测量与现场轨道表面不平顺测试相结合，提取由钢轨波磨引起的特征噪声，根据其时频分布特征提出了基于车厢噪声识别钢轨波磨的方法。Liu等［14］建立了轮轨噪声的数值模型，确定钢轨波磨幅值与噪声能级的非线性映射关系，以噪声能级作为钢轨波磨的评价指标。Han等［15］实测了轮轨粗糙度、轮轨噪声和车厢噪声，确定了轮轨噪声和车厢噪声之间的传递函数，并基于车内噪声限值确定钢轨打磨限值。研究发现，地铁钢轨波磨引起的振动频率约在100~200 Hz之间［16⁃17］，因钢轨波磨诱发的振动能量可以传递至车厢地板［18‑21］。Tsunashima等［22］ 介绍了日本普速铁路系统中基于车体振动加速度识别钢轨波磨的便携式车载传感系统。上述研究表明，钢轨波磨激发的特征振动能量可以传递至车厢底板。
笔者提出量化指标来描述钢轨波磨激发的振动能量在车体振动总能量的占比，验证了该指标用于钢轨波磨识别的有效性。结合地铁车辆的特点，提出了基于振动能量比的地铁钢轨波磨快速检测方法。该方法同样适用于轴箱振动加速度数据处理，能够分析轴箱加速度数据中与钢轨波磨相关的振动能量占轴箱振动总能量的比值。
1　地铁钢轨波磨快速检测技术
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钢轨波磨引起的车体振动频率的计算式为
其中：为列车行驶速度；为钢轨波磨波长。
采用高精度传感器监测地铁列车编组车体振动加速度，通过基于振动能量比的地铁钢轨波磨检测算法处理车体振动加速度，获取地铁钢轨波磨波长及其里程信息。基于振动能量比的地铁钢轨波磨检测技术路线如图 1所示。
1.1　列车编组车体振动监测
在列车编组各节车厢内的监测点位放置高精度传感器，实时监测列车车体振动加速度，并配备移动电源确保能够全程监测车体的振动信息。为减弱列车悬挂装置对数据监测的影响，根据《铁道车辆动力学性能评定和试验鉴定规范》［23］，将监测点位设置在各节车体前转向架正上方的车厢地板上，监测设备包括三向加速度传感器和数据采集设备。
1.2　基于振动能量比的地铁钢轨波磨检测方法
该方法基于高精度传感器收集车体振动加速度数据，能够快速识别钢轨波磨，输出钢轨波磨特征波长和里程信息。首先，通过高精度传感器监测车体振动加速度信息；其次，融合车体三向振动加速度估计实时车速及里程位置信息；然后，对车体垂向加速度进行小波包分解，识别钢轨波磨激发的车体振动特征频带，计算特征频带振动能量和振动总能量的比值，确定阈值对钢轨波磨进行自动识别；最后，利用移动窗法获取特征频率，根据式（1）计算钢轨波磨特征波长λ，并确定其分布里程。
实测分析地铁线路某区间车体振动加速度，将算法输出结果与钢轨波磨仪实测结果及车厢噪声的时频分析结果进行对比，验证了本算法的正确性。
2　振动能量比的定义
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2.1　特征频带分析
研究表明：钢轨波磨引起的轮轨高频振动能量经车辆一系、二系悬挂系统可传递至车厢地板［18‑22］，但从车体振动加速度时域信息中无法识别钢轨波磨的特征信息；基于频谱分析可以获取车体振动主频，但不能反映由于钢轨波磨引起的车体振动信号瞬时频率的变化；借助小波包分析可知钢轨波磨产生的信号频率成分及出现的具体时刻，即特征频带。
小波包分析通过在空间结构上按照二进制分法对小波子空间进行频率划分，得到更细的信号分辨率［24］。采用将尺度空间和小波子空间统一表示为
正交分解，可用的分解统一为
设函数为的闭包空，为函数的闭包并满足如下关系［35］
当时，式（4）化简为
式（5）中和为双尺度系数，满足正交关系，即
当时，有
对车体垂向加速度的小波包分解算法为由序列求序列和，即
其中：分别为尺度因子和位移因子。
小波包重构算法为
对车体垂向振动加速度进行层小波包分解，小波包分解树结构如图 2所示。其中，为车体垂向振动加速度原始信号。将每层节点信号均分解为低频信号和高频信号，依次分解后第层信号序号为，对应的节点数为，可以通过各节点信号对比确定特征频带，即
每个节点信号的带宽为
其中：为原始信号采样频率；为分解层数。
2.2　振动能量比
为获取全时段车体垂向振动加速度在频域上的变化，利用移动窗法对车体垂向振动加速度信号进行分割，则原始信号可以分为
其中：W为窗口数。
对移动窗下的车体垂向加速度信号进行小波包分析，单个移动窗下的小波包分解层，确定由钢轨波磨引起车体异常振动的特征频带，对特征频带的车体振动加速度进行时频转换，求得对应的特征频率，再由车速和特征频率即可计算钢轨波磨波长λ。具体计算式为
其中：为时频转换后的车体垂向振动加速度幅值信号；为特征频带内的车体垂向振动加速度峰峰值对应的频率位置；为输出位置对应的特征频率，记为。
钢轨波磨会引起车体产生异常的振动能量，小波包分解层后的第个频带的振动信号能量为，即
其中：，为频带号；，为信号的数据点。
由每个频带的振动信号能量可以求得该层振动总能量为
基于小波包分析节点能量系数，引入振动能量比的概念，其计算公式为
其中：、分别为第层的特征频带的能量和该层所有频带的能量总和。
和的计算公式为
其中：，为特征频带的数据点；为特征频带号。
3　实测分析
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3.1　车体振动加速度与车厢噪声测量
测试线路为我国某地铁运营线，其中A‑B为实例分析区间，其线路情况如图3所示。区间有两个曲线路段，曲线半径分别为400 m和405 m。根据现场调研，该区间曲线路段存在较为严重的钢轨波磨，波长范围为［100，200］ mm。
测试线路全线上下行共计50个区间，约68 km，测试过程中列车以正常运营速度运行，车厢内布置的车体振动加速度监测设备包括高精度传感器和数据采集设备。高精度传感器由3个正交的加速度传感器组成，可测量三轴（横向、垂向、纵向）加速度。根据车体振动特性，选用传感器量程为2g，采样频率为5 kHz。利用采样频率为40 kHz的麦克风实测车厢噪声，用于验证车体振动识别的钢轨波磨与车厢噪声识别的结果是否一致。为收集列车振动加速度信息，根据文献［33］中关于测定客车车体振动加速度的加速度传感器安装位置规定，将高精度传感器放置于车体与转向架连接处心盘一侧1 000 mm的车体地板上。现场测试布置如图 4所示。
3.2　列车车速与里程位置估计
以A站至B站的区间测试为例，通过高精度加速度传感器监测区间内地铁编组各车体振动加速度。单节车体振动加速度如图 5所示。
首先，对车体纵向加速度进行一次积分初步估计车速，再通过二次积分初步估计里程，即
其中：、分别为时刻的速度和里程估计值；。
利用数据融合的方法对初始估计车速进行修正，对不同车体的垂向和横向加速度进行波形匹配，获取任意时刻不同车厢内编号为、的传感器之间的信号时间延迟量和时间延迟量，则时刻编号为、的传感器估计的车速为
其中：为传感器设置距离。
对任意两个传感器的加速度均可进行波形匹配求得时间延迟，编号传感器相对编号传感器的估计车速可表示为
其中：为编号传感器相对于其他传感器的车速；为任意两个传感器之间的速度估计矩阵。
融合各传感器估计的车速，最优估计车速可表示为
其中：为计算加速度波形相似度构成的权重矩阵。
其中：为波形相似度；为相似度阈值；为编号传感器对应的权重向量；为权重矩阵。
时刻最优车速估计为
通过线性插值的方法获取各时刻对应的速度修正量，即
其中：为速度修正量；为离散时刻。
和 的计算公式为
其中：为离散时刻下的最优车速估计值与初始车速估计值的差值；为等时间间隔；为时间分割数。
数据融合后的车速计算公式为
对车速进行一次积分即可得到里程信息。列车运行速度如图6所示。
由图5（a）可以看出，车体垂向加速度在22~42 s、45~63 s振动剧烈。由图 6可知，列车以约60 km/h的速度经过里程范围14.9~15.1 km和15.3~15.6 km的两个曲线路段。
3.3　基于振动能量比的钢轨波磨识别
根据现场观察的钢轨波磨情况并结合车辆行驶速度，可知钢轨波磨激发的车体振动特征频率在［100，200］ Hz之间。选用db8小波基，对车体垂向加速度进行小波包分解，分解至第5层，根据式（11）得到节点带宽为78 Hz。车体垂向加速度小波包分解如图7所示。从图中 ［78，156］ Hz频带的振动信号中能识别钢轨波磨引起的车体异常振动。
根据式（14）~（17）计算特征频带及其附近的频带振动能量与总振动能量的比值，钢轨波磨激发的轮轨异常高频振动会传递至车厢地板，导致列车经过钢轨波磨区段时的振动能量响应更显著。振动能量比的对比如图 8所示。由图可知，特征频带［78，156］ Hz的振动能量比在里程14.9~15.1 km和15.3~15.6 km范围内达到0.7。根据现场调研，对应里程范围内是曲线路段，并且存在严重的钢轨波磨。
根据车体振动的特征频带［78，156］ Hz提取特征频率，取振动能量比阈值为0.2，并结合车速计算钢轨波磨的特征波长。
3.4　波磨仪实测及车厢噪声分析
为验证该方法的正确性，利用钢轨波磨仪对DK14+700-DK15.6+00区间路段0.9 km范围的线路内侧钢轨波磨进行现场测量，如图 9所示。实测钢轨波磨如图 10所示。钢轨波磨短波不平顺谱如图 11所示。分析可知，曲线段钢轨波磨主波长约为175 mm。基于振动能量比的钢轨波磨识别效果如图12所示。对比实测范围内振动能量比与实测波磨峰峰值可知，当振动能量比阈值为0.2时，识别钢轨波磨波长分布与实测波磨分布基本一致，表明本研究方法可以有效测量钢轨波磨波长并确定其分布里程。
车厢噪声能级与钢轨波磨幅值之间具有明显的相关性［13‑15］。通过麦克风收集车厢噪声，列车经过曲线段时有刺耳的轮轨噪音。车厢噪声时频分析如图 13所示。可知，车厢噪声主频在［100，180］ Hz之间，可以识别钢轨波磨激发的特征噪声成分，并结合车厢噪声时域信息识别出钢轨波磨区段。车体垂向振动加速度时频分析如图 14所示。整个区间的车体振动频率在1 300 Hz以内，车体振动主频在［100，200］ Hz之间，由图可以识别钢轨波磨引起的车体振动频率，并结合车体振动加速度时域信息识别出钢轨波磨区段。对比车厢噪声和车体垂向加速度的时频分析结果，二者识别的钢轨波磨区段在时域上基本吻合。
4　讨论与分析
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4.1　振动能量比与波磨幅值映射关系
钢轨波磨振动能量比与钢轨波磨波长、幅值及速度密切相关，三者以里程标签为基准，进行三维可视化，借用无监督学习K‑meas聚类方法可将数据集分为两类，与振动能量比0.2作为阈值分割的类别一致。速度‑波磨幅值‑振动能量比关系如图 15所示。其中：振动能量比大于0.2为红色；振动能量比小于0.2为蓝色。但是，图中未呈现出振动能量比与波磨幅值的单一线性映射关系，这是因为车体振动是一个综合响应，与轨道结构型式、曲线半径及扣件类型等因素有关。
振动能量比与钢轨波磨峰峰值之间不是单一线性映射关系。在工程实践中，针对不同线路区间提取车速、轨道结构型式、曲线半径及扣件类型等线路信息，结合深度学习训练模型，将振动能量比作为模型的输入，预测钢轨波磨幅值，以提高检测效率，实现地铁线路钢轨波磨的里程覆盖式、时间密集型的高效测量。
4.2　全线钢轨波磨检测结果分析
利用高精度传感器实时监测全线25个区间的车体振动加速度，测试前期由于设备校准，从里程K9+501处开始测量。利用本研究算法分析列车振动加速度数据，得到里程K9+501至里程K33+163的振动能量比变化情况。振动能量比分布如图 16所示。
统计分析实测线路的振动能量比在［，］的概率分布发现：振动能量比小于0.2的无波磨区段占比为76.56%；振动能量比大于0.2的波磨区段占比为23.44%。振动能量比概率分布直方图如图 17所示。
基于振动能量比对全线钢轨波磨进行自动识别，以10 m间隔计算全线钢轨波磨波长。由于不同区间的列车行驶速度、曲线半径、轨道结构和扣件类型不同，所以沿线分布的钢轨波磨波长存在差异。钢轨波磨波长分布如图 18所示。统计分析全线波磨波长在［，］的分布概率发现：波磨波长以60 mm以下为主，占比为77.88%；波长 60 mm以上的波磨占比为22.12%。钢轨波磨波长概率分布直方图如图 19所示。
5　结论
收起
1） 基于振动能量比可以自动识别钢轨波磨，通过小波包分解车体振动加速度，可以计算特征频带的能量占比是否超限。
2） 当实例分析区间的振动能量比阈值取0.2时识别效果最好，计算的钢轨波磨波长与波磨仪实测结果基本一致，识别的钢轨波磨里程范围与现场实际分布以及车厢噪声的时频分析结果吻合。
3） 通过统计聚类分析发现，振动能量比与钢轨波磨幅值之间不是单一因素线性映射关系，需要考虑其他线路结构信息。
4） 基于振动能量比快速检测全线钢轨波磨分布，发现测试线路无波磨区段占比为76.56%，波磨区段占比为23.44%。其中，钢轨波磨波长以60 mm以下为主，占比为77.88%，波长60 mm以上的波磨占比为22.12%。
基金
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  • 四川省科技计划资助项目(2024NSFTD0010)
文献
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2025年第45卷第5期
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doi: 10.16450/j.cnki.issn.1004-6801.2025.05.023
  • 接收时间：2023-02-10
  • 首发时间：2026-03-27
  • 出版时间：2025-10-01
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  • 收稿日期：2023-02-10
  • 修回日期：2023-07-20
基金
四川省科技计划资助项目(2024NSFTD0010)
作者信息
    1西南交通大学土木工程学院　成都，610031
    2西南交通大学高速铁路线路工程教育部重点实验室　成都，610031
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2种不同金属材料的力学参数
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Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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