Wigner-Ville Distribution Research Articles

Experimental Investigations Regarding the Structural Damage Monitoring of Strands Wire Rope within Mechanical Systems.

This paper deals with the area of structural damage monitoring of steel strands wire ropes embedded into various equipment and mechanical systems. Of the currently available techniques and methods for wire ropes health monitoring, the authors focused on the group of techniques based on operational dynamics investigation of such systems. Beyond the capability and efficiency of both occasionally and continuously monitoring application, the dynamics-based methods are able to provide additional information regarding the structural integrity and functional operability of the entire ensemble embedding the wire ropes. This paper presents the results gained by the authors using a laboratory setup that can simulate the operational condition usually used for regular applications of wire ropes. The investigations were conducted on three directions of acquired signals post-processing. Firstly, the classical fast Fourier transform was used to evaluate the potential changes within the spectral distribution of transitory response. The other two directions involved high-order spectral analyses in terms of bi-spectrum and Wigner–Ville distribution and multi-scale analysis based methods such as complex wavelet cross-correlation and complex wavelet coherency. The results indicate that each direction of analysis can provide suitable information regarding potential wire rope damage, but the ensemble of post-processing methods offers supplementary precision.

Multiscale dynamic distribution characteristics of dust collectors in wet scrubber based on image fields

ABSTRACT In order to reveal multiscale dynamic distribution characteristics of dust collectors in a wet scrubber, a method for scale decomposition of dust collectors based on Wigner–Ville distribution (WVD), empirical mode decomposition (EMD) and Hurst analysis of grayscale signals is reported. The WVD features of grayscale signals were used to observe the energy distribution details of dust collectors at different frequency bands and time periods. Then, the scale decomposition of dust collectors based on EMD and Hurst analysis of the grayscale signals was carried out. These analysis results showed that the motion behaviors of micro-, meso- and macro-scale subsets of dust collectors were determined: specifically, the single fractal features of micro-scale subsets conform to the motion characteristics of individual dust collectors. The dual fractal characteristics of meso-scale subsets denote the interactions among dust collector aggregations. Additionally, the fractal features of the macro-scale subsets reflect persistent liquid surface fluctuation behavior in wet scrubbers. Finally, the relative contribution of dust collectors at different scales to the effectiveness of dust removal was represented. This is not only an important innovation in the study of micro mechanism of wet dust removal but provides powerful theoretical support for technological innovations in wet scrubbers. Implications: The multiscale dynamic distribution characteristics of dust collectors in wet dust scrubber were explored, using a method for scale decomposition of dust collectors based on Wigner–Ville distribution, empirical mode decomposition and Hurst analysis of grayscale signals. The fractal characteristics of different scales of dust collectors are determined. Besides, the contribution of different scales of dust collectors to the effect of dust removal is quantized. Therefore, this research is very meaningful, which not only has important innovation in the study of micro mechanism of wet dust collectors but provides a powerful theoretical support for technological innovation of wet dust scrubbers.

Extraction and analysis of transient signals of a deployable structure vibration based on the sparse decomposition with mixed norms

This contribution deals with extraction and analysis of the transient component of a deployable structure vibration based on the sparse decomposition with mixed norms. The transient component is a critical nonlinear dynamical characteristic of the deployable structure. However, extraction of weak transient signals has always been a challenging problem in signal processing. To resolve this problem, we present an algorithm based on the sparse decomposition with the mixed norm. As redundant components may occur in the sparse decomposition, resulting from the end effect of time-frequency representations. Flip mirror extension is designed to address this question. The feasibilities of the short time Fourier transform, the Wigner-Ville distribution, the ensemble empirical mode decomposition, the stationary wavelet transform and the presented method to catch the transient component are verified with a sample example, and the result shows that the presented algorithm is more powerful. After that, the method is employed to extract transients from experimental signals of a deployable structure model; furthermore, characteristics of these components are analyzed, and are as follows: the transient components are complicated; the transient amplitudes decrease as a whole; the transient amplitudes are locally random. The algorithm is valuable for extracting the transient component from the vibrations, and the analysis may be valuable for the analysis of the nonlinear dynamics of the deployable structure.

Blind modal estimation using smoothed pseudo Wigner–Ville distribution and density peaks clustering

The determination of the number of active modes is always an obstacle to the identification of dynamic systems. To tackle this issue, a new blind modal estimation method is proposed through which the number of active modes does not need to be presupposed, even in underdetermined blind source separation cases. Firstly, the spatial time–frequency distribution matrices are constituted from the smoothed pseudo Wigner–Ville distribution of acceleration signals. The auto-source time–frequency points that contain modal information about only one mode are selected and then the density peaks clustering algorithm is introduced to identify the mode shape vectors. Finally, one can reconstruct the time–frequency distributions of modal coordinates and estimate the natural frequencies and damping ratios. The method is verified by a numerical study and a vibration experiment. The anti-noise study demonstrates that the method performs well.

Low Complexity Method for Recovering Continuous Phase Modulation Signals with Low Signal-to-noise Ratios

A low computational complexity scheme based on the modified Wigner–Ville distribution (MWVD) is developed for estimating the instantaneous frequency of continuous phase modulation (CPM) signals under low signal-to-noise ratio (SNR) scenario. To simplify the computation of the MWVD, a low order Chebyshev polynomial is chosen as the kernel function for suppressing the cross-terms. The implementation of this instantaneous frequency (IF) estimator is done through the Viterbi algorithm. The simulation results show that our scheme outperforms other estimating methods under low SNR scenario.

Tomographic and Entropic Analysis of Modulated Signals

We study an application of the quantum tomography framework for the time-frequency analysis of modulated signals. In particular, we calculate optical tomographic representations and Wigner-Ville distributions for signals with amplitude and frequency modulations. We also consider time-frequency entropic relations for modulated signals, which are naturally associated with the Fourier analysis. A numerical toolbox for calculating optical time-frequency tomograms based on pseudo Wigner-Ville distributions for modulated signals is provided.

Applications of Ceemdan in Dynamic Behavior of Defected Spur Gearbox Running Under Acyclism Regime

ABSTRACTEmpirical Mode Decomposition (EMD) and its approaches are powerful techniques in signal processing especially for the diagnosis of rotating machinery running in non-stationary regime. We are interested in this paper to the dynamic behavior of a defected one stage gearbox equipped with an elastic coupling and loaded under acyclism regime generated by a combustion engine. Actually, we adopt an approach to the EMD method called Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) as a technique to perform the diagnosis of the studied system. Since the obtained signals are modulated, all obtained Intrinsic Mode Functions (IMFs) are modulated and are processed and shown by the Wigner-Ville distributions (WVD) as well as the spectrum of their envelope in order to detect defects such as cracked tooth defect in the wheel of the spur gearbox and eccentricity defect in the gear.

Nonlinear Analysis of CCM Superbuck Converter Using Wigner-Ville Distribution

In order to analyze the bifurcation and chaos of Superbuck converter in Continuous Current Mode (CCM), a new method of time-frequency diagram based on Wigner-Ville distribution is proposed. The method is used to analyze the variation of the energy component of the output voltage with frequency and time. It reveals that the Superbuck converter exhibits period-1 bifurcation, period-2 bifurcation, period-4 bifurcation and chaos under different reference current. The results of the time-frequency diagram are consistent with the results of the bifurcation diagram, time-domain diagram, phase diagram and Poincare section. It proves that the method can deeply understand the nature of bifurcation and chaos in Superbuck converter, and it provides a new way to analyze the nonlinear phenomena of DC-DC converter

Structural-damage localization using ultrasonic guided waves based on the lossless filtering method

Ultrasonic guided waves have been widely used for structural-damage localization in recent decades, whose effectiveness depends on whether the damage on a structure reflects a wave pulse. The basic principle can be described as follows: the ratio between the times of flight (TOFs) of the excitation and damage signals is equal to that between their distances of flight. Because a number of disturbing factors occurred during the data-acquisition process, a large number of noise signals present in the experiment could cause a low signal-to-noise ratio (SNR). In addition, whereas the traditional filtering methods improved the SNR, the effective signals were weakened. To deal with this situation, an ultrasonic lossless filtering method based on the multi-coverage technique applied to a blasting seismic wave and the superposition technique to ultrasonic guided wave was first proposed to enhance the SNR. Compared with the traditional filtering techniques, the proposed method achieves better performance in that the effective signal remains unaltered and the noise level is reduced. The Wigner–Ville distribution (WVD) method, which could reflect the true energy distribution within the time and frequency domains, was applied to calculate the TOF of the signals. Finally, the damage localization of the structure was realized according to the abovementioned principle. Compared with the location result without a filter, the maximum WVD value becomes more perceivable, and the positioning accuracy is clearly improved. Compared with the location results using the Fourier and polynomial-smoothing filtering methods, the lossless filtering method allows an effective signal to remain unaltered. Finally, we can conclude that the proposed ultrasonic lossless filtering method can improve the SNR under the condition in which the effective signal remains unaltered, and the SNRs become higher and higher with the increase of superimposition times. The combination of ultrasonic lossless filtering method and the WVD method can perfectly realize the damage location with a high accuracy. Several damage-localization experiments demonstrate that the ultrasonic lossless filtering method is reliable.

Quantitative analysis of SNR in bilinear time frequency domain

Signal-to-noise ratio (SNR) is an essential concept or quantity on the result of a process or on the output of a filter, which helps us in designing, analyzing or evaluating a system. In this paper, we study SNR for bilinear time–frequency transform (TFT). Firstly, according to the definition of SNR in time domain, we define a proper form for SNR in time–frequency (T–F) plane for bilinear TFT; then, we extract SNR relation in terms of TFT kernel, signals power and noise power in time domain. The extracted relation of SNR for bilinear TFT that can be represented in terms of Wigner–Ville distribution (WVD) shows its dependence on the kernel used in the TFT. Finally, to illustrate the applicability of the proposed SNR, the relations of SNR for several distributions are extracted in the T–F domain, and the variation of SNR versus the noise variance is shown by curves. The results show that the WVD has higher SNR than the Rihaczek, Page, spectrogram and Levin respectively.

Low Complexity VLSI Architecture Design Methodology for Wigner Ville Distribution

In this brief, we propose a low complexity VLSI architecture design Methodology for Wigner Ville Distribution (WVD) computation. The proposed methodology performs both auto and cross WVD computations using only the half number of Fast Fourier transform (FFT) computations as opposed to the state of the art methodologies. The FPGA implementation for proposed methodology was performed for 16 bit fixed point and 32 bit single precision floating point numbers on the Xilinx Virtex-7 FPGA (XC7vx485tffg). The proposed methodology saves 49% energy consumption when compared with the state of the art methodology. However it can be noted that the proposed methodology is independent of the VLSI implementation platform and technology node.

Extraction of the pulse width and pulse repetition period of linear FM radar signal using time-frequency analysis

A common technique used by military to realize low probability of intercept (LPI) is linear frequency modulation (LFM) in the field of electronic intelligence (ELINT). This paper estimates the pulse width (PW) and the pulse repetition period (PRP) of LFM signal using instantaneous powers. The instantaneous powers were obtained either using time-marginal or power maxima approximated from a modified version of the Wigner-Ville distribution (WVD). The instantaneous power was also gotten directly from the signal by multiplication with its conjugate. Measurement was then carried out when the instantaneous power is ‘ON’ (the PW) and when it is ‘OFF’ (the PRP) at carefully selected thresholds. Thereafter, the mWVD-based algorithm was tested in the presence of additive white Gaussian noise (AWGN) at various signal-to-noise ratios. Results obtained during the test showed that the time marginal method emerged the best with minimum signal-to-noise ratio (SNR) of -5dB followed closely by the direct method with minimum SNR of -1dB at different thresholds. The results show that the proposed algorithm based on this modified WVD can be deployed in the practical field to determine radar’s performance and function

Modeling the acoustic repertoire of Cuvier's beaked whale clicks.

This paper investigates the evolution of spectral properties observed in Cuvier's beaked whale (Ziphius cavirostris) click trains recorded by fixed hydrophones in the Gulf of Mexico. In the context of deep water and high-frequency sounds and observed inter-click intervals, the authors assumed that the main effect responsible for the modification of the spectral content between adjacent clicks in the same click train is the source beam pattern. The spectral structure is studied by using the Wigner-Ville time-frequency distribution and is compared with the conventional Fourier spectrogram. The results show that the observed Cuvier's beaked whale clicks are a superposition of upsweep and downsweep chirps, unlike the currently accepted upsweep only structure of beaked whale clicks in bioacoustics literature. The spectral structure variations simulated by using a flat circular piston model as a beam pattern transmission model are consistent with the evolution of spectral click properties observed in experimental data. A better understanding of the properties of observed echolocation clicks of Cuvier's beaked whales will provide useful information for click annotations and, therefore, will contribute to improving accuracy of detecting, classifying, tracking, and estimating the density of Cuvier's beaked whales.

Characterization of Nonstationary Phase Noise Using the Wigner–Ville Distribution

Oscillators and atomic clocks, as well as lasers and masers, are affected by physical mechanisms causing amplitude fluctuations, phase noise, and frequency instabilities. The physical properties of the elements composing the oscillator as well as external environmental conditions play a role in the coherence of the oscillatory signal produced by the device. Such instabilities demonstrate frequency drifts, modulation, and spectrum broadening and are observed to be nonstationary processes in nature. Most of the tools which are being used to measure and characterize oscillator stability are based on signal processing techniques, assuming time invariance within a temporal window, during which the signal is assumed to be stationary. This letter proposes a new time-frequency approach for the characterization of frequency sources. Our technique is based on the Wigner–Ville time-frequency distribution, which extends the spectral measures to include the temporal nonstationary behavior of the processes affecting the coherence of the oscillator and the accuracy of the clock. We demonstrate the use of the technique in the characterization of nonstationary phase noise in oscillators.

Nonparametric Bayesian Prior Inducing Deep Network for Automatic Detection of Cognitive Status.

Pilots' brain fatigue status recognition faces two important issues. They are how to extract brain cognitive features and how to identify these fatigue characteristics. In this article, a gamma deep belief network is proposed to extract multilayer deep representations of high-dimensional cognitive data. The Dirichlet distributed connection weight vector is upsampled layer by layer in each iteration, and then the hidden units of the gamma distribution are downsampled. An effective upper and lower Gibbs sampler is formed to realize the automatic reasoning of the network structure. In order to extract the 3-D instantaneous time-frequency distribution spectrum of electroencephalogram (EEG) signals and avoid signal modal aliasing, this article also proposes a smoothed pseudo affine Wigner-Ville distribution method. Finally, experimental results show that our model achieves satisfactory results in terms of both recognition accuracy and stability.

Implementation of sparse recovery method with high‐resolution time‐frequency energy distributions for helicopter

AbstractIn this paper, an algorithm named the sparse Wigner‐Ville distribution (WVD) is applied for the time‐frequency analysis of signals. In this algorithm, the sampling for ambiguity function (AF) is regarded as a sparsity measurement of the WVD, and the Fourier transform matrix is treated as a sparsity redundant dictionary. The effectiveness of the algorithm is verified by using the liner frequency modulation and sinusoidal frequency modulation signals. Then the algorithm is employed to deal with the time‐frequency analysis of helicopters. The experiment results show that the time‐frequency images of helicopters obtained by utilizing this algorithm exhibit higher resolution without cross‐interference terms compared with that by WVD.

Automated phase classification in cyclic alternating patterns in sleep stages using Wigner–Ville Distribution based features

Sleep is one of the most important body mechanisms responsible for the proper functioning of human body. Cyclic alternating patterns (CAP) play an indispensable role in the analysis of sleep quality and related disorders like nocturnal front lobe epilepsy, insomnia, narcolepsy etc. The traditional manual segregation methods of CAP phases by the medical experts are prone to human fatigue and errors which may lead to inaccurate diagnosis of sleep stages. In this paper, we present an automated approach for the classification of CAP phases (A and B) using Wigner–Ville Distribution (WVD) and Rényi entropy (RE) features. The WVD provides a high-resolution time–frequency analysis of the signals whereas RE provides least time–frequency uncertainty with WVD. The classification is performed using medium Gaussian kernel-based support vector machine with 10-fold cross-validation technique. We have presented the results for randomly sampled balanced data sets. The proposed approach does not require any pre-processing or post-processing stages, making it simple as compared to the existing techniques. The proposed method is able to achieve an average classification accuracy of 72.35% and 87.45% for balanced and unbalanced data sets respectively. The proposed method can aid the medical experts to analyze the cerebral stability as well as the sleep quality of a person.

Railway Polygonized Wheel Detection Based on Numerical Time-Frequency Analysis of Axle-Box Acceleration

The increasing need for repairs of polygonized wheels on high-speed railways in China is becoming problematic. At high speeds, polygonized wheels cause abnormal vibrations at the wheel-rail interface that can be detected via axle-box accelerations. To investigate the quantitative relationship between axle-box acceleration and wheel polygonization in both the time and frequency domains and under high-speed conditions, a dynamics model was developed to simulate the vehicle-track coupling system and that considers both wheel and track flexibility. The calculated axle-box accelerations were analyzed by using the improved ensemble empirical mode decomposition and Wigner-Ville distribution time-frequency method. The numerical results show that the maximum axle-box accelerations and their frequencies are quantitatively related to the harmonic order and out-of-roundness amplitude of polygonized wheels. In addition, measuring the axle-box acceleration enables both the detection of wheel polygonization and the identification of the degree of damage.

Deep geometric convolutional network for automatic modulation classification

A recent trend of automatic modulation classification is to automatically learn high-level abstraction of signals, instead of manually designing features for further classification. In this paper, we propose a new deep geometric convolutional network (DGCN) to hierarchically extract discriminative features from Wigner–Ville distribution map of signals. A group of geometric filters are constructed from a least square support vector machine, to capture the linear singularity existed in maps. The filters are cascaded to construct a deep network for extracting discriminative features and classifying signals with different modulation types. Some experiments are taken to investigate the performance of DGCN, and the results show that it can achieve high accuracy in classifying 15 types of modulation signals.

A Comparison of Time-Frequency Methods for Nonlinear Dynamics and Chaos Analysis in an Energy Harvesting Model

In this paper, an energy harvesting model based on a portal frame structure, modeled as a duffing system, with a non-ideal excitation force, DC motor with an unbalanced mass, is presented and the piezoelectric coupling is designed to exhibit nonlinear characteristics. Nonlinearity included provides higher power output over a wide frequency range. This analysis was carried out by numerical simulation of the proposed mathematical formulation. Thus, the bifurcation diagram and the largest Lyapunov exponents are plotted to investigate the dynamic behavior by ranging the voltage applied to the DC motor. In this way, power harvesting is analyzed for two different dynamic responses: periodic and chaotic behavior. Furthermore, this work exhibits an application of frequency-domain techniques, such as short-time Fourier transform, continuous wavelet transform, synchrosqueezed wavelet transform, and Wigner-Ville distribution methods. These methods are often used to analyze non-stationary signals, allowing the verification of dynamic behavior and power harvesting. Therefore, this paper aims to apply the time-frequency methods, mentioned previously, to analyze the mechanical system response in different behaviors.