离散全矢谱校正方法及工程应用研究
|
摘要
全矢谱技术是大型旋转设备故障诊断分析领域发展起来的一项新技术,它提高了设备诊断的准确性和工程实用性。传统的单通道振动信号分析方法已经不能满足工程实际中故障特征提取和故障分析要求,全矢谱充分利用双通道同源信息融合技术,快速、稳健、准确地获得振动信号所包含的全部有用信息。
频谱校正的意义是提高频谱分析的精度。针对现有频谱校正技术只针对单源信号和同源的各单通道信号的频谱进行校正的研究现状,提出针对双通道融合矢量信号的全矢谱进行校正的方法。详细介绍内插法、能量重心法、FFT+FT法和相位差校正法的原理、方法及实现过程。分析和比较信号在三种不同窗函数条件下的内插法和三种不同相位差法的频谱校正结果。提出融合矢量信号的全矢谱和汉宁窗的内插法、连续等长的两段信号的相位差法相结合的校正法。
研究并实现了全矢谱和汉宁窗的内插法、连续等长的两段信号的相位差法相结合的校正法。两种方法的原理都是将针对单通道传统FFT分析方法的校正理论应用到全矢谱中,精确求得非同步整周期采集的双通道融合矢量信号的全矢谱参数。详细论述了基于全矢谱的内插法和相位差校正法的实现过程。仿真研究和工程应用表明,基于全矢谱的内插法和相位差校正的分析方法能够在频率分辨率不足的情况下得到准确的振动参数,提高了频谱分析的精度。
结合目前密集频谱校正的研究现状,客观分析了密集频谱对频谱分析精度的影响,分析将全矢谱技术和密集频谱校正方法相结合在故障诊断分析中的必要性。提出了复解析带通滤波器的选带细化方法和全矢谱相结合的分析方法,详细介绍了原理、算法步骤和实现过程,并进行了仿真试验。结果表明这种全矢谱细化有很好的实时性、准确性,从而提高频谱分析技术在密集频谱领域中的应用性。
Full vector spectrum is a novel technology which is developed from fault diagnosis and analysis of large rotating equipment enhances the precision of diagnosis and boost up the engineering practicability of the technology. The traditional vibration signal analysis based on single channel has not already been able to meet the need of fault signature abstraction and fault analysis in practical engineering. Full vector spectrum makes full use of fusion information using the source from two channels to get the fast, robust and accurate access to all the useful information that the vibration signals contain.
Correction of spectrum is to improve the accuracy of spectral analysis. In the view of the existing spectrum correction technology only for single source signal or the single channel signal of the same source, the correction methods for vector spectrum of fusion vector signals generated by two channels is proposed. The principle, methods and the realization process of the interpolation correction, the energy center of gravity correction, the FFT+FT spectrum zoom and several spectrum correction based on phase difference are introduced in detail. The correction of spectrum of signals with three different window functions is analyzed and compared as well as the results of three spectrum correction based on phase difference. The combination of full vector spectrum and interpolation method with Hanning window and its combination with phase difference correction of two consecutive signals are proposed.
The combination of full vector spectrum based on interpolation method with Hanning window and its combination with phase difference correction of two consecutive signals is researched and implemented. The principle of the two methods is that correction theory of traditional analysis method based on FFT is applied on the full vector spectrum, the accurate value of the full vector spectrum parameter of double channels'fusion vector signal which is not sampled in the way of synchronous integrated period. The implementing process of interpolation method and phase difference correction based on full vector spectrum is introduced in detail. Simulation results and Engineering Application demonstrate that interpolation method and phase difference correction based on the full vector spectrum can achieve the vibration parameters accurately under the condition of low frequency resolution and improve the applicability of spectrum technology.
Combined with the present research situation of intensive spectrum and objectively analyzing the impact of intensive spectrum on the accuracy of spectrum to propose the necessity of the combination of intensive spectrum correction method and full vector spectrum in fault diagnosis. The full vector spectrum combined with selected band zoom method, using multiple analytical band-pass filter is proposed. The principle, algorithm and implementing process are introduced in detail, simulation is carried out. The results show that the zoom vector spectrum implemented by this method has high accuracy and good real-time performance, thereby improving the applicability of spectrum analysis technique in intensive spectrum environment.
频谱校正的意义是提高频谱分析的精度。针对现有频谱校正技术只针对单源信号和同源的各单通道信号的频谱进行校正的研究现状,提出针对双通道融合矢量信号的全矢谱进行校正的方法。详细介绍内插法、能量重心法、FFT+FT法和相位差校正法的原理、方法及实现过程。分析和比较信号在三种不同窗函数条件下的内插法和三种不同相位差法的频谱校正结果。提出融合矢量信号的全矢谱和汉宁窗的内插法、连续等长的两段信号的相位差法相结合的校正法。
研究并实现了全矢谱和汉宁窗的内插法、连续等长的两段信号的相位差法相结合的校正法。两种方法的原理都是将针对单通道传统FFT分析方法的校正理论应用到全矢谱中,精确求得非同步整周期采集的双通道融合矢量信号的全矢谱参数。详细论述了基于全矢谱的内插法和相位差校正法的实现过程。仿真研究和工程应用表明,基于全矢谱的内插法和相位差校正的分析方法能够在频率分辨率不足的情况下得到准确的振动参数,提高了频谱分析的精度。
结合目前密集频谱校正的研究现状,客观分析了密集频谱对频谱分析精度的影响,分析将全矢谱技术和密集频谱校正方法相结合在故障诊断分析中的必要性。提出了复解析带通滤波器的选带细化方法和全矢谱相结合的分析方法,详细介绍了原理、算法步骤和实现过程,并进行了仿真试验。结果表明这种全矢谱细化有很好的实时性、准确性,从而提高频谱分析技术在密集频谱领域中的应用性。
Full vector spectrum is a novel technology which is developed from fault diagnosis and analysis of large rotating equipment enhances the precision of diagnosis and boost up the engineering practicability of the technology. The traditional vibration signal analysis based on single channel has not already been able to meet the need of fault signature abstraction and fault analysis in practical engineering. Full vector spectrum makes full use of fusion information using the source from two channels to get the fast, robust and accurate access to all the useful information that the vibration signals contain.
Correction of spectrum is to improve the accuracy of spectral analysis. In the view of the existing spectrum correction technology only for single source signal or the single channel signal of the same source, the correction methods for vector spectrum of fusion vector signals generated by two channels is proposed. The principle, methods and the realization process of the interpolation correction, the energy center of gravity correction, the FFT+FT spectrum zoom and several spectrum correction based on phase difference are introduced in detail. The correction of spectrum of signals with three different window functions is analyzed and compared as well as the results of three spectrum correction based on phase difference. The combination of full vector spectrum and interpolation method with Hanning window and its combination with phase difference correction of two consecutive signals are proposed.
The combination of full vector spectrum based on interpolation method with Hanning window and its combination with phase difference correction of two consecutive signals is researched and implemented. The principle of the two methods is that correction theory of traditional analysis method based on FFT is applied on the full vector spectrum, the accurate value of the full vector spectrum parameter of double channels'fusion vector signal which is not sampled in the way of synchronous integrated period. The implementing process of interpolation method and phase difference correction based on full vector spectrum is introduced in detail. Simulation results and Engineering Application demonstrate that interpolation method and phase difference correction based on the full vector spectrum can achieve the vibration parameters accurately under the condition of low frequency resolution and improve the applicability of spectrum technology.
Combined with the present research situation of intensive spectrum and objectively analyzing the impact of intensive spectrum on the accuracy of spectrum to propose the necessity of the combination of intensive spectrum correction method and full vector spectrum in fault diagnosis. The full vector spectrum combined with selected band zoom method, using multiple analytical band-pass filter is proposed. The principle, algorithm and implementing process are introduced in detail, simulation is carried out. The results show that the zoom vector spectrum implemented by this method has high accuracy and good real-time performance, thereby improving the applicability of spectrum analysis technique in intensive spectrum environment.
引文
[1]韩捷,张瑞林.旋转机械故障机理及诊断技术[M].北京：机械工业出版社,1997
[2]韩捷,石来德.全矢谱技术及工程应用[M].北京：机械工业出版社,2008
[3]韩捷.全矢谱技术及设备故障诊断应用研究[D].[博士学位论文].上海：同济大学,2005
[4]张瑞林.机械设备故障诊断技术的现状与发展趋势[J].振动工程学报,1998,11(s)：1-5
[5]彭浩.通用性旋转机械振动信号测试与分析系统的研制[D].[硕士学位论文].重庆：重庆大学,2006
[6]Qu L S, Cheng Y D, Liu X. Discovering the Holospectrum[J]. Noise & Vibration Control Worldwide,1989,20(2):58～62
[7]Qu L S, Liu X, Peyronne G, et al. The holospectrum:a new method for rotor surveillance and diagnosis[J]. Mechanical systems and signal processing,1989,3(3):255～267
[8]Don South Wick. Using Full Spectrum Plots[J]. Orbit,1993,14 (4):19～21
[9]Laws B. When you use spectrum, don't use it halfway[J]. Orbit,1998,18(2):23～26
[10]Southwick D. Plus and minus spectrum[J]. Orbit,1993,14(2):16～20
[11]Goldman P, Muszynska A. Application of full spectrum to rotating machinery diagnostics[J]. Orbit,1999,20(1):17～21
[12]Dong Xin min, Han Jie, SHI Lai de. Study on short time vector spectrum and its application[J]. Computer Engineering and Applications,2008,44(1):202～204
[13]Cooley J W, Tukey J W. An Algorithm for the Machine Calculation of Complex Fourier Series[J]. Mathematics of computation,1965,19(90):297～301
[14]丁康,张晓飞.频谱校正理论的发展[J].振动工程学报,2000(1)：18-26
[15]朱小勇,丁康.离散频谱校正方法的综合比较[J].信号处理,2001(1)：91-97
[16]丁康,谢明,杨志坚.离散频谱分析校正理论与技术[M].北京：科学出版社,2008
[17]Luo R C, Kay M G. Multisensor integration and fusion in intelligent systems[J]. Systems, Man and Cybernetics, IEEE Transactions on,1989,19(5):901～931
[18]Houzelle S, Giraudon G. Contribution to multisensor fusion formalization[J]. Robotics and autonomous systems,1994,13(2):69～85
[19]Luo R C, Yih C C, Su K L. Multisensor fusion and integration:approaches, applications, and future research directions[J]. Sensors Journal, IEEE,2002,2(2):107～119
[20]Hall D L, Llinas J. An introduction to multisensor data fusion[J]. Proceedings of the IEEE,1997,85(1):6～23
[21]左长青.基于全矢谱的齿轮系统故障诊断方法研究[D].[硕士学位论文],郑州：郑州大学,2011
[22]王宏超.基于全矢谱的旋转机械故障特征提取研究p].[硕士学位论文],郑州： 郑州大学,2011
[23]刘石,屈梁生.回转机械故障诊断中的三维全息谱技术[J].西安交通大学学报,2004(9)：900-903
[24]屈梁生,史东锋.全息谱十年：回顾与展望[J].振动、测试与诊断,1998(4)：3-10
[25]Liu S, Li Q, Zheng S.Unbalance identification of nonlinear rotor system based on holospectrum analysis[J]. Ji xie Gong cheng Xue bao(Chinese Journal of Mechanical Engineering),2010,46(17):62～67
[26]陈奎孚,张森林,高小蓉.对称窗函数的幅值谱特性[J].农业工程学报,1999,15(1)：36-40
[27]李杭生,陈丹.频谱分析中窗函数的研究[J].微计算机信息,2008(10)：272-273
[28]殷庆平,牛晓平.电力系统谐波测量中频谱泄漏问题的研究[J].工矿自动化,2007(4)：28-30
[29]丁康,江利旗.离散频谱的能量重心校正法[J].振动工程学报,2001,14(3)：354-358
[30]朱利明,熊有伦.一个通用的频谱误差校正快速算法[J].振动工程学报,2001,14(2)：166-171
[31]Schoukens J, Pintelon R, Van Hamme H. The interpolated fast Fourier transform: a comparative study [J]. Instrumentation and Measurement. IEEE Transactions on, 1992,41(2):226～232
[32]McFadden P D. Interpolation techniques for time domain averaging of gear vibration[J]. Mechanical Systems and Signal Processing,1989,3(1):87～97
[33]Andria G, Attivissimo F, Lanzolla A. Interpolation techniques for non-stationary signal analysis[J]. Measurement,1997,21(1):1～16.
[34]Offelli C, Petri D. The influence of windowing on the accuracy of multi-frequency signal parameter estimation[J]. Instrumentation and Measurement, IEEE Transactios on,1992,41(2):256～261
[35]Offelli C, Petri D. Weighting effect on the discrete time Fourier transform of noisy signals[J]. Instrumentation and Measurement, IEEE Transactions on,1991,40(6):972～ 981
[36]Burgess J C. On digital spectrum analysis of periodic signals[J]. The Journal of the Acoustical Society of America,1975,58:556
[37]Grandke T. Interpolation algorithms for discrete Fourier transforms of weighted signals[J]. Instrumentation and Measurement, IEEE Transactions on,1983,32(2):350～355
[38]Maeland E. On the comparison of interpolation methods[J].Medical Imaging, IEEE Transactions on,1988,7(3):213～217
[39]贲树俊,葛乃成,沈晓枉.基于相位差校正法的高精度电力谐波检测[J].电测与仪表,2007,44(2)：13-15
[40]黄云志,徐科军.基于相位差的频谱校正方法的研究[J].振动与冲击,2005,24(2)： 77-79
[41]Ding Kang,Yang Zhijian. Improvement and AntiNoise Performance Analysis of Window Length Changing Phase Difference Correction[J]. Journal of South China University of Technology,2007,35(10):210～213
[42]汤宝平,陈建波,章国稳.基于相位差校正法的全息谱研究[J].振动与冲击,2009(8)：99-102
[43]段明虎,秦树人,李宁.离散频谱的校正方法综述[J].振动与冲击,2007,26(11)：138-145
[44]韩捷,董新旻,郝伟等.旋转机械同源全信息倒频谱分析与应用[J].机械强度,2005,27(4)：452-455
[45]韩捷,石来德.旋转机械的全信息能量谱分析方法研究[J].机械强度,2003,26(4)：364-368
[46]韩捷,旋转机械的回转能量谱技术研究[C].2002年全国振动工程技术及应用会议
[47]钟一谔,何衍宗,王正等.转子动力学[M].北京：清华大学出版社,1987
[48]韩捷,关惠玲,梁川等.旋转机械故障诊断的进动谱研究[J].振动工程学报,1998,13(11)：67-71
[49]杜威.旋转机械全息谱分析精度提高方法的研究[D].[硕士学位论文],重庆：重庆大学,2011
[50]张正松,旋转机械振动检测机故障诊断[M].北京：清华大学出版社,1991
[51]Kang Y. An accuracy improvement for balancing[J]. Machine Theory,2003,38: 1449～1467
[52]佟德纯.工程信号处理及应用[M].上海：上海交通大学出版社,1989
[53]韩捷,张琳娜.旋转机械振动的谱强度计量[J].计量技术,1997,6：22-25
[54]杜永祚,秦志英.旋转机械动态信号全息谱分析[J].振动、测试与诊断,2002(2)：1-8
[55]马建仓,吴启彬,薛建武,等.基于小波变换的频谱细化分析方法[J].信号处理,1997(3)：274-279
[56]陈建波.基于相位差校正法的全息谱研究[D].[硕士学位论文],重庆：重庆大学,2009
[57]项春,董浩,周敏.基于频谱校正理论的全息谱研究[J].煤矿机械,2007(6)：55-58
[58]余佳兵,史铁林,杨叔子.窗谱校正方法的实用峰值搜索算法研究[J].振动工程学报,1997,10(2)：12-16
[59]杨志坚,丁康,徐传燕.基于离散频谱校正的发动机激励力识别方法仿真研究[J].振动工程学报.2010(6)：660-664
[60]李芳,曹长修.基于DFT的信号幅值谱分析[J].重庆工学院学报(自然科学版),2007(4)：64-66
[61]胡广书.数字信号处理—理论、算法与实现(第二版)[M].北京：清华大学出版社, 2003.8
[62]谢凯.基于全矢谱的全信息能量研究[D].[硕士学位论文],郑州：郑州大学,2008
[63]丁康,谢明,张彼德,等.基于复解析带通滤波器的复调制细化谱分析原理和方法[J].振动工程学报,2001(1)：33-39
[64]谢明,丁康,基于复解析带通滤波器的复调制细化谱分析的算法研究[J].振动工程学报,2002(4)：111-115
[65]项春,杨为,谢丽娟.提高全息谱分析精度方法的研究[J].机械设计与研究,2001(3)：63-65
[66]杜永祚,秦志英.旋转机械动态信号全息谱分析[J].振动、测试与诊断,2002(2)：1-8
[67]王力,张冰,徐伟.基于MATLAB复调制ZOOM-FFT算法的分析和实现[J].舰船电子工程,2006(4)：119-121
[68]丁康,郑春松,杨志坚.离散频谱能量重心法频率校正精度分析及改进[J].机械工程学报,2010(5)：43-48
[69]杜威,汤宝平,陈仁祥.基于频谱细化和相位差校正的全息谱研究[J].中国机械工程,2011(21)：2577-2582
[70]谢明,丁康,莫克斌.两个密集频率成分重叠频谱的校正方法[J].振动工程学报,1999,12(1)：109-114
[71]徐培民,杨积东,闻邦椿.离散频谱分析中两个邻近谱峰参数的识别[J].振动工程学报,2001,14(3)：254-258
[72]段虎明,秦树人,李宁.离散频谱的频率抽取校正法[J].振动与冲击,2007,26(7)：59-62
[73]候正信,王兆华,杨喜.全相位DFT数字滤波器的设计与实现[J].电子学报,2003,31(4)：539-542
[74]吴国乔,王兆华,黄晓红.离散频谱的全相位校正法[J].数据采集与处理,2005,20(3)：286-290
[75]Moravej Z, Pazoki M, Abdoos A A. Wavelet transform and multi-class relevance vector machines based recognition and classification of power quality disturbances[J]. European transactions on electrical power,2011,21(1):212～222
[76]Ma J C, Wu Q B, Xue J W, et al. Spectrum zoom analysis method based on wavelet transform[J]. Signal Processing,1997,13(3):274～279
[77]谢凯,韩捷.基于复调制的细化全矢谱分析研究[J].机械强度,2008(2)：184-188
[2]韩捷,石来德.全矢谱技术及工程应用[M].北京：机械工业出版社,2008
[3]韩捷.全矢谱技术及设备故障诊断应用研究[D].[博士学位论文].上海：同济大学,2005
[4]张瑞林.机械设备故障诊断技术的现状与发展趋势[J].振动工程学报,1998,11(s)：1-5
[5]彭浩.通用性旋转机械振动信号测试与分析系统的研制[D].[硕士学位论文].重庆：重庆大学,2006
[6]Qu L S, Cheng Y D, Liu X. Discovering the Holospectrum[J]. Noise & Vibration Control Worldwide,1989,20(2):58～62
[7]Qu L S, Liu X, Peyronne G, et al. The holospectrum:a new method for rotor surveillance and diagnosis[J]. Mechanical systems and signal processing,1989,3(3):255～267
[8]Don South Wick. Using Full Spectrum Plots[J]. Orbit,1993,14 (4):19～21
[9]Laws B. When you use spectrum, don't use it halfway[J]. Orbit,1998,18(2):23～26
[10]Southwick D. Plus and minus spectrum[J]. Orbit,1993,14(2):16～20
[11]Goldman P, Muszynska A. Application of full spectrum to rotating machinery diagnostics[J]. Orbit,1999,20(1):17～21
[12]Dong Xin min, Han Jie, SHI Lai de. Study on short time vector spectrum and its application[J]. Computer Engineering and Applications,2008,44(1):202～204
[13]Cooley J W, Tukey J W. An Algorithm for the Machine Calculation of Complex Fourier Series[J]. Mathematics of computation,1965,19(90):297～301
[14]丁康,张晓飞.频谱校正理论的发展[J].振动工程学报,2000(1)：18-26
[15]朱小勇,丁康.离散频谱校正方法的综合比较[J].信号处理,2001(1)：91-97
[16]丁康,谢明,杨志坚.离散频谱分析校正理论与技术[M].北京：科学出版社,2008
[17]Luo R C, Kay M G. Multisensor integration and fusion in intelligent systems[J]. Systems, Man and Cybernetics, IEEE Transactions on,1989,19(5):901～931
[18]Houzelle S, Giraudon G. Contribution to multisensor fusion formalization[J]. Robotics and autonomous systems,1994,13(2):69～85
[19]Luo R C, Yih C C, Su K L. Multisensor fusion and integration:approaches, applications, and future research directions[J]. Sensors Journal, IEEE,2002,2(2):107～119
[20]Hall D L, Llinas J. An introduction to multisensor data fusion[J]. Proceedings of the IEEE,1997,85(1):6～23
[21]左长青.基于全矢谱的齿轮系统故障诊断方法研究[D].[硕士学位论文],郑州：郑州大学,2011
[22]王宏超.基于全矢谱的旋转机械故障特征提取研究p].[硕士学位论文],郑州： 郑州大学,2011
[23]刘石,屈梁生.回转机械故障诊断中的三维全息谱技术[J].西安交通大学学报,2004(9)：900-903
[24]屈梁生,史东锋.全息谱十年：回顾与展望[J].振动、测试与诊断,1998(4)：3-10
[25]Liu S, Li Q, Zheng S.Unbalance identification of nonlinear rotor system based on holospectrum analysis[J]. Ji xie Gong cheng Xue bao(Chinese Journal of Mechanical Engineering),2010,46(17):62～67
[26]陈奎孚,张森林,高小蓉.对称窗函数的幅值谱特性[J].农业工程学报,1999,15(1)：36-40
[27]李杭生,陈丹.频谱分析中窗函数的研究[J].微计算机信息,2008(10)：272-273
[28]殷庆平,牛晓平.电力系统谐波测量中频谱泄漏问题的研究[J].工矿自动化,2007(4)：28-30
[29]丁康,江利旗.离散频谱的能量重心校正法[J].振动工程学报,2001,14(3)：354-358
[30]朱利明,熊有伦.一个通用的频谱误差校正快速算法[J].振动工程学报,2001,14(2)：166-171
[31]Schoukens J, Pintelon R, Van Hamme H. The interpolated fast Fourier transform: a comparative study [J]. Instrumentation and Measurement. IEEE Transactions on, 1992,41(2):226～232
[32]McFadden P D. Interpolation techniques for time domain averaging of gear vibration[J]. Mechanical Systems and Signal Processing,1989,3(1):87～97
[33]Andria G, Attivissimo F, Lanzolla A. Interpolation techniques for non-stationary signal analysis[J]. Measurement,1997,21(1):1～16.
[34]Offelli C, Petri D. The influence of windowing on the accuracy of multi-frequency signal parameter estimation[J]. Instrumentation and Measurement, IEEE Transactios on,1992,41(2):256～261
[35]Offelli C, Petri D. Weighting effect on the discrete time Fourier transform of noisy signals[J]. Instrumentation and Measurement, IEEE Transactions on,1991,40(6):972～ 981
[36]Burgess J C. On digital spectrum analysis of periodic signals[J]. The Journal of the Acoustical Society of America,1975,58:556
[37]Grandke T. Interpolation algorithms for discrete Fourier transforms of weighted signals[J]. Instrumentation and Measurement, IEEE Transactions on,1983,32(2):350～355
[38]Maeland E. On the comparison of interpolation methods[J].Medical Imaging, IEEE Transactions on,1988,7(3):213～217
[39]贲树俊,葛乃成,沈晓枉.基于相位差校正法的高精度电力谐波检测[J].电测与仪表,2007,44(2)：13-15
[40]黄云志,徐科军.基于相位差的频谱校正方法的研究[J].振动与冲击,2005,24(2)： 77-79
[41]Ding Kang,Yang Zhijian. Improvement and AntiNoise Performance Analysis of Window Length Changing Phase Difference Correction[J]. Journal of South China University of Technology,2007,35(10):210～213
[42]汤宝平,陈建波,章国稳.基于相位差校正法的全息谱研究[J].振动与冲击,2009(8)：99-102
[43]段明虎,秦树人,李宁.离散频谱的校正方法综述[J].振动与冲击,2007,26(11)：138-145
[44]韩捷,董新旻,郝伟等.旋转机械同源全信息倒频谱分析与应用[J].机械强度,2005,27(4)：452-455
[45]韩捷,石来德.旋转机械的全信息能量谱分析方法研究[J].机械强度,2003,26(4)：364-368
[46]韩捷,旋转机械的回转能量谱技术研究[C].2002年全国振动工程技术及应用会议
[47]钟一谔,何衍宗,王正等.转子动力学[M].北京：清华大学出版社,1987
[48]韩捷,关惠玲,梁川等.旋转机械故障诊断的进动谱研究[J].振动工程学报,1998,13(11)：67-71
[49]杜威.旋转机械全息谱分析精度提高方法的研究[D].[硕士学位论文],重庆：重庆大学,2011
[50]张正松,旋转机械振动检测机故障诊断[M].北京：清华大学出版社,1991
[51]Kang Y. An accuracy improvement for balancing[J]. Machine Theory,2003,38: 1449～1467
[52]佟德纯.工程信号处理及应用[M].上海：上海交通大学出版社,1989
[53]韩捷,张琳娜.旋转机械振动的谱强度计量[J].计量技术,1997,6：22-25
[54]杜永祚,秦志英.旋转机械动态信号全息谱分析[J].振动、测试与诊断,2002(2)：1-8
[55]马建仓,吴启彬,薛建武,等.基于小波变换的频谱细化分析方法[J].信号处理,1997(3)：274-279
[56]陈建波.基于相位差校正法的全息谱研究[D].[硕士学位论文],重庆：重庆大学,2009
[57]项春,董浩,周敏.基于频谱校正理论的全息谱研究[J].煤矿机械,2007(6)：55-58
[58]余佳兵,史铁林,杨叔子.窗谱校正方法的实用峰值搜索算法研究[J].振动工程学报,1997,10(2)：12-16
[59]杨志坚,丁康,徐传燕.基于离散频谱校正的发动机激励力识别方法仿真研究[J].振动工程学报.2010(6)：660-664
[60]李芳,曹长修.基于DFT的信号幅值谱分析[J].重庆工学院学报(自然科学版),2007(4)：64-66
[61]胡广书.数字信号处理—理论、算法与实现(第二版)[M].北京：清华大学出版社, 2003.8
[62]谢凯.基于全矢谱的全信息能量研究[D].[硕士学位论文],郑州：郑州大学,2008
[63]丁康,谢明,张彼德,等.基于复解析带通滤波器的复调制细化谱分析原理和方法[J].振动工程学报,2001(1)：33-39
[64]谢明,丁康,基于复解析带通滤波器的复调制细化谱分析的算法研究[J].振动工程学报,2002(4)：111-115
[65]项春,杨为,谢丽娟.提高全息谱分析精度方法的研究[J].机械设计与研究,2001(3)：63-65
[66]杜永祚,秦志英.旋转机械动态信号全息谱分析[J].振动、测试与诊断,2002(2)：1-8
[67]王力,张冰,徐伟.基于MATLAB复调制ZOOM-FFT算法的分析和实现[J].舰船电子工程,2006(4)：119-121
[68]丁康,郑春松,杨志坚.离散频谱能量重心法频率校正精度分析及改进[J].机械工程学报,2010(5)：43-48
[69]杜威,汤宝平,陈仁祥.基于频谱细化和相位差校正的全息谱研究[J].中国机械工程,2011(21)：2577-2582
[70]谢明,丁康,莫克斌.两个密集频率成分重叠频谱的校正方法[J].振动工程学报,1999,12(1)：109-114
[71]徐培民,杨积东,闻邦椿.离散频谱分析中两个邻近谱峰参数的识别[J].振动工程学报,2001,14(3)：254-258
[72]段虎明,秦树人,李宁.离散频谱的频率抽取校正法[J].振动与冲击,2007,26(7)：59-62
[73]候正信,王兆华,杨喜.全相位DFT数字滤波器的设计与实现[J].电子学报,2003,31(4)：539-542
[74]吴国乔,王兆华,黄晓红.离散频谱的全相位校正法[J].数据采集与处理,2005,20(3)：286-290
[75]Moravej Z, Pazoki M, Abdoos A A. Wavelet transform and multi-class relevance vector machines based recognition and classification of power quality disturbances[J]. European transactions on electrical power,2011,21(1):212～222
[76]Ma J C, Wu Q B, Xue J W, et al. Spectrum zoom analysis method based on wavelet transform[J]. Signal Processing,1997,13(3):274～279
[77]谢凯,韩捷.基于复调制的细化全矢谱分析研究[J].机械强度,2008(2)：184-188