Wigner-Ville distribution and cross Wigner-Ville distribution of noisy signals

The Wigner-Ville distribution （WVD） and the cross Wigner-Ville distribution （XWVD） have been shown to be efficient in the estimation of instantaneous frequency （IF）. But the statistical result of the IF estimation from XWVD peak is much better than using WVD peak. The reason is given from a statistical point of view. Theoretical studies show that XWVD of the analyzed signal can be estimated from XWVD of the noise-contaminated signal. The estimation is unbiased, and the variance is equal to that of noise. In this case, WVD cannot be estimated from W-VD of the noise-contaminated signal. Therefore, higher SNR is required when WVD is used to analyze signals.

Statistical Performance of the Wigner-Ville Distribution and the Cross Wigner-Ville Distribution

This paper analyzes statistical performances of the Wigner-Ville distribution (WVD) and the cross Wigner-Ville distribution (XWVD). Theoretical studies show that XWVD of the analyzed signal can be estimated from XWVD of the noise-contaminated signal . The estimation is unbiased, and the variance is equal to that of noise. In this case, WVD cannot be estimated from WVD of the noise-contaminated signal . Therefore higher SNR is required when using WVD.

Reservoir information extraction using a fractional Fourier transform and a smooth pseudo Wigner-Ville distribution

Currently, it is difficult for people to express signal information simultaneously in the time and frequency domains when analyzing acoustic logging signals using a simple-time or frequency-domain method. It is difficult to use a single type of time-frequency analysis method, which affects the feasibility of acoustic logging signal analysis. In order to solve these problems, in this paper, a fractional Fourier transform and smooth pseudo Wigner Ville distribution （SPWD） were combined and used to analyze array acoustic logging signals. The time-frequency distribution of signals with the variation of orders of fractional Fourier transform was obtained, and the characteristics of the time-frequency distribution of different reservoirs under different orders were summarized. Because of the rotational characteristics of the fractional Fourier transform, the rotation speed of the cross terms was faster than those of primary waves, shear waves, Stoneley waves, and pseudo Rayleigh waves. By choosing different orders for different reservoirs according to the actual circumstances, the cross terms were separated from the four kinds of waves. In this manner, we could extract reservoir information by studying the characteristics of partial waves. Actual logging data showed that the method outlined in this paper greatly weakened cross-term interference and enhanced the ability to identify partial wave signals.

Wigner-Ville distribution and its application in seismic attenuation estimation

The attenuation of seismic signals is often characterized in the frequency domain using statistical measures of the power spectrum. However, the conventional Fourier transform-based power spectrum estimation methods suffer from time-frequency resolution problems. Wigner-Ville distribution, which is a member of Cohen class time-frequency distributions, possesses many appealing properties, such as time-frequency marginal distribution, time-frequency localization, etc. Therefore, Wigner-Ville distribution offers a new way for estimating the attenuation of seismic signals. This paper initially gives a brief introduction to Wigner-Ville distribution and the smoothed Wigner-Ville distribution that is effective in reducing the cross-term effect, and then presents a method for seismic attenuation estimation based on the instantaneous energy spectrum of the Wigner-Ville distribution. A real data example from central Tarim Basin in western China is presented to illustrate the effectiveness of the proposed method. The results show that the Wigner-Ville distribution-based seismic attenuation estimation method can effectively detect the difference between reef, shoal and lagoon facies by their attenuation properties, indicating that the estimated seismic attenuation can be used for reef and shoal carbonate reservoir characterization.

Improvement on polynomial Wigner-Ville distribution for detecting higher-order polynomial phase signal

To detect higher order polynomial phase signals （HOPPSs）, the smoothed-pseudo polynomial Wigner-Ville distribution （SP-PVCVD）, an improved version of the polynomial Wigner-Ville distribution （PVCVD）, is presented using a separable kernel. By adjusting the lengths of the functions in the kernel, the balance between resolution retaining and interference suppressing can be adjusted conveniently. The proposed method with merits of interference terms reduction and noise suppression can provide time frequency representation of better readability and more accurate instantaneous frequency （IF） estimation with higher order SP-PVfVD. The performance of the SP-PWVD is verified by computer simulations.

SORTING RADAR SIGNAL BASED ON WAVELET CHARACTERISTICS OF WIGNER-VILLE DISTRIBUTION

Common sorting method have low sorting rates and is sensitive to the Signal-to-Noise Ratio(SNR),wavelet characteristics of Wigner-Ville distribution are applied to sort unknown complicated radar signal,high sorting accuracy can be got.The Wigner-Ville distribution of received signal is calculated,then it is predigested to two-dimensional characteristics.Using wavelet transformation to extract characteristics from two-dimensional of Wigner-Ville distribution,the best characteristics are selected to be used as sorting parameters.Experiment results demonstrated that the characteristics of eight typical radar emitter signals extracted by this method showed good performance of noise-resistance and clustering at large-scale SNR.

A microscopic ancient river channel identification method based on maximum entropy principle and Wigner-Ville Distribution and its application

In view of the problem of fine characterization of narrow and thin channels,the maximum entropy criterion is used to enhance the focusing characteristics of Wigner-Ville Distribution.On the basis of effectively improving the time-frequency resolution of seismic signal,a new method of microscopic ancient river channel identification is established.Based on the principle of the equivalence between the maximum entropy power spectrum and the AR model power spectrum,the prediction error and the autoregression coefficient of AR model are obtained using the Burg algorithm and Levinson-Durbin recurrence rule.Under the condition of the first derivative of autocorrelation function being 0,the Wigner-Ville Distribution of seismic signal is calculated,and the Wigner-Ville Distribution time-frequency power spectrum(MEWVD)is obtained under the maxi-mum entropy criterion of the microscopic ancient river channel.Through analysis of emulational seismic signal and forward numerical simulation signal of narrow thin model,it is found that MEWVD can effectively avoid the interference of cross term of Wigner-Ville Distribution,and obtain more accurate spectral characteristics than STFT and CWT signal analysis methods.It is also proved that the narrow and thin river channels of different scales can be identified effectively by MEWVD of different frequencies.The method is applied to the third member of Jurassic Shaximiao Formation(J2s33-2)gas reservoir of the Zhongji-ang gas field in Sichuan Basin.The spatial information of width and direction of narrow and thin river channels with width less than 500 m and sandstone thickness less than 35 m is accurately identified,providing bases for well deployment and horizontal well fracturing section selection.

Application of spectral decomposition technology in shallow gas detection based on Wigner-Ville distribution

Shallow gas is composed of all kinds of shallow buried natural gas resources( < 1500 m) with relatively small reserve for each gas resource. It has some advantages such as shallow burial depth,good physical properties and the huge accumulations. Based on the Wigner-Vill distribution,a general spectral decomposition method is applied in the shallow gas detection. Cone-shaped kernel function filtering method is used to suppress cross-terms of the Wigner-Ville distribution,which is tested on field seismic data. Because of shallow gas reservoir has a characteristic that low frequency energy is stronger and high frequency energy is weaker,it indicates the presence of shallow gas successfully.

STUDY OF ROLLING FORCE DISTRIBUTION ALONG THE ROLLING OF PAIR CROSS MILL

The theory of three-dimensional deformation is used.Based on rigid plastic assumption, the theory of stick friction and the sheet crown curve at the entry and the exit are used. The mathematical analytical formula of the rolling force in lateral distribution is deriven.

Dynamic Distribution Adaptation Based Transfer Network for Cross Domain Bearing Fault Diagnosis

In machinery fault diagnosis,labeled data are always difficult or even impossible to obtain.Transfer learning can leverage related fault diagnosis knowledge from fully labeled source domain to enhance the fault diagnosis performance in sparsely labeled or unlabeled target domain,which has been widely used for cross domain fault diagnosis.However,existing methods focus on either marginal distribution adaptation(MDA)or conditional distribution adaptation(CDA).In practice,marginal and conditional distributions discrepancies both have significant but different influences on the domain divergence.In this paper,a dynamic distribution adaptation based transfer network(DDATN)is proposed for cross domain bearing fault diagnosis.DDATN utilizes the proposed instance-weighted dynamic maximum mean discrepancy(IDMMD)for dynamic distribution adaptation(DDA),which can dynamically estimate the influences of marginal and conditional distribution and adapt target domain with source domain.The experimental evaluation on cross domain bearing fault diagnosis demonstrates that DDATN can outperformance the state-of-the-art cross domain fault diagnosis methods.

Three‑dimensional numerical simulation of dynamic strength and failure mode of a rock mass with cross joints

To study the dynamic mechanical properties and failure characteristics of intersecting jointed rock masses with different joint distributions under confining pressure,considering the cross angleαand joint persistence ratioη,a numerical model of the biaxial Hopkinson bar test system was established using the finite element method–discrete-element model coupling method.The validity of the model was verified by comparing and analyzing it in conjunction with laboratory test results.Dynamics-static combined impact tests were conducted on specimens under various conditions to investigate the strength characteristics and patterns of crack initiation and expansion.The study revealed the predominant factors influencing intersecting joints with different angles and penetrations under impact loading.The results show that the peak stress of the specimens decreases first and then increases with the increase of the cross angle.Whenα<60°,regardless of the value ofη,the dynamic stress of the specimens is controlled by the main joint.Whenα≥60°,the peak stress borne by the specimens decreases with increasingη.Whenα<60°,the initiation and propagation of cracks in the cross-jointed specimens are mainly controlled by the main joint,and the final failure surface of the specimens is composed of the main joint and wing cracks.Whenα≥60°orη≥0.67,the secondary joint guides the expansion of the wing cracks,and multiple failure surfaces composed of main and secondary joints,wing cracks,and co-planar cracks are formed.Increasing lateral confinement significantly increases the dynamic peak stress able to be borne by the specimens.Under triaxial conditions,the degree of failure of the intersecting jointed specimens is much lower than that under uniaxial and biaxial conditions.

Angular Distribution and Cross Section Measurements of ^(64)Zn(n,α)^(61)Ni Reaction for Neutron Energy 5 MeV

A twin gridded ionization chamber with dual parameter data acquisition sys-tem is used to study neutron induced charged particle emission reaction.The angulardistribution and cross section of n-particles from the 64Zn（n,α）61Ni reaction are meas-ured at neutron energy 5 MeV.

Configuration of propagator method for calculation of electron velocity distribution function in gas under crossed electric and magnetic fields

This paper presents a self-contained description on the configuration of propagator method(PM)to calculate the electron velocity distribution function(EVDF) of electron swarms in gases under DC electric and magnetic fields crossed at a right angle. Velocity space is divided into cells with respect to three polar coordinates v,θ and f. The number of electrons in each cell is stored in three-dimensional arrays. The changes of electron velocity due to acceleration by the electric and magnetic fields and scattering by gas molecules are treated as intercellular electron transfers on the basis of the Boltzmann equation and are represented using operators called the propagators or Green’s functions. The collision propagator, assuming isotropic scattering, is basically unchanged from conventional PMs performed under electric fields without magnetic fields. On the other hand, the acceleration propagator is customized for rotational acceleration under the action of the Lorentz force. The acceleration propagator specific to the present cell configuration is analytically derived. The mean electron energy and average electron velocity vector in a model gas and SF6 were derived from the EVDF as a demonstration of the PM under the Hall deflection and they were in a fine agreement with those obtained by Monte Carlo simulations. A strategy for fast relaxation is discussed, and extension of the PM for the EVDF under AC electric and DC/AC magnetic fields is outlined as well.

Distribution of the Classification Traits in the F_2 Progeny of Two Crosses of indica/japonica in Rice (Oryza sativa)

Comparison of seed setting rate, plant height and Cheng's morphological traits were made between the F_2 progeny of indica-japonica hybrids, 02428/Pei'ai 64 and Taichung 65/Teqing. There existed resemblance normal distribution in plant height, and the distribution had no relationship with the seed setting rate and plant height in F_1 progeny, suggesting that there were no gametic selection for the plant height in the F_2 progeny of indica-japoniea hybrids. An average seed setting rate of the F_2 was equal to the F_1 populations in the recombination of 02428/Pei'ai 64 in which there was an excellent cross compatibility, but the remarkable increase in the seed setting rate from the F_1 to F_2 in Taichung 65/Teqing, indicating that gametic selection only took place in the indica-japonica crosses with low cross compatibility while null or little in the hybrids with high compatibility. There were many intermediate types among the leaf pubescence, color of hull at heading, and length of the first and second panicle internode, and these Cheng's morphological traits was distributed normally; there were also a little intermediate types in hull hairness and phenol reaction with bi-peak distribution; while length to width ratio of grain was inclined to the japonica types obviously showing a skewed distribution in the F2 population. Although Cheng's morphological traits in F_2 populations had inconsistent distribution types, Cheng's morphological traits index showed normal distribution, which suggested that intermediate types, i.e. indicalinous or japonicalinous, were primary in F_2 population.

Extraction of Structure Function and Gluon Distribution Function at Low-x from Cross Section Derivative by Regge Behavior

An approximation method based on Regge behavior is presented. This new methodrelates the reduced cross section derivative and the structure function Regge behavior at low x.With the use of this approximation method, the C and λ parameters are calcuiated from the HERAreduced cross section data taken at low-x. Also, we calculate the structure functions F_2(x, Q~2)even for low-x values, which have not been investigated. To test the validity of calculatedstructure functions, we find the gluon distribution function in the Leading order approximationbased on Regge behaviour of structure function and compare to the NLO QCD fit to H1 data and NLOparton distribution function.

Experimental study for the particle size distribution of mine spoil pile cross section

The aim of the experiment is to analyze and view the distribution of gangue withdifferent particle sizes in mine spoil pile cross section.According to the Dimensionalmethod,'Pi'theorem was employed first to abbreviate ten physical and mechanical parametersto three dimensionless groups, and then the similarity criterion and coefficient ofthe experiment were determined and calculated based on particle size distribution curve.The similarity model was designed and constructed to represent the process of the minespoil pile.The profile of the final model shows that the small sized particles mainly composethe upper zone of the mine spoil pile, while the bottom of the pile is dominated bybigger sized particles, and the intermediate section presents a zigzag stripe cross-beddingstructure which is composed by small-medium scale particles and medium-large scaleparticles.Each stripe has two critical angles: one is the angle in which gangue particlescan maintain their stability condition, with approximate range from 24° to 26°; and theother is the angle in which particles can stop gliding downwards, approximately varyingfrom 34° to 36°.

Measurement of Angular Distribution and Cross Section for ^(58)Ni(n,α)^(55)Fe Reaction at 5.1 MeV

The α-particle angular distribution of 58Ni（n,α）55Fe was measured at incidentneutron energy 5.1 MeV using a grid ionization chamber.Neutron fluence was deter-mined by fission of 238U.The present results were compared with the theoretical calcu-lation based on the compound nucleus model.

基于EMD-Wigner-Ville的内燃机振动时频分析

在分析多分量信号时,WVD交叉项的出现极大干扰了对信号的时频分析,针对现有WVD交叉项抑制方法存在聚集性与交叉项成分抑制相互矛盾的问题,提出了一种基于经验模态分解(EMD)的WVD交叉项抑制方法。该方法首先利用EMD分解方法,将信号分解成相互独立的一系列具有不同特征时间尺度的固有模态函数(IMF),然后运用相关系数法对经验模式分解伪分量进行剔除,再对每个IMF进行Wigner-Ville分析,最后把各个IMF的Wigner-Ville分析结果线性叠加重构原始信号的时频分布。仿真实验结果表明,该方法既能有效抑制时频分布的交叉项,又保证了Wigner-Ville分布的时频聚集性。将EMD-Wigner-Ville应用在内燃机振动时频分析中,两个实例有效地揭示出了内燃机振动信号的特征信息,克服了HHT时频分布、Wigner-Ville时频分布在分析内燃机振动信号时的缺陷,是一种有效的时频分析方法。

基于互Wigner-Ville分布的SAR运动目标检测

本文针对机载合成孔径雷达 (SAR)运动目标回波信号的特点 ,提出了基于互Wigner Ville分布 (XWVD)的机载SAR运动目标检测方法 ,分析了它在单目标和多目标情况下的检测性能 .实验证明 ,该方法可以在较低的信噪比下实现目标的检测 ,其性能大大优于常用的Wigner Ville分布方法 .为了抑制多个目标之间交叉项的影响 ,本文还提出了一种基于逐次消去思想的互Wigner Ville分布检测方法 ,它可以解决强度相差较大的多目标检测问题 .