地铁列车轴承故障诊断及在途诊断系统研究
|
摘要
我国地铁的快速发展,大规模建设和投入运营,极大改善我国城市交通现状的同时,也给保障地铁安全带来了挑战。在地铁车辆的故障统计中,机械故障比例最高,而轴承故障在车辆机械故障中占有较高的比重。轴承故障不仅会影响地铁车辆的行车安全,还可能带来人员伤亡和经济损失,造成严重的社会影响,因此非常有必要研究轴承在途故障诊断系统。
国内试制的轴承故障诊断系统虽然不少,但是由于系统本身缺陷,最终形成产品并安装到轨道交通车辆上在线监控轴承状态的并不多,安装到地铁列车上的诊断装备则更少,基于以上考虑,本文重点研究适合于地铁列车轴承在途故障诊断的方法与系统,主要完成了以下几方面的研究工作：
1.提出了基于自适应傅里叶分解的轴承故障诊断方法。应用自适应傅里叶分解的方法处理轴承原始采集信号,将振动信号自适应分解为一系列单一分量信号,利用峭度值提取包含有故障信息的部分单一分量进行求和,然后对求和的信号做希尔伯特变换,进而做快速傅里叶变换,得到轴承信号的频谱,观察分析频谱图,诊断轴承故障。最后用实验数据验证了方法的有效性；
2.提出了基于新的非线性动力学模型的轴承故障诊断方法。根据轴承的物理结构和受力分析,利用弹簧质量阻尼系统首先建立轴承单个滚子与内圈、外圈的接触模型,分析在径向载荷力作用下,内圈、外圈和单个滚子在其法线方向上的实时位移；然后结合随机力干扰技术,建立内圈、外圈和滚子的轴承系统非线性动力学模型,并用该模型计算出在综合力作用下无故障振动的位移和加速度信号。在非线性动力学模型内植入内圈、外圈单表面故障,计算故障情形下的振动位移和加速度信号。最后应用自适应傅里叶分解的方法提取轴承模型内圈、外圈故障仿真加速度信号频谱特征,并与轴承故障特征频率相对比,验证滚动轴承非线性动力学故障模型的有效性；
3.提出了基于时频域特征参数融合的轴承故障在途诊断算法。分析了轴承时域特征参数和频域特征参数用于诊断轴承故障的优势和缺点,考虑到时域参数与轴承故障程度密切相关,频域参数可以准确地诊断轴承故障并分辨轴承的故障类型,提出了基于时频域特征融合的轴承故障在途诊断方法,新方法利用神经网络作为非线性分类器识别轴承的在途运行状态,不仅可以诊断轴承是否发生故障,还可以在一定程度上判断轴承的故障程度,同时保留了时域参数和频域参数的优势,最后通过实验数据验证了方法的有效性；
4.结合广州地铁列车现有的监控设备以及基于时频域特征参数融合的故障诊断算法,设计了地铁列车轴承故障在途诊断系统,并通过试验台数据验证了系统算法的有效性与实时性。
The rapid development, large-scale construction and operation of subway in our country has greatly improved the current situation of our urban traffic, but it also brings challenges to the subway security at the same time. The proportion of mechanical failure is highest in subway vehicle fault statistics, and bearing failure occupies a higher proportion of mechanical failure. Bearing fault not only affects the driving safety of subway vehicle, it may also lead to casualties and economic losses, and causes serious social impact, so is necessary to research on-board diagnosis system of bearing fault.
There are many bearing fault diagnosis systems of domestic trial-manufacture, but because of their own defects, very few of them are eventually formig products and installed on the rail transit vehicle to monitor the bearing operative state, so the diagnosis product installed on the subway train is much less. The paper emphasizes on the research of the bearing on-board fault diagnosis technologies and system of urban rail transit, and carries out the following task:
1. A new bearing fault diagnosis method is proposed based on Adaptive Fourier decomposition. Adaptive Fourier decomposition is applied to decompose the original bearing vibration signal into a series of mono-components, then part of mono-components with fault imformation is extracted and summed as the bearing fault signal, which is processinged by demodulated resonance technology, and finally the the bearing fault is identified from the obtained frequency spectrum.
2. A new bearing fault diagnosis model is proposed. The bearing model is constructed based on the bearing physical structure and force analysis. The contact of each bearing component is supposed as a sping-mass-damping system, and the affect of the number change of the pressure-bearing rollers is considered to contructed the bearing model. Then the bearing fault is described as an extra force and embedded into the bearing model. Finally the bearing fault diagnosis method based on adaptive Fourier decomposition is applied to verify the effectiveness of the proposed model.
3. The paper proposes a new bearing fault diagnosis method based on the fusion of time-domain parameters and frequency-domain parameters. It analyzes the advantage and disadvantage of time-domain parameters and frequency-domain parameters applied to diagnose the bearing fault, and proposes a new bearing fault diagnosis method based on the fusion of time-domain parameters and frequency-domain parameters, which has both the advantage of the two kinds of parameters. The new bearing fault diagnosis method is verified by experiment data.
4. The paper designs the bearing fault on-road diagnosis system of urban rail transit vehicle by combining the existing monitoring equipment on Guangzhou subway trains and the fault diagnosis algorithm based on the fusion of time-domain parameters and frequency-domain parameters. Finally the effectiveness and real-time of the system's algorithm is verified by experiment.
国内试制的轴承故障诊断系统虽然不少,但是由于系统本身缺陷,最终形成产品并安装到轨道交通车辆上在线监控轴承状态的并不多,安装到地铁列车上的诊断装备则更少,基于以上考虑,本文重点研究适合于地铁列车轴承在途故障诊断的方法与系统,主要完成了以下几方面的研究工作：
1.提出了基于自适应傅里叶分解的轴承故障诊断方法。应用自适应傅里叶分解的方法处理轴承原始采集信号,将振动信号自适应分解为一系列单一分量信号,利用峭度值提取包含有故障信息的部分单一分量进行求和,然后对求和的信号做希尔伯特变换,进而做快速傅里叶变换,得到轴承信号的频谱,观察分析频谱图,诊断轴承故障。最后用实验数据验证了方法的有效性；
2.提出了基于新的非线性动力学模型的轴承故障诊断方法。根据轴承的物理结构和受力分析,利用弹簧质量阻尼系统首先建立轴承单个滚子与内圈、外圈的接触模型,分析在径向载荷力作用下,内圈、外圈和单个滚子在其法线方向上的实时位移；然后结合随机力干扰技术,建立内圈、外圈和滚子的轴承系统非线性动力学模型,并用该模型计算出在综合力作用下无故障振动的位移和加速度信号。在非线性动力学模型内植入内圈、外圈单表面故障,计算故障情形下的振动位移和加速度信号。最后应用自适应傅里叶分解的方法提取轴承模型内圈、外圈故障仿真加速度信号频谱特征,并与轴承故障特征频率相对比,验证滚动轴承非线性动力学故障模型的有效性；
3.提出了基于时频域特征参数融合的轴承故障在途诊断算法。分析了轴承时域特征参数和频域特征参数用于诊断轴承故障的优势和缺点,考虑到时域参数与轴承故障程度密切相关,频域参数可以准确地诊断轴承故障并分辨轴承的故障类型,提出了基于时频域特征融合的轴承故障在途诊断方法,新方法利用神经网络作为非线性分类器识别轴承的在途运行状态,不仅可以诊断轴承是否发生故障,还可以在一定程度上判断轴承的故障程度,同时保留了时域参数和频域参数的优势,最后通过实验数据验证了方法的有效性；
4.结合广州地铁列车现有的监控设备以及基于时频域特征参数融合的故障诊断算法,设计了地铁列车轴承故障在途诊断系统,并通过试验台数据验证了系统算法的有效性与实时性。
The rapid development, large-scale construction and operation of subway in our country has greatly improved the current situation of our urban traffic, but it also brings challenges to the subway security at the same time. The proportion of mechanical failure is highest in subway vehicle fault statistics, and bearing failure occupies a higher proportion of mechanical failure. Bearing fault not only affects the driving safety of subway vehicle, it may also lead to casualties and economic losses, and causes serious social impact, so is necessary to research on-board diagnosis system of bearing fault.
There are many bearing fault diagnosis systems of domestic trial-manufacture, but because of their own defects, very few of them are eventually formig products and installed on the rail transit vehicle to monitor the bearing operative state, so the diagnosis product installed on the subway train is much less. The paper emphasizes on the research of the bearing on-board fault diagnosis technologies and system of urban rail transit, and carries out the following task:
1. A new bearing fault diagnosis method is proposed based on Adaptive Fourier decomposition. Adaptive Fourier decomposition is applied to decompose the original bearing vibration signal into a series of mono-components, then part of mono-components with fault imformation is extracted and summed as the bearing fault signal, which is processinged by demodulated resonance technology, and finally the the bearing fault is identified from the obtained frequency spectrum.
2. A new bearing fault diagnosis model is proposed. The bearing model is constructed based on the bearing physical structure and force analysis. The contact of each bearing component is supposed as a sping-mass-damping system, and the affect of the number change of the pressure-bearing rollers is considered to contructed the bearing model. Then the bearing fault is described as an extra force and embedded into the bearing model. Finally the bearing fault diagnosis method based on adaptive Fourier decomposition is applied to verify the effectiveness of the proposed model.
3. The paper proposes a new bearing fault diagnosis method based on the fusion of time-domain parameters and frequency-domain parameters. It analyzes the advantage and disadvantage of time-domain parameters and frequency-domain parameters applied to diagnose the bearing fault, and proposes a new bearing fault diagnosis method based on the fusion of time-domain parameters and frequency-domain parameters, which has both the advantage of the two kinds of parameters. The new bearing fault diagnosis method is verified by experiment data.
4. The paper designs the bearing fault on-road diagnosis system of urban rail transit vehicle by combining the existing monitoring equipment on Guangzhou subway trains and the fault diagnosis algorithm based on the fusion of time-domain parameters and frequency-domain parameters. Finally the effectiveness and real-time of the system's algorithm is verified by experiment.
引文
[1]李熙.城市轨道交通车辆走行部安全评估方法研究[D].北京：北京交通大学,2011.
[2]付军,胡晓依,陈亮等.BP神经网络方法在机车轴承故障诊断的应用[J].铁道机车车辆,2002,2(2)：25-26
[3]黄莉,汪曙俊.地铁车辆轮对轴承的检修[J].轴承,2012(10)：40-42.
[4]许六一,丛力群,欧阳树生,毛淑华.基于设备状态的智能化维修模式研究[J].信息技术与标准化,2009(11)：41-45.
[5]叶霞飞,李君,霍建平.国内外城市轨道交通车辆段对比研究[J].城市轨道交通研究,2003,6(1)：72-77.
[6]刘易平.便携式铁路车辆走行部故障在线诊断系统研究与开发[D].湖南：湖南大学,2005.
[7]宗清泉.地铁车辆维修模式的探讨[J].城市轨道交通研究,2007(5)：65-67.
[8]徐东.球轴承疲劳剩余寿命分析与预测方法研究[D].湖南：国防科学技术大学,2011.
[9]Liu C. Fault detection of rolling element bearings[D]. Washington:University of Washington, 2005.
[10]Cheung M, Li W. Probabilistic Fatigue and Fracture Analysis of Steel Bridges[J]. Journal of Structural Safety.2003,23:245-262.
[11]Zheng Jinde, Cheng Junsheng, Yang Yu. Generalized empirical mode decomposition and its applications to rolling element bearing fault diagnosis[J]. Mechanical systems and signal processing,2013,40(1):136-153.
[12]吴忠民.基于DSP的列车滚动轴承故障检测与分析系统研究[D].北京：北京交通大学,2007.
[13]吴德华.列车滚动轴承故障诊断与监测系统研究[D].湖南：中南大学,2005.
[14]詹捷等.机械信息学[M].重庆出版社,1994.
[15]贾天丽.轨道列车走行部滚动轴承故障诊断研究[D].北京：北京交通大学,2011.
[16]O.G. Gustantsson, T.Tallian. Detection of Damage in Assembled Roiling Bearing[J]. Transactions of the ASLE,1962:197-209.
[17]D. Dyer, R. M. Stewart. Detection of Rolling Element Bearing Damage by Statistical Vibration Analysis[J]. Transactions of the ASME, Journal of Mechanical Design,1978,100(4): 229-235.
[18]T. Koizumi. M. Kiso, R. Taniguchi. Preventive Maintenance for roller and Journal Bearings of introduction Motor based on the Diagnostic Signature Analysis[J]. Transactions of the ASME. Journal of Vibration, Acoustics, Stress and Reliability in Design,1986,108(1):26-31.
[19]Sohve J S. Trouble-shooting to stop vibration of centrifugal[J], Petro/Chem. Engeneer,1968, (11):22-23.
[20]Cvetkovic Z. On discrete short-time Fourier analysis[J]. IEEE Transactions on Signal Processing, 2000,48(9):2628-2640.
[21]赵新甫.电机轴承故障在线检测系统研究[D].杭州：杭州电子科技大学,2011.
[22]石丁丁.基于EMD的异步电动机轴承故障诊断技术的研究[D].太原：中北大学,2009.
[23]T. G. Wheeler. Bearing Analysis Equipment Keeps Down Time[J]. Plant Engineering.1968: 87-89.
[24]J. L. Taylor. Identification of Bearing Defects by Spectral Analysis. Transactions of the ASME[J]. Journal of Mechanical Design,1980,102(4):199-204.
[25]R. B. Randall. Analysis Techniques for Diagnosis of Gear and Bearing Faults[C]. Proceedings of CSMDT. Shenyang China,1986:387-393.
[26]J. Mathew. A. Szezepanik. B. T. Kuhnall. Incipient Damage Detection in Low Speed Bearings Using Demodulation Resonance Analysis Technique[C]. International Tribology Conference, Melborune, December,1987:366-369.
[27]Claasen TACM, Mecklenbrauker WFC. The Wigner distribution-a tool for time frequency analysis, Part 1:Continuous time signals[J]. Philips Journal of Research,1980,35(3): 217-250.
[28]Mallat S C. A theory for multi-resolution signal decomposition:the wavelet representation[J]. IEEE Transactions on Pattern Recognition and Machine Intelligence,1989:674-693.
[29]Norden E Huang, Zheng Shen, Steven R Long, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[R]. Proc. R. Soc, Lond. A,1998,454:903-995.
[30]余志红,王朝晖,陈志刚.基于数据挖掘的轴承故障特征模式提取[J].轴承,2006(7)：30-33.
[31]张星辉,康建设,刘占军,李志勇.轴承故障诊断与故障预测方法[J].轴承,2011(1)：148-152.
[32]乔保栋,陈果,葛科宇,曲秀秀.一种滚动轴承故障知识获取的新方法[J].轴承,2011(2)：39-44.
[33]邱阿瑞,尹彤.电动机滚动轴承的故障诊断[J].大电机技术,1996(2)：25-29.
[34]何正嘉.机械监测诊断中的小波应用技术[J].设备管理维修,1998,(8)：19-24.
[35]张中民,张英堂等.基于小波系数包络谱的滚动轴承故障诊断[J].振动工程学报1998,11(1)：65-69.
[36]缪荣松.基于小波-包络的重载货运列车滚动轴承振动故障诊断[D].长沙：中南大学, 2011.
[37]于德介,程军圣,杨宇.基于Hilbert边际谱的滚动轴承故障诊断方法[J].振动与冲击,2005,24(1)：70-72.
[38]扈炳涛.机车轴承工况监测与故障诊断系统开发[D].北京：北京交通大学,2008.
[39]冯赫.基于小波变换的旋转机械故障诊断方法研究[D].北京：北京化工大学,2008.
[40]Ka Mun Ho. Automatic recognition and demodulation of digitally modulated communications signals using wavelet-domain signatures [D]. New Jersey:Rutgers, The State University of New Jersey,2010.
[41]Michael Louis Adams. Analysis of rolling element bearing faults in rotating machinery Experiments, modeling, fault detection and diagnosis [C].8th International Conference on Vibrations in Rotating Machinery, Swansea,2004:511-520.
[42]XinSheng Lou. Fault detection and diagnosis for rolling element bearing [D]. Ohio:Case Western Reserve University,2000.
[43]Tony Boutros. Fault detection and diagnosis in machining processes and rotating machinery using fuzzy approach and hidden Markov model[D]. Ottawa:University of Ottawa,2006.
[44]Peng Xu. Neural network based wheel bearing fault detection and diagnosis using wavelets.[D]. Texas:Texas A&M University,2002.
[45]Hoonbin Hong. Rotating machinery monitoring. Feature extraction, signal separation, and fault severity evaluation[D]. Ottawa:University of Ottawa,2007.
[46]蒋静,郑国彦等.滚动轴承故障诊断中的Voiterra核-HMM识别方法[[J]. Coal Mine Machinery,2010,31(6):230-233..
[47]唐贵基等.基于分段线性分类器的滚动轴承的故障识别[J].轴承,2007(10)：31-34.
[48]李志农,王心怡等.基于核函数主元分析的滚动轴承故障模式识别方法[J].轴承,2008(5)：77-79.
[49]陆爽.基于奇异值分解和支持向量机的滚动轴承故障模式识别[J].农业工程学报,2007,23(4)：115-119.
[50]陆爽.基于双谱分析的滚动轴承故障模式识别[J].轴承,2005(5)：31-34.
[51]秦海勤,许可君等.基于图像奇异值分解的滚动轴承故障模式识别[[J].轴承,2010(6)：55-58.
[52]田野,陆爽.基于小波包和支持向量机的滚动轴承故障模式识别[[J].机床与液压,2006(6)：236-240.
[53]Venkat Venkatasubramanian, King Chan. A Neural Network Methodology for Process Fault Diagnosis[J]. Journal of American Institute of Chemical Engineers,1989,35(12):1993-2002.
[54]Ping Chen. Bearing condition monitoring and fault diagnosis[D). Calgary:University of Calgary,2000.
[55]何永勇,钟秉林,黄仁.基丁椭球单元网络的旋转机械多故障同时性诊断[J].振动工程学报,1997,10(2)：131-138.
[56]祝海龙,屈梁生.自组织包络解调及其在轴承诊断中的应用[J].西安交通大学学报,2000,34(7)：77-81.
[57]于江林,余永增等.滚动轴承声发射信号的人工神经网络模式识别技术[J].大庆石油学院学报,2008,32(5)：64-66
[58]陆爽,候跃谦.基于PCA和径向基函数神经网络的滚动轴承故障模式的识别[J].机床与液压,2005(3)：185-188.
[59]陆爽,杨斌等.基于小波和径向基函数神经网络的滚动轴承故障模式识别[J].农业工程学报,2004,20(6)：102-106.
[60]赵元喜,管永刚等.基于谐波小波包和BP神经网络的滚动轴承声发射故障模式识别技术[J].振动与冲击,2010,29(10)：162-165.
[61]MCFADDEN P D, SMITH J D. Model for the vibration produced by a single point defect in a rolling element bearing[J]. Journal of Sound and Vibration,1984,96(1):69-82.
[62]MCFADDEN P D, SMITH J D. The vibration produced by multiple point defect in a rolling element bearing[J]. Journal of Sound and Vibration,1985,98(2):263-273.
[63]ZOLADZ T, EARHART E, FIORUCCI T. Bearing defect signature analysis using advanced nonlinear signal analysis in a controlled environment[R]. Huntsville:National Aeronautics and Space Administration, Marshall Space Flight Center,1995.
[64]RAFSANJANI A, ABBASION S, FARSHIDIANFAR A. Nonlinear dynamic modeling of surface defects in rolling element bearing systems[J]. Journal of Sound and Vibration,2009, 319(3):1150-1174.
[65]HARSHA S P. Nonlinear dynamic analysis of a high-speed rotor supported by rolling element bearings[J]. Journal of Sound and Vibration,2006,290(1):65-100.
[66]NI Guangjian, ZHANG Junhong, CHENG Xiaoming. Characteristics of the main journal bearings of an engine based on non-linear dynamics[J]. Chinese Journal of Mechanical Engineering,2009,22(5):755-759.
[67]赵联春,马家驹.球轴承的弹性接触振动[J].机械工程学报,2003,39(5)：60-64.
[68]陈果.转子-滚动轴承-机匣耦合系统的不平衡/松动耦合故障非线性动力学[J].机械工程学报,2008,44(3)：82-88.
[69]谢里阳,王正.随机恒幅循环载荷疲劳可靠度异量纲干涉模型[J].机械工程学报,2008,44(1)：1-6.
[70]MA Zhenyue, SONG Zhiqiang. Nonlinear dynamic characteristic analysis of the shaft system in water turbine generator set[J]. Chinese Journal of Mechanical Engineering.2009,22(1): 124-131.
[71]徐东,徐永成,陈循等.单表面故障的滚动轴承系统非线性动力学研究[J].机械工程学报,2010,46(21)：61-68.
[72]M.F. While, Rolling Element Bearing Vibration Transfer Characteristics Effect of Stiffness[J]. Journal of Applied Mechanics,1979:677-684.
[73]Lin J, Qu L, Feature extraction based on morlet wavelet and its Application for mechanical fault diagnosis[J]. Journal of Sound and Vibration,2000.234(1):135-148.
[74]Seeker S, Ayaz E. Feature extraction related to bearing damage in electric motors by wavelet analysis[J]. Journal of the Franklin institute.2003,304:125-134.
[75]屈梁生,何正嘉.机械故障诊断学[M].上海科学技术出版社,1986.
[76]雷继尧,程善同,张思复.轴承疲劳诊断仪[R].重庆大学会议资料,重资(86)004号.
[77]王琳.机械设备故障诊断与监测的常用方法及其发展趋势[J].武汉工业大学学报,2000,22(3)：62-64.
[78]毛怀东,陈家骥.滚动轴承故障诊断参数的研究[C].第三届全国机械设备故障诊断学术会议论文集,1991：592-597.
[79]刘永斌.基于非线性信号分析的滚动轴承状态监测诊断研究[D].合肥：中国科学技术大学,2011.
[80]HARRIS T A, KOTZALAS M N. Advanced concepts of bearing technology(rolling bearing analysis)[M].5th ed. New York:Taylor& Francis,2006.
[81]周仕仁,钟声,章鹏·列车滚轴轴承故障诊断研究现状分析[J].中国铁路,2009(11)：35-39.
[82]James E and Berry. How to track rolling element bearing health with vibration signature analysis[R].1991.
[83]Gustafsson O. G. Tallian T. Detection of damage in assembled rolling bearings[J]. Trans. of ASLE,1962(5):197-209.
[84]Wheeler EG. Bearing analysis equipment keeps downtime down[N]. Plant Engineering.1968.
[85]Martin R. Detection of ball bearing malfunctions[N]. Instruments and Control Systems.1976.
[86]Martin R. Angelo and Brel Kjaer. Vibration monitoring of machines[M]. British Maritime Technology,1989.
[87]吴俊伟.Laplace小波在机车轴承故障诊断中的应用研究[D].北京：北京交通大学,2009.
[88]Ronald W, Jacobs. Detection of mechanical faults in rotary blowers[C]. Proceeding of Machinery Vibration Monitoring and Analysis Meeting,1983.
[89]Y Kim Paul, Cowe I. R. G. A review of rolling element bearing health monitoring[C]. Proceeding of Machinery Vibration Monitoring and Analysis Meeting,1983.
[90]岳建海,裘正定.信号处理技术在滚动轴承故障诊断中的应用与发展[J].信号处理,2005,2(21)：185-190
[91]徐尹格,颜玉玲.相关技术在滚动轴承故障诊断中的应用[J].应用数学和力学,1992,13(7)：593-598.
[92]汪林海.滚动轴承在线故障诊断冲击脉冲计[D].上海：上海大学,2009.
[93]赵佳萌.基于声信号小波变换的滚动轴承故障诊断[D].北京：北京交通大学,2009.
[94]林选.基于小波包和EMD相结合的电机轴承故障诊断[D].太原：太原理工大学,2010
[95]于明月.第二代小波变换在旋转机械故障诊断中的应用研究[D].南京：南京航空航天大学,2008.
[96]丁夏完.滚动轴承故障智能诊断方法的研究及应用[D]北京：中央民族大学,2006.
[97]曾刚.滚动轴承微弱故障信号检测方法研究[D].成都：成都理工大学,2010.
[98]张弛哲.共振解调技术在牵引电机轴承故障诊断中的应用[D].北京：北京交通大学,2011.
[99]范凯.基于LabWindows的泥浆泵故障诊断系统开发[D].青岛：石油大学(华东),2003.
[100]郭宙.滚动轴承故障模式识别方法研究[D].北京：北京化工大学,2011.
[101]欧阳土中,滚动轴承动力学分析中的理论问题(一)[J].轴承,1996(4)：14-19,34.
[102]高红斌.基于静动力学的滚动轴承故障模型分析及物理模拟[D].太原：太原理工大学,2006.
[103]陈雄,角接触球轴承静力学与动力学分析[D].南京：南京航空航天大学,2007.
[104]欧阳土中,滚动轴承动力学分析中的理论问题(二)[J].轴承,1996(5)：10-16.
[105]Sunnersjo C. S. Rolling bearing vibrations-the effects of geometrical imperfection and wear[J]. Journal of sound and vibration,1985,98(4):445-474.
[106]N. Tandon, A. Choud hury, An analytical model for the prediction of the vibration response of rolling element bearings due to a localized defect[J]. Journal of Sound and Vibration,1997, 205(3):275-292.
[107]白乙拉.非光滑分布参数系统参数辨识及其应用[D].大连,大连理工大学,2006.
[108]陆建.最小二乘法及其应用[J].中国西部科技,2007(12)：19-21.
[109]沈恒范.概率论与数理统计[M].北京：高等教育出版社,2007.
[110]张立新.基于最小二乘法的电容层析成像图像重建算法[D].哈尔滨：哈尔滨理工大学,2010.
[111]王萍,郭巧,赵静.极大似然法在间接测热系统参数估计中的应用[J].系统工程与电子技术,2003,25(11)：1404-1406
[112]NORDE E Huang, ZHENG Shen, STEVEN R Long, 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.
[113]INGRID Daubechies. Ten Lectures on Wavelets[M].2nd. Montpelier Vermont:Capital City Press,1992.
[114]WOLFGANG Martin, PATRICK Flandrin. Wigner-Ville Spectral Analysis of Non-stationary Processes[J]. IEEE Transactions on Acoustics. Speech, and Signal Processing,1985,33(6): 1461-1470.
[115]胡晓依,何庆复,王华胜等.基于STFT的振动信号解调方法及其在轴承故障检测中的应用[J].振动与冲击,2008,27(2)：82-86.
[116]CUI Hua, SONG Guoxiang. Study of the Wavelet Basis Selections[J]. Computational Intelligence and Security, Lecture Notes in Computer Science,2007(4456):1009-1017.
[117]QIAN Tao, ZHANG Liming, LI Zhixiong. Algorithm of Adaptive Fourier Decomposition[J]. IEEE Transactions on Signal Processing,2011,59(12):5899-5906.
[118]QIAN Tao, WANG Yanbo, DANG Pei. Adaptive Decomposition into Mono-Components[J]. Advances in Adaptive Data Analysis,2009,1 (4):703-709.
[119]刘金朝,丁夏完,王成国.自适应共振解调法及其在滚动轴承故障诊断中的应用[J].振动与冲击,26(1)：38-41.
[120]唐德尧.广义共振、共振解调故障诊断与安全工程-铁路篇[M].北京：中国铁道出版社,2006.
[121]周明珠.“信号与系统实验装置”的优化设计[D].郑州：郑州大学,2005.
[122]关庆,邓赵红,王士同.改进的模糊C均值聚类算法[J].计算机工程与应用,2011,47(10)：27-29,88.
[123]张铁新.峰值能量技术原理及其应用[J].电机技术,2010(3)：57-59.
[124]严保康,周凤星.齿轮箱故障识别系统的研究与应用[J].现代电子技术,2012,35(2)：77-80.
[125]杨建伟,蔡国强,姚德臣等.基于小波包变换和BP网络的铁道车辆滚动轴承故障诊断方法[J].中国铁道科学,2010,31(6)：68-73.
[126]张静.基于灰色——神经网络理论的西安市天然气中长期负荷预测[D].西安：西安建筑科技大学,2006.
[127]张俊.基于小波分形和神经网络的滚动轴承故障诊断[D].北京：北京交通大学,2009.
[128]杨克强.LVQ神经网络在齿轮箱故障诊断中的研究[D].安徽：安徽农业大学,2010.
[129]刘冬霞.滚动轴承故障诊断系统开发研究[D].江门：五邑大学,2008.
[130]刘海波.轨道车辆转向架电机轴承在线故障诊断系统开发[D].太原：太原科技大学,2010.
[2]付军,胡晓依,陈亮等.BP神经网络方法在机车轴承故障诊断的应用[J].铁道机车车辆,2002,2(2)：25-26
[3]黄莉,汪曙俊.地铁车辆轮对轴承的检修[J].轴承,2012(10)：40-42.
[4]许六一,丛力群,欧阳树生,毛淑华.基于设备状态的智能化维修模式研究[J].信息技术与标准化,2009(11)：41-45.
[5]叶霞飞,李君,霍建平.国内外城市轨道交通车辆段对比研究[J].城市轨道交通研究,2003,6(1)：72-77.
[6]刘易平.便携式铁路车辆走行部故障在线诊断系统研究与开发[D].湖南：湖南大学,2005.
[7]宗清泉.地铁车辆维修模式的探讨[J].城市轨道交通研究,2007(5)：65-67.
[8]徐东.球轴承疲劳剩余寿命分析与预测方法研究[D].湖南：国防科学技术大学,2011.
[9]Liu C. Fault detection of rolling element bearings[D]. Washington:University of Washington, 2005.
[10]Cheung M, Li W. Probabilistic Fatigue and Fracture Analysis of Steel Bridges[J]. Journal of Structural Safety.2003,23:245-262.
[11]Zheng Jinde, Cheng Junsheng, Yang Yu. Generalized empirical mode decomposition and its applications to rolling element bearing fault diagnosis[J]. Mechanical systems and signal processing,2013,40(1):136-153.
[12]吴忠民.基于DSP的列车滚动轴承故障检测与分析系统研究[D].北京：北京交通大学,2007.
[13]吴德华.列车滚动轴承故障诊断与监测系统研究[D].湖南：中南大学,2005.
[14]詹捷等.机械信息学[M].重庆出版社,1994.
[15]贾天丽.轨道列车走行部滚动轴承故障诊断研究[D].北京：北京交通大学,2011.
[16]O.G. Gustantsson, T.Tallian. Detection of Damage in Assembled Roiling Bearing[J]. Transactions of the ASLE,1962:197-209.
[17]D. Dyer, R. M. Stewart. Detection of Rolling Element Bearing Damage by Statistical Vibration Analysis[J]. Transactions of the ASME, Journal of Mechanical Design,1978,100(4): 229-235.
[18]T. Koizumi. M. Kiso, R. Taniguchi. Preventive Maintenance for roller and Journal Bearings of introduction Motor based on the Diagnostic Signature Analysis[J]. Transactions of the ASME. Journal of Vibration, Acoustics, Stress and Reliability in Design,1986,108(1):26-31.
[19]Sohve J S. Trouble-shooting to stop vibration of centrifugal[J], Petro/Chem. Engeneer,1968, (11):22-23.
[20]Cvetkovic Z. On discrete short-time Fourier analysis[J]. IEEE Transactions on Signal Processing, 2000,48(9):2628-2640.
[21]赵新甫.电机轴承故障在线检测系统研究[D].杭州：杭州电子科技大学,2011.
[22]石丁丁.基于EMD的异步电动机轴承故障诊断技术的研究[D].太原：中北大学,2009.
[23]T. G. Wheeler. Bearing Analysis Equipment Keeps Down Time[J]. Plant Engineering.1968: 87-89.
[24]J. L. Taylor. Identification of Bearing Defects by Spectral Analysis. Transactions of the ASME[J]. Journal of Mechanical Design,1980,102(4):199-204.
[25]R. B. Randall. Analysis Techniques for Diagnosis of Gear and Bearing Faults[C]. Proceedings of CSMDT. Shenyang China,1986:387-393.
[26]J. Mathew. A. Szezepanik. B. T. Kuhnall. Incipient Damage Detection in Low Speed Bearings Using Demodulation Resonance Analysis Technique[C]. International Tribology Conference, Melborune, December,1987:366-369.
[27]Claasen TACM, Mecklenbrauker WFC. The Wigner distribution-a tool for time frequency analysis, Part 1:Continuous time signals[J]. Philips Journal of Research,1980,35(3): 217-250.
[28]Mallat S C. A theory for multi-resolution signal decomposition:the wavelet representation[J]. IEEE Transactions on Pattern Recognition and Machine Intelligence,1989:674-693.
[29]Norden E Huang, Zheng Shen, Steven R Long, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[R]. Proc. R. Soc, Lond. A,1998,454:903-995.
[30]余志红,王朝晖,陈志刚.基于数据挖掘的轴承故障特征模式提取[J].轴承,2006(7)：30-33.
[31]张星辉,康建设,刘占军,李志勇.轴承故障诊断与故障预测方法[J].轴承,2011(1)：148-152.
[32]乔保栋,陈果,葛科宇,曲秀秀.一种滚动轴承故障知识获取的新方法[J].轴承,2011(2)：39-44.
[33]邱阿瑞,尹彤.电动机滚动轴承的故障诊断[J].大电机技术,1996(2)：25-29.
[34]何正嘉.机械监测诊断中的小波应用技术[J].设备管理维修,1998,(8)：19-24.
[35]张中民,张英堂等.基于小波系数包络谱的滚动轴承故障诊断[J].振动工程学报1998,11(1)：65-69.
[36]缪荣松.基于小波-包络的重载货运列车滚动轴承振动故障诊断[D].长沙：中南大学, 2011.
[37]于德介,程军圣,杨宇.基于Hilbert边际谱的滚动轴承故障诊断方法[J].振动与冲击,2005,24(1)：70-72.
[38]扈炳涛.机车轴承工况监测与故障诊断系统开发[D].北京：北京交通大学,2008.
[39]冯赫.基于小波变换的旋转机械故障诊断方法研究[D].北京：北京化工大学,2008.
[40]Ka Mun Ho. Automatic recognition and demodulation of digitally modulated communications signals using wavelet-domain signatures [D]. New Jersey:Rutgers, The State University of New Jersey,2010.
[41]Michael Louis Adams. Analysis of rolling element bearing faults in rotating machinery Experiments, modeling, fault detection and diagnosis [C].8th International Conference on Vibrations in Rotating Machinery, Swansea,2004:511-520.
[42]XinSheng Lou. Fault detection and diagnosis for rolling element bearing [D]. Ohio:Case Western Reserve University,2000.
[43]Tony Boutros. Fault detection and diagnosis in machining processes and rotating machinery using fuzzy approach and hidden Markov model[D]. Ottawa:University of Ottawa,2006.
[44]Peng Xu. Neural network based wheel bearing fault detection and diagnosis using wavelets.[D]. Texas:Texas A&M University,2002.
[45]Hoonbin Hong. Rotating machinery monitoring. Feature extraction, signal separation, and fault severity evaluation[D]. Ottawa:University of Ottawa,2007.
[46]蒋静,郑国彦等.滚动轴承故障诊断中的Voiterra核-HMM识别方法[[J]. Coal Mine Machinery,2010,31(6):230-233..
[47]唐贵基等.基于分段线性分类器的滚动轴承的故障识别[J].轴承,2007(10)：31-34.
[48]李志农,王心怡等.基于核函数主元分析的滚动轴承故障模式识别方法[J].轴承,2008(5)：77-79.
[49]陆爽.基于奇异值分解和支持向量机的滚动轴承故障模式识别[J].农业工程学报,2007,23(4)：115-119.
[50]陆爽.基于双谱分析的滚动轴承故障模式识别[J].轴承,2005(5)：31-34.
[51]秦海勤,许可君等.基于图像奇异值分解的滚动轴承故障模式识别[[J].轴承,2010(6)：55-58.
[52]田野,陆爽.基于小波包和支持向量机的滚动轴承故障模式识别[[J].机床与液压,2006(6)：236-240.
[53]Venkat Venkatasubramanian, King Chan. A Neural Network Methodology for Process Fault Diagnosis[J]. Journal of American Institute of Chemical Engineers,1989,35(12):1993-2002.
[54]Ping Chen. Bearing condition monitoring and fault diagnosis[D). Calgary:University of Calgary,2000.
[55]何永勇,钟秉林,黄仁.基丁椭球单元网络的旋转机械多故障同时性诊断[J].振动工程学报,1997,10(2)：131-138.
[56]祝海龙,屈梁生.自组织包络解调及其在轴承诊断中的应用[J].西安交通大学学报,2000,34(7)：77-81.
[57]于江林,余永增等.滚动轴承声发射信号的人工神经网络模式识别技术[J].大庆石油学院学报,2008,32(5)：64-66
[58]陆爽,候跃谦.基于PCA和径向基函数神经网络的滚动轴承故障模式的识别[J].机床与液压,2005(3)：185-188.
[59]陆爽,杨斌等.基于小波和径向基函数神经网络的滚动轴承故障模式识别[J].农业工程学报,2004,20(6)：102-106.
[60]赵元喜,管永刚等.基于谐波小波包和BP神经网络的滚动轴承声发射故障模式识别技术[J].振动与冲击,2010,29(10)：162-165.
[61]MCFADDEN P D, SMITH J D. Model for the vibration produced by a single point defect in a rolling element bearing[J]. Journal of Sound and Vibration,1984,96(1):69-82.
[62]MCFADDEN P D, SMITH J D. The vibration produced by multiple point defect in a rolling element bearing[J]. Journal of Sound and Vibration,1985,98(2):263-273.
[63]ZOLADZ T, EARHART E, FIORUCCI T. Bearing defect signature analysis using advanced nonlinear signal analysis in a controlled environment[R]. Huntsville:National Aeronautics and Space Administration, Marshall Space Flight Center,1995.
[64]RAFSANJANI A, ABBASION S, FARSHIDIANFAR A. Nonlinear dynamic modeling of surface defects in rolling element bearing systems[J]. Journal of Sound and Vibration,2009, 319(3):1150-1174.
[65]HARSHA S P. Nonlinear dynamic analysis of a high-speed rotor supported by rolling element bearings[J]. Journal of Sound and Vibration,2006,290(1):65-100.
[66]NI Guangjian, ZHANG Junhong, CHENG Xiaoming. Characteristics of the main journal bearings of an engine based on non-linear dynamics[J]. Chinese Journal of Mechanical Engineering,2009,22(5):755-759.
[67]赵联春,马家驹.球轴承的弹性接触振动[J].机械工程学报,2003,39(5)：60-64.
[68]陈果.转子-滚动轴承-机匣耦合系统的不平衡/松动耦合故障非线性动力学[J].机械工程学报,2008,44(3)：82-88.
[69]谢里阳,王正.随机恒幅循环载荷疲劳可靠度异量纲干涉模型[J].机械工程学报,2008,44(1)：1-6.
[70]MA Zhenyue, SONG Zhiqiang. Nonlinear dynamic characteristic analysis of the shaft system in water turbine generator set[J]. Chinese Journal of Mechanical Engineering.2009,22(1): 124-131.
[71]徐东,徐永成,陈循等.单表面故障的滚动轴承系统非线性动力学研究[J].机械工程学报,2010,46(21)：61-68.
[72]M.F. While, Rolling Element Bearing Vibration Transfer Characteristics Effect of Stiffness[J]. Journal of Applied Mechanics,1979:677-684.
[73]Lin J, Qu L, Feature extraction based on morlet wavelet and its Application for mechanical fault diagnosis[J]. Journal of Sound and Vibration,2000.234(1):135-148.
[74]Seeker S, Ayaz E. Feature extraction related to bearing damage in electric motors by wavelet analysis[J]. Journal of the Franklin institute.2003,304:125-134.
[75]屈梁生,何正嘉.机械故障诊断学[M].上海科学技术出版社,1986.
[76]雷继尧,程善同,张思复.轴承疲劳诊断仪[R].重庆大学会议资料,重资(86)004号.
[77]王琳.机械设备故障诊断与监测的常用方法及其发展趋势[J].武汉工业大学学报,2000,22(3)：62-64.
[78]毛怀东,陈家骥.滚动轴承故障诊断参数的研究[C].第三届全国机械设备故障诊断学术会议论文集,1991：592-597.
[79]刘永斌.基于非线性信号分析的滚动轴承状态监测诊断研究[D].合肥：中国科学技术大学,2011.
[80]HARRIS T A, KOTZALAS M N. Advanced concepts of bearing technology(rolling bearing analysis)[M].5th ed. New York:Taylor& Francis,2006.
[81]周仕仁,钟声,章鹏·列车滚轴轴承故障诊断研究现状分析[J].中国铁路,2009(11)：35-39.
[82]James E and Berry. How to track rolling element bearing health with vibration signature analysis[R].1991.
[83]Gustafsson O. G. Tallian T. Detection of damage in assembled rolling bearings[J]. Trans. of ASLE,1962(5):197-209.
[84]Wheeler EG. Bearing analysis equipment keeps downtime down[N]. Plant Engineering.1968.
[85]Martin R. Detection of ball bearing malfunctions[N]. Instruments and Control Systems.1976.
[86]Martin R. Angelo and Brel Kjaer. Vibration monitoring of machines[M]. British Maritime Technology,1989.
[87]吴俊伟.Laplace小波在机车轴承故障诊断中的应用研究[D].北京：北京交通大学,2009.
[88]Ronald W, Jacobs. Detection of mechanical faults in rotary blowers[C]. Proceeding of Machinery Vibration Monitoring and Analysis Meeting,1983.
[89]Y Kim Paul, Cowe I. R. G. A review of rolling element bearing health monitoring[C]. Proceeding of Machinery Vibration Monitoring and Analysis Meeting,1983.
[90]岳建海,裘正定.信号处理技术在滚动轴承故障诊断中的应用与发展[J].信号处理,2005,2(21)：185-190
[91]徐尹格,颜玉玲.相关技术在滚动轴承故障诊断中的应用[J].应用数学和力学,1992,13(7)：593-598.
[92]汪林海.滚动轴承在线故障诊断冲击脉冲计[D].上海：上海大学,2009.
[93]赵佳萌.基于声信号小波变换的滚动轴承故障诊断[D].北京：北京交通大学,2009.
[94]林选.基于小波包和EMD相结合的电机轴承故障诊断[D].太原：太原理工大学,2010
[95]于明月.第二代小波变换在旋转机械故障诊断中的应用研究[D].南京：南京航空航天大学,2008.
[96]丁夏完.滚动轴承故障智能诊断方法的研究及应用[D]北京：中央民族大学,2006.
[97]曾刚.滚动轴承微弱故障信号检测方法研究[D].成都：成都理工大学,2010.
[98]张弛哲.共振解调技术在牵引电机轴承故障诊断中的应用[D].北京：北京交通大学,2011.
[99]范凯.基于LabWindows的泥浆泵故障诊断系统开发[D].青岛：石油大学(华东),2003.
[100]郭宙.滚动轴承故障模式识别方法研究[D].北京：北京化工大学,2011.
[101]欧阳土中,滚动轴承动力学分析中的理论问题(一)[J].轴承,1996(4)：14-19,34.
[102]高红斌.基于静动力学的滚动轴承故障模型分析及物理模拟[D].太原：太原理工大学,2006.
[103]陈雄,角接触球轴承静力学与动力学分析[D].南京：南京航空航天大学,2007.
[104]欧阳土中,滚动轴承动力学分析中的理论问题(二)[J].轴承,1996(5)：10-16.
[105]Sunnersjo C. S. Rolling bearing vibrations-the effects of geometrical imperfection and wear[J]. Journal of sound and vibration,1985,98(4):445-474.
[106]N. Tandon, A. Choud hury, An analytical model for the prediction of the vibration response of rolling element bearings due to a localized defect[J]. Journal of Sound and Vibration,1997, 205(3):275-292.
[107]白乙拉.非光滑分布参数系统参数辨识及其应用[D].大连,大连理工大学,2006.
[108]陆建.最小二乘法及其应用[J].中国西部科技,2007(12)：19-21.
[109]沈恒范.概率论与数理统计[M].北京：高等教育出版社,2007.
[110]张立新.基于最小二乘法的电容层析成像图像重建算法[D].哈尔滨：哈尔滨理工大学,2010.
[111]王萍,郭巧,赵静.极大似然法在间接测热系统参数估计中的应用[J].系统工程与电子技术,2003,25(11)：1404-1406
[112]NORDE E Huang, ZHENG Shen, STEVEN R Long, 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.
[113]INGRID Daubechies. Ten Lectures on Wavelets[M].2nd. Montpelier Vermont:Capital City Press,1992.
[114]WOLFGANG Martin, PATRICK Flandrin. Wigner-Ville Spectral Analysis of Non-stationary Processes[J]. IEEE Transactions on Acoustics. Speech, and Signal Processing,1985,33(6): 1461-1470.
[115]胡晓依,何庆复,王华胜等.基于STFT的振动信号解调方法及其在轴承故障检测中的应用[J].振动与冲击,2008,27(2)：82-86.
[116]CUI Hua, SONG Guoxiang. Study of the Wavelet Basis Selections[J]. Computational Intelligence and Security, Lecture Notes in Computer Science,2007(4456):1009-1017.
[117]QIAN Tao, ZHANG Liming, LI Zhixiong. Algorithm of Adaptive Fourier Decomposition[J]. IEEE Transactions on Signal Processing,2011,59(12):5899-5906.
[118]QIAN Tao, WANG Yanbo, DANG Pei. Adaptive Decomposition into Mono-Components[J]. Advances in Adaptive Data Analysis,2009,1 (4):703-709.
[119]刘金朝,丁夏完,王成国.自适应共振解调法及其在滚动轴承故障诊断中的应用[J].振动与冲击,26(1)：38-41.
[120]唐德尧.广义共振、共振解调故障诊断与安全工程-铁路篇[M].北京：中国铁道出版社,2006.
[121]周明珠.“信号与系统实验装置”的优化设计[D].郑州：郑州大学,2005.
[122]关庆,邓赵红,王士同.改进的模糊C均值聚类算法[J].计算机工程与应用,2011,47(10)：27-29,88.
[123]张铁新.峰值能量技术原理及其应用[J].电机技术,2010(3)：57-59.
[124]严保康,周凤星.齿轮箱故障识别系统的研究与应用[J].现代电子技术,2012,35(2)：77-80.
[125]杨建伟,蔡国强,姚德臣等.基于小波包变换和BP网络的铁道车辆滚动轴承故障诊断方法[J].中国铁道科学,2010,31(6)：68-73.
[126]张静.基于灰色——神经网络理论的西安市天然气中长期负荷预测[D].西安：西安建筑科技大学,2006.
[127]张俊.基于小波分形和神经网络的滚动轴承故障诊断[D].北京：北京交通大学,2009.
[128]杨克强.LVQ神经网络在齿轮箱故障诊断中的研究[D].安徽：安徽农业大学,2010.
[129]刘冬霞.滚动轴承故障诊断系统开发研究[D].江门：五邑大学,2008.
[130]刘海波.轨道车辆转向架电机轴承在线故障诊断系统开发[D].太原：太原科技大学,2010.