Ville Distribution Research Articles

Adaptive stochastic resonance enhanced weak linear frequency modulated signal perception in low signal-to-noise ratio environments

Abstract The linear frequency modulated (LFM) signal has gained extensive utilization in radar, sonar and covert communication system due to its large time-bandwidth product, high-precision distance measurement and low detection probability. The perception of weak LMF signals holds significant importance yet encounters substantial challenges within the increasing complexity of the electromagnetic environments. Consequently, this paper proposes an adaptive stochastic resonance (ASR) enhanced approach for perceiving weak LFM signals in low signal-to-noise ratio (SNR) conditions. This approach initially commences a pioneering study on the quantitative synergistic resonance mechanism among LFM signals, random noise, and nonlinear stochastic resonance (SR) systems. Subsequently, the ASR system’s implementation becomes straightforward through the adaptive adjustment of SR system parameters according to the LFM signal and noise characteristics. This implementation leverages the inherent property of noise energy transfer to signal energy, facilitating the enhancement of ordered weak signals via random noise. Following the enhancement of the output signal by the ASR system, the Wigner–Ville distribution (WVD) transform’s time-frequency concentration property is employed to extract the time-frequency characteristics. Building on the WVD transform, the Radon transform with linear integral projection is applied to further harness the time-frequency domain energy concentration, thereby achieving the effective perception of weak LFM signals. Finally, the effectiveness of the proposed method in improving the perception performance of weak LFM signal in very low SNR conditions is verified through numerical simulations. It is anticipated that this method will have potential application value in fields such as radar, sonar, and communication under complex electromagnetic environments.

A Multi-Cycle Echo Energy Concentration Method for High-Mobility Targets Enveloped by Time-Varying Plasma Sheath

When a target moves at hypersonic speed, the aerodynamic thermal effect will cause air molecules to form a plasma sheath that envelopes the outer surface of the target, which consists of a large number of charged particles. The plasma sheath imposes a complicated modulation effect on the radar echo signal in terms of amplitude, phase, and frequency. When the plasma sheath is time-varying, the inter-pulse coherence of the multi-cycle echo signals is severely disrupted, resulting in the failure of coherent accumulation. To address the problem of abnormal inter-pulse energy accumulation in targets covered with time-varying plasma sheaths, we analyzed the dynamic modulation effects of time-varying plasma sheaths on echo signals and constructed a radar echo model enveloped with time-varying plasma sheaths. Based on this, we propose a method for inter-pulse energy concentration of multi-cycle echo signals based on range-frequency inversion, second-order Wigner–Ville distribution (WVD), and slow-time symmetric auto-correlation. The proposed method is capable of realizing energy concentration for targets enveloped with time-varying plasma sheaths and can accurately estimate the motion parameters of the target. The effectiveness of our proposed method has been verified via simulation analysis of multi-cycle echo signals from targets enveloped with time-varying plasma sheaths, and the reliability of the method has been further validated through statistical experimental analysis.

Vehicle Response-Based Bridge Modal Identification Using Different Time–Frequency Analysis Methods

Modal identification of bridges based on the responses of moving vehicles, termed as the indirect method, has drawn much attention in recent years. This indirect method has been proven to be capable of identifying bridge frequencies and mode shapes in the feasibility research. However, in the presence of additional factors such as vehicle speed and road surface roughness, it is difficult to identify high-order frequencies and high-resolution mode shapes of the bridge. The authors previously proposed a tractor-double-trailers model and the time–domain subtraction method to obtain the relative displacement of two trailers for bridge modal identification. In this study, the authors develop a methodology to improve the identification performance by combining the EMD technique and the time–frequency analysis method. The EMD technique is applied to separate the multi-source response signals of the trailers to obtain the signal component that contains only the bridge vibration. Then, different time–frequency analysis methods such as the short-time Fourier transform (STFT), Wigner–Ville distribution (WVD), and continuous wavelet transform (CWT) are adopted to construct the high-resolution bridge mode shapes. Numerical studies with one-dimensional and three-dimensional bridge models are conducted to verify the proposed method and investigate the effects of different factors. Finally, a laboratory test is implemented on a scaled bridge to verify the performance of the proposed method. The results show that the proposed method is able to separate the vehicle frequency and bridge frequencies, which facilitates the identification of bridge frequencies from the dynamic response of moving vehicles. Meanwhile, the CWT method performs the best in the identification of modal shapes among the three time–frequency analysis methods.

Automatic Wake and Deep-Sleep Stage Classification Based on Wigner-Ville Distribution Using a Single Electroencephalogram Signal.

This research paper outlines a method for automatically classifying wakefulness and deep sleep stage (N3) based on the American Academy of Sleep Medicine (AASM) standards. The study employed a single-channel EEG signal, leveraging the Wigner-Ville Distribution (WVD) for time-frequency analysis to determine EEG energy per second in specific frequency bands (δ, θ, α, and entire band). Particle Swarm Optimization (PSO) was used to optimize thresholds for distinguishing between wakefulness and stage N3. This process aims to mimic a sleep technician's visual scoring but in an automated fashion, with features and thresholds extracted to classify epochs into correct sleep stages. The study's methodology was validated using overnight PSG recordings from 20 subjects, which were evaluated by a technician. The PSG setup followed the 10-20 standard system with varying sampling rates from different hospitals. Two baselines, T1 for the wake stage and T2 for the N3 stage, were calculated using PSO to ascertain the best thresholds, which were then used to classify EEG epochs. The results showed high sensitivity, accuracy, and kappa coefficient, indicating the effectiveness of the classification algorithm. They suggest that the proposed method can reliably determine sleep stages, being aligned closely with the AASM standards and offering an intuitive approach. The paper highlights the strengths of the proposed method over traditional classifiers and expresses the intentions to extend the algorithm to classify all sleep stages in the future.

Online detection and assessment of cable insulation fault based on time–frequency domain reflectometry

The insulation performance of cables plays an important role in the safe and stable operation of aircraft. Time–frequency domain reflectometry (TFDR) is an effective method to detect the local insulation faults of cables. Usually, Wigner–Ville distribution (WVD) is used to analyze the energy distribution of reflected signals in TFDR. However, WVD can easily introduce cross-term interference to the detection results. In addition, most of the current studies have used TFDR to perform offline detection of cable insulation fault, and the performance of TFDR for online operation is unclear. In order to solve the above problems, first, this paper eliminates the interference of cross-term based on smoothed pseudo-Wigner–Ville distribution. Then, an online cable insulation fault detection platform based on non-contact signal injection is built. According to the requirements of the standard GJB181A, the interference degree of the incident signal of TFDR to the original signal of cable is analyzed, and the feasibility of using TFDR method to perform online detection is proved. Finally, the correlation between different features of reflected signals under different fault degrees of cable is analyzed. It is proved that time-domain correlation has a better correlation with the fault degree of cable compared to other four features.

The short-time Wigner–Ville distribution

The Wigner–Ville distribution (WD) and ambiguity function (AF) are serviceable tools for the global analysis of non-stationary signals. However, when dealing with time-varying signals that exhibit changing characteristics and require real-time signal processing, they have high limitations due to the existence of cross-items. In this paper, we propose the short-time Wigner–Ville distribution (STWD) as a novel approach that effectively analyzes time-varying signals with changing characteristics. First, the definition of STWD and short-time ambiguity function (STAF) and their properties are advanced. Next, three uncertainty principles that define the lower bound for the product of signal spread and its bandwidth are derived. Then, the discrete STWD (DSTWD) and the process of computerization are also proposed which can be used more widely in practice. Finally, the optimization of window functions based on Rényi entropy is discussed. Simulation experiments show that the STWD can be effectively applied for the analysis of local change characteristics and real-time processing of signals with valid and accurate results.

A Frangi filter aided deep learning approach for palaeochannel recognition

SUMMARY In view of the problem of identifying palaeochannels with high concealment and complex geological structures, this paper proposes an intelligent recognition method for palaeochannels based on Frangi filtering and deep learning. The methodology makes use of Maximum Entropy Wigner–Ville Distribution (MEWVD) method to process the original instantaneous amplitude data, which enhance the distinct features of micro palaeochannels in different sensitive frequency bands. The sample 2-D stratigraphic images generated from these data is labelled for the pre-training process of Attention R2U-Net neural network model. Subsequently, Frangi filter is used to identify and enhance the linear structures of river channels in target stratigraphic images, improving the identification effect of the neural network. Finally, RGB data fusion and 3-D visualization carving are performed on the identification data. This method not only eliminates redundant information using the Frangi filter but also proves that the Attention R2U-Net network model structure with attention mechanism and residual convolution structure can effectively improve the segmentation effect for river channels at different scales. Experimental examples show that this method achieves pixel-level feature segmentation of 3-D seismic data for palaeochannels, accurately depicting their shape, width, thickness, flow direction and other features, thus providing support for subsequent well deployment and horizontal well fracturing selection.

Sea Clutter Suppression Using Smoothed Pseudo-Wigner–Ville Distribution–Singular Value Decomposition during Sea Spikes

The detection of small targets within the background of sea clutter is a significant challenge faced in radar signal processing. Small target echoes are weak in energy, and can be submerged by sea clutter and sea spikes, which are caused by overturning waves and breaking waves. This severely affects the radar target detection performance. This paper proposes a smoothed pseudo-Wigner–Ville distribution–singular value decomposition (SPWVD-SVD) method for sea clutter suppression. This method determines the instantaneous frequency range of the target by contrasting the time–frequency characteristics of the sea spike and the target. Subsequently, it employs a singular value difference spectrum to reduce the rank of the Hankel matrix, thereby reducing the computational burden of the instantaneous frequency estimation step in the experiment. Based on the instantaneous frequency range of the target in the time–frequency domain, the singular values of the target signal are retained, while the singular values of clutter are set to zero. This process accomplishes the reconstruction of radar echo signals and effectively achieves the suppression of sea clutter. The suppression effect is verified using simulation data alongside ten sets of Intelligent Pixel processing X-band (IPIX) radar data against the background of sea spikes. By contrasting the clutter amplitudes before and after suppression, the SPWVD-SVD algorithm demonstrated an average clutter suppression of 15.06 dB, which proves the effectiveness of the proposed algorithm in suppressing sea clutter.

Modulation recognition of optical and electromagnetic waves based on transfer learning

Light is a type of electromagnetic wave. Research on the modulation recognition of communication signals, which are also electromagnetic waves, can be applied to the field of modulation and demodulation of optical waves. The limited signal data and varying data distribution have an impact on the automatic modulation recognition of signals. To address this, we proposed a method to enhance the characteristic information of modulation patterns carried by signal data. We used the Wigner–Ville distribution and short-time Fourier transform to convert the original I/Q multi-channel modulated communication signal into time–frequency representation images (TFRIs). Additionally, we adopted a transfer learning approach, the domain adaptation network (DAN), to identify modulation modes of signals under different SNRs. The combination of signal conversion and transfer learning significantly improved the identification of modulation recognition. Our experiments demonstrated that our proposed method outperformed existing state-of-the-art methods in terms of classification accuracy at both high and low signal-to-noise ratios (SNRs). Specifically, our method achieved a 10% increase in Top1-accuracy under high SNR, and overall improved the classification accuracy under low SNR compared to the adversarial transfer learning architecture (ATLA). This is attributed to the use of a more diverse and accurate dataset that provides a better representation of real-world communication signals. We also compared our experimental results with those of other papers, and the results show that our method achieved the best performance among the current state-of-the-art methods, considering the classification accuracy at different SNRs.

Wigner–Ville Distribution Associated with Clifford Geometric Algebra Cln,0, n=3(mod 4) Based on Clifford–Fourier Transform

In this study, the Wigner–Ville distribution is associated with the one sided Clifford–Fourier transform over Rn, n = 3(mod 4). Accordingly, several fundamental properties of the WVD-CFT have been established, including non-linearity, the shift property, dilation, the vector differential, the vector derivative, and the powers of τ∈Rn. Moreover, powerful results on the WVD-CFT have been derived such as Parseval’s theorem, convolution theorem, Moyal’s formula, and reconstruction formula. Eventually, we deduce a directional uncertainty principle associated with WVD-CFT. These types of results, as well as methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.

Research on Intelligent Monitoring of Boring Bar Vibration State Based on Shuffle-BiLSTM.

Due to its low stiffness, the boring bar used in deep-hole-boring is prone to violent vibration during the cutting process. It is often inaccurate and inefficient to judge the vibration state of the boring bar through artificial experience. To detect the change of the vibration state of the boring bar over time, guide the adjustment of the processing parameters, and avoid wastage of the workpiece and the loss of equipment, it is particularly important to intelligently monitor the vibration state of the boring bar during processing. In this paper, the boring bar is taken as the research object, and an intelligent monitoring technology of the boring bar's vibration state based on deep learning is proposed. Based on grouping convolution, channel shuffle, and BiLSTM, a shuffle-BiLSTM NET model is constructed, which is both lightweight and has a high classification accuracy. The boring experiment platform is built, and 192 groups of cutting experiments are carried out. The three-way acceleration and sound pressure signals are collected, and the signals are processed by smoothed pseudo-Wigner-Ville distribution. The original signals are transformed into a 256 × 256 × 3 matrix obtained by a two-dimensional time-frequency spectrum diagram. The matrix is input into the model to recognize the boring bar's vibration state. The final classification accuracy is 91.2%. A variety of typical deep learning models are introduced for performance comparison, which proves the superiority of the models and methods used in this paper.

Post-Earthquake Damage Identification of Buildings with LMSST

The structure is said to be damaged if there is a permanent shift in the post-event natural frequency of a structure as compared with the pre-event frequency. To assess the damage to the structure, a time-frequency approach that can capture the pre-event and post-event frequency of the structure is required. In this study, to determine these frequencies, a local maximum synchrosqueezing transform (LMSST) method is employed. Through the simulation results, we have shown that the traditional methods such as the Wigner distribution, Wigner–Ville distributions, pseudo-Wigner–Ville distributions, smoothed pseudo-Wigner–Ville distribution, and synchrosqueezing transforms are not capable of capturing the pre-event and post-event frequency of the structure. The amplitude of the signal captured by sensors during those events is very small compared with the signal captured during the seismic event. Thus, traditional methods cannot capture the frequency of pre-event and post-event, whereas LMSST employed in this work can easily identify these frequencies. This attribute of LMSST makes it a very attractive method for post-earthquake damage detection. In this study, these claims are qualitatively and quantitatively substantiated by comprehensive numerical analysis.

Using Deep Transfer Learning Technique to Protect Electrical Distribution Systems Against High-Impedance Faults

The dependence of high-impedance faults (HIFs) detection methods on a large amount of training data has always been a fundamental problem in electrical distribution systems. This article proposes a novel protection system based on the transfer learning technique and GoogleNet architecture to reduce this dependence. The proposed protection system uses a small amount of data to extend the knowledge of pretrained GoogleNet architecture to the HIF detection problem. In this system, a small amount of third harmonic angle data of the current at the measurement point are obtained from the understudy electrical distribution system. Then, the preprocessing phase is performed, and the extracted data are converted to image data using the Wigner–Ville distribution. Afterward, these converted images are fed to the GoogleNet architecture as an input dataset to update the GoogleNet pretrained knowledge. Finally, the process of fault detection and classification is accomplished only by transferring the GoogleNet pretrained knowledge. The simulation results of the modified IEEE 13-bus and 34-bus distribution systems in EMTP-RV and MATLAB indicate the high accuracy of the proposed protection system despite the use of a small amount of input training data.

LPI Waveform Recognition Using Adaptive Feature Construction and Convolutional Neural Networks

Low probability of intercept (LPI) radar waveform recognition is one of the crucial functions in electronic intelligence systems. Advances in artificial intelligence promote the performance of the LPI waveform recognition with various signal features defined with analytical expressions. However, noisy LPI waveform recognition is still a challenge for traditional approaches even with noise elimination techniques, especially for the heavily contaminated noisy LPI signals. Recently, the adaptive analysis techniques, such as variational mode decomposition (VMD) and empirical mode decomposition (EMD) provide potential methods that explore the inherent features of signals and formulate adaptive features for signal recognition. In this article, we propose an adaptive feature construction framework that utilizes both the adaptive features (via VMD and EMD) and predefined analytical features (via Wigner–Ville distribution, Choi–William distribution, and wavelet analysis) to construct the fusion feature, which is further applied on the convolutional neural networks-based LPI waveform recognition system. The experimental results show that the proposed feature adaptive LPI network-based exploitation (FALPINE) approach achieves higher probability of correct classification than the state-of-the-art works, which demonstrates the superior performance of the proposed approach.

A combined method to identify the rail irregularity at welded region

The track irregularities affect the safety and comfort of running vehicle and increase the dynamic responses of vehicle and track. There is the rail irregularity at the welded region, and the irregularity can be regarded as the superposition of two cosine waves with the long wavelength about 1 m and the short wavelength of 0.1–0.2 m. The welded location has both short-wavelength irregularity and long-wavelength irregularity. A combined method is presented to identify the rail irregularity at the welded region using the acceleration time history curve of wheelset. Firstly, the accelerations of wheelset are transformed into the different frequencies domain signals by wavelet transformation, and the rail irregularity with the short wavelength and high-frequency is determined. Secondly, the rail irregularity with the long wavelength and low-frequency is identified by the Wigner–Ville distribution or the short-time energy method. Finally, the rail irregularity at the welded region is determined by both of the above two steps met. The correctness of the proposed method is validated by numerical example. The proposed method can accurately and efficiently identify the high-frequency and low-frequency characteristics of the rail irregularity at the welded region.

Automated extraction of baleen whale calls based on the pseudo-Wigner–Ville distribution

Baleen whales produce a wide variety of frequency-modulated calls. Extraction of the time-frequency (TF) structures of these calls forms the basis for many applications, including abundance estimation and species recognition. Typical methods to extract the contours of whale calls from a spectrogram are based on the short-time Fourier transform and are, thus, restricted by a fixed TF resolution. Considering the low-frequency nature of baleen whale calls, this work represents the contours using a pseudo-Wigner-Ville distribution for a higher TF resolution at the cost of introducing cross terms. An adaptive threshold is proposed followed by a modified Gaussian mixture probability hypothesis density filter to extract the contours. Finally, the artificial contours, which are caused by the cross terms, can be removed in post-processing. Simulations were conducted to explore how the signal-to-noise ratio influences the performance of the proposed method. Then, in experiments based on real data, the contours of the calls of three kinds of baleen whales were extracted in a highly accurate manner (with mean deviations of 5.4 and 0.051 Hz from the ground-truth contours at sampling rates of 4000 and 100 Hz, respectively) with a recall of 75% and a precision of 78.5%.

Adaptive synchronous demodulation transform with application to analyzing multicomponent signals for machinery fault diagnostics

The combination of the complex structure and the nonstationary operating pattern makes the measured signal of the machinery a multi-component one with a complex time-varying spectral structure, challenging most time–frequency analysis methods in resolution, adaptability, and objectivity. As such, we propose a novel time–frequency analysis method, namely, the adaptive synchronous demodulation transform (ASDT), by adaptively designing a demodulation term according to the spectral structures of the target signals. The proposed demodulation term can make each component of the windowed signal stationary simultaneously without any prior knowledge, such as the number of components and the corresponding estimated instantaneous frequencies. ASDT possesses three main advantages: it can be used to analyze signals with nonlinear instantaneous frequencies; it can obtain the optimum frequency resolution when window width is set; and the demodulation term is flexible, implying that it can be specifically designed according to the frequency structures of different types of signals. Furthermore, ASDT allows for signal recovery. To testify the superiority of the proposed ASDT, two synthetic signals with parallel and proportional IFs structures were built, and several real-life signals, vibration signals collected from a planetary gearbox test rig and water turbine, and an echo signal collected from a brown bat were used. A comparison of the analysis results of ASDT with those of STFT, continuous wavelet transform, and Wigner–Ville distribution demonstrated the superiority of ASDT over conventional methods.

An Application of Analytic Wavelet Transform and Convolutional Neural Network for Radar Intrapulse Modulation Recognition.

This article analyses the possibility of using the Analytic Wavelet Transform (AWT) and the Convolutional Neural Network (CNN) for the purpose of recognizing the intrapulse modulation of radar signals. Firstly, the possibilities of using AWT by the algorithms of automatic signal recognition are discussed. Then, the research focuses on the influence of the parameters of the generalized Morse wavelet on the classification accuracy. The paper's novelty is also related to the use of the generalized Morse wavelet (GMW) as a superfamily of analytical wavelets with a Convolutional Neural Network (CNN) as classifier applied for intrapulse recognition purposes. GWT is used to obtain time-frequency images (TFI), and SqueezeNet was chosen as the CNN classifier. The article takes into account selected types of intrapulse modulation, namely linear frequency modulation (LFM) and the following types of phase-coded waveform (PCW): Frank, Barker, P1, P2, and Px. The authors also consider the possibility of using other time-frequency transformations such as Short-Time Fourier Transform(STFT) or Wigner-Ville Distribution (WVD). Finally, authors present the results of the simulation tests carried out in the Matlab environment, taking into account the signal-to-noise ratio (SNR) in the range from -6 to 0 dB.

An Interplay of Wigner–Ville Distribution and 2D Hyper-Complex Quadratic-Phase Fourier Transform

Two-dimensional hyper-complex (Quaternion) quadratic-phase Fourier transforms (Q-QPFT) have gained much popularity in recent years because of their applications in many areas, including color image and signal processing. At the same time, the applications of Wigner–Ville distribution (WVD) in signal analysis and image processing cannot be ruled out. In this paper, we study the two-dimensional hyper-complex (Quaternion) Wigner–Ville distribution associated with the quadratic-phase Fourier transform (WVD-QQPFT) by employing the advantages of quaternion quadratic-phase Fourier transforms (Q-QPFT) and Wigner–Ville distribution (WVD). First, we propose the definition of the WVD-QQPFT and its relationship with the classical Wigner–Ville distribution in the quaternion setting. Next, we investigate the general properties of the newly defined WVD-QQPFT, including complex conjugate, symmetry-conjugation, nonlinearity, boundedness, reconstruction formula, Moyal’s formula, and Plancherel formula. Finally, we propose the convolution and correlation theorems associated with WVD-QQPFT.

Parallel LSTM-CNN Network With Radar Multispectrogram for Human Activity Recognition

Owing to the ability of automatic feature extraction, deep learning is extensively applied in human activity recognition (HAR) based on radar. In this article, a recognition method based on a multispectrogram and deep-learning model is proposed. The radar echo data are transformed into spectrograms with different feature expressions by performing three time–frequency analyses, including short-time Fourier transform (STFT), reduced interference distribution with Hanning kernel (RIDHK), and smoothed pseudo-Wigner–Ville distribution (SPWVD), and then the spectrograms are sent to deep-learning model to realize HAR. The model employs three long short-term memory (LSTM) networks to learn the temporal features of the spectrograms and uses a 3-D convolutional neural network (3-DCNN) to extract the independent spatial features of a single spectrogram and the spatial correlation features between different kinds of spectrograms, named parallel LSTM-CNN network (PLCN). The PLCN is capable of effectively improving the degree of feature utilization in the spectrogram and the accuracy of human activity classification by fusing both temporal and spatial features. The final experimental results show that the average recognition accuracy of the method based on the PLCN for eight human activities reaches 94.75%, which is significantly higher than that of the three parallel LSTMs and the single 3-DCNN.