多分量调幅-调频信号的瞬时频率直接计算与畸变消除方法
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摘要
针对局部均值分解(LMD)在多分量调幅-调频(AM-FM)信号解调过程中的瞬时频率求解问题,提出了一种瞬时频率快速直接计算与畸变消除方法。首先通过LMD将多分量AM-FM信号分解为一系列单分量AM-FM信号,使用未展开瞬时相位的差分绝对值替代相位展开,有效提高了瞬时频率的计算效率;然后针对直接计算法求得的瞬时频率在极值点附近存在畸变的问题,根据畸变位置分布规律定位畸变位置并剔除畸变点,使用插值法补全被剔除数据,最终得到可用的瞬时频率。将提出的方法成功应用于转子碰磨故障诊断和语音信号基音频率识别,试验结果表明:与传统的基于相位展开的直接计算法相比,提出的快速直接计算法的运行效率更高;同时,求得的瞬时频率中的畸变能够被完整的定位和消除,最终得到正确可用的信号瞬时频率。
For extracting instantaneous frequency from multi-component amplitude modulationfrequency modulation(AM-FM)signals,an improved local mean decomposition(LMD)method with direct computing and aberration eliminating capability in extracting instantaneous frequencies is proposed.Firstly,a multi-component AM-FM signal is decomposed into a series of mono-component AM-FM signals.A difference operation for the absolute value of wrapped phase is utilized to directly compute the instantaneous frequency of mono-component AM-FM signals.Then,the aberration phenomena of instantaneous frequency near the extreme points are analyzed.The aberration points are located by a locating strategy and eliminated with the cubic spline interpolation.As a result,the undistorted instantaneous frequency is obtained.The simulation and experimental results show that the instantaneous frequency is effectively extracted and aberrations are eliminated successfully.
For extracting instantaneous frequency from multi-component amplitude modulationfrequency modulation(AM-FM)signals,an improved local mean decomposition(LMD)method with direct computing and aberration eliminating capability in extracting instantaneous frequencies is proposed.Firstly,a multi-component AM-FM signal is decomposed into a series of mono-component AM-FM signals.A difference operation for the absolute value of wrapped phase is utilized to directly compute the instantaneous frequency of mono-component AM-FM signals.Then,the aberration phenomena of instantaneous frequency near the extreme points are analyzed.The aberration points are located by a locating strategy and eliminated with the cubic spline interpolation.As a result,the undistorted instantaneous frequency is obtained.The simulation and experimental results show that the instantaneous frequency is effectively extracted and aberrations are eliminated successfully.
引文
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[11]唐贵基,王晓龙.LMD的LabVIEW实现及其在齿轮故障诊断中的应用[J].中国测试,2014,40(1):101-105.TANG Guiji,WANG Xiaolong.LMD realization by LabVIEW and its application in gear fault diagnosis[J].China Measurement&Test,2009,43(3):523-528.
[12]任达千,杨世锡,吴昭同,等.基于LMD的信号瞬时频率求取方法及实验[J].浙江大学学报(工学版),2009,43(3):523-528.REN Daqian,YANG Shixi,WU Zhaotong,et al.Instantaneous frequency extraction method and experiment based LMD[J].Journal of Zhejiang University(Engineering Science),2009,43(3):523-528.
[13]SCHLOTTHAUER G,TORRES M E,RUFINER H L.A new algorithm for instantaneous F0,speech extraction based on ensemble empirical mode decomposition[C]∥European Signal Processing Conference.Piscataway,NJ,USA IEEE,2015:2347-2351.
[2]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 Mathematical,Physical&Engineering Sciences,1998,454(1971):903-995.
[3]SMITH J S.The local mean decomposition and its application to EEG perception data[J].Journal of the Royal Society Interface,2005,2(5):443-454.
[4]MARAGOS P,KAISER J F,QUATIERI T F.On amplitude and frequency demodulation using energy operators[J].IEEE Transactions on Signal Processing,1993,41(4):1532-1550.
[5]ZENG M,YANG Y,ZHENG J.et al.Normalized complex Teager energy operator demodulation method and its application to fault diagnosis in a rubbing rotor system[J].Mechanical Systems and Signal Processing,2015(50/51):380-399.
[6]任达千,杨世锡,吴昭同,等.信号瞬时频率直接计算法与Hilbert变换及Teager能量法比较[J].机械工程学报,2013,49(9):42-48.REN Daqian,YANG Shixi,WU Zhaotong,et al.Comparison of instantaneous frequency directed computing method and Hilbert transform and Teager energy method[J].Journal of Mechanical Engineering,2013,49(9):42-48.
[7]张亢,程军圣,杨宇,等.基于分段波形的信号瞬时频率计算方法[J].湖南大学学报(自然科学版),2011,38(11):54-59.ZHANG Kang,CHENG Junsheng,YANG Yu,et al.A piece-wise based signal instantaneous frequency computing method[J].Journal of Hunan University(Natural Sciences),2011,38(11):54-59.
[8]SUN H,ZHANG X,WANG J.Online machining chatter forecast based on improved local mean decomposition[J].International Journal of Advanced Manufacturing Technology,2016,84(5/6/7/8):1045-1056.
[9]陈保家,何正嘉,陈雪峰,等.机车故障诊断的局域均值分解解调方法[J].西安交通大学学报,2010,44(5):40-44.CHEN Baojia,HE Zhengjia,CHEN Xuefeng,et al.Locomotive fault diagnosis based on local mean decomposition demodulating approach[J].Journal of Xi’an Jiaotong University,2010,44(5):40-44.
[10]任达千.基于局域均值分解的旋转机械故障特征提取方法及系统研究[D].杭州:浙江大学,2008:31-32.
[11]唐贵基,王晓龙.LMD的LabVIEW实现及其在齿轮故障诊断中的应用[J].中国测试,2014,40(1):101-105.TANG Guiji,WANG Xiaolong.LMD realization by LabVIEW and its application in gear fault diagnosis[J].China Measurement&Test,2009,43(3):523-528.
[12]任达千,杨世锡,吴昭同,等.基于LMD的信号瞬时频率求取方法及实验[J].浙江大学学报(工学版),2009,43(3):523-528.REN Daqian,YANG Shixi,WU Zhaotong,et al.Instantaneous frequency extraction method and experiment based LMD[J].Journal of Zhejiang University(Engineering Science),2009,43(3):523-528.
[13]SCHLOTTHAUER G,TORRES M E,RUFINER H L.A new algorithm for instantaneous F0,speech extraction based on ensemble empirical mode decomposition[C]∥European Signal Processing Conference.Piscataway,NJ,USA IEEE,2015:2347-2351.