A Method for Incipient Fault Diagnosis of Roller Bearings Based on the Wavelet Transform Correlation Filter and Hilbert Transform

Noise is the biggest obstacle that makes the incipient fault diagnosis results of roller bearings uncorrected; a new method for diagnosing incipient fault of roller bearings based on the Wavelet Transform Correlation Filter and Hilbert Transform was proposed. First, the weak fault information features are picked up from the roller bearings fault vibration signals by use of a de-noising characteristic of the Wavelet Transform Correlation Filter as the preprocessing of the Hilbert Envelope Analysis. Then, in order to get fault features frequency, de-noised wavelet coefficients of high scales which represent high frequency signal were analyzed by Hilbert Envelope Spectrum Analysis. The simulation signals and diagnosing examples analysis results reveal that the proposed method is more effective than the method of direct wavelet coefficients-Hilbert Transform in de-noising and clarifying roller bearing incipient fault.

Determination of Instantaneous Frequencies of Low Plasma Waves in the Magnetosheath Using Empirical Mode Decomposition (EMD) and Hilbert Transform (HT)

The observations of in-situ spacecraft mission in the magnetosheath and a region of thermalized subsonic plasma behind the bow shock reveal a non-linear behaviour of plasma waves. The study of waves and optics in Physics has given the understanding of the effect of many waves coming together to form a wave field or wave packet. The common aspect of such study shows that two or more waves can superimpose constructively or destructively. The sudden high magnetic field data in the magnetosheath displays such possibility of superposition of waves. In this paper, we use the empirical mode decomposition (EMD) and Hilbert transform (HT) techniques to determine the instantaneous frequencies of low frequency plasma waves in the magnetosheath. Our analysis has shown that the turbulent behavior of magnetic field in the magnetosheath within the selected period is due to superposition of waves.

The Coherence Cube Computing Method with Self-adaptive Time Window Based on Wavelet Transform

The coherence cube technology has become an important technology for the seismic attribute interpretation, which extracts the discontinuities of the events through analyzing the similarities of adjacent seismic channels to identify the fault form. The coherence cube technology which uses constant time window lengths can not balance the shallow layers and the deep layers, because the frequency band of seismic data varies with time. When analyzing the shallow layers, the time window will crossover a lot of events, which will lead to weak focusing ability and failure to delineate the details. While the time window will not be long enough for analyzing deep layers, which will lead to low accuracy because the coherences near the zero points of the events are heavily influenced by noise. For solving the problem, we should make a research on the coherence cube technology with self-adaptive time window. This paper determines the sample points＆#39; time window lengths in real time by computing the instantaneous frequency bands with Wavelet Transformation, which gives a coherence computing method with the self-adaptive time window lengths. The result shows that the coherence cube technology with self-adaptive time window based on Wavelet Transformation improves the accuracy of fault identification, and supresses the noise effectively. The method combines the advantages of long time window method and short time window method.

Properties of an improved Gabor wavelet transform and its applications to seismic signal processing and interpretation

This paper presents an analytical study of the complete transform of improved Gabor wavelets （IGWs）, and discusses its application to the processing and interpretation of seismic signals. The complete Gabor wavelet transform has the following properties. First, unlike the conventional transform, the improved Gabor wavelet transform （IGWT） maps time domain signals to the time-frequency domain instead of the time-scale domain. Second, the IGW＇s dominant frequency is fixed, so the transform can perform signal frequency division, where the dominant frequency components of the extracted sub-band signal carry essentially the same information as the corresponding components of the original signal, and the sub- band signal bandwidth can be regulated effectively by the transform＇s resolution factor. Third, a time-frequency filter consisting of an IGWT and its inverse transform can accurately locate target areas in the time-frequency field and perform filtering in a given time-frequency range. The complete IGW transform＇s properties are investigated using simulation experiments and test cases, showing positive results for seismic signal processing and interpretation, such as enhancing seismic signal resolution, permitting signal frequency division, and allowing small faults to be identified.

Chandler Wobble Period and Q Derived by Wavelet Transform

We apply complex Morlet wavelet transform to three polar motion data series,and derive quasi-instantaneous periods of the Chandler and annual wobble by differencing the wavelettransform results versus the scale factor, and then find their zero points. The results show thatthe mean periods of the Chandler (annual) wobble are 430.71+-1.07 (365.24+-0.11) and 432.71+-0.42(365.23+-0.18) mean solar days for the data sets of 1900-2001 and 1940-2001, respectively. Themaximum relative variation of the quasi-instantaneous period to the mean of the Chandler wobble isless than 1.5% during 1900-2001 (3%-5% during 1920-1940), and that of the annual wobble is less than1.6% during 1900-2001. Quasi-instantaneous and mean values of Q are also derived by using theenergy density―period profile of the Chandler wobble. An asymptotic value of Q = 36.7 is obtainedby fitting polynomial of exponential of σ^(-2) to the relationship between Q and σ during1940-2001.

Transient Power and Quality Events Analysed Using Hilbert Transforms

This work presents an advanced mathematical tool applicable to the recognition and classification of power system transients and disturbances. Disturbances without a periodic pattern or with a non-linear pattern require a more suitable tool than the Fourier series （Fast Fourier or Windowed Fourier Transforms）. To overcome these drawbacks, other tools have been broadly used, such as the wavelet transform. However, the wavelet transform also has some drawbacks such as the lack of adaptivity or interpretation of nonlinear phenomena that the Hilbert and Hilbert Huang Transform techniques could mitigate. The Hilbert techniques transform a time domain function into a space representation both in time and frequency. In the paper, the technique is applied to analyse several short-term and steady events, like a short circuit, a capacitor-switching transient, or a line energisation, showing the abilities of the Hilbert-based transforms.

Phase-unwrapping algorithm combined with wavelet transform and Hilbert transform in self-mixing interference for individual microscale particle detection

The self-mixing interferometry(SMI)technique is an emerging sensing technology in microscale particle classification.However,due to the nature of the SMI effect raised by a microscattering particle,the signal analysis suffers from many problems compared with a macro target,such as lower signal-to-noise ratio(SNR),short transit time,and time-varying modulation strength.Therefore,the particle sizing measurement resolution is much lower than the one in typical displacement measurements.To solve these problems,in this paper,first,a theoretical model of the phase variation of a singleparticle SMI signal burst is demonstrated in detail.The relationship between the phase variation and the particle size is investigated,which predicts that phase observation could be another alternative for particle detection.Second,combined with continuous wavelet transform and Hilbert transform,a novel phase-unwrapping algorithm is proposed.This algorithm can implement not only efficient individual burst extraction from the noisy raw signal,but also precise phase calculation for particle sizing.The measurement shows good accuracy over a range from 100 nm to 6μm with our algorithm,proving that our algorithm enables a simple and reliable quantitative particle characteristics retrieval and analysis methodology for microscale particle detection in biomedical or laser manufacturing fields.

Bark-Wavelet Analysis and Hilbert -Huang Transform for Underwater Target Recognition

Recognizing the underwater targets by the radiated noise information is one of the most significant subjects in the area of underwater acoustics. Based on the theory of auditory perception, a novel recognition approach which consists of the algorithms of Bark-wavelet analysis, Hilbert-Huang transform and support vector machine is proposed. The performance of the proposed method is validated by comparing with traditional method and evaluated by the recognition experiments for SNRs of 0 dB, 5 dB, 10 dB, 15 dB and 20 dB.The results show that the average recognition rate of the method is above 88% and can be increased by 0.75 % to 6.25% under various SNR conditions compared to the baseline system.

Hilbert-Huang transform and wavelet analysis of time history signal

The brief theories of wavelet analysis and Hilbert-Huang transform (HHT) are introduced firstly in the present paper. Then several signal data were analyzed by using wavelet and HHT methods, respectively. The comparison shows that HHT is not only an effective method for analyzing non-stationary data, but also is a useful tool for examining detailed characters of time history signal.

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.

Seismic signal analysis based on the dual-tree complex wavelet packet transform

We tried to apply the dual-tree complex wavelet packet transform in seismic signal analysis. The complex wavelet packet transform (CWPT) combine the merits of real wavelet packet transform with that of complex continuous wavelet transform (CCWT). It can not only pick up the phase information of signal, but also produce better ″focal- izing″ function if it matches the phase spectrum of signals analyzed. We here described the dual-tree CWPT algo- rithm, and gave the examples of simulation and actual seismic signals analysis. As shown by our results, the dual-tree CWPT is a very effective method in analyzing seismic signals with non-linear phase.

IMPROVED METHOD FOR HILBERT INSTANTANEOUS FREQUENCY ESTIMATION

In the mechanical fault detection and diagnosis field, it is more and more important to analyze the instantaneous frequency （IF） character of complex vibration signal. The improved IF estimation method is put forward aiming at the shortage of traditional Hilbert transform. It is based on Hilbert transform in wavelet domain. With the help of relationship between the real part and the imaginary part obtained from the complex coefficient of continuous wavelet transform or the analyti- cal signal reconstructed in wavelet packet decomposition, the instantaneous phase function of the subcomponent is extracted. In order to improve the precise of IF estimated out, some means such as Linear regression, adaptive filtering, resampling are applied into the instantaneous phase obtained, then, the central differencing operator is used to get desired IF. Simulation results with synthetic and gearbox fault signals are included to illustrate the proposed method.

Extracting Power Transformer Vibration Features by a Time-Scale-Frequency Analysis Method

In order to take advantage of the merits of WPT and HHT in feature extraction from vibration signals of power transformer, a time-scale-frequency analysis method is developed based on the combination of these two techniques. This method consists of two steps. First, the desirable wavelet packet nodes corresponding to characteristic frequency bands of power transformer are selected through a Correlation Degree Threshold Screening (CDTS) technique for reconstructing a time-domain signal that contains useful information of power transformer. Second, the HHT is then conducted on the reconstructed signal to track the instantaneous frequencies corresponding to natural characteristics of power transformer. Experimental results are provided by analyzing a real power transformer vibration signal. Compared with the features extracted by directly using HHT, the features obtained by the proposed method reveal clearer condition pattern of the transformer, which shows the potential of this method in condition monitoring of power transformer.

Exploration of instantaneous frequency for local control assessment in real-time hybrid simulation

Local control parameters such as instantaneous delay and instantaneous amplitude play an essential role in evaluating the performance and maintaining the stability of real-time hybrid simulation(RTHS).However,existing methods have limitations in obtaining this local assessment in either the time domain or frequency domain.In this study,the instantaneous frequency is introduced to determine local control parameters for actuator tracking assessment in a real-time hybrid simulation.Instantaneous properties,including amplitude,delay,frequency and phase,are then calculated based on analytic signals translated from actuator tracking signals through the Hilbert transform.Potential issues are discussed and solutions are proposed for calculation of local control parameters.Numerical simulations are first conducted for sinusoidal and chirp signals with time varying amplitude error and delay to demonstrate the potential of the proposed method.Laboratory tests also are conducted for a predefined random signal as well as the RTHS of a single degree of freedom structure with a self-centering viscous damper to experimentally verify the effectiveness of the proposed use of the instantaneous frequency.Results from the ensuing analysis clearly demonstrate that the instantaneous frequency provides great potential for local control assessment,and the proposed method enables local tracking parameters with good accuracy.

基于Hilbert-Huang变换的电网故障行波定位方法

正确辨识和检测故障行波信号是实现电网故障行波定位的关键。提出了一种新的故障行波信号时频分析方法,采用Hilbert-Huang变换(HHT)对故障行波信号进行检测,通过经验模态分解(EMD)法提取故障行波信号的固有模态函数(IMF),再进行Hilbert变换,得到各自的瞬时频率,由瞬时频率进行行波到达时刻的准确检测。HHT与小波变换比较,不存在变换参数的选取难题,变换结果具有唯一性。仿真结果表明HHT能更准确地提取电网故障行波波头位置,有效提高故障行波定位精度。

Hilbert-Huang变换在电力系统过电压识别中的应用

将希尔伯特-黄变换(HHT)方法引入到过电压信号分类识别研究中,该方法由经验模态分解(EMD)与Hilbert变换两部分组成,能够定量、准确地对信号幅值及频率特征进行刻画。采用HHT方法对7种电力系统中常见的过电压信号进行了分析计算,结果表明HHT方法计算得到的瞬时幅值谱、Hilbert边际谱、Hilbert时频谱,能够作为特征量对不同种类型过电压进行分类识别。基于HHT算法与RBF神经网络搭建了过电压信号分层识别系统,并以实测过电压数据对其进行验证,结果表明,该分类识别系统能够有效地对过电压信号进行分类识别,并具有较高的识别率。

在频率域基于小波变换和Hilbert解析包络的CSEM噪声评价

传统CSEM一般只提取主频信号,或以谐波与主频的振幅比为依据提取部分低阶谐波信号,但缺乏判断标准,实际操作中存在很大的不确定性.本文基于小波变换和希尔伯特解析包络提出一种新的CSEM信号噪声评价方法,首先在时间域中基于混合基快速傅里叶变换获得原始信号准确功率谱;其次在频率域中根据CSEM频率位置相邻频率幅值进行频谱预处理,基于离散小波变换将预处理后的频谱分成低频部分和高频部分,基于希尔伯特变换识别高频部分的上包络线,并与低频部分重构得到频谱的整体上包络线;最后根据包络线与对应CSEM频率振幅的比值估计噪声的影响幅度,根据阈值筛选出高信噪比的主频和谐波信号.本方法不需增加野外工作量即可提取大量的频率信号,特别是高阶谐波信号,实现频率加密,提高CSEM的纵向分辨能力和能源利用率.

信号瞬时频率直接计算法与Hilbert变换及Teager能量法比较

针对Hilbert变换求取信号瞬时频率时会出现没有物理意义的负频率现象,研究基于局域均值分解的瞬时频率直接计算方法。给出相位展开分段计算方法的详细计算步骤。直接法与直接正交法进行了比较,直接法和直接正交法在数学上相等,计算结果相同,可以认为是同一种方法。直接法也与Hilbert变换、Teager能量方法进行比较。仿真和试验结果表明,直接法计算结果能很好地反映信号的相位调制现象,没有明显的端点效应,不会出现负频率现象。直接法应用于旋转机械振动信号的分析,取得良好效果。

利用Hilbert变换提取信号瞬时特征参数的问题研究

解析Hilbert变换利用其实部与虚部的关系,定义出任意时刻的瞬时频率、瞬时相位及瞬时幅度,因而工程中人们设法将其应用对实际信号的瞬时参数提取中。然而,在利用Hilbert变换提取瞬时特征参数的工程实现中存在一些问题,如何解决这些问题,特别是如何高精度提取瞬时频率特征参数问题是文中的研究重点。