Smoothed Pseudo Wigner-Ville Distribution Research Articles

SPWVD-PSD 겹침 이미지를 이용한 전이학습기반 GNSS 재밍식별기법

In this paper, a transfer learning-based global navigation satellite system (GNSS) jamming classification scheme using overlapped images of the smoothed pseudo-Wigner-Ville distribution (SPWVD) and power spectral density (PSD) is proposed. Five types of jamming are considered: amplitude modulation jamming (continuous wave interference), linear chirp jamming, frequency modulation jamming, narrow-band noise jamming, and distance measurement equipment jamming (pulse jamming). The performance of the proposed scheme is shown to be the F1 score and the confusion matrix for pre-mentioned 5 jamming types with no jamming case. A representative conventional transfer learning-based GNSS jamming classification scheme uses a concatenated image comprising a spectrogram, in-phase and quadrature constellation, PSD, and histogram. However, in conventional schemes, the spectrogram

Signal fingerprint feature extraction and recognition method for communication satellite

ABSTRACT Due to the complex maritime environment, communication satellite signals are inevitably subjected to various unpredictable situations which results in the noisy signal. To tackle the fickle ocean environment, we propose a novel scheme to extract and identify the fingerprint feature of communication satellite signals. K-means clustering algorithm is utilised to optimise the conventional Smooth Pseudo Wigner-Ville Distribution (SPWVD), which makes the final result of SPWVD closer to the feature of the original data and improves the accuracy of signal fingerprinting. Basing on the improved SPWVD, the singular value entropy is calculated by time-frequency analysis. Then, the entropy of diagonal slices is generated by the ameliorated bispectrum method which is enhanced by using the fractional low-order covariance method. Consequently, a two-dimensional signal fingerprint feature vector can be calculated. For the fingerprint feature recognition, the XGBoost classifier which is more efficient in machine learning classification is employed. Finally, we simulate the Iridium satellite signal for experiments with MATLAB. The experimental result shows the superiority of the improved SPWVD method and the improved bispectrum method, which proves the scheme's feasibility.

Frame Selection Method for ISAR Imaging of 3-D Rotating Target Based on Time–Frequency Analysis and Radon Transform

When a target has 3-D rotation accompanying roll–pitch–yaw movement, it yields an additional phase component, which cannot be compensated for by any of the existing inverse synthetic aperture radar (ISAR) imaging methods. Under this condition, the resulting ISAR image will be severely distorted. Accordingly, selecting a proper imaging frame, where the target has only 2-D rotation, becomes the only solution, especially for range-Doppler (RD) algorithm. To do this, the conventional approach is to directly use the phase of the received signal, and however, this approach is vulnerable to noise and the cross-term interference of multiple scattering centers (SCs) in the range bin. To address these issues, we propose a new frame selection method using the range-instantaneous Doppler (RID) technique and Radon transform to detect the presence of 3-D rotation of the target within imaging frame. The proposed method comprises three steps: 1) obtain joint time–frequency distribution (JTFD) via the smoothed pseudo Wigner–Ville distribution (SPWVD); 2) estimate the orientation angle of the Radon image of the JTFD spectrum; and 3) select the suitable imaging frame using the estimated angle. Furthermore, to demonstrate the effectiveness of the proposed method, experimental results based on simulated and real measured data are provided.

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.

Rotating machinery faults detection method based on deep echo state network

This paper aims to develop an accurate and efficient end-to-end fault detection model trained by small-scale data for the rotating machinery. The echo state network (ESN) is promising thanks to the training process by linear regression, but it struggles in mining spatial information. Thus, a deep ESN based on fixed convolution kernels (FCK-DESN) is proposed. The Prewitt, the Sobel, and the Gaussian lowpass filters are designed as the fixed convolution kernels for spatial feature extraction without training. The one hidden layer autoencoder is built to compress the dimensionality and improve the applicability. Based on the pre-process modules, the ESN could realize pattern recognition under complex conditions. The fault detection approach is then constructed based on the time–frequency information provided by the smoothed pseudo-Wigner–Ville distribution. Case studies of a rotor-bearing system and a diesel engine show that the proposed FCK-DESN approach has better recognition rates than popular deep learning methods with high efficiency and lower data size requirements, which has more practical significance.

An online stress monitoring strategy based on Wigner–Ville time–frequency energy extraction of single-frequency dual mode Lamb waves

In this paper, a new online uniaxial stress monitoring methodology has been developed. Based on the acoustoelastic effect of Lamb waves, multimodal information at a single frequency, in which the approximate linear fitting between group velocity ratio of two modes and stress is obtained, is fused to characterize stress. The transceiver distance can be eliminated, which is essential knowledge for existing methods, in stress coefficient calibration and practical application by using the ratio of acoustic time. The semi-analytical finite element method(SAFE) is adopted to calibrate the stress coefficient. Next, the time–energy assignment algorithm derived from the smoothed pseudo-Wigner–Ville distribution(SPWVD) is evaluated on the ideal dataset obtained by time-domain finite element(TDFE) simulation. The arrival times of different modes are extracted accurately, and the fitting results are consistent with the theoretical analysis. Finally, the laboratory experiments employing a pair of piezoelectric wafer active sensors(PWAS) are conducted to calibrate unknown coefficients. The same calibration process is carried out at three different distances, and almost the same calibration results are obtained, indicating the distance-dependent nature of the stress coefficients. According to the completed calibration, the actual measurements from the same batch show the maximum absolute error of stress measurement is 4.2MPa within the applied stress range from 20MPa to 100MPa and the standard deviation is less than 3MPa, demonstrating good measurement accuracy and consistency. It shows the great potential of the proposed strategy to measure stress at unknown propagation distances.

Spectral analysis of ultrasonic signals backscartted by mortar: Effect of sand size and temperatures

This paper presents results of application of Ultrasonic Waves UW in civil engineering. The measurement has been performed by ultrasonic reflection technique using a transducer with central frequency 0,5MHz. Several methods of analysis and signal processing have been applied to detect the position of reflections and to measure the time of flight between two echoes related to the reflection at the mortar interfaces. The experiments performed in the laboratory are carried to determine the ultrasonic velocity of the wave backscattered by samples. This allowed determining the ultrasonic velocity of UW in the mortar in order to deduce the durability of each mortar according to its microstructure. The objective is to make a comparative study of the various methods of analysis of the ultrasonic signals as: Continuous Wavelet Transform (CWT), Wigner Ville (WVD), Pseudo Wigner–Ville distribution (PWVD), Smoothed Pseudo Wigner–Ville Distribution (SPWVD) and Hilbert Transform (HT).

Hyp-Net: Automated detection of hypertension using deep convolutional neural network and Gabor transform techniques with ballistocardiogram signals

Hypertension (HPT) is a physiological abnormality characterized by high blood pressure, headache, wooziness, and fainting that may lead to various heart, kidney, or brain diseases. Detection and continuous monitoring of HPT by sphygmometer is arduous and hectic. Nowadays, ballistocardiogram (BCG) signals are used to determine HPT as it indicates the vibration of the heart. Usual linear and nonlinear hand-crafted machine learning methods are subjective, involve decomposition of signal, features elicitation, selection, and classification steps. In this work, a completely automated HPT detection system is proposed using time–frequency (T-F) spectral images and a convolutional neural network (CNN) for the accurate detection of HPT using BCG signals. The BCG signals are subjected to Gabor transform (GT), smoothed pseudo-Wigner Ville distribution (SPWVD), and short-time Fourier transform (STFT) techniques to obtain T-F spectral images. These T-F spectral images are fed to benchmarked Alex-Net, Res-Net50, and proposed CNN (Hyp-Net) to develop the automated HPT detection model with a 10-fold cross-validation scheme. The proposed Hyp-Net obtained the highest detection accuracy of 97.65% with GT-based spectral images. In comparison to Alex-Net and Res-Net50 pre-trained models, our developed Hyp-Net needs minimal learnable parameters, makes it computationally fast and more efficient. This shows that our proposed model has outperformed other two transfer learning methods. The experimental results with collected BCG signals from a public dataset are provided to show the effectiveness of the presented technique for automated detection of HPT.

Contact delamination detection of anisotropic composite plates using non-elliptical probability imaging of nonlinear ultrasonic guided waves

Contact delamination damage easily occurs inside the composite. The extension and accumulation of the damage occupy most of the time from damage appearance to failure. However, the anisotropy of materials and the small size of early damage make accurate detection difficult. In this paper, a non-elliptical probability imaging (NEPI) method based on nonlinear ultrasonic guided waves is proposed for the delamination damage detection in anisotropic composites. Firstly, the anisotropic characteristics of the composite are analyzed theoretically, and the velocity in all directions is obtained by numerical simulation. Secondly, the arrival time is obtained by the intersection of the upper and lower envelope fitting lines, and nonlinear coefficient is calculated based on the smooth pseudo Wigner–Ville distribution (SPWVD). Then, the time coefficient (CT) and nonlinear damage index (NDI) are defined and applied in the NEPI. By comparison with a reference point, the problem that the damage location of anisotropic composite cannot be solved analytically is avoided skillfully. Finally, the NEPI method is used to present the damage. The experiment results show that the NEPI method can accurately display the damage location. The sensitivity and reliability of NDI based on SPWVD are further verified by comparison with damage index of scattered signal and time–frequency analysis methods such as fast Fourier transform, short-time Fourier transform, and S-transform. The proposed NEPI method based on nonlinear ultrasonic guided waves can detect the delamination damage with good location accuracy and high damage sensitivity.

Frequency information extraction based on time-frequency ridges for characterizing thin sand bodies

Abstract Time-frequency analysis (TFA) is a widely used reservoir prediction technology. During the identification of sand bodies using TFA, abnormally high values in the high-frequency portion of the spectrum usually indicate the presence of thin sand bodies. However, owing to the complexity of the depositional environment, the spatial distribution of thin sand bodies is often variable, and multiple phases of sand bodies—superimposed on each other—can occur with uneven thicknesses. A frequency information extraction technique based on time-frequency ridges (TFRs) is proposed in this study to identify stable TFRs in the time-frequency spectrum of a rearranged smooth pseudo-Wigner–Ville distribution with high energy aggregation, as well as to extract the main- and high-frequency energy contents relative to them. To enhance the ability of these energy components to detect thin sand bodies, a frequency-energy weighting factor is computed. By performing the aforementioned steps, information about each frequency band can be obtained and a comprehensive depiction of sand bodies with different thicknesses achieved. It is concluded that by using the proposed method thin sand bodies such as small riverbeds can be effectively characterized using seismic data.

Time-frequency readability enhancement of compact support kernel-based distributions using image post-processing: Application to instantaneous frequency estimation of M-ary frequency shift keying signals

Time-frequency distributions (TFDs) based on time-lag kernels with compact support (KCS) have proved their high performance in terms of resolution and crossterms suppression. However, as for all kernel-based quadratic TFDs, these distributions suffer from spreading out signal terms. This is due to the unavoidable smoothing effects of the kernel in the ambiguity domain. The main objective of this paper is to improve concentration, interference rejection and so time-frequency localization of this representation class. The latter has the advantage of being tuned using a single parameter while external windows are no longer needed. The KCS-TFDs, referred to as KCSDs, are first optimized using a selection of the most used objective performance measures in the literature. Important signal features are extracted as well through analysis of time slice plots. The obtained TF diagrams are then enhanced using a specific method that includes two-dimensional Wiener filter, automatic binarization and morphological image processing techniques. The enhanced plots are compared to those obtained from the original TFDs using several tests on real-life and multicomponent frequency modulated (FM) signals including the noise effects. Moreover, a comparative study involving a selection of the best-performing reassignment time-frequency distributions is provided. The obtained results show a significant improvement of concentration, time-frequency localization of the autoterms as well as interference and noise suppression. As viable applications, the proposed approach is used first to instantaneous frequency (IF) estimation of several synthetic and real-life M-ary frequency shift keying (MFSK) signals. It is shown that the IF estimator from the enhanced plots performs better than smoothed pseudo Wigner-Ville distribution (SPWVD) and reassignment post-processing-based TFDs in terms of mainlobe width (MLW) and variance, respectively, even at low signal-to-noise ratio (SNR). On the other hand, time-frequency characterization of continuous wave linear frequency modulation (CW-LFM) and pulse linear FM (PLFM) radar signals is also investigated.

SP-WVD with Adaptive-Filter-Bank-Supported RF Sensor for Low RCS Targets' Nonlinear Micro-Doppler Signature/Pattern Imaging System.

In this study, the authors present the accurate imaging of the behavior of simultaneous operations of multiple low radar cross-section (RCS) aerial targets. Currently, the popularity of low RCS targets is increasing day by day, and detection and identification of these targets have become critical issues. Micro-Doppler signatures are key components for detecting and identifying these low RCS targets. For this, an innovative approach is proposed along with the smooth pseudo-Wigner–Ville distribution (SP-WVD) and adaptive filter bank to improve the attenuation of cross-term interferences to generate more accurate images for the micro-Doppler signatures/patterns of simultaneous multiple targets. A C-band (5.3 GHz) radio-frequency (RF) sensor is designed and used to acquire the micro-Doppler signatures of aerial rotational, flapping, and motional low RCS targets. Digital pipelined-parallel architecture is designed inside the Xilinx field-programable gate array (FPGA) for fast sensor data collection, data preprocessing, and interface to the computer (imaging algorithm). The experimental results of the proposed approach are validated with the results of the classical short-term Fourier transform (STFT), continuous wavelet transform (CWT), and smooth pseudo-Wigner Ville distribution (SP-WVD). Realistic open-field outdoor experiments are conducted covering different simultaneous postures of (i) two-/three-blade propeller/roto systems, (ii) flapping bionic bird, and (iii) kinetic warhead targets. The associated experimental results and findings are reported and analyzed in this paper. The limitations and possible future research studies are also discussed in the conclusion.

Hardware Implementation of Stockwell Transform and Smoothed Pseudo Wigner Ville Distribution Transform on FPGA using CORDIC Algorithm

A comparison of linear and quadratic transform implementation on field programmable gate array (FPGA) is presented. Popular linear transform namely Stockwell Transform and Smoothed Pseudo Wigner Ville Distribution (SPWVD) transform from Quadratic transforms is considered for the implementation on FPGA. Both the transforms are coded in Verilog hardware description language (Verilog HDL). Complex calculations of transformation are performed by using CORDIC algorithm. From FPGA family, Spartan-6 is chosen as hardware device to implement. Synthetic chirp signal is taken as input to test the both designed transforms. Summary of hardware resource utilization on Spartan-6 for both the transforms is presented. Finally, it is observed that both the transforms S-Transform and SPWVD are computed with low elapsed time with respect to MATLAB simulation.

Interference Mitigation Based on Low Complexity Subspace Tracking Method for Vehicle Positioning

Advanced driver assistance systems and automatic driving have drawn lots of attentions due to user’s multiapplication needs. Among different technologies, the integration of Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) is a key technique with the decreasing costs of Inertial Measurement Unit (IMU) and the increasing deployment of GNSS for navigation applications. Although the integration may have immune ability to interference in a certain extent, interference suppression strategy applied on the integration system can greatly improve the performance. A complete framework including interference monitor, detection, and mitigation is provided jointly using subspace tracking method and Kalman filter measurements innovation of INS and GNSS. The proposed monitor is simple, efficient, and can decide when to start the interference mitigation procedure, which can reduce the computation complexity significantly; Subspace‐based method is introduced to track the interference basis matrix that can be feed to RootMUSIC to detect the frequency of interference, followed by the interference mitigation with a notch filter. The proposed framework has superior performance than the well‐known time‐frequency algorithm, such as short‐time Fourier transform (STFT) and smoothed pseudo Wigner‐Ville distribution (SPWVD), and can improve the performance of INS/GNSS system in the presence of interference with simulation verification.

Cross-Term Suppression Method for Time-Frequency Spectrum of Engineering Blasting Signals

Abstract Engineering blasting vibration signals are affected by the test environment and contain noise and trend components, which leads to significant cross-term in the time-frequency (TF) distribution. To address these problems, a combined algorithm of matching pursuit (MP) and smooth pseudo-Wigner-Ville distribution (SPWVD) is proposed to suppress the TF spectrum cross-term and extract the signal features. An overcomplete atom library is constructed for signal feature matching according to sparse signal representation theory. Atomic reconstruction of the subsignal is achieved by MP decomposition, and the SPWVD distribution of the reconstructed subsignal is calculated and superimposed, yielding a more accurate TF expression of the blasting signal. The results show that the combined MP-SPWVD method can accurately suppress cross-term and improve the TF identification and feature analysis ability, which verifies the accuracy of its application in signal TF analysis. The combined algorithm is thus suitable for TF feature extraction of engineering blasting signals.

Human Activity Recognition Based on Mixed CNN With Radar Multi-Spectrogram

Deep learning makes radar-based human activity recognition (HAR) attract more attention in the fields of intelligent security, traffic management, medical rehabilitation and military operation, because it has the ability to automatically extract comprehensive features of human activity. This paper proposes a recognition method based on multi-spectrogram and mixed convolutional neural network (MCNN). Specifically, three time-frequency analyses, including short-time Fourier transform (STFT), reduced interference distribution with Hanning kernel (RIDHK) and smoothed pseudo Wigner-Ville distribution (SPWVD), are performed on radar echo data to obtain the time-frequency spectrograms with different feature expressions, and then the spectrograms are fed into the MCNN for recognition and classification. In the MCNN, three two-dimensional CNNs (2DCNNs) are used to extract the independent spatial features from three types of spectrograms, and one three-dimensional CNN (3DCNN) with unit convolution kernel is employed to focus on extracting the correlation features between three kinds of spectrograms. The behavioral features in the spectrograms are characterized comprehensively by fusing these two kinds of features, which is able to improve the recognition accuracy. Experimental results illustrate that the proposed method improves the average recognition accuracy of eight human activities by at least 2.16% compared with other methods.

Lamb wave damage severity estimation using ensemble-based machine learning method with separate model network

Lamb wave-based damage estimation have great potential for structural health monitoring. However, designing a generalizable model that predicts accurate and reliable damage quantification result is still a practice challenge due to complex behavior of waves with different damage severities. In the recent years, machine learning (ML) algorithms have been proven to be an efficient tool to analyze damage-modulated Lamb wave signals. In this study, ensemble-based ML algorithms are employed to develop a generalizable crack quantification model for thin metallic plates. For this, the scattering of Lamb wave signals due to different configuration of crack dimension and orientation is extensively studied. Various finite element simulations signals, representing distinct crack severities in term of crack length, penetration and orientation are acquired. Realizing that both temporal and spectral information of signal is extremely important to damage quantification, three time-frequency (TF) based damage sensitive indices namely energy concentration, TF flux and coefficient of energy variance are proposed. These damage features are extracted by employing smoothed-pseudo Wigner–Ville distribution. After that data augmentation technique based on the spline-based interpolation is applied to enhance the size of the dataset. Eventually, these fully developed damage dataset is deployed to train ensemble-based models. Here we propose separate model network, in which different models are trained and then link together to predict new and unseen datasets. The performance of the proposed model is demonstrated by two cases: first simulated data incorporated with high artificial noises are employed to test the model and in the second scenario, experimental data in raw form are used. Results indicate that the proposed model has the potential to develop a general model that yields reliable answer for crack quantification.

Identification of Epileptogenic and Non-epileptogenic High-Frequency Oscillations Using a Multi-Feature Convolutional Neural Network Model.

Accurately identifying epileptogenic zone (EZ) using high-frequency oscillations (HFOs) is a challenge that must be mastered to transfer HFOs into clinical use. We analyzed the ability of a convolutional neural network (CNN) model to distinguish EZ and non-EZ HFOs. Nineteen medically intractable epilepsy patients with good surgical outcomes 2 years after surgery were studied. Five-minute interictal intracranial electroencephalogram epochs of slow-wave sleep were selected randomly. Then 5 s segments of ripples (80–200 Hz) and fast ripples (FRs, 200–500 Hz) were detected automatically. The EZs and non-EZs were identified using the surgery resection range. We innovatively converted all epochs into four types of images using two scales: original waveforms, filtered waveforms, wavelet spectrum images, and smoothed pseudo Wigner–Ville distribution (SPWVD) spectrum images. Two scales were fixed and fitted scales. We then used a CNN model to classify the HFOs into EZ and non-EZ categories. As a result, 7,000 epochs of ripples and 2,000 epochs of FRs were randomly selected from the EZ and non-EZ data for analysis. Our CNN model can distinguish EZ and non-EZ HFOs successfully. Except for original ripple waveforms, the results from CNN models that are trained using fixed-scale images are significantly better than those from models trained using fitted-scale images (p < 0.05). Of the four fixed-scale transformations, the CNN based on the adjusted SPWVD (ASPWVD) produced the best accuracies (80.89 ± 1.43% and 77.85 ± 1.61% for ripples and FRs, respectively, p < 0.05). The CNN using ASPWVD transformation images is an effective deep learning method that can be used to classify EZ and non-EZ HFOs.

A two-stage deep transfer learning for localisation of forced oscillations disturbance source

Accurately locating forced oscillations (FOs) disturbance source in a large-scale power system is a challenging task. In this paper, a localisation method featuring system-level and area-level localisation is proposed. Compared with traditional localisation methods which process the FOs signals only in control centre phasor data concentrator (PDC), the proposed method can not only relieve the data communication pressure, but also meets the data privacy and confidentiality requirements of utility companies. Besides, with the two-stage deep transfer learning, high accuracy of localisation can be realised with far less training. Firstly, by adopting principle component analysis (PCA) to extract the most representative information at system-level and smooth pseudo Wigner-Ville distribution (SPWVD) to characterize FOs signals, graphical representations of FOs at system-level and area-level are obtained respectively, transforming the localisation problem to image recognition problem. Subsequently, a two-stage deep transfer learning (DTL) algorithm is developed to locate FOs disturbance source. The first stage involves repurposing the learnt features from a pre-trained deep convolutional neural network (previously trained for universal image recognition) to improve the learning of system-level localisation. In a similar logic, the second stage entails transferring the knowledge acquired from the first stage is exploited to aid area-level localisation learning. Case studies carried out on the WECC 179-bus system demonstrate that the proposed method achieves a significantly higher accuracy in the presence of measurement noise, topology variation and load disturbances of the system with respect to the traditional machine learning method. The proposed method also exhibits a more favorable computational performance and learning efficiency due to the employment of the tactfully designed two-stage DTL approach.

PDCNNet: An Automatic Framework for the Detection of Parkinson’s Disease Using EEG Signals

Parkinson's disease (PD) is a neurodegenerative ailment which causes changes in the neuronal, behavioral, and physiological structures. During the early stages of PD, these changes are very subtle and hence accurate diagnosis is challenging. Pathological and neurological experts assess the PD patients by examining their drawing, writing, walking, tremor, facial expressions, and speech. The manual analysis performed by specialists is time-consuming and prone to errors. Electroencephalogram (EEG) signals represent changes in the brain activities, but it is difficult to manually analyze these signals due to their non-linear, non-stationary, and complex nature. Traditional machine learning methods require several manual steps, such as decomposition, extraction of features, and classification. To overcome these limitations, automated PD detection using smoothed pseudo-Wigner Ville distribution (SPWVD) coupled with convolutional neural networks (CNN) called Parkinson's disease CNN (PDCNNet) is proposed. First the EEG signals are subjected to SPWVD to obtain time-frequency representation (TFR). Then these two-dimensional plots are fed to an CNN. The proposed model is developed using two public databases. We have obtained an accuracy of 100% and 99.97% for dataset 1 and 2, respectively in detecting PD automatically using our proposed PDCNNet model. Our developed prototype has outperformed all existing state-of-the-art techniques and ready to be validated with more diverse datasets.