Optimization of the End Effect of Hilbert-Huang transform(HHT)

In fault diagnosis of rotating machinery, Hil- bert-Huang transform （HHT） is often used to extract the fault characteristic signal and analyze decomposition results in time-frequency domain. However, end effect occurs in HHT, which leads to a series of problems such as modal aliasing and false IMF （Intrinsic Mode Func- tion）. To counter such problems in HHT, a new method is put forward to process signal by combining the general- ized regression neural network （GRNN） with the bound- ary local characteristic-scale continuation （BLCC）. Firstly, the improved EMD （Empirical Mode Decompo- sition） method is used to inhibit the end effect problem that appeared in conventional EMD. Secondly, the gen- erated IMF components are used in HHT. Simulation and measurement experiment for the cases of time domain, frequency domain and related parameters of Hilbert- Huang spectrum show that the method described here can restrain the end effect compared with the results obtained through mirror continuation, as the absolute percentage of the maximum mean of the beginning end point offset and the terminal point offset are reduced from 30.113% and 27.603% to 0.510% and 6.039% respectively, thus reducing the modal aliasing, and eliminating the false IMF components of HHT. The proposed method caneffectively inhibit end effect, reduce modal aliasing and false IMF components, and show the real structure of signal components accuratelX.

基于自适应小波变换与HHT的混合储能容量配置

混合储能系统能有效缓解风电输出功率强波动性与随机性造成电网频率不稳定问题。本文以蓄电池和超级电容组成的混合储能系统为研究对象,提出了一种混合储能容量配置方法。该方法首先采用自适应小波变换对风电输出功率进行功率一次分配,得到满足条件的并网功率和储能功率。然后采用HHT变换对储能功率进行分解,得到一系列波动功率分量以及各分量的瞬时频率。再根据瞬时频率确定分界频率,将高于分界频率的功率分量分配给超级电容,剩余的功率分量分配给蓄电池。最后根据蓄电池与超级电容各自的储能功率,对储能系统的额定容量与额定功率进行配置。该仿真结果表明,本文采用自适应小波变换与HHT变换能够有效地将风电输出功率进行分解,实现风电输出功率的平抑与混合储能系统的容量与功率配置。

基于EEMD-HHT的边坡爆破振动信号分析

爆破工程所处的环境一般复杂多变,爆破振动信号大多呈现瞬时非平稳性特征。因此,为了准确分析爆破振动的信号特征以及传播规律,以首都环线高速公路承平段路基爆破工程为背景,通过引入EEMD分解方法,解决了传统EMD分解方法存在模态混叠的不足;结合HHT变换,对承平段典型路堑边坡岩体爆破振动信号进行了分析。研究结果表明:采用EEMD分解方法提取爆破振动信号中主要的IMF能量层,并对振动信号进行重构,可以达到良好的去噪效果;对施工现场爆破振动信号进行主成分分析、提取之后,瞬时能量和质点振速曲线整体平滑度显著提高,振动信号主成分提取效果良好;Hilbert能量谱可以清晰地体现时间、频率与能量三者之间的关系,展现出了爆破振动信号的时频特性和传播规律;测点振动主频主要分布在10~40 Hz的频率段范围内,近似呈现出随着传播距离的增加而衰减、随着距离的增加衰减幅度减弱的趋势。该分析成果对边坡稳定性分析和邻近建筑物的安全控制具有重要的现实意义。

Fault Diagnosis for Buckling Friction Components in Wet Multi-Disc Clutches Using IHHT

The wet multi-disc clutches are extensively used in various transmission systems,withone of the most prevalent failure modes being the buckling deformation of friction components.Animproved Hilbert-Huang transform method(IHHT)is proposed to address the limitations of tradi-tional time-domain vibration analyses,such as low accuracy and mode mixing.This paper first clas-sifies the buckling degree of the friction components.Next,wavelet packet transform(WPT)isapplied to the vibration signals of different buckling plates to partition them into distinct fre-quency bands.Then,the instantaneous features are extracted by empirical mode decomposition(EMD)and Hilbert transform(HT)to discarding extraneous intrinsic mode function(IMF)com-ponents.Comparative analyses of Hilbert spectral entropy and time-domain features confirm theenhanced precision of IHHT under specific classifiers,which is better than traditional methods.

Efficacy of Hilbert-Huang Transform (HHT) in the Analysis of Instantaneous Low Frequency Waves of Magnetosheath

The flow of supersonic plasma is accompanied by a highly thermalized region called the Magnetoshealth found after the bow shock. Enclosed within this region are different wave modes associated with classes of boundaries which have been determined by different methods. The efficacy of Hilbert-Huang transform (HHT) is based on the conditionality of allowing for the local analysis of frequencies, which presents the physical meaning of the original signal at that instant. The observed data have been taken from Cluster II Fluxgate Magnetometer (FGM) instrument that provides advantage for the analysis in three dimensions. The result compares favourably with instantaneous frequencies computed using simple Hilbert transform (SHT) with electric field measurements of Cluster II mission already carried out in literatures. The result of this study has shown that HHT provides the best applicability in the magnetosheath data analysis than the wavelet and Fast Fourier Transform (FFT). The application of HHT based on its advantages over other methods is viewed to be very critical in the analysis of multi-frequency signals where different frequencies could be determined distinctively at a point.

Efficacy of Hilbert-Huang Transform (HHT) in the Analysis of Instantaneous Low Frequency Waves of Magnetosheath

The flow of supersonic plasma is accompanied by a highly thermalized region called the Magnetoshealth found after the bow shock. Enclosed within this region are different wave modes associated with classes of boundaries which have been determined by different methods. The efficacy of Hilbert-Huang transform (HHT) is based on the conditionality of allowing for the local analysis of frequencies, which presents the physical meaning of the original signal at that instant. The observed data have been taken from Cluster II Fluxgate Magnetometer (FGM) instrument that provides advantage for the analysis in three dimensions. The result compares favourably with instantaneous frequencies computed using simple Hilbert transform (SHT) with electric field measurements of Cluster II mission already carried out in literatures. The result of this study has shown that HHT provides the best applicability in the magnetosheath data analysis than the wavelet and Fast Fourier Transform (FFT). The application of HHT based on its advantages over other methods is viewed to be very critical in the analysis of multi-frequency signals where different frequencies could be determined distinctively at a point.

基于Hilbert-Huang Transform的心音信号谱分析

心音信号是一种典型的非平稳信号 ,传统信号处理方法的应用受到很大限制。针对此本文提出了基于Hilbert-HuangTransform(HHT)的心音信号的分析方法 ,对冠心病患者的心音信号进行了分析。通过把心音信号分解为内蕴模式函数 ,利用Hilbert变换建立了心音信号的时间 -频率 -能量三维Hilbert谱分布以及边界谱分布 ;Hilbert谱及其边界谱在时域以及频域以较高的分辨率表征了心音信号的时频变化特性 ,揭示了冠心病患者心音信号的病理特征 ;为冠心病的早期无损诊断奠定了坚实基础 ,临床实践中有较大的指导价值。

Analysis of the characteristics of gastrointestinal motility based on Hilbert-Huang transform method

Pressure activity data as an important index of gastrointestinal （GI） motility can be obtained from the wireless radiotelemetry capsule. The Hilbert-Huang transform （HHT） method, which is more effective to process non-stationary signal, is proposed to identify the characteristics of GI motility. We decompose the pressure activity data into intrinsic mode functions （IMFs）, calculate the Hi/bert marginal spectrum and attain the peristalsis characteristics of GI tract. The IMFs represent the peristalses modes of GI tract activity embedded in the pressure data. The time-varying characteristic of the method suggests that the HHT is suitable to accommodate other non-stationary biomedical data analysis.

基于小波阈值去噪与HHT滚动轴承故障诊断

针对噪音比较强烈环境下的故障诊断问题,提出了一种小波阈值去噪与希尔伯特黄变换(HHT)相结合提取轴承信号故障的方法。首先采集滚动轴承在运作时的振动信号,选取合适的小波阈值对采集到的时域信号进行去噪处理。采用HHT对信号进行时频分析,将去噪信号分解为若干个固有模态函数分量(IMF)并对其进行希尔伯特变换(HT),最终从希尔伯特边际谱得到故障频率从而判定轴承是否发生故障。试验结果表明,上述方法可以有效地降低噪声信号对HHT对轴承故障诊断的影响,更好的保留了有用的信息,提高故障诊断的准确性和可靠性。

Practical implementation of Hilbert-Huang Transform algorithm

Hilbert-Huang Transform (HHT) is a newly developed powerful method for nonlinear and non-stationary time series analysis. The empirical mode decomposition is the key part of HHT, while its algorithm was protected by NASA as a US patent, which limits the wide application among the scientific community. Two approaches, mirror periodic and extrema extending methods, have been developed for handling the end effects of empirical mode decomposition. The implementation of the HHT is realized in detail to widen the application. The detailed comparison of the results from two methods with that from Huang et al. (1998, 1999), and the comparison between two methods are presented. Generally, both methods reproduce faithful results as those of Huang et al. For mirror periodic method (MPM), the data are extended once forever. Ideally, it is a way for handling the end effects of the HHT, especially for the signal that has symmetric waveform. The extrema extending method (EEM) behaves as good as MPM, and it is better than MPM for the signal that has strong asymmetric waveform. However, it has to perform extrema envelope extending in every shifting process.

基于改进的HHT-SVM微震信号特征提取及分类识别研究

为了解决实际工程中微震信号与爆破信号在波形上具有较强相似性,难以识别的问题,提出基于改进HHT-SVM的微震信号识别方法。分析2种信号的瞬时能量变化规律,发现微震信号具有孕育速度慢、持续时间短及峰后衰减速度慢的特点,对其进行量化处理并提取特征,构建多维特征向量。对输入的特征向量经功率谱熵特征加权算法赋予权重,并使用GSWOA算法对SVM进行参数寻优,建立信号识别网络对微震信号、爆破信号进行识别。研究结果表明:方法的综合识别成功率达到96.250%,能够有效识别微震、爆破信号。研究结果可为后续利用微震信号进行灾害预警提供有力支撑。

AE waveform characteristics of rock mass under uniaxial loading based on Hilbert-Huang transform

Acoustic Emission(AE)waveforms contain information on microscopic structural features that can be related with damage of coal rock masses.In this paper,the Hilbert-Huang transform(HHT)method is used to obtain detailed structural characteristics of coal rock masses associated with damage,at different loading stages,from the analyses of the characteristics of AE waveforms.The results show that the HHT method can be used to decompose the target waveform into multiple intrinsic mode function(IMF)components,with the energy mainly concentrated in the c1−c4 IMF components,where the c1 component has the highest frequency and the largest amount of energy.As the loading continues,the proportion of energy occupied by the low-frequency IMF component shows an increasing trend.In the initial compaction stage,the Hilbert marginal spectrum is mainly concentrated in the low frequency range of 0−40 kHz.The plastic deformation stage is associated to energy accumulation in the frequency range of 0−25 kHz and 200−350 kHz,while the instability damage stage is mainly concentrated in the frequency range of 0−25 kHz.At 20 kHz,the instability damage reaches its maximum value.There is a relatively clear instantaneous energy peak at each stage,albeit being more distinct at the beginning and at the end of the compaction phase.Since the effective duration of the waveform is short,its resulting energy is small,and so there is a relatively high value from the instantaneous energy peak.The waveform lasts a relatively long time after the peak that coincides with failure,which is the period where the waveform reaches its maximum energy level.The Hilbert three-dimensional energy spectrum is generally zero in the region where the real energy is zero.In addition,its energy spectrum is intermittent rather than continuous.It is therefore consistent with the characteristics of the several dynamic ranges mentioned above,and it indicates more clearly the low-frequency energy concentration in the critical stage of instability failure.This study well reflects the response law of geophysical signals in the process of coal rock instability and failure,providing a basis for monitoring coal rock dynamic disasters.

Structural modal parameter identifi cation and damage diagnosis based on Hilbert-Huang transform

Traditional modal parameter identifi cation methods have many disadvantages,especially when used for processing nonlinear and non-stationary signals.In addition,they are usually not able to accurately identify the damping ratio and damage.In this study,methods based on the Hilbert-Huang transform(HHT) are investigated for structural modal parameter identifi cation and damage diagnosis.First,mirror extension and prediction via a radial basis function(RBF) neural network are used to restrain the troublesome end-effect issue in empirical mode decomposition(EMD),which is a crucial part of HHT.Then,the approaches based on HHT combined with other techniques,such as the random decrement technique(RDT),natural excitation technique(NExT) and stochastic subspace identifi cation(SSI),are proposed to identify modal parameters of structures.Furthermore,a damage diagnosis method based on the HHT is also proposed.Time-varying instantaneous frequency and instantaneous energy are used to identify the damage evolution of the structure.The relative amplitude of the Hilbert marginal spectrum is used to identify the damage location of the structure.Finally,acceleration records at gauge points from shaking table testing of a 12-story reinforced concrete frame model are taken to validate the proposed approaches.The results show that the proposed approaches based on HHT for modal parameter identifi cation and damage diagnosis are reliable and practical.

A technique to improve the empirical mode decomposition in the Hilbert-Huang transform

The Hilbert-based time-frequency analysis has promising capacity to reveal the time-variant behaviors of a sys- tem.To admit well-behaved Hilbert transforms,component decomposition of signals must be performed beforehand.This was first systematically implemented by the empirical mode decomposition(EMD)in the Hilbert-Huang transform,which can provide a time-frequency representation of the signals.The EMD,however,has limitations in distinguishing different components in narrowband signals commonly found in free-decay vibration signals.In this study,a technique for decompo- sing components in narrowband signals based on waves' beating phenomena is proposed to improve the EMD,in which the time scale structure of the signal is unveiled by the Hilbert transform as a result of wave beating,the order of component ex- traction is reversed from that in the EMD and the end effect is confined.The proposed technique is verified by performing the component decomposition of a simulated signal and a free decay signal actually measured in an instrumented bridge structure.In addition,the adaptability of the technique to time-variant dynamic systems is demonstrated with a simulated time-variant MDOF system.

Application of Hilbert-Huang transform to denoising in vortex flowmeter

Due to piping vibration, fluid pulsation and other environmental disturbances, variations of amplitude and frequency to the raw signals of vortex flowmeter are imposed. It is difficult to extract vortex frequencies which indicate volumetric flowrate from noisy data, especially at low flowrates. Hilbert-Huang transform was adopted to estimate vortex frequency. The noisy raw signal was decomposed into different intrinsic modes by empirical mode decomposition, the time-frequency characteristics of each mode were analyzed, and the vortex frequency was obtained by calculating partial mode’s instantaneous frequency. Experimental results show that the proposed method can estimate the vortex frequency with less than 2% relative error; and in the low flowrate range studied, the denoising ability of Hilbert-Huang transform is markedly better than Fourier based algorithms. These findings reveal that this method is accurate for vortex signal processing and at the same time has strong anti-disturbance ability.

基于EEMD-HHT的隧道爆破振动信号分析

为准确分析隧道爆破振动信号特征,基于EEMD-HHT方法对现场实测的爆破振动信号进行时频和能量分析。结果表明:EEMD算法可有效改善EMD分解产生的信号模态混叠效应;采用去噪指标对EMD和EEMD分解的信号进行量化评价,其中EEMD分解得到的信号去噪比较大,均方根差更小,即EEMD算法的去噪效果优于EMD;通过EEMD-HHT分析,能有效反映爆破振动信号的时间-频率-能量之间的关系;通过对爆破信号频带能量提取,发现在试验条件下爆破振动信号主振频带范围在41~50Hz,其余各频带能量围绕主频带呈现正态分布,0~10Hz低频带占据总能量的7.84%,爆破施工时应采取相应措施避免隧道衬砌结构发生共振现象。

Application of Hilbert-Huang Transform to the Analysis of the Landslides Triggered by the Wenchuan Earthquake

A steep rock hill with two side slopes located at DK30＋256 of National Road 213 was used as a prototype for analysis. The full process from initial deformation to sliding of the slope during ground shaking was simulated by using a new Continuum-based Discrete Element Method. During the earthquake, when shaking amplitudes were lower, the stress concentration points firstly appeared at the top of the slip mass, and then some tension failure points appeared, followed by shear failure points. At the same time, both the instantaneous frequencies of accelerations in the bedrock and that in the slip mass basically stayed in two different ranges. The energy transmittance coefficients of the sliding surface also stayed in a high range. As the ground shaking lasted, the number of failure points gradually increased until landslide occurrence. The instantaneous frequencies of accelerations in the slip mass and the energy transmittance coefficients of sliding surface gradually decreased, and both finally converged to a lower range. And then, the reasons triggering landslides are analysis in the joint time-frequency domain using Hilbert-Huang Transform, as follows： the differenees of distribution and dissipation of the earthquake energy and the inconsistency of movements between the slip mass and the bedrock were the two major influence factors.

Modal identification based on Hilbert-Huang Transform of structural response with S VD preprocessing

In recent years, Empirical mode decomposition and Hilbert spectral analysis have been combined to identify system parameters. Singular-Value Decomposition is pro- posed as a signal preprocessing technique of Hilbert-Huang Transform to extract modal parameters for closely spaced modes and low-energy components. The proposed method is applied to a simulated airplane model built in Automatic Dynamic Analysis of Mechanical Systems software. The results demonstrate that the identified modal parameters are in good agreement with the baseline model.

Mode Recognition of Lamb Wave Detecting Signals in Metal Plate Using the Hilbert-Huang Transform Method

The dispersion and multiple modes characteristics which exist in the propagation of Lamb waves (LW) in metal plates make it extremely hard to analyze and recognize the detection echo signals of defects. As a newly developed time-frequency analysis method in recent years, Hilbert-Huang transform (HHT) is one of the powerful tools to analyze non-stationary signals. The experimental LW detecting system for single aluminum plate is setup in this work, and the LW detecting signals are analyzed by HHT. The overlapped LW detecting signals of different modes are recognized by the means of extracting flight time of intrinsic mode functions (IMFs) after Hilbert transform (HT). The experiment results, agreeing well with the theoretical analysis, indicate that the HHT method can clearly recognize overlapped LW detecting signals of different modes in metal plates, but could hardly recognize that of the same mode. HHT can be an effective method to recognize LW detecting signals of different modes in metal plates.

利用声信号基于HHT方法识别螺旋桨模态参数

为了对螺旋桨的模态参数进行无接触式测量,首先基于声学边界元方法,建立了螺旋桨在冲击载荷作用下辐射声信号与模态参数之间的数学模型,该模型相比于已公开文献采用的模型,从理论上揭示了采样声信号不必须取自于结构近场。在此基础上,借助希尔伯特-黄变换(Hilbert-Huang transform, HHT)方法处理非平稳、非线性信号,对采样声信号进行处理来识别结构模态参数。以一螺旋桨缩尺模型为研究对象,分别采用数值模拟和试验手段对该方法的实用性和有效性进行了验证,并评估了环境噪声的影响程度。结果显示该方法能准确识别模态频率和阻尼比,且具有自适应频率分辨率,为工程上精细结构的模态参数识别提供一种新途径。