经验模态分解理论与应用研究
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摘要
本文对经验模态分解(empirical mode decomposition,EMD)方法进行了深入的研究。在总结新近有关研究热点和进展的基础上,对离散Hilbert变换估计IMF的幅度包络和瞬时频率进行了误差分析。提出了改进的离散Teager能量算子(Teager energy operator,TEO)算法改善了求取幅度包络和瞬时频率的精度;提出了基于过零点和极点估计(zero-crossing and extremum estimation,ZCEE)求取幅度包络和瞬时频率的算法。讨论了EMD时频幅度谱的离散时频分辨率。将改进的离散TEO算法和ZCEE方法引入EMD理论,比较了三种算法求取EMD时频幅度谱和边际谱的时频特性。
基于EMD方法的应用,结合EMD方法的自适应滤波特性,对于具有噪声干扰的调制信号解调问题,提出了基于时延相关以及WVD切片算法降噪预处理的算法。时延相关降噪是对信号自相关函数的无偏估计采用矩形窗截断得到较长时间差的部分,WVD切片算法是对信号Wiger-Ville分布求得零频率处的切片,而后利用EMD方法对其进行自适应滤波得到IMF,最终求得解调结果。不同噪声强度仿真数据和实验数据分析表明,该方法比直接解调或仅采用时延相关(对称自相关)解调能更有效地抑制噪声,凸现信号调制信息。
共振解调法是诊断滚动轴承故障的重要方法。共振解调法需要预先设计中心频率为某一元件固有频率的带通滤波器对原始信号进行带通滤波,有时会出现时域相加信号的频率成分在调制边频带附近不被滤除的情况,从而在解调谱上出现误诊断或无法分析的频率成分。因此,本文提出了基于EMD的共振解调法,在带通滤波后,进一步采用EMD方法自适应滤波提取故障轴承振动信号中的调制信息,最后解析出故障频率。仿真信号和实验验证结果均表明,和仅仅采用带通滤波器滤波比较,该方法能更加突出故障频率成分,避免误诊断。
对于非线性、非稳态、含噪原始信号混合且混合信号数目小于源信号数目的旋转机械调制故障源信号盲分离问题,本文提出了基于EMD和主成分分析(principle component analysis,PCA)相结合的方法。提出了对混合信号进行EMD提取嵌入在信号中的所有振荡模式,应用PCA方法对所提取的模式进行共性分析,得到模式中的主要成分。应用该方法对仿真数据和两通道滚动轴承加速度振动数据进行了分析。结果表明,该方法能有效地突出旋转机械的故障特征频率成分,避免误诊断,适用范围优于独立分量分析(independent component analysis,ICA)方法。
This paper studied the empirical mode decomposition (EMD) method. After summarizing recent research hotspots and progresses about EMD, the errors of EMD's intrinic mode function(IMF) s' amplitude envelope and instantaneous frequency obtained by Hilbert transform were analyzed. The advanced discrete Teager energy operator (TEO) was put forward to improve the computation precision of the amplitude envelope and instantaneous frequency. The zero-crossing and extremum estimation (ZCEE) algorithm was put forward to compute the amplitude envelope and instantaneous frequency. The discrete time-frequency resolution of EMD's time-frequency spectrum was discussed. With advanced discrete TEO algorithm and ZCEE method being introduced to EMD theory, the time-frequency attribution of the time-frequency amplitude spectrum and marginal spectrum obtained by those three methods were compared.Combined with the self-adapting filtering attribution of EMD, the delayed autocorrelation and the slice of Wigner-Ville distribution (WVD) algorithm, named as the de-noise pre-disposal method, were introduced to deal with the noised signal demodulation problem. The delayed autocorrelation function is the longer time interval part of the unbiased estimation of signal's autocorrelation function which is intercepted by rectangle window. The slice of WVD function is the slice at the zero frequency of WVD. Then the result was filtered adaptively by EMD method and the intrinsic mode functions (IMFs) were obtained. The demodulation result was thus obtained by applying Hilbert transform to IMFs. It is shown that the proposed method is more effective to de-noise and to make the modulation information more clear than direct modulation or delayed autocorrelation demodulation.Demodulated resonance method is an important method to identify rolling bearing fault but It must use a band-pass filter, of which the center frequency is one component's intrinsic frequency, to filtrate original signal. Sometimes the frequency components of the added signals near the modulated sideband are not filtrated. Thus there will be wrong diagnosis or unanalysable frequency components on the demodulation spectrum. Therefore the demodulated resonance method based on EMD was proposed. After the vibration signal of rolling bearing was filtered by band-pass filter, the EMD method was introduced to filter the signal self-adaptively and to extract the modulated information. At last, the fault frequency was extracted by Hilbert transform. Simulation and experiment results show that, compared with the method of band-pass filter, this method can make fault frequency more clear and avoid fault diagnoses.An approach based on EMD and principle component analysis (PCA) was proposed to deal with the rotation machine blind sources separation (BSS) problem in the case of nonlinear,
non-stationary, noisy source mixing and the number of observed mixtures being less than that of contributing sources. EMD method extracted all oscillatory modes embedded in the observed signals. PCA aggregated similar modes into unifying components. The method was applied to analyze simulation signals and two-way rolling bearing acceleration vibration signals. Result shows that this method can efficiently identify rotation machine's fault characteristic frequencies and the application scope of this method is larger than that of independent component analysis (ICA) method.
基于EMD方法的应用,结合EMD方法的自适应滤波特性,对于具有噪声干扰的调制信号解调问题,提出了基于时延相关以及WVD切片算法降噪预处理的算法。时延相关降噪是对信号自相关函数的无偏估计采用矩形窗截断得到较长时间差的部分,WVD切片算法是对信号Wiger-Ville分布求得零频率处的切片,而后利用EMD方法对其进行自适应滤波得到IMF,最终求得解调结果。不同噪声强度仿真数据和实验数据分析表明,该方法比直接解调或仅采用时延相关(对称自相关)解调能更有效地抑制噪声,凸现信号调制信息。
共振解调法是诊断滚动轴承故障的重要方法。共振解调法需要预先设计中心频率为某一元件固有频率的带通滤波器对原始信号进行带通滤波,有时会出现时域相加信号的频率成分在调制边频带附近不被滤除的情况,从而在解调谱上出现误诊断或无法分析的频率成分。因此,本文提出了基于EMD的共振解调法,在带通滤波后,进一步采用EMD方法自适应滤波提取故障轴承振动信号中的调制信息,最后解析出故障频率。仿真信号和实验验证结果均表明,和仅仅采用带通滤波器滤波比较,该方法能更加突出故障频率成分,避免误诊断。
对于非线性、非稳态、含噪原始信号混合且混合信号数目小于源信号数目的旋转机械调制故障源信号盲分离问题,本文提出了基于EMD和主成分分析(principle component analysis,PCA)相结合的方法。提出了对混合信号进行EMD提取嵌入在信号中的所有振荡模式,应用PCA方法对所提取的模式进行共性分析,得到模式中的主要成分。应用该方法对仿真数据和两通道滚动轴承加速度振动数据进行了分析。结果表明,该方法能有效地突出旋转机械的故障特征频率成分,避免误诊断,适用范围优于独立分量分析(independent component analysis,ICA)方法。
This paper studied the empirical mode decomposition (EMD) method. After summarizing recent research hotspots and progresses about EMD, the errors of EMD's intrinic mode function(IMF) s' amplitude envelope and instantaneous frequency obtained by Hilbert transform were analyzed. The advanced discrete Teager energy operator (TEO) was put forward to improve the computation precision of the amplitude envelope and instantaneous frequency. The zero-crossing and extremum estimation (ZCEE) algorithm was put forward to compute the amplitude envelope and instantaneous frequency. The discrete time-frequency resolution of EMD's time-frequency spectrum was discussed. With advanced discrete TEO algorithm and ZCEE method being introduced to EMD theory, the time-frequency attribution of the time-frequency amplitude spectrum and marginal spectrum obtained by those three methods were compared.Combined with the self-adapting filtering attribution of EMD, the delayed autocorrelation and the slice of Wigner-Ville distribution (WVD) algorithm, named as the de-noise pre-disposal method, were introduced to deal with the noised signal demodulation problem. The delayed autocorrelation function is the longer time interval part of the unbiased estimation of signal's autocorrelation function which is intercepted by rectangle window. The slice of WVD function is the slice at the zero frequency of WVD. Then the result was filtered adaptively by EMD method and the intrinsic mode functions (IMFs) were obtained. The demodulation result was thus obtained by applying Hilbert transform to IMFs. It is shown that the proposed method is more effective to de-noise and to make the modulation information more clear than direct modulation or delayed autocorrelation demodulation.Demodulated resonance method is an important method to identify rolling bearing fault but It must use a band-pass filter, of which the center frequency is one component's intrinsic frequency, to filtrate original signal. Sometimes the frequency components of the added signals near the modulated sideband are not filtrated. Thus there will be wrong diagnosis or unanalysable frequency components on the demodulation spectrum. Therefore the demodulated resonance method based on EMD was proposed. After the vibration signal of rolling bearing was filtered by band-pass filter, the EMD method was introduced to filter the signal self-adaptively and to extract the modulated information. At last, the fault frequency was extracted by Hilbert transform. Simulation and experiment results show that, compared with the method of band-pass filter, this method can make fault frequency more clear and avoid fault diagnoses.An approach based on EMD and principle component analysis (PCA) was proposed to deal with the rotation machine blind sources separation (BSS) problem in the case of nonlinear,
non-stationary, noisy source mixing and the number of observed mixtures being less than that of contributing sources. EMD method extracted all oscillatory modes embedded in the observed signals. PCA aggregated similar modes into unifying components. The method was applied to analyze simulation signals and two-way rolling bearing acceleration vibration signals. Result shows that this method can efficiently identify rotation machine's fault characteristic frequencies and the application scope of this method is larger than that of independent component analysis (ICA) method.
引文
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[3] 朱景清,王向东.傅立叶变换在热轧无缝钢管壁厚不均研究中的应用[J].钢铁,1994,29(2):40-45
[4] 李振然,吴杰康.基于傅里叶变换和自适应采样的微机电量变送器[J].中国电力,1995,28(6):68-71
[5] 程玉宝,何宗平.用快速傅里叶变换精确测定激光波长[J].红外与激光工程,1998,27(5):52-54
[6] 李维华,段玉然.傅里叶变换垃曼探针测定九种气体的定量因子[J].1999,18(2):111-112
[7] 许伯强,陆保义.笼型异步电动机转子断条综合在线检测方法[J].2000,27(4):23-28
[8] 段海峰,杨泽平.快速傅里叶算法在哈特曼—夏克传感器波前重构算法中的应用[J].光学学报,2003,23(2):240-244
[9] 杜太行,陈培颖,弭艳芝.基于FFT算法的交流电器选相分合闸技术[J].电工技术学报,2003,18(6):80-83
[10] 王宏禹.非平稳随机信号分析与处理[M].北京:国防工业出版社,1999
[11] Gabor D. Theory of communication[M]. J.Inst.Elec.Eng, 1946, 93:429-457
[12] POTTER R K, KOPP G, GREEN H C. Visible speech[M]. New York: Van Nostrand, 1947,
[13] Classen T C M, Mecklenbrauker W F G The Wigner distribution-part Ⅰ[J]. Philips Res.J., 1980, 35:217-250
[14] Classen T C M, Mecklenbrauker W F G. The Wigner distribution-part Ⅱ[J]. Philips Res.J., 1980, 35: 276-300
[15] Classan T C M, Mecklenbrauker W F G The Wigner distribution-part Ⅲ[J]. Philips Res. J., 1980, 35: 372-389
[16] VILLE J. Theorie et applications de la notion de signal analytique[J]. Cables et transmission, 1948, 2A: 61-94
[17] DAUBECHIES I. Where do wavelets come from?-A personal points of view[J]. Proc.IEEE, 1996, 84(5): 510-513
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