高速铁路轨道不平顺参数多尺度相关性分析
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摘要
基于多元经验模态分解的多分辨率特性,提出从不同尺度分析轨道不平顺参数之间相关性的方法。首先,利用多元希尔伯特-黄变换,分析轨道不平顺的能量分布及对应的波长特征;然后,利用改进的时变内在相关方法分析轨道不平顺在不同尺度下的相关性。对实测的轨道不平顺数据分析表明:样本数据的能量主要分布在空间波长4～36m的尺度内;左、右轨道在轨向和高低两方面整体上具有较强的相关性,轨距与轨向较差以及水平与高低较差在4～60m尺度内相关性较强。提出的轨道不平顺相关性分析方法可为科学地评价轨道质量奠定方法基础。
Based on the multi-resolution characteristics of multivariate empirical mode decomposition,a method was proposed to analyze the correlation between track irregularity parameters at different scales.First,the energy distribution and corresponding wavelength characteristics of track irregularities were analyzed using multivariate Hilbert-Huang Transform.Then,the modified timedependent intrinsic correlation method was used to analyze the correlation of track irregularities at different scales.The analysis results of track dynamic irregularity show that the energy of track irregularity sample data is mainly distributed in the spatial wavelength of 4 mto 36 m,and there exists a strong correlations in both alignment and longitudinal level between the left and left tracks.The correlations between gauge and difference of double track alignment,and also between cross leveland difference of double track longitudinal level are strong in the wavelength range of 4 mto 60 m.The proposed method in this research lays foundation for scientific evaluation of track geometry quality.
Based on the multi-resolution characteristics of multivariate empirical mode decomposition,a method was proposed to analyze the correlation between track irregularity parameters at different scales.First,the energy distribution and corresponding wavelength characteristics of track irregularities were analyzed using multivariate Hilbert-Huang Transform.Then,the modified timedependent intrinsic correlation method was used to analyze the correlation of track irregularities at different scales.The analysis results of track dynamic irregularity show that the energy of track irregularity sample data is mainly distributed in the spatial wavelength of 4 mto 36 m,and there exists a strong correlations in both alignment and longitudinal level between the left and left tracks.The correlations between gauge and difference of double track alignment,and also between cross leveland difference of double track longitudinal level are strong in the wavelength range of 4 mto 60 m.The proposed method in this research lays foundation for scientific evaluation of track geometry quality.
引文
[1]罗林,张格明,吴旺青,等.轮轨系统轨道平顺状态的控制[M].北京:中国铁道出版社,2006:1-42.
[2]BS EN 13848-1:2003+A1:2008.Railway applications-track-track geometry quality-part 1:characterisation of track geometry[S].
[3]BS EN 13848-2:2006.Railway applications-tracktrack geometry quality-part 2:measuring systemsTrack recording vehicles[S].
[4]BS EN 13848-6:2014.Railway applications-tracktrack geometry quality-part 6:characterisation of track geometry quality[S].
[5]刘金朝,刘秀波.轨道质量状态评价方法[J].铁路技术创新,2012(1):106-109.Liu Jin-zhao,Liu Xiu-bo.Evaluation method of track geometry quality[J].Railway Technical Innovation,2012(1):106-109.
[6]李海锋,吴纪才,许玉德.铁路轨道几何状态评价方法比较[J].同济大学学报:自然科学版,2005,33(6):772-776.Li Hai-feng,Wu Ji-cai,Xu Yu-de.Comparison of railway track geometry status evaluation methods[J].Journal of Tongji University(Natural Science),2005,33(6):772-776.
[7]Sadeghi J.Development of railway track geometry indexes based on statistical distribution of geometry data[J].Journal of Transportation Engineering,2010,136(8):693-700.
[8]练松良,黄俊飞.客货共运线路轨道不平顺不利波长的分析研究[J].铁道学报,2004,26(2):111-115.Lian Song-liang,Huang Jun-fei.Study of the detrimental wavelengths of track irregularities for railways with passenger and freight traffic[J].Journal of the China Railway Society,2004,26(2):111-115.
[9]练松良,刘扬,杨文忠.沪宁线轨道不平顺谱的分析[J].同济大学学报:自然科学版,2007,35(10):1342-1346.Lian Song-liang,Liu Yang,Yang Wen-zhong.Analysis of track irregularity spectrum of shanghainanjing railway[J].Journal of Tongji University(Natural Science),2007,35(10):1342-1346.
[10]宁迎智,周小林,徐庆元,等.基于小波的轨道不平顺和车体振动响应分析[J].铁道科学与工程学报,2013,10(3):28-32.Ning Ying-zhi,Zhou Xiao-lin,Xu Qing-yuan,et al.Analysis of track irregularity and car-body vibration response based on wavelet transform[J].Journal of Railway Science and Engineering,2013,10(3):28-32.
[11]金守华,曾志平.京津城际铁路博格板式无砟轨道不平顺分析[J].铁道科学与工程学报,2009,6(1):48-52.Jin Shou-hua,Zeng Zhi-ping.Analysis of boglslab track irregularity of Beijing-Tianjin intercity high speed railway[J].Journal of Railway Science and Engineering,2009,6(1):48-52.
[12]左玉云,向俊.郑武线轨道不平顺的相关性分析[J].铁道科学与工程学报,2006,3(1):46-49.Zuo Yu-yun,Xiang Jun.Correlation analysis of track irregularities of Zhengzhou-Wuhan railway[J].Journal of Railway Science and Engineering,2006,3(1):46-49.
[13]Chen X Y,Wu Z H,Huang N E.The time-dependent intrinsic correlation based on the empirical mode decomposition[J].Advances in Adaptive Data Analysis,2011,2(2):233-265.
[14]侯卫星.0号高速综合检测列车[M].北京:中国铁道出版社,2010:40-61.
[15]魏世斌,刘伶萍,赵延峰,等.高速轨道检测系统[J].铁路技术创新,2012(1):29-32.Wei Shi-bin,Liu Ling-ping,Zhao Yan-feng,et al.High speed rail detection system[J].Railway Technical Innovation,2012(1):29-32.
[16]Rehman N, Mandic D P.Multivariate empirical mode decomposition[J].Proceedings Mathematical Physical&Engineering Sciences,2010,466(2117):1291-1302.
[17]Rehman N,Mandic D P.Filter bank property of multivariate empirical mode decomposition[J].IEEE Transactions on Signal Processing,2011,59(5):2421-2426.
[18]Huang N E,Wu Z H,Long S R,et al.On instantaneous frequency[J].Advances in Adaptive Data Analysis,2009,1(2):177-229.
[19]康熊,刘秀波,李红艳,等.高速铁路无砟轨道不平顺谱[J].中国科学:技术科学,2014,44(7):687-696.Kang Xiong,Liu Xiu-bo,Li Hong-yan,et al.PSD of ballastless track irregularities of high-speed railway[J].Scientia Sinica(Technologica),2014,44(7):687-696.
[20]许贵阳,史天运,刘金朝,等.高速铁路轨道几何检测数据自动预处理方法研究[J].中国铁道科学,2013,34(6):8-12.Xu Gui-yang,Shi Tian-yun,Liu Jin-zhao,et al.Research on automatic preprocessing methods for track geometry inspection data of high speed railway[J].China Railway Science,2013,34(6):8-12.
[21]Huang G Q,Su Y,Kareem A,et al.Time-frequency analysis of nonstationary process based on multivariate empirical mode decomposition[J].Journal of Engineering Mechanics,2015,142(1):1-15.
[2]BS EN 13848-1:2003+A1:2008.Railway applications-track-track geometry quality-part 1:characterisation of track geometry[S].
[3]BS EN 13848-2:2006.Railway applications-tracktrack geometry quality-part 2:measuring systemsTrack recording vehicles[S].
[4]BS EN 13848-6:2014.Railway applications-tracktrack geometry quality-part 6:characterisation of track geometry quality[S].
[5]刘金朝,刘秀波.轨道质量状态评价方法[J].铁路技术创新,2012(1):106-109.Liu Jin-zhao,Liu Xiu-bo.Evaluation method of track geometry quality[J].Railway Technical Innovation,2012(1):106-109.
[6]李海锋,吴纪才,许玉德.铁路轨道几何状态评价方法比较[J].同济大学学报:自然科学版,2005,33(6):772-776.Li Hai-feng,Wu Ji-cai,Xu Yu-de.Comparison of railway track geometry status evaluation methods[J].Journal of Tongji University(Natural Science),2005,33(6):772-776.
[7]Sadeghi J.Development of railway track geometry indexes based on statistical distribution of geometry data[J].Journal of Transportation Engineering,2010,136(8):693-700.
[8]练松良,黄俊飞.客货共运线路轨道不平顺不利波长的分析研究[J].铁道学报,2004,26(2):111-115.Lian Song-liang,Huang Jun-fei.Study of the detrimental wavelengths of track irregularities for railways with passenger and freight traffic[J].Journal of the China Railway Society,2004,26(2):111-115.
[9]练松良,刘扬,杨文忠.沪宁线轨道不平顺谱的分析[J].同济大学学报:自然科学版,2007,35(10):1342-1346.Lian Song-liang,Liu Yang,Yang Wen-zhong.Analysis of track irregularity spectrum of shanghainanjing railway[J].Journal of Tongji University(Natural Science),2007,35(10):1342-1346.
[10]宁迎智,周小林,徐庆元,等.基于小波的轨道不平顺和车体振动响应分析[J].铁道科学与工程学报,2013,10(3):28-32.Ning Ying-zhi,Zhou Xiao-lin,Xu Qing-yuan,et al.Analysis of track irregularity and car-body vibration response based on wavelet transform[J].Journal of Railway Science and Engineering,2013,10(3):28-32.
[11]金守华,曾志平.京津城际铁路博格板式无砟轨道不平顺分析[J].铁道科学与工程学报,2009,6(1):48-52.Jin Shou-hua,Zeng Zhi-ping.Analysis of boglslab track irregularity of Beijing-Tianjin intercity high speed railway[J].Journal of Railway Science and Engineering,2009,6(1):48-52.
[12]左玉云,向俊.郑武线轨道不平顺的相关性分析[J].铁道科学与工程学报,2006,3(1):46-49.Zuo Yu-yun,Xiang Jun.Correlation analysis of track irregularities of Zhengzhou-Wuhan railway[J].Journal of Railway Science and Engineering,2006,3(1):46-49.
[13]Chen X Y,Wu Z H,Huang N E.The time-dependent intrinsic correlation based on the empirical mode decomposition[J].Advances in Adaptive Data Analysis,2011,2(2):233-265.
[14]侯卫星.0号高速综合检测列车[M].北京:中国铁道出版社,2010:40-61.
[15]魏世斌,刘伶萍,赵延峰,等.高速轨道检测系统[J].铁路技术创新,2012(1):29-32.Wei Shi-bin,Liu Ling-ping,Zhao Yan-feng,et al.High speed rail detection system[J].Railway Technical Innovation,2012(1):29-32.
[16]Rehman N, Mandic D P.Multivariate empirical mode decomposition[J].Proceedings Mathematical Physical&Engineering Sciences,2010,466(2117):1291-1302.
[17]Rehman N,Mandic D P.Filter bank property of multivariate empirical mode decomposition[J].IEEE Transactions on Signal Processing,2011,59(5):2421-2426.
[18]Huang N E,Wu Z H,Long S R,et al.On instantaneous frequency[J].Advances in Adaptive Data Analysis,2009,1(2):177-229.
[19]康熊,刘秀波,李红艳,等.高速铁路无砟轨道不平顺谱[J].中国科学:技术科学,2014,44(7):687-696.Kang Xiong,Liu Xiu-bo,Li Hong-yan,et al.PSD of ballastless track irregularities of high-speed railway[J].Scientia Sinica(Technologica),2014,44(7):687-696.
[20]许贵阳,史天运,刘金朝,等.高速铁路轨道几何检测数据自动预处理方法研究[J].中国铁道科学,2013,34(6):8-12.Xu Gui-yang,Shi Tian-yun,Liu Jin-zhao,et al.Research on automatic preprocessing methods for track geometry inspection data of high speed railway[J].China Railway Science,2013,34(6):8-12.
[21]Huang G Q,Su Y,Kareem A,et al.Time-frequency analysis of nonstationary process based on multivariate empirical mode decomposition[J].Journal of Engineering Mechanics,2015,142(1):1-15.