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。

基于改进Hilbert-Huang变换的管路环向裂纹故障诊断研究

在制造、加工、装配以及服役过程中,航空液压管路可能存在平面型缺陷。在适航载荷作用下,这些缺陷会萌生裂纹并发生扩展,最终导致管路破裂和油液泄漏。为了在管路产生微裂纹时对其进行故障诊断,采用了自行搭建的航空液压管路模态试验平台和测控系统,对存在环向裂纹航空液压管路的振动信号进行了采集和预处理。而在对管路振动信号进行分解时,由于经验模态分解(Empirical Mode Decomposition,EMD)算法存在模态混叠问题难以获得准确的本征模态函数(Intrinsic Mode Functions,IMF)。为提高信号处理精度,提出一种基于自适应噪声完备经验模态分解(Complete Ensemble Empirical Mode Decomposition with Adaptive Noise,CEEMDAN)和Hilbert变换理论相结合的改进Hilbert-Huang变换方法对航空液压管路环向裂纹进行故障诊断。研究结果表明,该方法能够更准确地诊断航空液压管路的环向裂纹故障。

基于Hilbert变换的条纹-灰度线性投影三维测量

针对传统的条纹投影测量中绝对相位求解方法存在投影图像数量较多以及算法复杂程度高的问题,提出了一种基于Hilbert变换的条纹-灰度线性投影策略及相位求解方法,该方法仅使用3幅投影图像——1幅高频条纹图和2幅灰度线性变化图,通过Hilbert变换求得包裹相位,采用灰度线性变化图像得到基础相位,联立包裹相位和基础相位可得到条纹级数,进而得到绝对相位。通过构建的主动双目系统得到的三维重构结果发现,该方法可以有效恢复被测物体的三维形状,测量精度可达0.1 mm。

基于CEEMDAN-Hilbert变换的水下爆炸信号时频分析方法研究

研究水下爆炸冲击波信号的时频特性,对于舰艇利用弹药水下爆炸信号对抗自导鱼雷具有重要的实际意义。本文针对EMD-Hilbert方法中经验模态分解(EMD)存在模态混叠的问题,提出CEEMDAN-Hilbert方法实现水下爆炸冲击波信号精确的时频分析。在水深100 m处单发炸药爆炸,产生爆炸信号的频率主要分布在56.5 kHz以下的低频段,特别是0~28.3 kHz以下的能量最大,高于56.5 kHz的能量较少。通过与EMD-Hilbert方法相比,CEEMDAN-Hilbert方法在28.3~56.5 kHz频段的能量分布会更加明显,具有一定的优越性。

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.

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.

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.

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.

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.

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.

Quantum Mechanical Hilbert Transformation for Normally Ordering Coulomb Potential-Type Operators

We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.

Hilbert C^(*)-模中g-Riesz基的对偶性

本文研究Hilbert C^(*)-模中g-Riesz基的对偶性问题.利用算子理论方法,获得了Hilbert C^(*)-模中的给定序列是g-Riesz基且有唯一对偶g-框架的充要条件,g-Riesz基的对偶g-框架是g-Riesz基的充要条件,以及g-Riesz基成为无冗g-框架的充分条件,所得结果进一步展示了g-框架理论在Hilbert C^(*)-模与Hilbert空间中的差异性.

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.

Causes and solutions of overshoot and undershoot and end swing in Hilbert-Huang transform

There are overshoot and undershoot phenomenon and end swing phenomenon in the cubic spline fitting in Hil- bert-Huang transform. The two problems influence data quality of the empirical mode decomposition seriously. The cubic spline fitting has been analysed, and the causes of producing the overshoot and undershoot phenomenon and the end swing phenomenon have been pointed out in this paper. Two new methods of cubic spline fitting and sine spline fitting and the new technique of handling the end points of the original data curve can completely re- move the overshoot and undershoot phenomenon and the end swing phenomenon on the condition of unchanging original data, and have the advantages of the continuous fitting functions and its continuous one order derivative, the simple and convenient calculations, the small calculation amount and the easy work on it.

Transmission Lines Distance Protection Using Differential Equation Algorithm and Hilbert-Huang Transform

This paper proposed the scheme of transmission lines distance protection based on differential equation algorithms (DEA) and Hilbert-Huang transform (HHT). The measured impedance based on EDA is affected by various factors, such as the distributed capacitance, the transient response characteristics of current transformer and voltage transformer, etc. In order to overcome this problem, the proposed scheme applies HHT to improve the apparent impedance estimated by DEA. Empirical mode decomposition (EMD) is used to decompose the data set from DEA into the intrinsic mode functions (IMF) and the residue. This residue has monotonic trend and is used to evaluate the impedance of faulty line. Simulation results show that the proposed scheme improves significantly the accuracy of the estimated impedance.

Phase Error Compensation of Three-Dimensional Reconstruction Combined with Hilbert Transform

Nonlinear response is an important factor affecting the accuracy of three-dimensional image measurement based on the fringe structured light method.A phase compensation algorithm combined with a Hilbert transform is proposed to reduce the phase error caused by the nonlinear response of a digital projector in the three-dimensional measurement system of fringe structured light.According to the analysis of the influence of Gamma distortion on the phase calculation,the algorithm establishes the relationship model between phase error and harmonic coefficient,introduces phase shift to the signal,and keeps the signal amplitude constant while filtering out the DC component.The phase error is converted to the transform domain,and compared with the numeric value in the space domain.The algorithm is combined with a spiral phase function to optimize the Hilbert transform,so as to eliminate external noise,enhance the image quality,and get an accurate phase value.Experimental results show that the proposed method can effectively improve the accuracy and speed of phase measurement.By performing phase error compensation for free-form surface objects,the phase error is reduced by about 26%,and about 27%of the image reconstruction time is saved,which further demonstrates the feasibility and effectiveness of the method.

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.

Hilbert-Huang变换与大地电磁噪声压制

大地电磁信号具有非线性、非平稳、非最小相位特征,不符合以Fourier变换为基础的传统功率谱估计的基本要求.Hilbert-Huang变换是近年发展起来的处理非线性、非平稳信号的完全局部时频分析方法.本文在简要介绍Hilbert-Huang变换基本原理与算法基础上,以实际数据分析为例,探讨了它在大地电磁信号处理及噪声压制中的应用.提出利用Hilbert时-频能量谱对大地电磁信号进行时段筛选,以提高信号品质,增强数据处理的质量和资料的可解释性.利用经验模态分解方法及其多尺度滤波特征,可以有效地分析MT信号中的噪声分布特征,并进行干扰压制.