HHT理论及其在结构健康监测中的应用研究
|
摘要
信号处理是结构健康监测方法中的一个重要环节。基于Lamb波的损伤监测方法是结构健康监测中一个研究热点，而Lamb波是典型的非平稳信号。常规傅里叶分析理论在时频联合分析方面存在局限。希尔伯特-黄变换（Hilbert-Huang transform,HHT）是目前公认的适用于分析非平稳、非线性信号的一种信号分析理论。它通过经验模式分解（Empirical Mode Decomposition,EMD）自适应特点，在时域上将信号分解为有限个特征模式函数（Intrisical Mode Function, IMF），再对每个IMF进行Hilbert变换，得到频率变化的精确表达。HHT方法在Lamb波分析中具有很好的应用前景。本文对HHT信号处理方法开展系统研究，并将结果应用于结构健康监测中。本文主要研究内容如下：
1.对比了广义延拓插值与传统插值、直接均值线生成与传统均值线生成的效果，分析了边端效应原因及其选用原则，深入研究了三种常用IMF筛选停止条件原理。在此基础上，引入分解面概念，评估了这些EMD实现技术对EMD分解效果的影响，提出了基于剔除余量的IMF筛选停止条件，验证了基于该方案的EMD分解效果。
2.利用实验分析了信号幅值、频率、相位的变化对极值点的影响，研究了极值点变化趋势对EMD分解效果影响。将幅值、频率、相位变化与EMD分解效果之间联系起来，通过实验归纳与数学公式推导，发现了信号影响EMD分解效果的关系式，最后利用实验对该关系式进行了验证。
3.在EMD实现技术及信号自身条件对EMD分解效果影响的研究基础上，分析了模式混叠原因，提出了模式混叠可分为三种基本类型，深入研究了三种典型模式混叠解决方案原理，分析了它们的局限性，提出了基于频段EMD提取法的模式混叠处理方案，利用实验验证了该方案的模式混叠处理效果。
4.研究了直达波叠加损伤散射信号后的瞬时相位变化，并利用实验对研究结果进行了验证；分析了主动Lamb波信号EMD分解非稳定的原因，引入了基于频段EMD提取法以提高分解的稳定性，并用实验进行了验证；在此基础上，利用边际谱研究了损伤散射信号对直达波的瞬时频率影响，并与信号的频谱进行了比较。
5.从理论上分析了板结构冲击损伤Lamb波模式特点，利用断铅实验验证了分析结论；利用Lamb波A0模态波速计算验证了频段EMD提取法的窄带信号提取功能，在冲击实验引入该方法以实现冲击源定位；在冲击损伤诊断，利用EMD自适应分解信号的特点，得到了结构损伤激发的IMF，并用频段EMD提取法对损伤进行定位。
Signal processing is important in helping the development of Structural Health Monitoring (SHM)techniques. Lamb wave based Structural Health Monitoring method is one of the most interesting hotspots for SHM. Lamb wave is a typical non-stationary signal. However, the traditional FFT analysistheory is limited for time-frequency combined analysis. Hilbert-Huang transform(HHT) is known as atheory used for non-stationary and nonlinear signal. In HHT, a signal is first decomposed into finiteIMFs by EMD, and then, with the Hilbert transform, the meaning instantaneous frequency of everyIMF that gives precise description of the varying frequency is obtained. Hence HHT shows apromising application in Lamb wave analysis. In this paper the HHT signal processing is researchedsystematically, and the research result is applied in SHM. The main research contents of this paper areas follows:
Firstly, this paper compared generalized extended interpolation to Cubic Spline Interpolation andthe mean from the local maxima and the local minima to the mean of the upper and lower envelopes,then analyzed the reason of the end effects and choosing principles and researched deeply the criterionfor stoppage of three common IMF filtering. Based on the above research, the concept of thedecomposition plane was introduced and EMD realization techniques’ influence on EMDdecomposition effect was assessed. Then an IMF criterion for sifting stoppage based on excludingmargin was put forward, which verified the EMD decomposition effect based on this method.
Secondly, the influence on the extreme value point by signal amplitude, frequency and phasevariation was analyzed by experiments, and then the influence on EMD decomposition effect byextreme value variation trend was researched. Combining the variation of signal amplitude, frequencyand phase with EMD decomposition, signals’ influence on EMD decomposition effect was discoveredby both experimental induction and theoretical deduction. The relationship was validated byexperiments.
Thirdly, based on the research about EMD realization technique and the influence on EMDdecomposition effect by signal, the reason of mode mixing is analyzed. Three basic types of modemixing are proposed. The solution principles to the three typical mode mixing were researched deeply,and their limitations were also analyzed. EMD based on frequency bands was proposed to solve modemixing, whose mode mixing solution effect was validated by experiments.
Fourthly, the instantaneous phase variation when the direct arrival wave was superimposed by damage scattering signal was researched and its result was validated by experiments. The reason whyEMD decomposition of the active Lamb wave signal is unstable is analyzed and BF-EMD wasintroduced to improve the decomposition stability. The experimental validation was followed. Basedon that, the marginal spectrum was applied to research damage’s influence on the instantaneousfrequency of direct arrival wave and the research result was compared to signal’s frequency spectrum.
Fifthly, the mode feature of Lamb wave generated by impact damage was analyzed theoreticallyand validated by lead cutting experiment. The propagation velocity calculation of A0mode wasutilized to validate the extraction ability of BF-EMD about signals of narrow frequency. This methodwas introduced to realize impact source localization. During the prognosis of impact damage, IMFprovoked by structural damage was obtained by EMD self-adaptive signal decomposition and damagelocalization was realized by BF-EMD extraction method.
1.对比了广义延拓插值与传统插值、直接均值线生成与传统均值线生成的效果，分析了边端效应原因及其选用原则，深入研究了三种常用IMF筛选停止条件原理。在此基础上，引入分解面概念，评估了这些EMD实现技术对EMD分解效果的影响，提出了基于剔除余量的IMF筛选停止条件，验证了基于该方案的EMD分解效果。
2.利用实验分析了信号幅值、频率、相位的变化对极值点的影响，研究了极值点变化趋势对EMD分解效果影响。将幅值、频率、相位变化与EMD分解效果之间联系起来，通过实验归纳与数学公式推导，发现了信号影响EMD分解效果的关系式，最后利用实验对该关系式进行了验证。
3.在EMD实现技术及信号自身条件对EMD分解效果影响的研究基础上，分析了模式混叠原因，提出了模式混叠可分为三种基本类型，深入研究了三种典型模式混叠解决方案原理，分析了它们的局限性，提出了基于频段EMD提取法的模式混叠处理方案，利用实验验证了该方案的模式混叠处理效果。
4.研究了直达波叠加损伤散射信号后的瞬时相位变化，并利用实验对研究结果进行了验证；分析了主动Lamb波信号EMD分解非稳定的原因，引入了基于频段EMD提取法以提高分解的稳定性，并用实验进行了验证；在此基础上，利用边际谱研究了损伤散射信号对直达波的瞬时频率影响，并与信号的频谱进行了比较。
5.从理论上分析了板结构冲击损伤Lamb波模式特点，利用断铅实验验证了分析结论；利用Lamb波A0模态波速计算验证了频段EMD提取法的窄带信号提取功能，在冲击实验引入该方法以实现冲击源定位；在冲击损伤诊断，利用EMD自适应分解信号的特点，得到了结构损伤激发的IMF，并用频段EMD提取法对损伤进行定位。
Signal processing is important in helping the development of Structural Health Monitoring (SHM)techniques. Lamb wave based Structural Health Monitoring method is one of the most interesting hotspots for SHM. Lamb wave is a typical non-stationary signal. However, the traditional FFT analysistheory is limited for time-frequency combined analysis. Hilbert-Huang transform(HHT) is known as atheory used for non-stationary and nonlinear signal. In HHT, a signal is first decomposed into finiteIMFs by EMD, and then, with the Hilbert transform, the meaning instantaneous frequency of everyIMF that gives precise description of the varying frequency is obtained. Hence HHT shows apromising application in Lamb wave analysis. In this paper the HHT signal processing is researchedsystematically, and the research result is applied in SHM. The main research contents of this paper areas follows:
Firstly, this paper compared generalized extended interpolation to Cubic Spline Interpolation andthe mean from the local maxima and the local minima to the mean of the upper and lower envelopes,then analyzed the reason of the end effects and choosing principles and researched deeply the criterionfor stoppage of three common IMF filtering. Based on the above research, the concept of thedecomposition plane was introduced and EMD realization techniques’ influence on EMDdecomposition effect was assessed. Then an IMF criterion for sifting stoppage based on excludingmargin was put forward, which verified the EMD decomposition effect based on this method.
Secondly, the influence on the extreme value point by signal amplitude, frequency and phasevariation was analyzed by experiments, and then the influence on EMD decomposition effect byextreme value variation trend was researched. Combining the variation of signal amplitude, frequencyand phase with EMD decomposition, signals’ influence on EMD decomposition effect was discoveredby both experimental induction and theoretical deduction. The relationship was validated byexperiments.
Thirdly, based on the research about EMD realization technique and the influence on EMDdecomposition effect by signal, the reason of mode mixing is analyzed. Three basic types of modemixing are proposed. The solution principles to the three typical mode mixing were researched deeply,and their limitations were also analyzed. EMD based on frequency bands was proposed to solve modemixing, whose mode mixing solution effect was validated by experiments.
Fourthly, the instantaneous phase variation when the direct arrival wave was superimposed by damage scattering signal was researched and its result was validated by experiments. The reason whyEMD decomposition of the active Lamb wave signal is unstable is analyzed and BF-EMD wasintroduced to improve the decomposition stability. The experimental validation was followed. Basedon that, the marginal spectrum was applied to research damage’s influence on the instantaneousfrequency of direct arrival wave and the research result was compared to signal’s frequency spectrum.
Fifthly, the mode feature of Lamb wave generated by impact damage was analyzed theoreticallyand validated by lead cutting experiment. The propagation velocity calculation of A0mode wasutilized to validate the extraction ability of BF-EMD about signals of narrow frequency. This methodwas introduced to realize impact source localization. During the prognosis of impact damage, IMFprovoked by structural damage was obtained by EMD self-adaptive signal decomposition and damagelocalization was realized by BF-EMD extraction method.
引文
[1]杜崇壮.先进复材技术的发展现状与展望.第三届全球华人航空科技研讨会论文集,西安,2005,37-43.
[2]袁慎芳,邱雷,吴键等.大型飞机的发展对结构健康监测的需求与挑战.航空制造技术,2009(22):62-67.
[3] Goggin P. Challenges for SHM transition to future aerospace systems. Structural HealthMonitoring2003: From Diagnostics&Prognostics to Structural Health Management:Proceedings of the4th International Workshop on Structural Health Monitoring, StanfordUniversity, Stanford, CA,2003,30-41.
[4]陈祥宝,张宝艳译.工程复合材料.北京:化学工业出版社,2004.
[5] Farrar C R, Sohn H, Hemez F M. et al. Damage prognosis: current status and future needs, LosAlamos National Laboratory report. LA-14051-MS,2003.
[6] Hickinbotham S J, Austin J. Novelty Detection for Flight Data from Airframe Strain Gauges.European COST F3Conference on System Identification and Structural Health Monitoring,Madrid, Spain,2000:773-780.
[7] Ganguli R, Chopra I, Haas D J. Helicopter Rotor System Health Monitoring Using NumericalSimulation and Neural Networks. The53rd AHS Annual forum,1997:1285-1296.
[8] Giurgiutiu V, Cuc A, Goodman P. Review of Vibration-based Helicopters Health and UsageMonitoring Methods. The Shock&Vibration Digest33,2001,5:387~443.
[9] Keilers C H, Chang F K, Identifying delaminations in composite beams using built-inpiezoelectrics: Part i–experiments and analysis; Part ii an identification method, Journal ofIntelligent Material Systems and Structures,1995,6:649-672
[10] Takeda N, Jajima N, Sakurai T, et al. Structural health monitoing issues in Japanese compositefuselage demonstrator program for damage detection and suppression, Proceedings of3rdInternational workshop on structural health monitoring, Stanford, USA,2003:88-95
[11]陶宝祺.智能材料结构.北京:国防工业出版社,1997.
[12]梁大开,陶宝祺,朱晓荣.光纤智能复合材料结构的研究.仪器仪表学报,1999,20(6)：582-585.
[13]梁大开,杨红,陶宝祺.液芯光纤在机敏结构自修复功能中的初步试验.自然科学进展,2001,25(5):102-106.
[14]梁大开.基于空心光纤的智能结构自诊断、自修复系统.航空维修与工程,2004,35(3):20~23.
[15] Shenfang Yuan, Lei Wang, Lihua Shi, Active monitoring for on-line damage detection incomposite structures， Proceedings of the US-Japan Workshop on Smart Structures forImproved Seismic Performances in Urban Seismic Performance in Urban Regions, Seatle,USA, Aug.2001:45-56.
[16]王磊,袁慎芳,朱安华.基于主动监测技术的蜂窝夹心结构损伤监测研究,仪器仪表学报,2002,23(4):422-425.
[17] Lei Wang, Shenfang Yuan. Application of neural networks to active damage detectiontechnique of composites, Proceedings of SPIE,2003, Vol.5058:569-575.
[18] Shenfang Yuan, Lei Wang, Lihua Shi. On-line damage monitoring in composite structures,Journal of Vibration and Acoustics,2003,125:178-186.
[19]彭鸽,袁慎芳.基于主动监测技术的结构冲击损伤BP神经网络识别.仪器仪表学报,2005,26(6):574~577.
[20]徐欣,袁慎芳.结构健康监测中压电元件的温度效应的软件补偿方法.江苏省计量测试学术论文集,2005:258-264.
[21]王帮峰,李迎,施益峰.复合材料结构健康主动监测中激励信号的优化.南京航空航天大学学报,2006,38（5）:613~618.
[22]袁慎芳.结构健康监控.北京:国防工业出版社,2007.
[23]赵霞,袁慎芳,周恒保等.基于声发射技术的损伤诊断Agent研究.中国机械工程,2008,19(14):1697-1702.
[24]王强,袁慎芳.复合材料板脱层损伤的时间反转成像监测.复合材料学报,2009,26(3):99-104.
[25]王强. Lamb波时间反转方法及其在结构健康监测中的应用研究，[博士学位论文].南京:南京航空航天大学,2009.
[26]苏永振.航空材料结构低速冲击健康监测研究,[博士学位论文].南京:南京航空航天大学,2010.
[27]孙亚杰.基于超声相控阵原理的结构健康监测技术研究,[博士学位论文],南京:南京航空航天大学,2010.
[28]杜善义,冷劲松,王殿富.智能材料系统与结构.北京:科学出版社,2001.
[29]张晓晶.复合材料壳体结构健康监测研究.[博士学位论文].哈尔滨:哈尔滨工业大学,2005.
[30]李顺利,张博明,李庆芬等.形状记忆合金混杂复合材料弯曲变形的研究.哈尔滨工业大学学报,2005,37(1):80-83.
[31]杜善义,张博明.飞行器结构智能化研究及其发展趋势,宇航学报,2007,28（4）,773-778.
[32]杜善义.先进复合材料与航空航天.复合材料学报,2007,24(1):1-12.
[33]杨晓宁.含损伤复合材料结构修补技术研究及软件开发.[硕士学位论文],西安:西北工业大学硕士学位论文,2002.
[34]孙晓波.复合材料蜂窝夹芯结构脱胶修补研究与软件开发.[硕士学位论文],西安:西北工业大学硕士学位论文,2003.
[35]李秋龙.复合材料蜂窝结构损伤修补试验技术与分析研究.[硕士学位论文],西安:西北工业大学硕士学位论文,2003.
[36]刘凤楠.复合材料层合板静压痕及分层损伤分析研究.[硕士学位论文],西安:西北工业大学硕士学位论文,2010.
[37]王瑜,赵美英,余明.复合材料层压板分层损伤扩展与压缩强度预测.机械科学与技术,2011,30(7):1051-1055.
[38]谢小林.基于电阻法碳布增强环氧树脂复合材料损伤自诊断的研究,[博士学位论文],武汉:武汉理工大学,2010.
[39]孙九霄.基于布拉格光栅传感的复合材料固化及冲击损伤监测研究,[博士学位论文],武汉:武汉理工大学,2011.
[40] Wigner E. P. On the Quantum Correction for Thermodynamic Equilibrium, Physical Review,1932,40:749-759.
[41] L科恩,时频分析:理论与应用（白居宪译）,西安:西安交通大学出版社,2000.
[42] Gabor D. Theory of communication. J Inst Elec Eng,1946,93:429-457.
[43] Ville J. Theorie et applications de la notion de signal analytique. Cables et Transmission,1948,2A:61-74.
[44]秦前清,杨宗凯.实用小波分析.西安:西安电子科学出版社,1994.
[45]石钧.多小波理论和应用,信号处理,1999,15:4329-4334.
[46]张贤达,保铮.非平稳信号分析与处理.北京:国防工业出版社,1998.
[47]邹红星,戴琼海,李衍达等.不含交叉项干扰且具有WVD聚集性的时频分布之不存在性.中国科学（E辑）,2001,31(4):348-354.
[48] Huang N E, Shen Z, Long S. R, et al. The empirical mode decomposition and the Hilbertspectrum for nonlinear and non-stationary time series analysis.Proc.Roy.Soc, London. A.1998,454,903-995.
[49] Boashash B. Estimating and Interpreting The Instantaneous Frequency of a Signal—Part1:Fundamentals, Proc. IEEE, April1992,80(4):520-538.
[50] Cohen L, Lee C. Instantaneous Frequency, Its Standard Deviation, and MulticomponentSignals. In Advanced Algorithms and Architectures for Signal Processing III,1988,975:186-208.
[51] Wei D, Bovik A. On the Instantaneous Frequencies of Multicomponent AM-FM Signals. IEEESignal Processing Letters,1998,5:84–86.
[52] Oliveira P M, Barroso V. Instantaneous Frequency of Multicomoponent Signals. IEEE SingnalProcessing Letters,1999,6(4):81-83.
[53] http://tco.gsfc.nasa.gov/HHT/index.html#hhtawards
[54] Huang W, Shen Z, Huang N E, et al. Engineering analysis of Biological Variables: an exampleof blood pressure over one day. Proceeding of the National Academy of Science(USA),1998,95(9):4816-4821.
[55] Hwang P A, Huang N E, Wang D W. A note on analyzing nonlinear and nonstationary oceanwave data. Applied Ocean Research,2003,25:187-193.
[56] Huang N E, Shin H H, Long S R. The Ages of Large Amplitude Coastal Seiches on theCaribbean Coast of Puerto Rice, J. Phy. Oceanograhy, Aug2000,30(8):2001-2012.
[57]钟佑明.希尔伯特—黄变换局瞬信号分析理论的研究,[博士学位论文].重庆:重庆大学,2002.
[58] Rilling G, Flandrin P, Goncalves P. On empirical mode decomposition and its algorithms.IEEEEURASIP Workshop on Nonlinear Signal and Image Processing, Grado(I),2003.
[59]邓拥军,王伟,钱成春等. EMD方法及Hilbert变换中边界问题的处理.科学通报,2001,46(3):257-263.
[60]张郁山,梁建文,胡聿贤.应用自回归模型处理EMD方法中的边界问题.自然科学进展,2003,13(10):1054-1059.
[61]盖强.局域波时频分析法的理论研究与应用,[博士学位论文].大连:大连理工大学,2001.
[62]黄大吉,赵进平,苏纪兰.希尔伯特-黄变换的端点延拓.海洋学报,2003,25(1):1-11.
[63]刘慧婷,张旻,程家兴.基于多项式拟合算法的EMD端点问题的处理.计算机工程与应用,2004,(16):84-86.
[64]余泊.自适应时频分析方法及其在故障诊断中的应用,[博士学位论文].大连:大连理工大学,1998.
[65] Chen Q H, Huang N E, Riemenschneider S.A B-spline approach for empirical modedecompositions. Advances in Computational Mathematics,2006,24:171–195.
[66] Huang N E, Shen Z, Long S R. A new view of nonlinear water waves: the Hilbert spectrum.Annual Review of Fluid Mechanics,1999,31:417-457.
[67] Huang N E, Wu M L, Long S R, et al. A confidence limit for the empirical modedecomposition and the Hilbert spectral analysis, Proceeding of the Royal Society of London,2003(459):2317-2345.
[68] Cheng J, Yu D, Yang Y. Research on the Intrinsic Mode Function (IMF) Criterion in EMDMethod. Mechanical Systems and Signal Processing,2006,20:817-824.
[69] Xuan B, Xie Q, Peng S. EMD Sifting Based on Bandwidth, IEEE Signal Processing Letters,2007,14(8):537-540.
[70]谭善文.多分辨希尔伯特-黄（Hilbert-Huang）变换方法的研究,[博士学位论文].重庆:重庆大学,2001.
[71] Yang J N, Lei Y, Pan S W, et al. System Identification of Linear Structures Based onHilbert-Huang Spectral Analysis. Part1: Normal Modes. Earthquake Engineering andStructural Dynamics,2003, Vol.32:1443-1467.
[72] Yang J. N, Lei Y, Pan S. W, et al.System Identification of Linear Structures Based onHilbert-Huang Spectral Analysis. Part2: Complex Modes. Earthquake Engineering andStructural Dynamics,2003, Vol.32:1533-1554.
[73] Wu Z H, Huang N E. A study of the characteristics of white noise using the empirical modedecomposition method. Proceedings of the Royal Society London A,2004,460（2046）:1597-1611.
[74] Wu Z H, Huang N E. Ensemble empirical mode decomposition: a noise assisted data analysismethod. Center for Ocean Land Atmosphere Studies, Technical Report,2004,(193):51.
[75] Deering R, Kaiser J F. The use of masking signal to improve empirical mode decomposition. inProc. IEEE Int. Conf. Acoustics, Speech Signal Processing,2005,4:485-488.
[76] Helong Li,Lihua Yang,Daren Huang. The study of the intermittency test filtering character ofHilbert-Huang transform. Mathematics and Computers in Simulation,2005,70:22-32.
[77] Senroy N, Suryanarayanan S.Two techniques to enhance empirical mode decomposition forpower quality applications. IEEE Power Eng. Society General Meeting, Tampa, USA,2007.
[78]陈隽,徐幼麟.经验模分解在信号趋势项提取中的应用,振动、测试与诊断,2005,25(2):101-153.
[79] Flandrin P, Rilling G, Goncalves P. Empirical mode decomposition as a filter bank. IEEESignal Processing Letters,2004,11(2):112-114.
[80] Kizhner S, Blank K, Flatley T, et al. On certain theoretical developments underlying theHilbert-Huang transform. Aerospace Conference, IEEE, Paris,2006:1-14.
[81]张海勇.基于局域波法的非平稳随机信号分析中若干问题的研究,[博士学位论文].大连:大连理工大学,2001.
[82]张海勇,马孝江,盖强.一种新的时频分析方法.火力与指挥控制,2000,25(3):39-42.
[83]盖强,马孝江,张海勇等.几种局域波分解方法的比较研究.系统工程与电子技术,2002,24(2):57-59.
[84]盖强,马孝江,张海勇等.一种消除局域波法中边界效应的新方法.大连理工大学学报,2002,42(l):115-117.
[85]邹岩崑.局域波分析的理论方法研究及应用,[博士学位论文].大连:大连理工大学,2004.
[86]钟佑明,秦树人.希尔伯特-黄变换的统一理论依据研究,振动与冲击,2006,25（3）:40-43.
[87]钟佑明,秦树人. HHT的理论依据探讨——Hilbert变换的局部乘积定理.振动与冲击,2006,25(2):12-19.
[88]徐冠雷,王孝通,徐晓刚等.多分量到单分量可用EMD分解的条件及判据.自然科学进展,2006,16(10):1356-1360.
[89]沈国际,陶利民,陈仲生.多频信号经验模态分解的理论研究及应用,振动工程学报,2005,18(1):91~94.
[90] Rilling G，Flandrin P. One or two frequencies? the empiricalmode decomposition answers.IEEE Transactions on Signal Processing.2008,56:85–95.
[91] Michael Feldman.Analytical basics of the EMD: Two harmonics decomposition.MechanicalSystems and Signal Processing,2009,23:2059~2071.
[92] Huang N E, Chern C C, Huang K, et al. A new spectral representation of earthquake data:Hilbert spectral analysis of Station TCU129, Chi-Chi, Taiwan,21September1999. Bulletin ofthe Seismological Society of America,2001,91(5):1310-1338.
[93]张郁山.希尔伯特－黄变换（HHT）与地震动时程的希尔伯特谱－方法与应用研究,[博士学位论文].北京:中国地震局地球物理研究所,2003.
[94]胡聿贤,张郁山,梁建文.应用HHT方法从竖向地震动记录识别场地液化的物理过程.地震工程与工程振动,2004,24(3):1-11.
[95] Zhang R R, Lance V D, Liang J.W, et al. On estimating site damping with soil non-linearityfrom earthquake recordings, International Journal of Non-linear Mechanics,2003,(39):1501-1517.
[96] Molla K. I, Hirose K, Minematsu N, et al. Voiced/Unvoiced Detection of Speech Signals UsingEmpirical Mode Decomposition Model. IEEE Inter-national Conference on Information andCommunication Technology, Dhaka, Bangladesh,2007.
[97] Khaldi K, Boudraa A O, Bouchikhi A, et al. Speech Signal Noise Reduction by EMD. IEEEInternational Symposium on Communications, Control and Signal Processing, St. Julians,Malta,2008.
[98] Chatlani N, Soraghan J J. Adaptive Empirical Mode Decomposition for Signal Enhancementwith Application to Speech. IEEE International Conference on Systems, Signals and ImageProcessing, Bratislava, Slovak Republic,2008.
[99] Aicha Bouzid, Noureddine Ellouze. Empircal mode decomosition of voiced speech signal. FirstInternational Symposium on Control, Communications and Signal Processing,2004:603-606.
[100] Weng B, Blanco-Velasco M, Barner K E. ECG Denoising Based on the Empirical ModeDecomposition. IEEE International Conference on Engineering in Medicine and BiologySociety, NY, USA,2006.
[101] Ye Y, Garcia-Casado J, J. Martinesde-Juan L,et al.Combined Method for Artifact Reduction inSurface Electro-enterogram.IEEE International Conference on Engineering in Medicine andBiology Society, France, Lyon,2007.
[102] Liu S, He Q, Gao R X, et al. Empirical Mode Decomposition Applied to Tissue ArtifactRemoval from Respiratory Signal. IEEE International Conference on Engineering in Medicineand Biology Society, Canada, Vancouver,2008.
[103] Echeverría J C, Crowe J A, Woolfson M S, et al. Application of empirical mode decompositionto heart rate variability analysis. Medical&Biological Engineering&Computing,2001,(39):471-479.
[104] Blanco-Velasco M, Cruz-Roldán F, Godino-Llorente JI, et al. Nonlinear Trend Estimation ofthe Ventricular Repolarization Segment for T-Wave Alternans Detection. IEEE BiomedicalEngineering,2010,57(10):2402-2412.
[105] Arafat A, Hasan K. Automatic detection of ECG wave boundaries using empirical modedecomposition. Acoustics Speech and Signal Processing, taipei, china,2009.
[106] Agarwal V, Tsoukalas L H. De-noising Electrical Signal via Empirical Mode Decomposition.2007IREP Symposium-Bulk Power System Dynamics and Control-VII, RevitalizingOperational Reliability, South Carolina, USA,2007.
[107] Lu Z, Smith J S, Wu Q H. Empirical Mode Decomposition For Power Quality.2005IEEE/PES Transmission and Distribution Conference&Exhibition: Asia and Pacific, China,2005.
[108] Senroy N, Suryanarayanan S, Ribeiro P F. An improved Hilbert-Huang method for analysis oftime varying distortions in power quality. IEEE Transcactons on power systems,2007,22(4):1843-1850.
[109] Silian Lin, Jann N Yang, Li Zhou. Damage identification of a benchmark building for structuralhealth monitoring. Smart Masterials and Structures,2005,14, S162-S169.
[110] Quek S T, Tua P S, Wang Q. Detecting anomalies in beams and plate based on theHilbert-Huang transform of real signals. Smart Masterials and Structures,2003,12,447-460.
[111] Yang J N, Lei Y, Lin S,et al. Hilbert-Huang Based Approach for Structural Damage Detection.Journal of Engineering Mechanics.2004,1:85-95.
[112] Yang J N, Lei Y, Lin S,et al. Identification of natural frequencies and dampings of In Situ tallbuildings using Ambient wind vibration data. Journal of Engineering mechanics,2004,130(5):570-577.
[113] Pines D, Salvino L. Structural health monitoring using empirical mode decomposition and theHilbert phase. Journal of Sound and Vibration,2006,294:97-124.
[114] Peng Z K, Peter W T, Chu FL. An improved Hilbert-Huang transform and its application invibration signal analysis. Journal of Sound and Vibration,2005,286:187-205.
[115] Rai V K, Mohanty A R. Bearing fault diagnosis using FFT of intrinsic mode functions inHilbert-Huang transform..Mechanical Systems and Signal Processing,2007,21:2607-2615.
[116] Babu T R, Srikanth S, Sekhar A S. Hilbert-Huang transform for detection and moinoring ofcrack in a transient rotor. Mechanical Systems and Signal Processing,2008,22:905-914.
[117] Yan R Q,Robert X G. Hilbert-Huang Transform-Based Vibration Signal Analysis for MachineHealth Monitoing.Transactions on Instrumentation and Measurement,2006,55(6):2320-2329.
[118] Mao Y M, Que P W. Application of Hilbert-Huang signal processing to ultrasonicnon-destructive testing of oil pipelines. Journal of Zhejiang University Science A,2006,7(2):130-134.
[119] Kazys R, Tumsys O, Pagodinas D. Ultrasonic detection of defects in strongly attenuatingstructures using the Hilbert-Huang transform. NDT&E Int,2008,41(6):457-466.
[120] Lu B, Upadhyaya B R, Perez R B.Structural Integrity Monitoring of Steam Generator TubingUsing Transient Acoustic Signal Analysis. Transactions on Nuclear Science,2005,52(1):484-493.
[121] Huang N E.,Martin J B, Liming S. Hilbert-Huang Transform Stability Spectral AnalysisApplied to Flutter Flight Test Data. AIAA Journal,2006,44(4):772-786.
[122] Chen H G, Yan Y J, Jiang J S. Vibration-based damage detectiong in composite wingboxstructures by HHT. Mechanical Systems and Signal Processing,2007,21:307-321.
[123]常鸣,袁慎芳.基于HHT技术的复合材料结构损伤定位研究.宇航学报.2006,27(1),144-150.
[124]孙亚杰,袁慎芳,王帮峰.基于HHT技术的二维结构损伤定位研究.压电与声光.2007,29(6):736-739.
[125]胡爱军. Hilbert-Huang变换在旋转机械振动信号分析中的应用研究,[博士学位论文].北京:华北电力大学,2008.
[126] Chapra S C, Canale R P.工程数值方法（于艳华，傅效群，赵红宇等译）.北京:清华大学出版社,2010.
[127]施浒立,颜毅华,徐国华.工程科学中的广义延拓逼近法.北京:科学出版社,2005.
[128]余波.自适应时频方法及其在故障诊断方法中的应用研究,[博士学位论文].大连:大连理工大学,1998.
[129]程军圣,于德介,杨宇.基于支持矢量回归机的Hilbert-Huang变换端点效应问题的处理方法.机械工程学报,2006,42(4):23-31.
[130]邓蕾,胡小林,李锋等.基于支持向量机的BS-EMD端点效应消除法.振动、测试与诊断,2011,31(3):344-347.
[131] Zhao J P. Improvement of the mirror extending in empirical mode decomposition method andthe technology for eliminating frequency mixing. High Technology Letters,2002，8(3):40-47.
[132]杨建文,贾民平.希尔伯特-黄谱的端点效应分析及处理方法研究.振动工程学报,2006,19(2):283-288.
[133] Huang D J. Practical implementaion of Hilbert-Huang transform algorithm. Acta OceanologicaSinica,2003,22(1):1-14.
[134]郑天翔,杨力华.经验模式分解算法的探讨和改进.中山大学学报,2007,46(1):2-6.
[135] Marcus D, Torsten S. Performance and limitations of the Hilbert–Huang transform (HHT) withan application to irregular water waves. Ocean Engineering,2004,31:1783-1834.
[136]杨世锡,胡劲松,吴昭同等.基于高次样条插值的经验模态分解方法研究.浙江大学学报(工学版),2004,38(3):267-270.
[137] Albena D V, Soares C G. Analysis of abnormal wave records by the Hilbert-Huang transformmethod. Journal of Atmospheric and Oceanic Technology,2007,24:1678-1689.
[138] http://perso.ens-lyon.fr/patrick.flandrin/emd.html
[139] Boashash B. Estimating and interpreting the instantaneous frequency of a signal-part II:Fundamentals. Proc. IEEE,1992,80(4):540-568.
[140]胡维平,莫家玲,杜明辉.经验模态分解中的频域分辨率及其改进方法.华南理工大学学报（自然科学版）,2007,35(5):15-19.
[141]郑祥明,赵玉珍,史耀武.兰姆波频散曲线的计算.无损检测,2003,25(3):66-68.
[142]彭鸽.基于Lamb波的结构健康监测主动监测技术研究,[博士学位论文].南京:南京航空航天大学,2006.
[143]耿荣生,沈功田,刘时风.模态声发射基本理论.无损检测,2002,24(7):302-306.
[144] Crawley E F, Luis J D. Use of piezoelectric actuators as elements of intelligent structures.AIAA Journal,1987,25(10):1373-1385.
[145] Crawley E F, Anderson E H. Detailed Models of Piezoceramic Actuation of Beams. Journal ofIntelligent Material Systems and Structures,1990,1(1):4-25.
[146]邱雷,袁慎芳.集成压电结构健康监测系统的研制及其应用.压电与声光,2008,30(1):39-42.
[147] Yuan S F, Xu Y D, Peng G. New Developments in Structural Health Monitoring Based onDiagnostic Lamb Wave. Journal of Material Science&Technology,2004,20(5):490-496.
[148]彭鸽,袁慎芳,徐颖娣.基于主动LAMB波和小波变换得二维结构损伤定位研究.振动工程学报,2004,17(4):488-493.
[149]马玉华,林文华.解析信号的瞬时相位与原始信号的等价关系.黑龙江大学自然科学学报,1995,12(3):56-60.
[150]李辉,郑海起,唐力伟.基于经验模态分解的瞬时相位分析方法的应用.振动、测试与诊断,2007,27(1):9-12.
[151]马宏伟,杨桂通.结构损伤探测的基本方法和研究进展.力学进展,1999,29(4):513-527.
[152] Gorman M R. Plate wave acoustic emission. JASA,1991,90(1):358-364.
[153]赵霞.多主体协作结构健康监测系统的关键技术研究,[博士学位论文].南京:南京航天航天大学,2008.
[154]耿荣生,沈功田,刘时风.模态声发射—声发射信号处理的得力工具,无损检测,2002,24（8）:341-345.
[2]袁慎芳,邱雷,吴键等.大型飞机的发展对结构健康监测的需求与挑战.航空制造技术,2009(22):62-67.
[3] Goggin P. Challenges for SHM transition to future aerospace systems. Structural HealthMonitoring2003: From Diagnostics&Prognostics to Structural Health Management:Proceedings of the4th International Workshop on Structural Health Monitoring, StanfordUniversity, Stanford, CA,2003,30-41.
[4]陈祥宝,张宝艳译.工程复合材料.北京:化学工业出版社,2004.
[5] Farrar C R, Sohn H, Hemez F M. et al. Damage prognosis: current status and future needs, LosAlamos National Laboratory report. LA-14051-MS,2003.
[6] Hickinbotham S J, Austin J. Novelty Detection for Flight Data from Airframe Strain Gauges.European COST F3Conference on System Identification and Structural Health Monitoring,Madrid, Spain,2000:773-780.
[7] Ganguli R, Chopra I, Haas D J. Helicopter Rotor System Health Monitoring Using NumericalSimulation and Neural Networks. The53rd AHS Annual forum,1997:1285-1296.
[8] Giurgiutiu V, Cuc A, Goodman P. Review of Vibration-based Helicopters Health and UsageMonitoring Methods. The Shock&Vibration Digest33,2001,5:387~443.
[9] Keilers C H, Chang F K, Identifying delaminations in composite beams using built-inpiezoelectrics: Part i–experiments and analysis; Part ii an identification method, Journal ofIntelligent Material Systems and Structures,1995,6:649-672
[10] Takeda N, Jajima N, Sakurai T, et al. Structural health monitoing issues in Japanese compositefuselage demonstrator program for damage detection and suppression, Proceedings of3rdInternational workshop on structural health monitoring, Stanford, USA,2003:88-95
[11]陶宝祺.智能材料结构.北京:国防工业出版社,1997.
[12]梁大开,陶宝祺,朱晓荣.光纤智能复合材料结构的研究.仪器仪表学报,1999,20(6)：582-585.
[13]梁大开,杨红,陶宝祺.液芯光纤在机敏结构自修复功能中的初步试验.自然科学进展,2001,25(5):102-106.
[14]梁大开.基于空心光纤的智能结构自诊断、自修复系统.航空维修与工程,2004,35(3):20~23.
[15] Shenfang Yuan, Lei Wang, Lihua Shi, Active monitoring for on-line damage detection incomposite structures， Proceedings of the US-Japan Workshop on Smart Structures forImproved Seismic Performances in Urban Seismic Performance in Urban Regions, Seatle,USA, Aug.2001:45-56.
[16]王磊,袁慎芳,朱安华.基于主动监测技术的蜂窝夹心结构损伤监测研究,仪器仪表学报,2002,23(4):422-425.
[17] Lei Wang, Shenfang Yuan. Application of neural networks to active damage detectiontechnique of composites, Proceedings of SPIE,2003, Vol.5058:569-575.
[18] Shenfang Yuan, Lei Wang, Lihua Shi. On-line damage monitoring in composite structures,Journal of Vibration and Acoustics,2003,125:178-186.
[19]彭鸽,袁慎芳.基于主动监测技术的结构冲击损伤BP神经网络识别.仪器仪表学报,2005,26(6):574~577.
[20]徐欣,袁慎芳.结构健康监测中压电元件的温度效应的软件补偿方法.江苏省计量测试学术论文集,2005:258-264.
[21]王帮峰,李迎,施益峰.复合材料结构健康主动监测中激励信号的优化.南京航空航天大学学报,2006,38（5）:613~618.
[22]袁慎芳.结构健康监控.北京:国防工业出版社,2007.
[23]赵霞,袁慎芳,周恒保等.基于声发射技术的损伤诊断Agent研究.中国机械工程,2008,19(14):1697-1702.
[24]王强,袁慎芳.复合材料板脱层损伤的时间反转成像监测.复合材料学报,2009,26(3):99-104.
[25]王强. Lamb波时间反转方法及其在结构健康监测中的应用研究，[博士学位论文].南京:南京航空航天大学,2009.
[26]苏永振.航空材料结构低速冲击健康监测研究,[博士学位论文].南京:南京航空航天大学,2010.
[27]孙亚杰.基于超声相控阵原理的结构健康监测技术研究,[博士学位论文],南京:南京航空航天大学,2010.
[28]杜善义,冷劲松,王殿富.智能材料系统与结构.北京:科学出版社,2001.
[29]张晓晶.复合材料壳体结构健康监测研究.[博士学位论文].哈尔滨:哈尔滨工业大学,2005.
[30]李顺利,张博明,李庆芬等.形状记忆合金混杂复合材料弯曲变形的研究.哈尔滨工业大学学报,2005,37(1):80-83.
[31]杜善义,张博明.飞行器结构智能化研究及其发展趋势,宇航学报,2007,28（4）,773-778.
[32]杜善义.先进复合材料与航空航天.复合材料学报,2007,24(1):1-12.
[33]杨晓宁.含损伤复合材料结构修补技术研究及软件开发.[硕士学位论文],西安:西北工业大学硕士学位论文,2002.
[34]孙晓波.复合材料蜂窝夹芯结构脱胶修补研究与软件开发.[硕士学位论文],西安:西北工业大学硕士学位论文,2003.
[35]李秋龙.复合材料蜂窝结构损伤修补试验技术与分析研究.[硕士学位论文],西安:西北工业大学硕士学位论文,2003.
[36]刘凤楠.复合材料层合板静压痕及分层损伤分析研究.[硕士学位论文],西安:西北工业大学硕士学位论文,2010.
[37]王瑜,赵美英,余明.复合材料层压板分层损伤扩展与压缩强度预测.机械科学与技术,2011,30(7):1051-1055.
[38]谢小林.基于电阻法碳布增强环氧树脂复合材料损伤自诊断的研究,[博士学位论文],武汉:武汉理工大学,2010.
[39]孙九霄.基于布拉格光栅传感的复合材料固化及冲击损伤监测研究,[博士学位论文],武汉:武汉理工大学,2011.
[40] Wigner E. P. On the Quantum Correction for Thermodynamic Equilibrium, Physical Review,1932,40:749-759.
[41] L科恩,时频分析:理论与应用（白居宪译）,西安:西安交通大学出版社,2000.
[42] Gabor D. Theory of communication. J Inst Elec Eng,1946,93:429-457.
[43] Ville J. Theorie et applications de la notion de signal analytique. Cables et Transmission,1948,2A:61-74.
[44]秦前清,杨宗凯.实用小波分析.西安:西安电子科学出版社,1994.
[45]石钧.多小波理论和应用,信号处理,1999,15:4329-4334.
[46]张贤达,保铮.非平稳信号分析与处理.北京:国防工业出版社,1998.
[47]邹红星,戴琼海,李衍达等.不含交叉项干扰且具有WVD聚集性的时频分布之不存在性.中国科学（E辑）,2001,31(4):348-354.
[48] Huang N E, Shen Z, Long S. R, et al. The empirical mode decomposition and the Hilbertspectrum for nonlinear and non-stationary time series analysis.Proc.Roy.Soc, London. A.1998,454,903-995.
[49] Boashash B. Estimating and Interpreting The Instantaneous Frequency of a Signal—Part1:Fundamentals, Proc. IEEE, April1992,80(4):520-538.
[50] Cohen L, Lee C. Instantaneous Frequency, Its Standard Deviation, and MulticomponentSignals. In Advanced Algorithms and Architectures for Signal Processing III,1988,975:186-208.
[51] Wei D, Bovik A. On the Instantaneous Frequencies of Multicomponent AM-FM Signals. IEEESignal Processing Letters,1998,5:84–86.
[52] Oliveira P M, Barroso V. Instantaneous Frequency of Multicomoponent Signals. IEEE SingnalProcessing Letters,1999,6(4):81-83.
[53] http://tco.gsfc.nasa.gov/HHT/index.html#hhtawards
[54] Huang W, Shen Z, Huang N E, et al. Engineering analysis of Biological Variables: an exampleof blood pressure over one day. Proceeding of the National Academy of Science(USA),1998,95(9):4816-4821.
[55] Hwang P A, Huang N E, Wang D W. A note on analyzing nonlinear and nonstationary oceanwave data. Applied Ocean Research,2003,25:187-193.
[56] Huang N E, Shin H H, Long S R. The Ages of Large Amplitude Coastal Seiches on theCaribbean Coast of Puerto Rice, J. Phy. Oceanograhy, Aug2000,30(8):2001-2012.
[57]钟佑明.希尔伯特—黄变换局瞬信号分析理论的研究,[博士学位论文].重庆:重庆大学,2002.
[58] Rilling G, Flandrin P, Goncalves P. On empirical mode decomposition and its algorithms.IEEEEURASIP Workshop on Nonlinear Signal and Image Processing, Grado(I),2003.
[59]邓拥军,王伟,钱成春等. EMD方法及Hilbert变换中边界问题的处理.科学通报,2001,46(3):257-263.
[60]张郁山,梁建文,胡聿贤.应用自回归模型处理EMD方法中的边界问题.自然科学进展,2003,13(10):1054-1059.
[61]盖强.局域波时频分析法的理论研究与应用,[博士学位论文].大连:大连理工大学,2001.
[62]黄大吉,赵进平,苏纪兰.希尔伯特-黄变换的端点延拓.海洋学报,2003,25(1):1-11.
[63]刘慧婷,张旻,程家兴.基于多项式拟合算法的EMD端点问题的处理.计算机工程与应用,2004,(16):84-86.
[64]余泊.自适应时频分析方法及其在故障诊断中的应用,[博士学位论文].大连:大连理工大学,1998.
[65] Chen Q H, Huang N E, Riemenschneider S.A B-spline approach for empirical modedecompositions. Advances in Computational Mathematics,2006,24:171–195.
[66] Huang N E, Shen Z, Long S R. A new view of nonlinear water waves: the Hilbert spectrum.Annual Review of Fluid Mechanics,1999,31:417-457.
[67] Huang N E, Wu M L, Long S R, et al. A confidence limit for the empirical modedecomposition and the Hilbert spectral analysis, Proceeding of the Royal Society of London,2003(459):2317-2345.
[68] Cheng J, Yu D, Yang Y. Research on the Intrinsic Mode Function (IMF) Criterion in EMDMethod. Mechanical Systems and Signal Processing,2006,20:817-824.
[69] Xuan B, Xie Q, Peng S. EMD Sifting Based on Bandwidth, IEEE Signal Processing Letters,2007,14(8):537-540.
[70]谭善文.多分辨希尔伯特-黄（Hilbert-Huang）变换方法的研究,[博士学位论文].重庆:重庆大学,2001.
[71] Yang J N, Lei Y, Pan S W, et al. System Identification of Linear Structures Based onHilbert-Huang Spectral Analysis. Part1: Normal Modes. Earthquake Engineering andStructural Dynamics,2003, Vol.32:1443-1467.
[72] Yang J. N, Lei Y, Pan S. W, et al.System Identification of Linear Structures Based onHilbert-Huang Spectral Analysis. Part2: Complex Modes. Earthquake Engineering andStructural Dynamics,2003, Vol.32:1533-1554.
[73] Wu Z H, Huang N E. A study of the characteristics of white noise using the empirical modedecomposition method. Proceedings of the Royal Society London A,2004,460（2046）:1597-1611.
[74] Wu Z H, Huang N E. Ensemble empirical mode decomposition: a noise assisted data analysismethod. Center for Ocean Land Atmosphere Studies, Technical Report,2004,(193):51.
[75] Deering R, Kaiser J F. The use of masking signal to improve empirical mode decomposition. inProc. IEEE Int. Conf. Acoustics, Speech Signal Processing,2005,4:485-488.
[76] Helong Li,Lihua Yang,Daren Huang. The study of the intermittency test filtering character ofHilbert-Huang transform. Mathematics and Computers in Simulation,2005,70:22-32.
[77] Senroy N, Suryanarayanan S.Two techniques to enhance empirical mode decomposition forpower quality applications. IEEE Power Eng. Society General Meeting, Tampa, USA,2007.
[78]陈隽,徐幼麟.经验模分解在信号趋势项提取中的应用,振动、测试与诊断,2005,25(2):101-153.
[79] Flandrin P, Rilling G, Goncalves P. Empirical mode decomposition as a filter bank. IEEESignal Processing Letters,2004,11(2):112-114.
[80] Kizhner S, Blank K, Flatley T, et al. On certain theoretical developments underlying theHilbert-Huang transform. Aerospace Conference, IEEE, Paris,2006:1-14.
[81]张海勇.基于局域波法的非平稳随机信号分析中若干问题的研究,[博士学位论文].大连:大连理工大学,2001.
[82]张海勇,马孝江,盖强.一种新的时频分析方法.火力与指挥控制,2000,25(3):39-42.
[83]盖强,马孝江,张海勇等.几种局域波分解方法的比较研究.系统工程与电子技术,2002,24(2):57-59.
[84]盖强,马孝江,张海勇等.一种消除局域波法中边界效应的新方法.大连理工大学学报,2002,42(l):115-117.
[85]邹岩崑.局域波分析的理论方法研究及应用,[博士学位论文].大连:大连理工大学,2004.
[86]钟佑明,秦树人.希尔伯特-黄变换的统一理论依据研究,振动与冲击,2006,25（3）:40-43.
[87]钟佑明,秦树人. HHT的理论依据探讨——Hilbert变换的局部乘积定理.振动与冲击,2006,25(2):12-19.
[88]徐冠雷,王孝通,徐晓刚等.多分量到单分量可用EMD分解的条件及判据.自然科学进展,2006,16(10):1356-1360.
[89]沈国际,陶利民,陈仲生.多频信号经验模态分解的理论研究及应用,振动工程学报,2005,18(1):91~94.
[90] Rilling G，Flandrin P. One or two frequencies? the empiricalmode decomposition answers.IEEE Transactions on Signal Processing.2008,56:85–95.
[91] Michael Feldman.Analytical basics of the EMD: Two harmonics decomposition.MechanicalSystems and Signal Processing,2009,23:2059~2071.
[92] Huang N E, Chern C C, Huang K, et al. A new spectral representation of earthquake data:Hilbert spectral analysis of Station TCU129, Chi-Chi, Taiwan,21September1999. Bulletin ofthe Seismological Society of America,2001,91(5):1310-1338.
[93]张郁山.希尔伯特－黄变换（HHT）与地震动时程的希尔伯特谱－方法与应用研究,[博士学位论文].北京:中国地震局地球物理研究所,2003.
[94]胡聿贤,张郁山,梁建文.应用HHT方法从竖向地震动记录识别场地液化的物理过程.地震工程与工程振动,2004,24(3):1-11.
[95] Zhang R R, Lance V D, Liang J.W, et al. On estimating site damping with soil non-linearityfrom earthquake recordings, International Journal of Non-linear Mechanics,2003,(39):1501-1517.
[96] Molla K. I, Hirose K, Minematsu N, et al. Voiced/Unvoiced Detection of Speech Signals UsingEmpirical Mode Decomposition Model. IEEE Inter-national Conference on Information andCommunication Technology, Dhaka, Bangladesh,2007.
[97] Khaldi K, Boudraa A O, Bouchikhi A, et al. Speech Signal Noise Reduction by EMD. IEEEInternational Symposium on Communications, Control and Signal Processing, St. Julians,Malta,2008.
[98] Chatlani N, Soraghan J J. Adaptive Empirical Mode Decomposition for Signal Enhancementwith Application to Speech. IEEE International Conference on Systems, Signals and ImageProcessing, Bratislava, Slovak Republic,2008.
[99] Aicha Bouzid, Noureddine Ellouze. Empircal mode decomosition of voiced speech signal. FirstInternational Symposium on Control, Communications and Signal Processing,2004:603-606.
[100] Weng B, Blanco-Velasco M, Barner K E. ECG Denoising Based on the Empirical ModeDecomposition. IEEE International Conference on Engineering in Medicine and BiologySociety, NY, USA,2006.
[101] Ye Y, Garcia-Casado J, J. Martinesde-Juan L,et al.Combined Method for Artifact Reduction inSurface Electro-enterogram.IEEE International Conference on Engineering in Medicine andBiology Society, France, Lyon,2007.
[102] Liu S, He Q, Gao R X, et al. Empirical Mode Decomposition Applied to Tissue ArtifactRemoval from Respiratory Signal. IEEE International Conference on Engineering in Medicineand Biology Society, Canada, Vancouver,2008.
[103] Echeverría J C, Crowe J A, Woolfson M S, et al. Application of empirical mode decompositionto heart rate variability analysis. Medical&Biological Engineering&Computing,2001,(39):471-479.
[104] Blanco-Velasco M, Cruz-Roldán F, Godino-Llorente JI, et al. Nonlinear Trend Estimation ofthe Ventricular Repolarization Segment for T-Wave Alternans Detection. IEEE BiomedicalEngineering,2010,57(10):2402-2412.
[105] Arafat A, Hasan K. Automatic detection of ECG wave boundaries using empirical modedecomposition. Acoustics Speech and Signal Processing, taipei, china,2009.
[106] Agarwal V, Tsoukalas L H. De-noising Electrical Signal via Empirical Mode Decomposition.2007IREP Symposium-Bulk Power System Dynamics and Control-VII, RevitalizingOperational Reliability, South Carolina, USA,2007.
[107] Lu Z, Smith J S, Wu Q H. Empirical Mode Decomposition For Power Quality.2005IEEE/PES Transmission and Distribution Conference&Exhibition: Asia and Pacific, China,2005.
[108] Senroy N, Suryanarayanan S, Ribeiro P F. An improved Hilbert-Huang method for analysis oftime varying distortions in power quality. IEEE Transcactons on power systems,2007,22(4):1843-1850.
[109] Silian Lin, Jann N Yang, Li Zhou. Damage identification of a benchmark building for structuralhealth monitoring. Smart Masterials and Structures,2005,14, S162-S169.
[110] Quek S T, Tua P S, Wang Q. Detecting anomalies in beams and plate based on theHilbert-Huang transform of real signals. Smart Masterials and Structures,2003,12,447-460.
[111] Yang J N, Lei Y, Lin S,et al. Hilbert-Huang Based Approach for Structural Damage Detection.Journal of Engineering Mechanics.2004,1:85-95.
[112] Yang J N, Lei Y, Lin S,et al. Identification of natural frequencies and dampings of In Situ tallbuildings using Ambient wind vibration data. Journal of Engineering mechanics,2004,130(5):570-577.
[113] Pines D, Salvino L. Structural health monitoring using empirical mode decomposition and theHilbert phase. Journal of Sound and Vibration,2006,294:97-124.
[114] Peng Z K, Peter W T, Chu FL. An improved Hilbert-Huang transform and its application invibration signal analysis. Journal of Sound and Vibration,2005,286:187-205.
[115] Rai V K, Mohanty A R. Bearing fault diagnosis using FFT of intrinsic mode functions inHilbert-Huang transform..Mechanical Systems and Signal Processing,2007,21:2607-2615.
[116] Babu T R, Srikanth S, Sekhar A S. Hilbert-Huang transform for detection and moinoring ofcrack in a transient rotor. Mechanical Systems and Signal Processing,2008,22:905-914.
[117] Yan R Q,Robert X G. Hilbert-Huang Transform-Based Vibration Signal Analysis for MachineHealth Monitoing.Transactions on Instrumentation and Measurement,2006,55(6):2320-2329.
[118] Mao Y M, Que P W. Application of Hilbert-Huang signal processing to ultrasonicnon-destructive testing of oil pipelines. Journal of Zhejiang University Science A,2006,7(2):130-134.
[119] Kazys R, Tumsys O, Pagodinas D. Ultrasonic detection of defects in strongly attenuatingstructures using the Hilbert-Huang transform. NDT&E Int,2008,41(6):457-466.
[120] Lu B, Upadhyaya B R, Perez R B.Structural Integrity Monitoring of Steam Generator TubingUsing Transient Acoustic Signal Analysis. Transactions on Nuclear Science,2005,52(1):484-493.
[121] Huang N E.,Martin J B, Liming S. Hilbert-Huang Transform Stability Spectral AnalysisApplied to Flutter Flight Test Data. AIAA Journal,2006,44(4):772-786.
[122] Chen H G, Yan Y J, Jiang J S. Vibration-based damage detectiong in composite wingboxstructures by HHT. Mechanical Systems and Signal Processing,2007,21:307-321.
[123]常鸣,袁慎芳.基于HHT技术的复合材料结构损伤定位研究.宇航学报.2006,27(1),144-150.
[124]孙亚杰,袁慎芳,王帮峰.基于HHT技术的二维结构损伤定位研究.压电与声光.2007,29(6):736-739.
[125]胡爱军. Hilbert-Huang变换在旋转机械振动信号分析中的应用研究,[博士学位论文].北京:华北电力大学,2008.
[126] Chapra S C, Canale R P.工程数值方法（于艳华，傅效群，赵红宇等译）.北京:清华大学出版社,2010.
[127]施浒立,颜毅华,徐国华.工程科学中的广义延拓逼近法.北京:科学出版社,2005.
[128]余波.自适应时频方法及其在故障诊断方法中的应用研究,[博士学位论文].大连:大连理工大学,1998.
[129]程军圣,于德介,杨宇.基于支持矢量回归机的Hilbert-Huang变换端点效应问题的处理方法.机械工程学报,2006,42(4):23-31.
[130]邓蕾,胡小林,李锋等.基于支持向量机的BS-EMD端点效应消除法.振动、测试与诊断,2011,31(3):344-347.
[131] Zhao J P. Improvement of the mirror extending in empirical mode decomposition method andthe technology for eliminating frequency mixing. High Technology Letters,2002，8(3):40-47.
[132]杨建文,贾民平.希尔伯特-黄谱的端点效应分析及处理方法研究.振动工程学报,2006,19(2):283-288.
[133] Huang D J. Practical implementaion of Hilbert-Huang transform algorithm. Acta OceanologicaSinica,2003,22(1):1-14.
[134]郑天翔,杨力华.经验模式分解算法的探讨和改进.中山大学学报,2007,46(1):2-6.
[135] Marcus D, Torsten S. Performance and limitations of the Hilbert–Huang transform (HHT) withan application to irregular water waves. Ocean Engineering,2004,31:1783-1834.
[136]杨世锡,胡劲松,吴昭同等.基于高次样条插值的经验模态分解方法研究.浙江大学学报(工学版),2004,38(3):267-270.
[137] Albena D V, Soares C G. Analysis of abnormal wave records by the Hilbert-Huang transformmethod. Journal of Atmospheric and Oceanic Technology,2007,24:1678-1689.
[138] http://perso.ens-lyon.fr/patrick.flandrin/emd.html
[139] Boashash B. Estimating and interpreting the instantaneous frequency of a signal-part II:Fundamentals. Proc. IEEE,1992,80(4):540-568.
[140]胡维平,莫家玲,杜明辉.经验模态分解中的频域分辨率及其改进方法.华南理工大学学报（自然科学版）,2007,35(5):15-19.
[141]郑祥明,赵玉珍,史耀武.兰姆波频散曲线的计算.无损检测,2003,25(3):66-68.
[142]彭鸽.基于Lamb波的结构健康监测主动监测技术研究,[博士学位论文].南京:南京航空航天大学,2006.
[143]耿荣生,沈功田,刘时风.模态声发射基本理论.无损检测,2002,24(7):302-306.
[144] Crawley E F, Luis J D. Use of piezoelectric actuators as elements of intelligent structures.AIAA Journal,1987,25(10):1373-1385.
[145] Crawley E F, Anderson E H. Detailed Models of Piezoceramic Actuation of Beams. Journal ofIntelligent Material Systems and Structures,1990,1(1):4-25.
[146]邱雷,袁慎芳.集成压电结构健康监测系统的研制及其应用.压电与声光,2008,30(1):39-42.
[147] Yuan S F, Xu Y D, Peng G. New Developments in Structural Health Monitoring Based onDiagnostic Lamb Wave. Journal of Material Science&Technology,2004,20(5):490-496.
[148]彭鸽,袁慎芳,徐颖娣.基于主动LAMB波和小波变换得二维结构损伤定位研究.振动工程学报,2004,17(4):488-493.
[149]马玉华,林文华.解析信号的瞬时相位与原始信号的等价关系.黑龙江大学自然科学学报,1995,12(3):56-60.
[150]李辉,郑海起,唐力伟.基于经验模态分解的瞬时相位分析方法的应用.振动、测试与诊断,2007,27(1):9-12.
[151]马宏伟,杨桂通.结构损伤探测的基本方法和研究进展.力学进展,1999,29(4):513-527.
[152] Gorman M R. Plate wave acoustic emission. JASA,1991,90(1):358-364.
[153]赵霞.多主体协作结构健康监测系统的关键技术研究,[博士学位论文].南京:南京航天航天大学,2008.
[154]耿荣生,沈功田,刘时风.模态声发射—声发射信号处理的得力工具,无损检测,2002,24（8）:341-345.