Analysis Of Multicomponent Signals Research Articles

Improved Lv’s Distribution for Noisy Multicomponent LFM Signals Analysis

This paper presents the improved Lv’s distribution (ImLVD) for noisy multicomponent linear frequency-modulated (LFM) signals analysis, which is of significant importance in radar signal processing. Two goals of this paper are (i) to overcome drawbacks of the Lv’s distribution (LVD), and (ii) to study mechanisms of the constant delay introduction. Theoretical comparisons in cross-term suppression, resolution, peak-to-sidelobe level, anti-noise performance and implementation are performed for the maximum likelihood (ML) method, Wigner–Hough transform (WHT), LVD, parameterized centroid frequency–chirp rate distribution (PCFCRD) and ImLVD. Based on theoretical comparisons and illustrative examples, superiorities of the ImLVD are demonstrated and several unclear mechanisms of the introduced constant delay are interpreted. Finally, three numerical examples are given to illustrate that, because of the high cross-term suppression, resolution, peak-to-sidelobe level and anti-noise performance without the non-uniform integration variable, the ImLVD is more suitable for noisy multicomponent LFM signals analysis.

On refinements to QMFD based chirp parameter estimation

Commuting matrix methods furnish a full basis of orthogonal eigenvectors for the discrete Fourier transform or its centered version needed for computing the discrete fractional Fourier transform and multicomponent chirp signal analysis. However, these approaches suffer from ill-conditioning issues at higher matrix sizes, and require a computationally expensive eigenvalue decomposition.In this paper, ill-conditioning issues associated with the QMFD approach developed previously by the authors are addressed via diagonal modification. Further symmetries of the eigenvectors are used to reduce the size of the underlying eigenvalue problem. These modifications are then incorporated into the real-arithmetic implementation of the QMFD approach that is shown to be significantly superior to the conventional implementation and the corresponding MSE of the chirp parameter estimates are shown to approach their Cramer–Rao lower bounds.

Tunable hyperbolic Cohen-class kernel for cross-term diminishing in time–frequency distributions

Nonstationary signals are found in many engineering applications. The analysis of nonstationary signals trough bi-dimensional functions allows tracing their time and frequency evolution. In this regard, energy-distribution representations allocate the analyzed-signal power over two description variables, time and frequency, and offer a large number of mathematical properties, such as an ideal infinite resolution in both domains. Unfortunately, energy-distribution representations generate cross terms for multi-component nonstationary signals, which might mislead the analysis interpretation. Cross-term effects can be lessened by applying an appropriate smoothing kernel; they distort the shape of auto terms at the same time. In this work, a novel tunable signal-independent hyperbolic kernel function is introduced for reducing cross-term effects, preserving valuable properties, during the analysis of multi-component nonstationary signals. Obtained results from computer-model and real-life cases of study validate and demonstrate the performance superiority of the proposed kernel function, in terms of cross-term suppression and time–frequency resolution, against the well-known and widely used the Choi-Williams distribution and the cone-shape distribution.

Sparse spectrum based swarm decomposition for robust nonstationary signal analysis with application to sleep apnea detection from EEG

Background and motivationTime–frequency representation (TFR) of a signal finds its application in numerous fields for non-stationary multicomponent signal analysis. Due to underlying difficulties and improvement scope in the current methodology, developing a new time–frequency method can improve spectral analysis of real-life signals and further can be extended to practical applications. Materials and methodsThe proposed new method swarm-sparse decomposition method (SSDM) is an advanced version of swarm decomposition (SWD) for decomposing nonstationary multicomponent signals into a finite number of oscillatory components (OCs). Benefiting from sparse spectrum and SWD, the proposed SSDM method delivers optimal estimation of boundary frequencies in the sparse spectrum, resulting in improved filter banks. In addition to SSDM, we have also proposed the spectrum approximator function, i.e., fused least absolute shrinkage and selection operator to modify sparse spectrum and get significant OCs. The performance of the proposed SSDM has been evaluated by TFR analysis and compared to SWD and Hilbert-Huang transform methods. Also, it has been tested for automated sleep apnea classification using a convolutional neural network (CNN) and bidirectional long short-term memory (BiLSTM) on the publicly available EEG database. ResultsThe proposed SSDM-TFR-CNN and SSDM-feature-fusion-BiLSTM frameworks outperformed all the compared methods used for sleep apnea detection and achieved the highest classification accuracy of 96.24% and 95.86%, respectively, in the subject-independent cross-validation scheme. ConclusionSimulation result shows that the proposed SSDM method delivers substantial improvement in time–frequency analysis. Our developed sleep apnea detection model could be a vital aid in clinical solutions.

Kernel ridge regression-based chirplet transform for non-stationary signal analysis and its application in machine fault detection under varying speed conditions

The vibration signals of variable speed rotating machines are non-stationary. Time-frequency analysis (TFA) can effectively analyze non-stationary signals in time–frequency (TF) plane and polynomial chirplet transform (PCT) is one of widely adopted TFA methods. In PCT, a vital step is to approximate the instantaneous frequency (IF) of signals through polynomial approximation. However, the solution of polynomial approximation is easily affected by noise or disturbance, which greatly limits the ability of PCT to analyze noisy signals. To solve this issue, kernel ridge regression-based chirplet transform (KRR-CT) is developed to precisely characterize the TF features of non-stationary signals and produce an energy concentrated TF plane. In the KRR-CT, even in the presence of severe noise, a stable solution can be obtained in the approximation step implemented through KRR. Moreover, KRR-CT based iterative algorithm is further constructed for the analysis of common multi-component signals. The efficacy of proposed KRR-CT based iterative algorithm is confirmed by synthetic and real signals, and the feasibility of applying it for machine fault detection is illustrated. The results indicate that the proposed methods can produce a more energy concentrated TF plane and provide more precise IF information for machine fault detection under varying speed conditions than four comparison methods.

An improved signal-dependent quadratic time-frequency distribution using regional compact kernels for analysis of nonstationary multicomponent LFM signals

The time-frequency analysis of nonstationary multicomponent linear frequency modulation (LFM) signals is still a challenging task due to their cross-term interferences. In this paper, a novel signal-dependent adaptive compact kernel based time-frequency distribution (CKD) named regional adaptive CKD (RACKD) is proposed. The proposed RACKD firstly represents the signal in the Doppler-lag (ν, τ) ambiguity domain, and then applies a signal-dependent regional compact kernel to filter the cross-term interferences, with preserving the auto-terms in the ambiguity domain. By automatically selecting the auto-terms' distribution area which represents the signals in the ambiguity domain, the parameters of the newly designed signal-dependent regional compact kernel can be adaptively set according to the signals to be processed. The proposed RACKD shows a more stable performance in the ability of cross-term rejection and component energy of signals concentration around their respective instantaneous frequency, compared to several existing state-of-the-art methods. Both simulation results and experimental results based on sea-truth data have validated the improved performance of the proposed method. For the simulated signal composed of one weak and two strong LFM components with crossing frequency, the proposed RACKD shows up to 2.6% gain as compared to the signal-dependent multidirectional distribution (MDD) approach.

A pde-Based Analysis of the Spectrogram Image for Instantaneous Frequency Estimation

Instantaneous frequency (IF) is a fundamental feature in multicomponent signals analysis and its estimation is required in many practical applications. This goal can be successfully reached for well separated components, while it still is an open problem in case of interfering modes. Most of the methods addressing this issue are parametric, that is, they apply to a specific IF class. Alternative approaches consist of non-parametric time filtering-based procedures, which do not show robustness to destructive interference—the most critical scenario in crossing modes. In this paper, a method for IF curves estimation is proposed. The case of amplitude and frequency modulated two-component signals is addressed by introducing a spectrogram time-frequency evolution law, whose coefficients depend on signal IFs time derivatives, that is, the chirp rates. The problem is then turned into the resolution of a two-dimensional linear system which provides signal chirp rates; IF curves are then obtained by a simple integration. The method is non-parametric and it results quite robust to destructive interference. An estimate of the estimation error, as well as a numerical study concerning method sensitivity and robustness to noise are also provided in the paper.

ECG Signals Processing by Using Wavelet Analysis: Diagnostic Capabilities

The problem of recognition and classification of biomedical signals is a complex problem related to the interdisciplinary field of computer science and medicine. Within the framework of the project implementation of the development of the new defibrillation equipment, it is necessary to solve the problems of analyzing biomedical signals of the electrocardiogram to obtain a diagnostic solution with the possibility of assigning a specific condition to the pathological condition of the patient. This article presents the analysis of electrocardiogram signals, considering the technical aspects of the analysis of multicomponent signals, and describes the diagnostic possibility of wavelet analysis of ECG signals. The paper considers the limited tools of analyzing the electrocardiogram signal, in particular, limitation of parametric data. Wavelet analysis may significantly expand the analysis of signals and transfer them into the time-frequency domain. Thus, the use of various basic functions of the wavelet transform leads to the determination of the additional diagnostically significant information formalized in the parameters extracted from the wavelet scalogram.

Fast-training feedforward neural network for multi-scale power quality monitoring in power systems with distributed generation sources

In this paper, a deep learning approach for power quality monitoring in systems with distributed generation sources is presented. The proposed method focuses in the multi-scale analysis of multi-component signals for power quality disturbances classification. The proposed methodology combines a signal processing stage using variational mode decomposition (VMD) to obtain the times scales of multi-component signals, and a deep learning stage using a simple feedforward neural network (FFNN) to classify the disturbances. The simple proposed architecture allows minimum training time of the classification model. In addition, the proposed method is able to classify different disturbance combinations based on a reduced training-set. The proposed VMD-FFNN method is tested using synthetic and simulated signals, and it is compared with other well-known methods based on convolutional and recurrent deep neuronal networks. Finally, the proposed method is assessed using lab measurements in order to shown its performance in a real-world environment.

Instantaneous Frequency Estimation Based on Modified Kalman Filter for Cone-Shaped Target

The instantaneous frequency (IF) is a vital parameter for the analysis of non-stationary multicomponent signals, and plays an important role in space cone-shaped target recognition. For a cone-shaped target, IF estimation is not a trivial issue due to the proximity of the energy of the IF components, the intersections among different IF components, and the existence of noise. Compared with the general parameterized time-frequency (GPTF), the traditional Kalman filter can perform better when the energy of different signal components is close. Nevertheless, the traditional Kalman filter usually makes association mistakes at the intersections of IF components and is sensitive to the noise. In this paper, a novel IF estimation method based on modified Kalman filter (MKF) is proposed, in which the MKF is used to associate the intersecting IF trajectories obtained by the synchroextracting transform (SET). The core of MKF is the introduction of trajectory correction strategy in which a trajectory survival rate is defined to judge the occurrence of association mistakes. When the trajectory survival rate is below the predetermined threshold, it means that an association mistakes occurs, and then the new trajectories generated by the random sample consensus algorithm are used to correct the wrong associations timely. The trajectory correction strategy can effectively obviate the association mistakes caused by the intersections of IF components and the noise. The windowing technique is also used in the trajectory correction strategy to improve computational speed. The experimental results based on the electromagnetic computation data show that the proposed method is more robust and precise than the traditional Kalman filter. Moreover, the proposed method has great performance advantages compared with other methods (i.e., the multiridge detection, the ant colony optimization, and the GPTF methods) especially in the case of low signal noise ratio (SNR).

Radon spectrogram-based approach for automatic IFs separation

The separation of overlapping components is a well-known and difficult problem in multicomponent signals analysis and it is shared by applications dealing with radar, biosonar, seismic, and audio signals. In order to estimate the instantaneous frequencies of a multicomponent signal, it is necessary to disentangle signal modes in a proper domain. Unfortunately, if signal modes supports overlap both in time and frequency, separation is only possible through a parametric approach whenever the signal class is a priori fixed. In this work, time-frequency analysis and Radon transform are jointly used for the unsupervised separation of modes of a generic frequency modulated signal in noisy environment. The proposed method takes advantage of the ability of the Radon transform of a proper time-frequency distribution in separating overlapping modes. It consists of a blind segmentation of signal components in Radon domain by means of a near-to-optimal threshold operation. The inversion of the Radon transform on each detected region allows us to isolate the instantaneous frequency curves of each single mode in the time-frequency domain. Experimental results performed on constant amplitudes chirp signals confirm the effectiveness of the proposed method, opening the way for its extension to more complex frequency modulated signals.

Radar Signal Intra-Pulse Modulation Recognition Based on Convolutional Neural Network and Deep Q-Learning Network

Intra-pulse modulation recognition of radar signals is an important part of modern electronic intelligence reconnaissance and electronic support systems. With the increasing density of radar signals, the analysis and processing of multi-component radar signals have become an urgent problem in the current radar reconnaissance system. In this paper, an intra-pulse modulation recognition approach for single-component and dual-component radar signals is proposed. First, in order to adapt to the time-frequency energy distribution characteristics of various radar signals, we propose to extract the time-frequency images (TFIs) of received signals by Cohen class time-frequency distribution (CTFD) with multiple kernel functions. Besides, the image processing methods are used to suppress noise and adjust the size and amplitude of the TFIs. Second, we design and pre-train a TFI feature extraction network for radar signals based on a convolutional neural network (CNN). Finally, to improve the probability of successful recognition (PSR) of the recognition system in the pulse overlapping environment, a multi-label classification network based on a deep Q-learning network (DQN) is explored. Besides, two sub-networks take TFIs based on special kernel functions as input and re-judge the recognition results of some specific signals to further enhance the recognition effect of the recognition system. The proposed approach can identify 8 kinds of random overlapping radar signals. The simulation results show that the overall PSR of dual-component radar signals and single-component radar signals can reach 94.83% and 94.43%, respectively, when the signal-to-noise ratio (SNR) is −6 dB.

A multi-perspective architecture for high-speed train fault diagnosis based on variational mode decomposition and enhanced multi-scale structure

The performance degradation and failure of high-speed train bogie would directly threaten the safe long-term operation of the vehicle. The fault diagnosis based on vibration signals is encountering difficulties as nonlinearity, high complexity, strong coupling, and high uncertainty. To address these challenges, this paper proposes a multi-perspective architecture for fault diagnosis, based on variational mode decomposition and enhanced multi-scale convolutional neural network. The proposed method provides multiple perspectives for the multi-channel and multi-component signal analysis, including perspectives from channel, component and time scale, with low input dimension and reduced model complexity. Signal features under different perspectives can be adaptively extracted. The effectiveness of the proposed method is validated on high-speed train fault data and rolling element bearings dataset. The experimental results show that the proposed scheme not only improves the accuracy of fault diagnosis but also has superior noise robustness which could be valuable for practical applications of complex systems, especially in dynamic environments.

A new modified sliding window empirical mode decomposition technique for signal carrier and harmonic separation in non-stationary signals: Application to wind turbines

Modern control applications justify the need for improved techniques capable of coping with the non-stationary nature of measured signals while being able to monitor systems in real-time. Empirical Mode Decomposition (EMD) is known for its efficiency in time domain analysis of multi-component signals through Intrinsic Mode Functions (IMFs) extraction. Recent years witnessed the introduction of Sliding Window EMD (SWEMD) capable of analyzing signals in real time applications. However, complex signals require several sifting iterations while a rather increased number of IMFs might result in impracticality for on-line applications. This paper introduces a new modified faster SWEMD capable of extracting harmonics from non-stationary signals in real-time operation. The method uses the traditional EMD properties in the first pass for a small number of sifting processes. In addition, a new section is added to the algorithm based on inflection point tracking of the residue derivative from the first pass is added, in order to track low frequency waves and render the analysis faster. The method is validated for non-stationary signals with and without added colored noise and applied on measured turbine side angular velocity for harmonic extraction in wind turbines as an application. The proposed method may well be used for fault detection and disturbance rejection in mechanical systems.

Adaptive iterative generalized demodulation for nonstationary complex signal analysis: Principle and application in rotating machinery fault diagnosis

Abstract Effective identification of signal frequency contents and their time variability is a key to success in rotating machinery fault diagnosis under nonstationary conditions. Fine time-frequency resolution and free from both inner and outer interferences are necessary to achieve this purpose. Iterative generalized demodulation (IGD) can separate a nonstationary multi-component signal into constituent mono-components, and derive quality time-frequency representation based on Hilbert spectrum of each mono-component, thus offering an effective approach to nonstationary complex signal analysis. Nevertheless, it requires prior expertise knowledge about signal structure to ascertain true constituent components and construct proper demodulation phase functions. This leads to a major difficulty in real signal analysis tasks, where expertise knowledge is usually unavailable and signal time-frequency structure identification via visual observation is susceptible to noise interferences. To address this issue, the capability of surrogate test technique in recognizing true signal components is exploited, and thereby an adaptive iterative generalized demodulation (AIGD) is proposed. Proper demodulation phase functions corresponding to constituent components are derived accordingly, and Hilbert spectra of all constituent mono-components are superposed to generate time-frequency representation (TFR). This method features good merits, such as fine time-frequency resolution and free of both inner and outer interferences. Additionally, it neither relies on prior expertise knowledge about signals, nor needs to construct any basis function. It is highly adaptive to reveal the frequency contents and track their time variability of a signal, and provides an effective approach to nonstationary complex multi-component signal analysis. It is illustrated and validated via numerical simulations, lab experiments of a planetary gearbox and rolling bearings, and on-site tests of a hydraulic turbine in a hydraulic power plant.

Bispectrum-based technique to remove cross-terms in quadratic systems and Wigner–Ville distribution

In the analysis of multicomponent signals using quadratic nonlinear transforms or systems, along with the desired auto-terms unwanted cross-terms are also generated. In this paper, a novel bispectrum-based technique is proposed to remove these cross-terms. The concept of accumulated modified bispectrum (AMB) is developed. The cross-term removal property of the AMB is demonstrated, and its use in quadratic system analysis in presence of additive noise is illustrated. The application of AMB in interference reduction in the analysis of multicomponent non-stationary signals using Wigner–Ville distribution (WVD) is illustrated. For performance comparison, we compute an information theoretic measure, the Renyi entropy, which indicates that the performance of the proposed method is better than the smoothed pseudo-WVD in the analysis of multicomponent signals that have same support in time or frequency domain.

Time-frequency representation based on robust local mean decomposition for multicomponent AM-FM signal analysis

Local mean decomposition (LMD) is a promising approach to implement time-frequency representation (TFR) for multicomponent amplitude-modulated (AM) and frequency-modulated (FM) signal analysis; however, its performance usually suffers from end effect and mode mixing problems. To address this issue, this paper proposes a novel comprehensive scheme to improve LMD performance. The novel scheme can automatically determine the fix subset size of the moving average algorithm and the optimal number of sifting iterations in a sifting process. Extensive simulations have been explored for multicomponent AM-FM signal analysis by means of TFR with the improved LMD. Moreover, the improved LMD shows potential application in bearing fault diagnosis in conjunction with the well-known fast kurtogram.

PCFCRD for multicomponent LFM signals analysis

A novel extension of the cubic phase function (CPF), known as the parameterised centroid frequency-chirp rate distribution (PCFCRD), is proposed for multicomponent linear frequency modulated signals analysis. The PCFCRD is coherent and introduces a constant delay to reduce the noise correlation. Mathematic analysis and numerical simulations demonstrate that, compared with the coherent integrated CPF, the PCFCRD can obtain a higher anti-noise performance.

Theoretical analysis of the second-order synchrosqueezing transform

We consider in this article the analysis of multicomponent signals, defined as superpositions of modulated waves also called modes. More precisely, we focus on the analysis of a variant of the second-order synchrosqueezing transform, which was introduced recently, to deal with modes containing strong frequency modulation. Before going into this analysis, we revisit the case where the modes are assumed to be with weak frequency modulation as in the seminal paper of Daubechies et al. [8] , to show that the constraint on the compactness of the analysis window in the Fourier domain can be alleviated. We also explain why the hypotheses made on the modes making up the multicomponent signal must be different when one considers either wavelet or short-time Fourier transform-based synchrosqueezing. The rest of the paper is devoted to the theoretical analysis of the variant of the second order synchrosqueezing transform [16] and numerical simulations illustrate the performance of the latter.

An algorithm of matched pursuit with compensation for the analysis of multicomponent Doppler signals

The problem of decomposition of multicomponent Doppler signals in order to increase the operation efficiency of systems based on the use of Doppler radars for a wide range of applications is considered. To study the structure of these signals, a matched pursuit algorithm and its modification—matched pursuit with compensation, which have been developed for the analysis of signals represented by functions of time and their spectrograms, respectively, are used. Obtained and analyzed the Results of decomposition of a simulated three-component signal against the background of noise for a signal-to-noise ratio of 20 dB as well as actual Doppler signals by these algorithmsare obtained and analyzed.