Review on Detection Principle, Method, and Device of Rail Corrugation

doi:10.3901/JME.2025.10.191

Abstract

Abstract: A systematic review is conducted on the detection principles of rail corrugation, with advantages, limitations, and applicable scope summarized. Detection methods based on different principles are elucidated, and an overview of common static and dynamic detection devices for corrugation is provided, along with research progress on next-generation detection and monitoring devices. Research prospects for corrugation detection are discussed. Detection principles for rail corrugation are categorized into five types: chord measurement method, inertial reference method, signal reconstruction method, machine vision method, and time-series modeling method. Inherent drawbacks, such as non-unit transfer function and severe amplitude oscillation for shorter wavelengths, are associated with the chord measurement method. Corrugation can be measured effectively using a combination of chord models. The inertial reference method, based on inertia, can be installed at multiple positions, such as axle boxes, frames, and the car body. At low speeds, inertial sensor responses diminish, while noise and trend components gradually dominate. Digital signal processing techniques are used by the signal reconstruction method to decompose data from sources like axle box acceleration, frame acceleration, wheel-rail noise, and in-car noise, extracting valuable information about corrugation. Rail images are perceived, understood, and interpreted by computers using the machine vision method, which is based on image processing and pattern recognition technologies. This method mainly comprises three approaches: image processing-based, laser camera-based, and 3D point cloud reconstruction-based methods for corrugation measurement. Corrugation recognition is transformed into classification or regression problems by the time-series modeling method. Through machine learning and deep learning techniques, mapping relationships between corrugation and responses like vibration and noise are established, achieving corrugation detection. Detection and monitoring devices for rail corrugation are advancing towards intelligent, integrated, and portable measurement solutions.

Key words: rail corrugation, detection principle, detection device, machine vision, deep learning

CLC Number:

U213

XIAO Hong, WANG Yang, LIU Xiubo, CUI Xuhao, ZHANG Zhihai, JIN Feng. Review on Detection Principle, Method, and Device of Rail Corrugation[J]. Journal of Mechanical Engineering, 2025, 61(10): 191-214.

References

[1] LI X，HU Z，ZOU C. Noise annoyance and vibration perception assessment on passengers during train operation in Guangzhou metro[J]. Environmental Science and Pollution Research，2022，29(3)：4246-4259.
[2] MA M，RAN W，WU J，et al. Evaluating the impact of metro interior noise on passenger annoyance：An experimental study[J]. International Journal of Environmental Research and Public Health，2022，19(9)：5041.
[3] 朱海燕，袁遥，肖乾，等. 钢轨波磨研究进展[J]. 交通运输工程学报，2021，21(3)：110-133. ZHU Haiyan，YUAN Yao，XIAO Qian，et al. Research progress on rail corrugation[J]. Journal of Traffic and Transportation Engineering，2021，21(3)：110-133.
[4] 温泽峰. 钢轨波浪形磨损研究[D]. 成都：西南交通大学，2006. WEN Zefeng. Study on rail corrugation[D]. Chengdu：Southwest Jiaotong University，2006.
[5] 徐晓迪. 轨道短波病害时频特征提取和动态诊断方法研究[D]. 北京：中国铁道科学研究院，2019. XU Xiaodi. Time-frequency feature extraction and dynamic diagnosis method for track short-wave defects[D]. Beijing：China Academy of Railway Sciences，2019.
[6] 崔旭浩，马超智，金锋. 重载铁路钢轨波磨对有砟道床动力特性的影响[J]. 华中科技大学学报，2021，49(1)：110-115. CUI Xuhao，MA Chaozhi，JIN Feng. The effect of rail corrugation on dynamic characteristics of heavy haul railway ballast bed[J]. Journal of Huazhong University of Science and Technology，2021，49(1)：110-115.
[7] 金学松，李霞，李伟，等. 铁路钢轨波浪形磨损研究进展[J]. 西南交通大学学报，2016，2(51)：264-273. JIN Xuesong，LI Xia，LI Wei，et al. Review of rail corrugation progress[J]. Journal of Southwest Jiaotong University，2016，2(51)：264-273.
[8] 崔晓璐. 地铁线路钢轨波磨现象发生机理研究[D]. 成都：西南交通大学，2017. CUI Xiaolu. Research on occurrence mechanisms of rail corrugation phenomena in metros[D]. Chengdu：Southwest Jiaotong University，2017.
[9] GRASSIE S L，KALOUSEK J. Rail corrugation：Characteristics，causes and treatments[J]. Proceedings of the Institution of Mechanical Engineers，Part F：Journal of Rail and Rapid Transit，1993，207(1)：57-68.
[10] HIENSCH M，NIELSEN J C O，VERHEIJEN E. Rail corrugation in the Netherlands—measurements and simulations[J]. Wear，2002，253(1)：140-149.
[11] SATO Y，MATSUMOTO A，KNOTHE K. Review on rail corrugation studies[J]. Wear，2002，253(1-2)：130-139.
[12] GRASSIE S L. Rail corrugation：Advances in measurement，understanding and treatment[J]. Wear，2005，258(7-8)：1224-1234.
[13] OOSTERMEIJER K H. Review on short pitch rail corrugation studies[J]. Wear，2008，265(9-10)：1231-1237.
[14] GRASSIE S L. Rail irregularities，corrugation and acoustic roughness：Characteristics，significance and effects of reprofiling[J]. Proceedings of the Institution of Mechanical Engineers，Part F：Journal of Rail and Rapid Transit，2012，226(5)：542-557.
[15] 关庆华，张斌，熊嘉阳，等. 地铁钢轨波磨的基本特征、形成机理和治理措施综述[J]. 交通运输工程学报，2021，21(1)：316-337. GUAN Qinghua，ZHANG Bin，XIONG Jiayang，et al. Review on basic characteristics，formation mechanisms，and treatment measures of rail corrugation in metro systems[J]. Journal of Traffic and Transportation Engineering，2021，21(1)：316-337.
[16] 刘学毅，王平，万复光. 重载线路钢轨波形磨耗成因研究[J]. 铁道学报，2000，22(1)：98-103. LIU Xueyi，WANG Ping，WAN Fuguang. Formation mechanism of rail corrugations in heavy-haul railline[J]. Journal of the China Railway Society，2000，22(1)：98-103.
[17] GRASSIE S L. Short wavelength rail corrugation：Field trials and measuring technology[J]. Wear，1996，191(1)：149-160.
[18] GRASSIE S L，SAXON M J，SMITH J D. Measurement of longitudinal rail irregularities and criteria for acceptable grinding[J]. Journal of Sound and Vibration，1999，227(5)：949-964.
[19] GRASSIE S L. The corrugation of railway rails：2. Monitoring and conclusions[J]. Proceedings of the Institution of Mechanical Engineers，Part F：Journal of Rail and Rapid Transit，2023，237(5)：597-605.
[20] 金学松，温泽峰，王开云. 钢轨磨耗型波磨计算模型与数值方法[J]. 交通运输工程学报，2005，5(2)：12-18. JIN Xuesong，WEN Zefeng，WANG Kaiyun. Theoretical model and numerical method of rail corrugation[J]. Journal of Traffic and Transportation Engineering，2005，5(2)：12-18.
[21] 金学松，温泽峰，肖新标. 曲线钢轨初始波磨形成的机理分析[J]. 机械工程学报，2008，44(3)：1-8，15. JIN Xuesong，WEN Zefeng，XIAO Xinbiao. Investigation into mechanism of initial rail corrugation formation at a curved track[J]. Journal of Mechanical Engineering，2008，44(3)：1-8，15.
[22] DU X，JIN X，ZHAO G，et al. Rail corrugation of high-speed railway induced by rail grinding[J]. Shock and Vibration，2021，2021：1-14.
[23] 陈光雄. 金属往复滑动摩擦噪声的研究[D]. 成都：西南交通大学，2002. CHEN Guangxiong. Investigation into friction-induced noise under metal reciprocating sliding conditions[D]. Chengdu：Southwest Jiaotong University，2002.
[24] CHEN G X，ZHOU Z R，OUYANG H，et al. A finite element study on rail corrugation based on saturated creep force-induced self-excited vibration of a wheelset–track system[J]. Journal of Sound and Vibration，2010，329(22)：4643-4655.
[25] 陈光雄，钱韦吉，莫继良，等. 轮轨摩擦自激振动引起小半径曲线钢轨波磨的瞬态动力学[J]. 机械工程学报，2014，50(9)：71-76. CHEN Guangxiong，QIAN Weiji，MO Jiliang，et al. A transient dynamics study on wear-type rail corrugation on a tight curve due to the friction-induced self-excited vibration of a wheelset-track system[J]. Journal of Mechanical Engineering，2014，50(9)：71-76.
[26] BELLETTE P A，MEEHAN P A，DANIEL W J T. Effects of variable pass speed on wear-type corrugation growth[J]. Journal of Sound and Vibration，2008，314(3-5)：616-634.
[27] MEEHAN P A，BELLETTE P A，BATTEN R D，et al. A case study of wear-type rail corrugation prediction and control using speed variation[J]. Journal of Sound and Vibration，2009，325(1-2)：85-105.
[28] BATTEN R D，BELLETTE P A，MEEHAN P A，et al. Field and theoretical investigation of the mechanism of corrugation wavelength fixation under speed variation[J]. Wear，2011，271(1-2)：278-286.
[29] MEEHAN P A，BATTEN R D，BELLETTE P A. The effect of non-uniform train speed distribution on rail corrugation growth in curves/corners[J]. Wear，2016，366-367：27-37.
[30] SUN Y Q，SIMSON S. Wagon-track modelling and parametric study on rail corrugation initiation due to wheel stick-slip process on curved track[J]. Wear，2008，265(9-10)：1193-1201.
[31] 王志强，雷震宇. 基于黏滑扭振的地铁小半径曲线钢轨波磨形成机理[J]. 东南大学学报，2022，52(5)：998-1011. WANG Zhiqiang，LEI Zhenyu. Formation mechanism of rail corrugation on the small radius curve of metro based on stick-slip torsional vibration[J]. Journal of Southeast University，2022，52(5)：998-1011.
[32] WANG Z，LEI Z. Trend analysis of rail corrugation on the metro based on wheel-rail stick-slip characteristics[J]. Vehicle System Dynamics，2024，62(1)：147-176.
[33] EGANA J I，VINOLAS J，GIL-NEGRETE N. Effect of liquid high positive friction (HPF) modifier on wheel-rail contact and rail corrugation[J]. Tribology International，2005，38(8)：769-774.
[34] EADIE D T，SANTORO M，OLDKNOW K，et al. Field studies of the effect of friction modifiers on short pitch corrugation generation in curves[J]. Wear，2008，265(9-10)：1212-1221.
[35] 肖祥龙，陈光雄，莫继良，等. 摩擦调节剂抑制钢轨波磨的机理研究[J]. 振动与冲击，2013，32(8)：166-170. XIAO Xianglong，CHEN Guangxiong，MO Jiliang，et al. Mechanism for friction to suppress a wear-type rail corrugation[J]. Journal of Vibration and Shock，2013，32(8)：166-170.
[36] JIN X S，WEN Z F，WANG K Y. Effect of track irregularities on initiation and evolution of rail corrugation[J]. Journal of Sound and Vibration，2005，285：121-148.
[37] TYFOUR W R. Predicting the effect of grinding corrugated rail surface on the wear behavior of pearlitic rail steel[J]. Tribology Letters，2008，29(3)：229-234.
[38] WEN Z，JIN X，XIAO X，et al. Effect of a scratch on curved rail on initiation and evolution of plastic deformation induced rail corrugation[J]. International Journal of Solids and Structures，2008，45(7-8)：2077-2096.
[39] BÖHMER A，KLIMPEL T. Plastic deformation of corrugated rails—A numerical approach using material data of rail steel[J]. Wear，2002，253(1)：150-161.
[40] JIN X S，WEN Z F. Effect of discrete track support by sleepers on rail corrugation at a curved track[J]. Journal of Sound and Vibration，2008，315(1-2)：279-300.
[41] 李伟，杜星，王衡禹，等. 地铁钢轨一种波磨机理的调查分析[J]. 机械工程学报，2013，49(16)：26-32. LI Wei，DU Xing，WANG Hengyu，et al. Investigation into the mechanism of type of rail corrugation of metro[J]. Journal of Mechanical Engineering，2013，49(16)：26-32.
[42] WANG Y，XIAO H，NADAKATTI M M，et al. Mechanism of rail corrugation combined with friction self-excited vibration and wheel-track resonance[J]. Construction and Building Materials，2023，400：132782.
[43] DANIEL W J T，CHENG C Y，MEEHAN P A. Modelling the effects of friction modifiers on rail corrugation in cornering[J]. Vehicle System Dynamics，2008，46(9)：845-866.
[44] 钱韦吉，黄志强. 蠕滑力饱和条件下钢轨吸振器抑制短波波磨的理论研究[J]. 振动与冲击，2019，38(14)：68-73，111. QIAN Weiji，HUANG Zhiqiang. Theoretical study on the suppression of short pitch rail corrugation induced vibration by rail vibration absorbers under saturated creep forces condition[J]. Journal of Vibration and Shock，2019，38(14)：68-73，111.
[45] 王平，刘奕斌，高原，等. 表面选区强化对钢轨波磨处轮轨滚动接触行为的影响[J]. 铁道学报，2020，42(5)：105-112. WANG Ping，LIU Yibin，GAO Yuan，et al. A study on influence of surface strengthening on wheel-rail rolling contact behavior at rail corrugation[J]. Journal of the China Railway Society，2020，42(5)：105-112.
[46] TANG X，CAI X，PENG H，et al. Experimental and simulation investigation into the cause and treatment of rail corrugation for metro[J]. Journal of Central South University，2022，29(12)：3925-3938.
[47] 周坤，王文健，刘启跃，等. 钢轨打磨机理研究进展及展望[J]. 中国机械工程，2019，30(3)：284-294. ZHOU Kun，WANG Wenjian，LIU Qiyue，et al. Research progresses and prospect of rail grinding mechanism[J]. China Mechanical Engineering，2019，30(3)：284-294.
[48] 殷华. 钢轨波磨多中点弦测理论及检测技术研究[D]. 南昌：南昌大学，2017. YIN Hua. Research on multi-midpoint chord measurement theory and detection technique of rail corrugation[D]. Nanchang：Nanchang University，2017.
[49] 尹贤贤. 城市轨道交通轨道服役性能劣化机理分析及病害智能检测研究[D]. 北京：北京交通大学，2021. YIN Xianxian. Degradation mechanism analysis of track service performance and intelligent detection of track defects in urban rail transit[D]. Beijing：Beijing Jiaotong University，2021.
[50] GABOR D. Theory of communication. Part 1：The analysis of information[J]. Journal of the Institution of Electrical Engineers-part III：Radio and Communication Engineering，1946，93(26)：429-441.
[51] MALLAT S G. A theory for multiresolution signal decomposition：The wavelet representation[J]. IEEE Transactions On Pattern Analysis and Machine Intelligence，1989，11(7)：674-693.
[52] HUANG N E，SHEN Z，LONG S R，et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J]. Proceedings of the Royal Society A，1998，454(1971)：903-995.
[53] MANDRIOTA C，STELLA E，NITTI M，et al. Rail corrugation detection by Gabor filtering[C]// Proceedings 2001 International Conference on Image Processing (Cat. No. 01CH37205)，October 07-10，2001，Makedonia Palace Hotel，Thessaloniki，Greece. New York：IEEE，2001，2：626-628.
[54] MANDRIOTA C，NITTI M，ANCONA N，et al. Filter-based feature selection for rail defect detection[J]. Machine Vision and Applications，2004，15(4)：179-185.
[55] 李艳福. 基于激光位移的钢轨磨耗动态检测方法研究[D]. 长沙：湖南大学，2018. LI Yanfu. Research on dynamic measurement method of rail wear based on laser displacement sensors[D]. Changsha：Hunan University，2018.
[56] 魏振忠，张广军，徐园. 一种线结构光视觉传感器标定方法[J]. 机械工程学报，2005，41(2)：210-214. WEI Zhenzhong，ZHANG Guangjun，XU Yuan. Calibration approach for structured-lighted-stripe vision sensor[J]. Journal of Mechanical Engineering，2005，41(2)：210-214.
[57] QU W，FAN C，LI X. Analysis of an augmented moving least squares approximation and the associated localized method of fundamental solutions[J]. Computers & Mathematics with Applications，2020，80(1)：13-30.
[58] SERIN G，SENER B，OZBAYOGLU A M，et al. Review of tool condition monitoring in machining and opportunities for deep learning[J]. The International Journal of Advanced Manufacturing Technology，2020，109(3-4)：953-974.
[59] 谢清林，陶功权，温泽峰. 基于一维卷积神经网络的地铁钢轨波磨识别方法[J]. 中南大学学报，2021，52(4)：1371-1379. XIE Qinglin，TAO Gongquan，WEN Zefeng. Detection method of metro rail corrugation based on 1-dimensional convolutional neural network[J]. Journal of Central South University，2021，52(4)：1371-1379.
[60] 朱洪涛，魏晖，王志勇，等. 轨检仪弦测法“以小推大”检查轨道轨向不平顺的理论研究[J]. 铁道学报，2007，29(1)：36-40. ZHU Hongtao，WEI Hui，WANG Zhiyong，et al. Discussion on inspection of track alignment irregularities according to method of chord measuring and its “using small fetch big”[J]. Journal of the China Railway Society，2007，29(1)：36-40.
[61] 熊丽娟，朱洪涛，王志勇，等. 轨道长波不平顺半测回法测量精度的研究(I)[J]. 铁道学报，2019，41(6)：130-136. XIONG Lijuan，ZHU Hongtao，WANG Zhiyong，et al. Study on improving accuracy of track long-wave irregularity measured by semi-observation method (I)[J]. Journal of the China Railway Society，2019，41(6)：130-136.
[62] 熊丽娟，朱嫣，朱洪涛，等. 轨道长波不平顺半测回法测量精度的研究(II)[J]. 铁道学报，2021，43(8)：118-125. XIONG Lijuan，ZHU Yan，ZHU Hongtao，et al. Study on improving accuracy of track long-wave irregularity measured by semi-observation method (II)[J]. Journal of the China Railway Society，2021，43(8)：118-125.
[63] 毛晓君，许玉德，周宇. 基于四点弦测法的轨面不平顺检测及复原方法[J]. 华东交通大学学报，2013(5)：13-17. MAO Xiaojun，XU Yude，ZHOU Yu. Rail surface irregularities detection and restoration based on four-point chord reference method[J]. Journal of East China Jiaotong University，2013(5)：13-17.
[64] 王源，李帅，陈嵘，等. 基于逆滤波的轨道不平顺测评误差分析及滤波参数优化[J]. 铁道学报，2017，39(10)：102-109. WANG Yuan，LI Shuai，CHEN Rong，et al. Error analysis of track irregularity measuring and filter parameters optimization based on inverse filtering method[J]. Journal of the China Railway Society，2017，39(10)：102-109.
[65] 殷华，朱洪涛. 基于ZFFT的轨道波磨高精度弦测算法研究[J]. 铁道科学与工程学报，2017，14(9)：1851-1858. YIN Hua，ZHU Hongtao. A discussion about high-precision chord measurement algorithm for rail corrugation based upon ZFFT[J]. Journal of Railway Science and Engineering，2017，14(9)：1851-1858.
[66] WANG P，WANG Y，TANG H，et al. Error theory of chord-based measurement system regarding track geometry and improvement by high frequency sampling[J]. Measurement，2018，115：204-216.
[67] 殷华，朱洪涛，魏晖，等. 基于中点弦测模型的钢轨波磨量值估计[J]. 振动、测试与诊断，2016，36(5)：954-959. YIN Hua，ZHU Hongtao，WEI Hui，et al. Estimation of rail corrugation value based on midpoint chord measurement model[J]. Journal of Vibration，Measurement & Diagnosis，2016，36(5)：954-959.
[68] 殷华，朱洪涛，王志勇，等. 基于多弦模型的轨道短波不平顺测量研究[J]. 振动与冲击，2017，36(14)：178-182，193. YIN Hua，ZHU Hongtao，WANG Zhiyong，et al. Rail short-wave irregularity measurement based upon a multi-midpoint chord model[J]. Journal of Vibration and Shock，2017，36(14)：178-182，193.
[69] 殷华，万灵. 基于多中点弦测法的钢轨波磨测量不确定度分析[J]. 铁道科学与工程学报，2020，17(12)：3036-3044. YIN Hua，WAN Ling. Uncertainty evaluation for rail corrugation measurement based upon multi-chord method[J]. Journal of Railway Science and Engineering，2020，17(12)：3036-3044.
[70] LI Y，LIU H，MA Z，et al. Rail corrugation broadband measurement based on combination-chord model and LS[J]. IEEE Transactions on Instrumentation and Measurement，2018，67(4)：938-949.
[71] CHEN L，LI Y，MA Z，et al. Vision-based position deviation measurement of rail corrugation chord measuring points under bi-linear laser assistance[J]. IEEE Access，2021，9：36207-36217.
[72] WANG C，ZENG J. Combination-chord measurement of rail corrugation using triple-line structured-light vision：Rectification and optimization[J]. IEEE Transactions on Intelligent Transportation Systems，2021，22(11)：7256-7265.
[73] CHEN L，LI Y，ZHONG X，et al. An automated system for position monitoring and correction of chord-based rail corrugation measuring points[J]. IEEE Transactions on Instrumentation and Measurement，2019，68(1)：250-260.
[74] WARD C P，WESTON P F，STEWART E J C，et al. Condition monitoring opportunities using vehicle-based sensors[J]. Proceedings of the Institution of Mechanical Engineers，Part F：Journal of Rail and Rapid Transit，2011，225(2)：202-218.
[75] REAL J，SALVADOR P，MONTALBÁN L，et al. Determination of rail vertical profile through inertial methods[J]. Proceedings of the Institution of Mechanical Engineers，Part F：Journal of Rail and Rapid Transit，2011，225(1)：14-23.
[76] LEE J S，CHOI S，KIM S，et al. A mixed filtering approach for track condition monitoring using accelerometers on the axle box and bogie[J]. IEEE Transactions on Instrumentation and Measurement，2012，61(3)：749-758.
[77] XU X，LIU J，SUN S，et al. Dynamic diagnosis method and quantitative characterization of rail corrugation[J]. Proceedings of the Institution of Mechanical Engineers，Part F：Journal of Rail and Rapid Transit，2023，237(3)：297-308.
[78] CARRIGAN T D，TALBOT J P. A new method to derive rail roughness from axle-box vibration accounting for track stiffness variations and wheel-to-wheel coupling[J]. Mechanical Systems and Signal Processing，2023，192：110232.
[79] CHIA L，BHARDWAJ B，LU P，et al. Railroad track condition monitoring using inertial sensors and digital signal processing：A review[J]. IEEE Sensors Journal，2019，19(1)：25-33.
[80] HUANG W，ZHANG W，DU Y，et al. Detection of rail corrugation based on fiber laser accelerometers[J]. Measurement Science and Technology，2013，24(9)：94014.
[81] BAGSHAWE M J. Investigating inertial measurements using mems devices in train-borne automatic track condition monitoring applications[C]// 2013 IET Conference on Control and Automation：Uniting Problems and Solutions，June 04-05，2013，Conference Aston Lakeside Centre，Birmingham，United Kingdom. London：IET，2013：1-6.
[82] HEUSEL J，BAASCH B，RIEDLER W，et al. Detecting corrugation defects in harbour railway networks using axle-box acceleration data[J]. Insight (Northampton)，2022，64(7)：404-410.
[83] TUO W，LI X，JI Y，et al. Mechanical design and determination of bandwidth for a two-axis inertial reference unit[J]. Mechanical Systems and Signal Processing，2022，172：108962.
[84] KOBAYASHI T，NAGANUMA Y，TSUNASHIMA H. Condition monitoring of shinkansen tracks based on inverse analysis[J]. International Journal of Performability Engineering，2014，10(5)：443-452.
[85] ZHANG X，JIA L，WEI X，et al. Railway track condition monitoring based on acceleration measurements[C]// 27th Chinese Control and Decision Conference，May 23-25，2015，Northeastern University，Qingdao，China. New York：IEEE，2015：923-928.
[86] ESCALONA J L. Vertical track geometry monitoring using inertial sensors and complementary filters[C]// Proceedings of the ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference，August 21-24, 2016，Charlotte, North Carolina. New York：ASME，2016，50183.
[87] WEI X，LIU F，JIA L. Urban rail track condition monitoring based on in-service vehicle acceleration measurements[J]. Measurement，2016，80：217-228.
[88] GOMES R，BATISTA A，ORTIGUEIRA M，et al. Railscan：A tool for the detection and quantification of rail corrugation[C]// Emerging Trends in Technological Innovation：First IFIP WG 5.5/SOCOLNET Doctoral Conference on Computing, Electrical and Industrial Systems，DoCEIS 2010，Costa de Caparica, Portugal，February 22-24，2010. Proceedings 1. Berlin：Springer Heidelberg，2010：401-408.
[89] NG A K，MARTUA L，SUN G. Dynamic modelling and acceleration signal analysis of rail surface defects for enhanced rail condition monitoring and diagnosis[C]// 2019 4th International Conference on Intelligent Transportation Engineering，September 05-07，2019，Singapore. New York：IEEE，2019：69-73.
[90] HOPKINS B M，TAHERI S. Track health monitoring using wavelets[C]// ASME 2010 Rail Transportation Division Fall Technical Conference，October 12-13，2010，Roanoke，Virginia. USA：ASMEDC，2010：9-15.
[91] LIANG B，IWNICKI S D，ZHAO Y，et al. Railway wheel-flat and rail surface defect modelling and analysis by time-frequency techniques[J]. Vehicle System Dynamics，2013，51(9)：1403-1421.
[92] LI S，NÚÑEZ A，LI Z，et al. Automatic detection of corrugation：Preliminary results in the dutch network using axle box acceleration measurements[C]// Proceedings of the 2015 Joint Rail Conference，March 23-26，2015，Rail Transportation Division，San Jose， California. USA：ASME，2015：1-7.
[93] SALVADOR P，NARANJO V，INSA R，et al. Axlebox accelerations：Their acquisition and time–frequency characterisation for railway track monitoring purposes[J]. Measurement，2016，82：301-312.
[94] SHADFAR M，MOLATEFI H. Detection of rail local defects using in-service trains[J]. Proceedings of the Institution of Mechanical Engineers，Part F：Journal of Rail and Rapid Transit，2022，236(9)：1114-1123.
[95] ZHANG Y，LI B，LI J，et al. Rail corrugation identification method based on parameter optimization VMD and SPWVD[C]// 2019 IEEE 16th International Conference on Networking，Sensing and Control，May 09-11，2019，Banff，Alberta，Canada. New York：IEEE，2019：110-115.
[96] DRAGOMIRETSKIY K，ZOSSO D. Variational mode decomposition[J]. IEEE Transactions on Signal Processing，2014，62(3)：531-544.
[97] 晏兆晋，高翠香，徐晓迪，等. 基于车辆响应的高速铁路周期性轨道短波病害时频特性分析[J]. 中国铁道科学，2020，41(1)：10-17. YAN Zhaojin，GAO Cuixiang，XU Xiaodi，et al. Time-frequency characteristics analysis of periodic short wave disease of track for high-speed railway based on vehicle response[J]. China Railway Science，2020，41(1)：10-17.
[98] PIERINGER A，KROPP W. Model-based estimation of rail roughness from axle box acceleration[J]. Applied Acoustics，2022，193：108760.
[99] 刘金朝，陈东生，赵钢，等. 评判高铁轨道短波不平顺病害的轨道冲击指数法[J]. 中国铁道科学，2016，37(4)：34-41. LIU Jinzhao，CHEN Dongsheng，ZHAO Gang，et al. Track impact index method for evaluating track short wave irregularity of high-speed railway[J]. China Railway Science，2016，37(4)：34-41.
[100] 牛留斌，刘金朝，孙善超，等. 钢轨波磨指数与轨道短波不平顺关系研究[J]. 中国铁道科学，2020，41(5)：46-55. NIU Liubin，LIU Jinzhao，SUN Shanchao，et al. Study on the relationship between rail corrugation index and track shortwave irregularity[J]. China Railway Science，2020，41(5)：46-55.
[101] 刘金朝，徐晓迪，牛留斌，等. 高速铁路轨道短波健康状态动态诊断模型和方法[J]. 铁道学报，2021，43(10)：69-74. LIU Jinzhao，XU Xiaodi，NIU Liubin，et al. Dynamic inspection model and methodology for track short wave health management for high-speed railway[J]. Journal of the China Railway Society，2021，43(10)：69-74.
[102] 黄哲昊，刘金朝，徐晓迪，等. 高速铁路钢轨波磨声振结合识别方法[J]. 中国铁道科学，2023，44(1)：97-105. HUANG Zhehao，LIU Jinzhao，XU Xiaodi，et al. Identification method for rail corrugation by acoustics and vibration combination on high-speed railway[J]. China Railway Science，2023，44(1)：97-105.
[103] CAPRIOLI A，CIGADA A，RAVEGLIA D. Rail inspection in track maintenance：A benchmark between the wavelet approach and the more conventional Fourier analysis[J]. Mechanical Systems and Signal Processing，2007，21(2)：631-652.
[104] WEI X，YIN X，HU Y，et al. Squats and corrugation detection of railway track based on time-frequency analysis by using bogie acceleration measurements[J]. Vehicle System Dynamics，2020，58(8)：1167-1188.
[105] 邓小军，曹源，张玉琢，等. 改进希尔伯特黄变换分析波磨对列车时频特征的影响[J]. 电子学报，2016，44(10)：2294-2299. DENG Xiaojun，CAO Yuan，ZHANG Yuzhuo，et al. Influence of corrugation on time-frequency characteristics of a train based on improved Hilbert-Huang transform[J]. Acta Electronica Sinica，2016，44(10)：2294-2299.
[106] GUO X，LI C，LUO Z，et al. Identification of track irregularities with the multi-sensor acceleration measurements of vehicle dynamic responses[J]. Vehicle System Dynamics，2024，62(4)：906-931.
[107] 王阳，肖宏，张智海，等. 基于车内振动噪声响应的钢轨波磨状态评估方法[J/OL].机械工程学报，1-15 [2024-09-30]. http://kns.cnki.net/kcms/detail/11.2187.th.20231129.1502.028.html. WANG Yang，XIAO Hong，ZHANG Zhihai，et al. Rail corrugation state assessment method based on train interior vibration and noise response [J/OL]. Journal of Mechanical Engineering，1-15[2024-09-30]. http://kns.cnki.net/kcms/detail/11.2187.th.20231129.1502.028.html.
[108] 何庆，利璐，李晨钟，等. 基于深度学习的轨道不平顺与车体垂向加速度映射模型[J]. 铁道学报，2023，45(6)：106-113. HE Qing，LI Lu，LI Chenzhong，et al. A mapping model between track irregularity and vertical car-body acceleration based on deep learning[J]. Journal of the China Railway Society， 2023，45(6)：106-113.
[109] TSUNASHIMA H，HIROSE R. Condition monitoring of railway track from car-body vibration using time-frequency analysis[J]. Vehicle System Dynamics，2022，60(4)：1170-1187.
[110] WEI Z，SUN X，YANG F，et al. Carriage interior noise-based inspection for rail corrugation on high-speed railway track[J]. Applied Acoustics，2022，196：108881.
[111] 从建力，王源，徐舟，等. 振噪融合的地铁钢轨波磨快速测量方法[J]. 西南交通大学学报，2023，58(3)：677-684. CONG Jianli，WANG Yuan，XU Zhou，et al. Rail corrugation measurement method based on vibration-noise fusion in metro system[J]. Journal of Southwest Jiaotong University，2023，58(3)：677-684.
[112] LI Q，REN S. A real-time visual inspection system for discrete surface defects of rail heads[J]. IEEE Transactions on Instrumentation and Measurement，2012，61(8)：2189-2199.
[113] LI Q，TAN Y，ZHANG H，et al. A visual inspection system for rail corrugation based on local frequency features[C]// 2016 IEEE 14th Intl Conf on Dependable，Autonomic and Secure Computing，August 08-12，2016， Auckland，New Zealand. New York：IEEE，2016：18-23.
[114] 李清勇，章华燕，任盛伟，等. 基于钢轨图像频域特征的钢轨波磨检测方法[J]. 中国铁道科学，2016，37(1)：24-30. LI Qingyong ，ZHANG Huayan，REN Shengwei，et al. Detection method for rail corrugation based on rail image feature in frequency domain[J]. China Railway Science，2016，37(1)：24-30.
[115] 贺振东，王耀南，毛建旭，等. 基于反向P-M扩散的钢轨表面缺陷视觉检测[J]. 自动化学报，2014(8)：1667-1679. HE Zhendong，WANG Yaonan，MAO Jianxu，et al. Research on inverse P-M diffusion-based rail surface defect detection[J]. Acta Automatica Sinica，2014(8)：1667-1679.
[116] VIJAYKUMAR V R，SANGAMITHIRAI S. Rail defect detection using Gabor filters with texture analysis[C]// 3rd International Conference on Signal Processing，March 26-28，2015，Chennai，India. New York：IEEE，2015：1-6.
[117] WEI D，WEI X，LIU Y，et al. The identification and assessment of rail corrugation based on computer vision[J]. Applied Sciences，2019，9(18)：3913.
[118] ZHUANG L，QI H，ZHANG Z. The automatic rail surface multi-flaw identification based on a deep learning powered framework[J]. IEEE Transactions on Intelligent Transportation Systems，2022，23(8)：12133-12143.
[119] YANG H，WANG Y，HU J，et al. Deep learning and machine vision-based inspection of rail surface defects[J]. IEEE Transactions on Instrumentation and Measurement，2022，71：1-14.
[120] CHEN Z，WANG Q，YANG K，et al. Deep learning for the detection and recognition of rail defects in ultrasound b-scan images[J]. Transportation Research Record：Journal of the Transportation Research Board，2021，2675(11)：888-901.
[121] UYGUN E，TERZI S. Acoustic monitoring of railway defects using deep learning with audio to spectrogram conversion[J]. Journal of Vibration Engineering & Technologies，2024，12(2)：2585-2594.
[122] 陈仕明. 基于视觉/惯性融合的轨道长波不平顺动态检测系统研究及应用[D]. 北京：中国铁道科学研究院，2022. CHEN Shiming. Research and application of dynamic inspection system for track longwave irregularities based on vision/inertial fusion[D]. Beijing：China Academy of Railway Sciences，2022.
[123] 陈新禹，马孜，陈天飞. 线结构光传感器模型的简易标定[J]. 光学精密工程，2012，20(11)：2345-2352. CHEN Xinyu，MA Zi，CHEN Tianfei. Calibration model for line structured light vision sensor[J]. Optics and Precision Engineering，2012，20(11)：2345-2352.
[124] 占栋，于龙，肖建，等. 轨道检测中激光摄像式传感器标定方法研究[J]. 机械工程学报，2013，49(16)：39-47. ZHAN Dong，YU Long，XIAO Jian，et al. Calibration approach study for the laser camera transducer of track inspection[J]. Journal of Mechanical Engineering，2013，49(16)：39-47.
[125] WANG C，LI Y，MA Z，et al. Distortion rectifying for dynamically measuring rail profile based on self-calibration of multiline structured light[J]. IEEE Transactions on Instrumentation and Measurement，2018，67(3)：678-689.
[126] GUERRIERI M，PARLA G，CELAURO C. Digital image analysis technique for measuring railway track defects and ballast gradation[J]. Measurement，2018，113：137-147.
[127] GAZAFRUDI S M M，YOUNESIAN D，TORABI M. A high accuracy and high-speed imaging and measurement system for rail corrugation inspection[J]. IEEE Transactions on Industrial Electronics，2021，68(9)：8894-8903.
[128] 马骙骙，杨新文，张昭，等. 基于结构光视觉的钢轨波磨检测与定位方法研究[J]. 机械工程学报，2022，58(22)：140-147. MA Kuikui，YANG Xinwen，ZHANG Zhao，et al. Research on detection and positioning method of rail corrugation based on structural light vision[J]. Journal of Mechanical Engineering，2022，58(22)：140-147.
[129] 江航，尚春阳，高瑞鹏. 基于EMD和神经网络的轮轨故障噪声诊断识别方法研究[J]. 振动与冲击，2014，33(17)：34-38. JIANG Hang，SHANG Chunyang，GAO Ruipeng. Wheel /rail fault noise diagnosis method based on EMD and neural network[J]. Journal of Vibration and Shock，2014，33(17)：34-38.
[130] LI J，SHI H. Rail corrugation detection of high-speed railway using wheel dynamic responses[J]. Shock and Vibration，2019，2019：1-12.
[131] LI J，SHI H. Rail corrugation diagnosis of high-speed railway based on dynamic responses of the vehicle[C]// Prognostics and Health Management Conference，June 08-10，2020，Besancon，France. New York：IEEE，2020：148-152.
[132] DE ROSA A，KULKARNI R，QAZIZADEH A，et al. Monitoring of lateral and cross level track geometry irregularities through onboard vehicle dynamics measurements using machine learning classification algorithms[J]. Proceedings of the Institution of Mechanical Engineers Part F-Journal of Rail and Rapid Transit，2021，235(1)：107-120.
[133] XIAO B，LIU J，ZHANG Z. A heavy-haul railway corrugation diagnosis method based on WPD-ASTFT and SVM[J]. Shock and Vibration，2022，2022：1-14.
[134] LI S，MAO X，SHANG P，et al. Intelligent detection of rail corrugation using ACMP-based energy entropy and LSSVM[J]. Nonlinear Dynamics，2023，111(9)：8419-8438.
[135] IYER S，VELMURUGAN T，GANDOMI A H，et al. Structural health monitoring of railway tracks using IOT-based multi-robot system[J]. Neural Computing and Applications，2021，33(11)：5897-5915.
[136] ILIOPOULOS I A，SAKELLARIOU J S，FASSOIS S D. Track segment automated characterisation via railway-vehicle-based random vibration signals and statistical time series methods[J]. Vehicle System Dynamics，2022，60(10)：3336-3357.
[137] XIE Q，TAO G，HE B，et al. Rail corrugation detection using one-dimensional convolution neural network and data-driven method[J]. Measurement，2022，200：111624.
[138] XIE Q，TAO G，LO S M，et al. A data-driven convolutional regression scheme for on-board and quantitative detection of rail corrugation roughness[J]. Wear，2023，524-525：204770.
[139] LI C，SUN H，LI W，et al. A multitask learning method for rail corrugation detection using in-vehicle responses and noise data[J]. IEEE Transactions on Intelligent Transportation Systems，2024，6(25)：1-14.
[140] EDWARDS R S，DIXON S，JIAN X. Characterisation of defects in the railhead using ultrasonic surface waves[J]. NDT & E International，2006，39(6)：468-475.
[141] 孙玉华，王平，徐井芒，等. 钢轨波磨自感知原位检测系统试验研究[J]. 机械工程学报，2021，57(18)：107-117. SUN Yuhua，WANG Ping，XU Jingmang，et al. Experimental study of self-powered and self-sensing system for the rail corrugation in-situ inspection[J]. Journal of Mechanical Engineering，2021，57(18)：107-117.
[142] CLARK R. Rail flaw detection：Overview and needs for future developments[J]. NDT & E International，2004，37(2)：111-118.
[143] LEE H，HONG J，WENDIMAGEGN T W，et al. Rail corrugation detection and characterization using computer vision[J]. Sensors，2021，21(24)：8335.
[144] 马子骥，董艳茹，刘宏立，等. 基于多线结构光视觉的钢轨波磨动态测量方法[J]. 仪器仪表学报，2018，39(6)：189-197. MA Ziji，DONG Yanru，LIU Hongli，et al. Rail corrugation dynamic measurement method based on multi-line structured-light vision[J]. Chinese Journal of Scientific Instrument，2018，39(6)：189-197.
[145] LIU X，HAN J，XU H，et al. An indirect method for rail corrugation measurement based on numerical models and wavelet packet decomposition[J]. Measurement，2022，191：110726.
[146] LU J，GAO M，WANG Y，et al. Health monitoring of urban rail corrugation by wireless rechargeable sensor nodes[J]. Structural Health Monitoring，2019，18(3)：838-852.
[147] MORI H，SATO Y，OHNO H，et al. Development of compact size onboard device for condition monitoring of railway tracks[J]. Journal of Mechanical Systems for Transportation and Logistics，2013，6(2)：142-149.