Smoothed Pseudo Wigner-Ville Research Articles

A novel approach for modeling of the ultrasonic signal backscattered in immersed multilayer structures at normal incidence: Time, Frequency, and Velocity dispersion representation

This study proposes a theoretical procedure for modeling ultrasonic signal backscattered in normal incidence by a multilayer structure (MS) immersed in water. The propagation of a longitudinal ultrasonic wave in a MS is studied analytically by using the transfer matrix method (TMM), in which each layer is established as a quadrupole formalism combining the stresses and velocities. The transfer matrices allow us to determine the reflection coefficient of the multilayer structure. The MS solid/liquid/solid case is studied in both insonation configurations (direct and reverse). The modeled ultrasonic response is represented in both time and frequency domains and validated by comparison with experimental data published previously. The time–frequency methods such as spectrogram (SP) and the smoothed pseudo-Wigner–Ville (SPWV) are also used to investigate the character and the value of the non-dispersive of the longitudinal wave. Moreover, the TMM method is used under different conditions (different layer thicknesses, non-uniform distribution of layers, and any frequency range), which are among the causes of MS dispersion. TMM method is able to show this behavior and is exploited to produce (Distance versus Time) and (Distance versus Frequency) representations of wave propagation for each studied MS. The perfect agreement of the comparison of TMM dispersion results with the results is achieved by using time–frequency methods in the case of a 5 MHz central frequency.

A Unique Method for Detecting and Characterizing Low Probability of Intercept Frequency Hopping Radar Signals by means of the Wigner-Ville Distribution and the Reassigned Smoothed Pseudo Wigner-Ville Distribution

Low probability of intercept radar signals, which are may times difficult to detect and characterize, have as their goal ‘to see but not be seen’. Digital intercept receivers are currently moving away from Fourier-based techniques and toward classical time-frequency techniques for analyzing low probability of intercept radar signals. This paper brings forth the unique approach of both detecting and characterizing low probability of intercept frequency hopping radar signals by employing and comparing the Wigner-Ville Distribution and the Reassigned Smoothed Pseudo Wigner-Ville Distribution. Four-component frequency hopping low probability of intercept radar signals were analyzed. The following metrics were used for evaluation: percent error of: carrier frequency, modulation bandwidth, modulation period, and time-frequency localization. Also used were: percent detection, lowest signal-to-noise ratio for signal detection, and relative processing time.

Application of the Reassigned Smoothed Pseudo Wigner-Ville Distribution in Gear Defect Diagnosis

Gear is one of the most omnipresent components in the mechanical and industrial fields. Some defects can occur causing a change in the vibration signature. In the dynamic of gears system, several sources of excitation are considered. The principal objective of the present work is to study the use of the Reassigned Smoothed Pseudo Wigner Ville Distribution (RSPWVD) in the gear vibration monitoring. The used signals are obtained by the simulation of an eight degrees of freedom gearbox system for the healthy and cracked case. The considered model takes into account the presence of friction force inter teeth in contact, backlash and time varying mesh stiffness. Also, the presence of noise is highlighted. A comparison with the Smoothed Pseudo Wigner Ville Distribution (SPWVD) is done.

Using Time-Frequency Analysis to Characterize Altered Knee Dynamics in Post ACL Reconstruction Individuals.

More than 250,000 individuals suffer an anterior cruciate ligament (ACL) injury in the United States each year requiring surgery and rehabilitation. However, despite exhaustive rehabilitation individuals are often plagued by neuromuscular deficits that lead to detrimental knee loading and knee osteoarthritis. Traditionally, time domain-based metrics like peak sagittal plane knee angle are used to quantify differences in knee mechanics; however, additional information can potentially be elucidated from time-frequency analyses. Here Smoothed Pseudo Wigner-Ville (SPWV), a time-frequency analysis technique, was used to investigate differences in knee loading dynamics between healthy controls and post ACL reconstruction individuals during running. The results indicated that post ACL reconstruction individuals adopt significantly different loading strategies in their injured limb than their non-injured limb. Individuals adopt a stiffer, more restrictive movement strategy delineated by a stronger low frequency to high frequency (LF/HF) ratio while the non-injured limb exhibit a more oscillatory motion (p<; 0.001). The time domain metrics were unable to identify differences between the ACL injured and non-injured limbs. The ability of SPWV to provide both quantitative and visual means to detect these differences supports its use as a clinical tool to track and monitor joint health.

Investigation into the bistatic evolution of the acoustic scattering from a cylindrical shell using time-frequency analysis

The time and frequency analyses of the acoustic scattering by an elastic cylindrical shell in bistatic method show that the arrival times of the echoes and the resonance frequencies of the elastic waves propagating in and around the cylindrical shell are a function of the bistatic angle, β, between the emitter and receiver transducers. The aim of this work is to explain the observed results in time and frequency domains using time-frequency analysis and graphical interpretations. The performance of four widely used time-frequency representations, the Smoothed Pseudo Wigner-Ville (SPWV), the Spectrogram (SP), the reassignment SPWV, and the reassignment SP, are studied. The investigation into the evolution of the time-frequency plane as a function of the bistatic angle β shows that there are the waves propagating in counter-clockwise direction (labeled wave+) and the waves which propagate in clockwise direction (labeled waves−). In this paper the A, S0, and A1 circumferential waves are investigated. The graphical interpretations are used to explain the formation mechanism of these waves and the acoustic scattering in monostatic and bistatic configurations. The delay between the echoes of the waves+ and those of the waves− is expressed in the case of the circumnavigating wave (Scholte-Stoneley wave). This study shows that the observed waves at β=0° and β=180° are the result of the constructive interferences between the waves+ and the waves−. A comparative study of the physical properties (group velocity dispersion and cut-off frequency) of the waves+, the waves− and the waves observed in monostatic configuration is conducted. Furthermore, it is shown that the ability of the time-frequency representation to highlight the waves+ and the waves− is very useful, for example, for the detection and the localization of defaults, the classification purposes, etc.

Acoustic scattering from immersed composite cylindrical shells: Existence of zero group velocity circumferential waves

Some Lamb waves in a plate and some circumferential waves in a one-layer cylinder are characterized by the resonance frequencies where the group velocity is vanishing while the phase velocity remains finite. This paper investigates on the existence of these special waves which call zero group velocity waves (ZGV waves) in the case of the copper/polymer composite cylindrical shell immersed in water and filled with air. The acoustic scattering of a plane wave from this composite cylindrical shell is analyzed in the reduced frequency range (0.1<k1a1<200; k1 is the wave number and a1 is the outer radius of the composite cylindrical shell). The study of the respective influence of the inner layer thickness (polymer) and the outer layer thickness (copper) shows that the existence of these waves is a function of these thicknesses. Moreover, this study depicts that the dispersion curves of the considered bilayer shell tend towards the dispersion curves of the one-layer cylindrical shell made from the material of the thicker layer of the bi-layer cylindrical shell (polymer or copper). The time-frequency representation of smoothed pseudo Wigner-Ville (SPWV) is used to extract some properties of the circumferential waves propagating in and around the bi-layer cylindrical shell. The obtained results by this representation are in good agreement with those obtained by the theoretical approach.

Characterization and prediction of the backscattered form function of an immersed cylindrical shell using hybrid fuzzy clustering and bio-inspired algorithms

The acoustic scattering of a plane wave by an elastic cylindrical shell is studied. A new approach is developed to predict the form function of an immersed cylindrical shell of the radius ratio b/a (‘b’ is the inner radius and ‘a’ is the outer radius). The prediction of the backscattered form function is investigated by a combined approach between fuzzy clustering algorithms and bio-inspired algorithms. Four famous fuzzy clustering algorithms: the fuzzy c-means (FCM), the Gustafson-Kessel algorithm (GK), the fuzzy c-regression model (FCRM) and the Gath-Geva algorithm (GG) are combined with particle swarm optimization and genetic algorithm. The symmetric and antisymmetric circumferential waves A, S0, A1, S1 and S2 are investigated in a reduced frequency (k1a) range extends over 0.1<k1a<225 (k1 is the wave number). The time-frequency representation of Smoothed Pseudo Wigner-Ville (SPWV) is applied on the predicted and calculated acoustic backscattered form functions. This representation is used as a comparison criterion between the calculated form function by the analytical method and that predicted by the proposed approach on the one hand and is used to extract the predicted cut-off frequencies on the other hand. Moreover, the transverse velocity of the material constituting the cylindrical shell is extracted. The computational results show that the proposed approach is very efficient to predict the form function and consequently, for acoustic characterization purposes.

A Signal Decomposition Method for Ultrasonic Guided Wave Generated from Debonding Combining Smoothed Pseudo Wigner-Ville Distribution and Vold–Kalman Filter Order Tracking

Carbon fibre composites have a promising application future of the vehicle, due to its excellent physical properties. Debonding is a major defect of the material. Analyses of wave packets are critical for identification of the defect on ultrasonic nondestructive evaluation and testing. In order to isolate different components of ultrasonic guided waves (GWs), a signal decomposition algorithm combining Smoothed Pseudo Wigner-Ville distribution and Vold–Kalman filter order tracking is presented. In the algorithm, the time-frequency distribution of GW is first obtained by using Smoothed Pseudo Wigner-Ville distribution. The frequencies of different modes are computed based on summation of the time-frequency coefficients in the frequency direction. On the basis of these frequencies, isolation of different modes is done by Vold–Kalman filter order tracking. The results of the simulation signal and the experimental signal reveal that the presented algorithm succeeds in decomposing the multicomponent signal into monocomponents. Even though components overlap in corresponding Fourier spectrum, they can be isolated by using the presented algorithm. So the frequency resolution of the presented method is promising. Based on this, we can do research about defect identification, calculation of the defect size, and locating the position of the defect.

Power Consumption Profiling Using Energy Time-Frequency Distributions in Smart Grids

Smart grids are power distribution networks that include a significant communication infrastructure, which is used to collect usage data and monitor the operational status of the grid. As a consequence of this additional infrastructure, power networks are at an increased risk of cyber-attacks. In this letter, we address the problem of detecting and attributing anomalies that occur in the sub-meter power consumption measurements of a smart grid, which could be indicative of malicious behavior. We achieve this by clustering a set of statistical features of power measurements that are determined using the Smoothed Pseudo Wigner Ville (SPWV) energy Time-Frequency (TF) distribution. We show how this approach is able to more accurately distinguish clusters of energy consumption than simply using raw power measurements. Our ultimate goal is to apply the principles of profiling power consumption measurements as part of an enhanced anomaly detection system for smart grids.

A New Method for Interference Reduction in the Smoothed Pseudo Wigner-Ville Distribution

Abstract This article presents a new method facilitating interference reduction in the Wigner-Ville distribution, which is used for nonstationary signal analysis, for example in machine condition monitoring. The algorithm is based on multiple Smoothed Pseudo Wigner-Ville distributions: differently smoothed time-frequency planes are compared and, for every point, a cross-term free value is calculated on the basis of optimal smooth estimation. The proposed approach is compared with the Gabor-Wigner transform, the Zhao-Atlas-Marks distribution, and the Choi-Williams distribution. Five time-frequency Gaussian atoms and a bat echolocation chirp are used as the testing signals. The Rényi entropy, the ratio of norms, the Stanković measure, and the mean squared error are used as quantitative measures to demonstrate the promising results of the proposed method.

Parametric and Non Parametric Time-Frequency Analysis of Biomedical Signals

Due to non-stationary multicomponent nature of the electrocardiogram (ECG) signal its analysis by the monodimensional techniques temporal and frequenctial can be very difficult. The use of the time-frequency techniques can be inevitable to achieve to a correct diagnosis. Between the different existing parametric and non-parametric time-frequency techniques the Periodgram Capon Choi-Williams and Smoothed Pseudo Wigner-Ville were chosen to deal with analysis of this biomedical signal. In a first time a comparison between these time-frequency techniques was made by analyzing modulated signal to make in evidence the technique that gives a good resolution and low level of cross-terms. In a second time the Periodogram which presents a powerful technique was applied to a normal and abnormal ECG signal. The results show the effectiveness of this time-frequency in analyzing this type of biology signal.

A novel approach for detection of deception using Smoothed Pseudo Wigner-Ville Distribution (SPWVD)

For many years, the uncertainty of lie-detection systems has been one of the concerns of defense related agencies. Clearly the results of these systems must be generalized by a high value of accuracy to be acceptable by judicial systems. In this paper, a new method based on P300-based component has been proposed for lie-detection. In this regard, the test protocol is designed based on Odd-ball paradigm concealed information recognition. This test was done on 32 people and their brain signals were acquired. After preprocessing, the classic features are extracted from each single trial. After that, time-frequency (TF) transformation is applied on the sweeps and TF features are produced thereupon. Then, the best combinational feature vector is selected in order to improve classifier accuracy. Finally, Guilty and Innocent persons are classified by KNN and MLP. We found that combination of Time-Frequency and Classic features have better ability to achieve higher amount of accuracy. The obtained results show that the proposed method can detect deception by the accuracy of 89.73% which is better than other previously reported methods.

Application of the reassignment time–frequency method on an acoustic signals backscattered by an air-filled circular cylindrical shell immersed in water

In this paper, the time–frequency representations of the Spectrogram (SP), the Reassigned Spectrogram (RSP), the Smoothed Pseudo-Wigner–Ville (SPWV) and the Wavelet Transform (WT) were used. These techniques are applied for analyzing experimental acoustic signal backscattered by an air-filled tube immersed in water. From the time–frequency images obtained, one can go up easily with certain characteristics of the acoustic waves such as the attenuation and the group delay of each circumferential wave. A comparative performance study of these four time–frequency representations was used. The reassigned spectrogram was chosen for its better localization and good resolution of the signal components in the time–frequency plane. It allows a better visibility of the circumferential waves which are propagated around the target. The estimated parameters from the reassigned spectrogram time–frequency image are in very good agreement with those obtained by the theoretical methods.

A comparative study of bilinear time-frequency transforms of isar signals for air target imaging

In this paper a comparative study of bilinear time-frequency (TF) transforms for Inverse Synthetic Aperture Radar (ISAR) imaging is presented. Following a concise presentation of the ISAR imaging method used in this work, as well as of the theory of the bilinear TF transforms involved in our numerical simulations, extended numerical results are presented for a reference simulated radar target and for various noise conditions. The constructed ISAR images are presented and analyzed quantitatively using an entropy cost function criterion, while corresponding run-time considerations have also been taken into account. As a result, it appears that the Smoothed Pseudo Wigner-Ville (SPWV) distribution provides us with images of superior quality. Furthermore, the analysis of the results demonstrates the usefulness of bilinear TF methods in ISAR imaging and showcases the relative performance advantages and disadvantages of the various distributions. Ill. 7, bibl. 22 (in English; summaries in English, Russian and Lithuanian).

Guided ultrasound wave propagation in intact and healing long bones

Ultrasonic evaluation of bone fracture healing has been traditionally based on the measurement of the propagation velocity of the first arriving signal (FAS). However, the FAS in general corresponds to a lateral wave that propagates along the bone’s subsurface. In this work, we study guided ultrasound propagation in intact and healing bones. We developed a 2-D model of a bone-mimicking plate in which the healing process was simulated as a 7-stage process, and we also carried out ex vivo experiments on an intact tibia. Guided waves were represented in the time-frequency (t-f) domain of the signal by incorporating the Lamb wave theory. Three t-f distribution functions were examined, namely the reassigned Spectrogram, the smoothed-pseudo Wigner-Ville, and the reassigned version of it. For the intact plate case, we found that the S2, A3 Lamb modes were the dominant waves for a broadband 1-MHz excitation, and the S2, S0 for a 500-kHz excitation. During the simulated healing process, the mechanical and geometrical callus properties affected the theoretically anticipated Lamb modes. The propagation of guided waves throughout the thickness of the cortical bone and their sensitivity to both the mechanical and structural changes during healing can supplement velocity measurements so as to enhance the monitoring capabilities of ultrasonic evaluation. Nevertheless, the applicability of the Lamb wave theory to real bones has several limitations mostly associated with neglecting the inhomogeneity, anisotropy and irregular geometry of bone. (E-mail: fotiadis@cs.uoi.gr)