Analysis Of Non-stationary Signals Research Articles

Applications of Fractional Lower Order Synchrosqueezing Transform Time Frequency Technology to Machine Fault Diagnosis

Synchrosqueezing transform (SST) is a high resolution time frequency representation technology for nonstationary signal analysis. The short time Fourier transform-based synchrosqueezing transform (FSST) and the S transform-based synchrosqueezing transform (SSST) time frequency methods are effective tools for bearing fault signal analysis. The fault signals belong to a non-Gaussian and nonstationary alpha (α) stable distribution with 1<α<2 and even the noises being also α stable distribution. The conventional FSST and SSST methods degenerate and even fail under α stable distribution noisy environment. Motivated by the fact that fractional low order STFT and fractional low order S-transform work better than the traditional STFT and S-transform methods under α stable distribution noise environment, we propose in this paper the fractional lower order FSST (FLOFSST) and the fractional lower order SSST (FLOSSST). In addition, we derive the corresponding inverse FLOSST and inverse FLOSSST. The simulation results show that both FLOFSST and FLOSSST perform better than the conventional FSSST and SSST under α stable distribution noise in instantaneous frequency estimation and signal reconstruction. Finally, FLOFSST and FLOSSST are applied to analyze the time frequency distribution of the outer race fault signal. Our results show that FLOFSST and FLOSSST extract the fault features well under symmetric stable (SαS) distribution noise.

Classification of Task-State fMRI Data Based on Circle-EMD and Machine Learning.

In the research work of the brain-computer interface and the function of human brain work, the state classification of multitask state fMRI data is a problem. The fMRI signal of the human brain is a nonstationary signal with many noise effects and interference. Based on the commonly used nonstationary signal analysis method, Hilbert–Huang transform (HHT), we propose an improved circle-EMD algorithm to suppress the end effect. The algorithm can extract different intrinsic mode functions (IMFs), decompose the fMRI data to filter out low frequency and other redundant noise signals, and more accurately reflect the true characteristics of the original signal. For the filtered fMRI signal, we use three existing different machine learning methods: logistic regression (LR), support vector machine (SVM), and deep neural network (DNN) to achieve effective classification of different task states. The experiment compares the results of these machine learning methods and confirms that the deep neural network has the highest accuracy for task-state fMRI data classification and the effectiveness of the improved circle-EMD algorithm.

Seismic Reservoir Delineation via Hankel Transform Based Enhanced Empirical Wavelet Transform

To better describe features of nonstationary seismic signals, mode decomposition-based approaches are widely used for seismic processing and analysis, such as empirical mode decomposition (EMD) and empirical wavelet transform (EWT). EWT builds an adaptive filter bank and then decomposes a nonstationary seismic trace into several intrinsic mode functions (IMFs), which has been applied for analyzing the nonstationary seismic signal. In this letter, we propose an enhanced EWT (EEWT) using Hankel transform (HT), which is an integral transform whose kernels are Bessel functions. Compared with sinusoidal functions of Fourier transform (FT), Bessel functions are more effective for describing features of nonstationary signals. Moreover, HT obtains a more compact spectrum than FT for wideband and nonstationary signal analysis, which contributes to the detection of spectral segmentation. To demonstrate the effectiveness of the proposed algorithm, we apply it to both synthetic and field data. Compared with the results provided by EWT, EEWT provides a time–frequency spectrum with higher resolution and offers potentials in precisely highlighting reservoirs.

End-to-End Noisy Speech Recognition Using Fourier and Hilbert Spectrum Features

Despite the progress of deep neural networks over the last decade, the state-of-the-art speech recognizers in noisy environment conditions are still far from reaching satisfactory performance. Methods to improve noise robustness usually include adding components to the recognition system that often need optimization. For this reason, data augmentation of the input features derived from the Short-Time Fourier Transform (STFT) has become a popular approach. However, for many speech processing tasks, there is an evidence that the combination of STFT-based and Hilbert–Huang transform (HHT)-based features improves the overall performance. The Hilbert spectrum can be obtained using adaptive mode decomposition (AMD) techniques, which are noise-robust and suitable for non-linear and non-stationary signal analysis. In this study, we developed a DeepSpeech2-based recognition system by adding a combination of STFT and HHT spectrum-based features. We propose several ways to combine those features at different levels of the neural network. All evaluations were performed using the WSJ and CHiME-4 databases. Experimental results show that combining STFT and HHT spectra leads to a 5–7% relative improvement in noisy speech recognition.

RETRACTED ARTICLE: Feasibility of spectral domain techniques for the classification of non-stationary signals

Extensive research is carried out in the analysis of non stationary signals. Most of the real time signals are non-stationary in nature. In most cases, these non stationary signals are of types viz defect / non defect, normal / abnormal etc. Hence analysis refers to categorising the signals. Developing a signal processing algorithm for performing the above task is a major challenge. In Machine learning, features are extracted and classifiers are used for categorizing the signals. Feature extraction can be done in time domain, frequency domain and spectral domain. In this paper, feasibility of Singular Value Decomposition (SVD), Framelet Transforms, Discrete Wavelet Transform (DWT) and Discrete Cosine Transform (DCT) for feature extraction is studied. These features are aggregated using statistical parameters, namely mean, skewness and kurtosis. These aggregated features are then fed to Back Propagation Network (BPN). Performance of Back Propagation Network is measured in terms of sensitivity, specificity and accuracy.

New results for the ADF statistic in nonstationary signal analysis with a view towards structural health monitoring

This paper presents some new results relating to nonstationary signal analysis, particularly relating to the ADF test statistic. The first main result is a simple interpretation of the ADF statistic motivated by dimensional analysis. It is argued that the ADF statistic essentially counts the number of cycles of the dominant frequency component in a sample. The analysis also points to a critical frequency fc, such that frequency components with content lower than fc will be judged nonstationary; components with content higher than fc will be judged stationary. The existence of fc leads to the idea of a simple decomposition into stationary and nonstationary components; such a decomposition is then demonstrated using wavelet/multiresolution analysis. The new decomposition is illustrated using two data sets acquired during the well known Structural Health Monitoring campaign on the Z24 Bridge. The paper should be of interest not just to engineers, but also to econometricians, or anyone concerned with time series analysis and the impact of nonstationarity.

FinFET‐based power‐efficient, low leakage, and area‐efficient DWT lifting architecture using power gating and reversible logic

SummaryFor ultra‐low‐power applications, the computing components are smaller in size and consume less energy. In nonstationary signal analysis, the transformation plays an important role. Out of different transformation techniques, the most famous and dominant architecture is the discrete wavelet transform. The building block of the architecture should be optimized by all parameters. In this paper, the optimization was done on the power reduction and leakage current reduction. A new FinFET‐based lifting‐based wavelet architecture was proposed. Power gating and reversible logic methodology are proposed for the FinFET‐based transform to reduce the dynamic power by about 30%. The proposed FinFET‐based processing elements were utilized in the various blocks of the lifting‐based DWT architecture. The implementation was done in 32‐nm CMOS and FinFET technology. From the results, it has been investigated that the FinFET‐based circuits are efficient when compared with CMOS technology. This is due to the second‐order effects happening in CMOS circuits below 45 nm. The proposed design consumes less area and low leakage current and power when compared with the CMOS technology. Future trends of using multigate devices below 14 nm technology are presented finally.

A wavelet-based hybrid islanding detection system applied for distributed generators interconnected to AC microgrids

The modern distribution system widely uses renewable energy sources (RESs) as a distributed generation that introduces some problems like unintentional islanding, protection concerns, and reverse power flow. Islanding or fault occurrences must be detected and treated to ensure system stability. The literature presents several islanding detection methods classified as passive (PDM), active (ADM), or hybrid detection methods (HDM). HDMs present advantages of both PDM and ADM methods and overcome their inherent drawbacks. This paper proposes a modification on the CWT for accomplishing its real-time implementation (RT-CWT), and the use of its nonstationary signal analysis for implementing a wavelet-based hybrid islanding detection scheme (WB-HIDS). The evaluation of some power quality-related indices: power grid voltage, frequency deviation, grid impedance, and power angle enables the detection of islanding condition or fault occurrence. The simultaneous use of various indices mitigates the non-detection zone related to the PDM. Also, the use of a transient detection scheme for triggering the signal injection implementation minimizes undesired disturbances introduced by ADM schemes. Experimental results obtained from an ac microgrid laboratory setup validate the proposed solution and demonstrate its effectiveness.

Horizontal Synchrosqueezing Transform: Algorithm and Applications

Advancements in the synchrosqueezing transform as a postprocessing time-frequency method have received considerable attention in the past few decades for the analysis of nonstationary signals. Many studies have focused on improving the accuracy of the estimated instantaneous frequency (IF). In some fields, the IF spectra of signals exhibit fast varying behavior or even some times parallel to the frequency axis. Thus, a majority of the existing methods may fail to adequately handle the transient signals such as guided waves and vibration waves. To address this problem, a new method called the horizontal synchrosqueezing transform (HST) is introduced in the present research study. By applying a local estimation of the group delay (GD), the proposed technique can yield a compact time-frequency representation for a transient signal while retaining its invertibility. For the purpose of validation, the proposed approach is implemented in both synthetic and real signals. The results are observed in a convincing manner in terms of the smaller value of the Rényi entropy and better reconstruction accuracy. The HST is supposed to be a reliable and accurate method for the analysis of transient signals with extensive usefulness.

Statistical Interpretation of the Allan Variance as a Characteristic of Measuring and Navigation Devices

The Allan variance was originally meant to be a characteristic of time and frequency standards, but now it is widely used in many fields, including the development of navigation devices. The paper considers different applications of the Allan variance to various tasks, among which is estimation of characteristics of navigation devices. However, sometimes the Allan variance does not seem to be very effective; besides, its physical interpretation may be vague. This is due to its empirical definition as an alternative estimate of variance. The paper considers the definition of the Allan variance based on a model of random processes with stationary increments that include both stationary and Wiener processes. In this model, the main characteristic is the structure function, whereas the Allan variance turns out to be its empirical estimate. This representation makes the statistical meaning of the Allan variance clear and explains its high effectiveness in the analysis of nonstationary signals and noise. It also allows the Allan variance to be used as a general characteristic describing stability of measuring and navigation devices, the one that is different from variance.

Study on T-Connection Transmission Line Fault Location Method Based on Transient Fault Traveling Wave Signal

Aiming at the fault location of T-type transmission lines, which are susceptible to the influence of wave speed and transmission line length, this paper proposes a method of T-type transmission line fault location based on transient fault traveling wave information. Based on the fault reflection traveling wave generated at the fault point of the transmission line when a fault occurs, this paper detects the current and voltage traveling wave of the transmission line before and after the fault occurs through a current and voltage collector, and uses the non-stationary signal analysis to obtain the fault line The initial time of the wave reflection to the transmission line port is obtained by simplifying the formula to obtain the modal maximum value of the initial time of the transient fault traveling wave. The modal maximum value of the initial reflected traveling wave time is brought into the calculation formula of the fault branch location criterion. Finally determine the fault distance. Experimental results based on PSCAD show that the method has better accuracy and efficiency than traditional fault analysis methods.

Iterative filtering as a direct method for the decomposition of nonstationary signals

The Iterative Filtering method is a technique developed recently for the decomposition and analysis of nonstationary and nonlinear signals. In this work, we propose two alternative formulations of the original algorithm which allows to transform the iterative filtering method into a direct technique, making the algorithm closer to an online algorithm. We present a few numerical examples to show the effectiveness of the proposed approaches.

Wavelet decomposition and nonlinear prediction of nonstationary vibration signals

In order to overcome the shortcomings (such as the time–frequency localization and the nonstationary signal analysis ability) of the Fourier transform, time–frequency analysis has been carried out by wavelet packet decomposition and reconstruction according to the actual nonstationary vibration signal from a large equipment located in a large Steel Corporation in this article. The effect of wavelet decomposition on signal denoising and the selection of high-frequency weight coefficients for each layer on signal denoising were analyzed. The nonlinear prediction of the chaotic time series was made by global method, local method, weighted first-order local method, and maximum Lyapunov exponent prediction method correspondingly. It was found the multi-step prediction method is better than other prediction methods.

An optimized design of seizure detection system using joint feature extraction of multichannel EEG signals.

The detection of seizure onset and events using electroencephalogram (EEG) signals are important tasks in epilepsy research. The literature available on seizure detection has discussed the implementation of advanced signal processing algorithms using tools accessed over the cloud. However, seizure monitoring application needs near sensor processing due to privacy and latency issues. In this paper, a real time seizure detection system has been implemented using an embedded system. The proposed system is based on ensemble empirical mode decomposition (EEMD) and tunable-Q wavelet transform (TQWT) algorithms. The analysis and classification of non-stationary EEG signals require the wavelet transform with high Q-factor. However, direct use of TQWT increases the computational complexity of feature extraction from multivariate EEG signals. In this paper, the first step is to process the signal by using EEMD to obtain 8 intrinsic mode functions (IMFs). The Kraskov (KraEn), sample (SampEn), and permutation (PermEn) entropy features of IMFs are extracted and based on optimum values, and 4 IMFs are decomposed using TQWT. Secondly, centered correntropy (CenCorrEn) features of the 1st and 16th sub-band of TQWT have been used as classifier inputs. The performance of multilayer perceptron neural networks (MLPNN), least squares support vector machine (LSSVM), and random forest (RF) classifiers has been tested on the multichannel EEG data recorded from a local hospital. The RF classifier has produced the highest accuracy of 96.2% in classifying the signals. The proposed scheme has been employed in developing an embedded seizure detection system to assist neurologists in making seizure diagnostic decisions.

A New Perspective of Wind Power Grid Codes Under Unbalanced and Distorted Grid Conditions

Increasing penetration of wind power has led power system operators worldwide to develop new grid codes for integration of a wind power plant (WPP) onto the grid. According to the grid codes issued by Federal Energy Regulatory Commission (FERC) in the US, a WPP must have low voltage ride through (LVRT) capability, power factor design criteria, and supervisory control and data acquisition (SCADA) system to ensure power system reliability. Fast Fourier transform (FFT) is frequently used to measure root mean square (RMS) voltage, power factor, and for supervisory data acquisition in order to verify that a WPP conforms to the grid code requirements. However, FFT inherently assumes signal is periodic in nature, and it provides misleading results under unbalanced and distorted grid conditions. To overcome these issues, this work proposes a new method for wind power grid codes based on time-frequency analysis technique. Unlike FFT, it provides accurate result both in steady-state and transient conditions. The efficacy of the proposed method is verified by applying it to computer simulated and real-world cases provided by National Renewable Energy Laboratory (NREL) in the US. Time-frequency analysis is performed utilizing Time-Frequency Toolbox (TFTB) in MATLAB ® developed for the analysis of non-stationary signals.

Research of the method the time-frequency signal analysis based on the behavior functions and arithmetic series

Introduction. The study results of the method of time-frequency signal analysis are shown in the article. The study of the method was carried out based on the behavior functions and arithmetic series (BFAS method). Also, the article presents the comparison results of the BFAS method and the short-term Fourier transform method (STFT). The non-stationary signal in the infrasonic frequency range with low frequency resolution was used for comparison. BFAS method. We’ve proposed to use the properties of the systems behavior functions, which are represented as the distribution of the possibility measure to solve the problem of non-stationary signals analyzing. We’ve used the mathematical basis of the p-adic calculus to construct the behavior function. The behavior of a system that generates a signal has locally invariant areas in which the signal spectrum is relatively stable. To identify these areas, we’ve used a method for identifying the metasystem. It is based on the changes analysis in the uncertainty index of system behavior function. The change moments in the behavior function are determine the coordinates of the impulse function that models the original signal. The coordinates of the pulses are described by arithmetic series, which are used to estimate the frequency spectrum of the original signal. The pulses of the signal under study are formed when there is a balance of pulses in signal vicinity. The balance is caused by the harmonic functions that form this signal. Based on the formed balance equations, we have proposed an approach to determining the estimates of the current signal spectra. The use of balance equations in the vicinity of the pulses of the analyzed signal allows to form adaptive temporal localization  that allows to estimate current spectra. This made it possible to use the proposed approach for time-frequency analysis of non-stationary signals. To smooth the estimates, we’ve used fuzzy filtering. The results of the study. We have conducted a studies of the BFAS method usage for the analysis of non-stationary signals and compared the obtained results with the results of using the STFT method. In the article, we analyzed in detail the results of a discrete low-resolution infrasonic signal study. Such signals are the most difficult for time-frequency analysis. We’ve used the spectral contrast angle to quantitatively compare the results of spectra estimation and to compare reconstructed signals we’ve used the correlation coefficient. Studies of the BFAS method showed that the estimation accuracy of the current spectrum using the cosine of the contrast spectral angle is not lower than 0.9, and the correlation coefficient of the reconstructed and true signals is not lower than 0.87. Conclusions. Studies have shown that the BFAS method is effective for time-frequency analysis of non-stationary signals and in many cases exceeds in accuracy the use of the STFT method.

Analysis of laser radiation using the Nonlinear Fourier transform

Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions.

Generalized adaptive mode decomposition for nonstationary signal analysis of rotating machinery: Principle and applications

Abstract Rotating machinery signals are usually intricate and often nonstationary. The analysis of such signals is further complicated because of the spectral overlaps between constituent frequency components under time-varying running conditions. Most conventional signal processing methods are unable to effectively extract the embedded meaningful information. Adaptive mode decomposition (AMD) methods are flexible to describe complex signals, free from the limitations inherent in conventional basis expansion and thus more suited to unveiling the underlying physical nature. However, as those methods work in a way similar to filter banks, i.e. via rectangular partition of time-frequency plane, they are effective only for signals with constituent frequency components that are almost constant and parallel to each other. As such, it would be inappropriate to apply such methods when signal constituent frequency components vary considerably over time and particularly overlap in frequency domain. To address this issue, this paper proposes a general framework by exploiting the unique capability of generalized demodulation to transform an arbitrary time-varying instantaneous frequency into a constant frequency. In doing so, many state-of-the-art AMD methods (including empirical mode composition, local mean decomposition, intrinsic time-scale decomposition, local characteristic scale decomposition, Hilbert vibration decomposition, empirical wavelet transform, variational mode decomposition, and adaptive local iterative filtering) can be extended to analyze highly nonstationary complex signals with spectral overlaps. The principle and advantage of generalized adaptive mode decomposition (GAMD) are illustrated through numerical simulation. The GAMD’s performance in monitoring different rotating machinery components (including a planetary gearbox, an aircraft engine rolling bearing and a hydraulic turbine rotor) is demonstrated and validated under time-varying conditions.

A Novel Fault Detection Method for Rolling Bearings Based on Non-Stationary Vibration Signature Analysis.

To realize the accurate fault detection of rolling element bearings, a novel fault detection method based on non-stationary vibration signal analysis using weighted average ensemble empirical mode decomposition (WAEEMD) and modulation signal bispectrum (MSB) is proposed in this paper. Bispectrum is a third-order statistic, which can not only effectively suppress Gaussian noise, but also help identify phase coupling. However, it cannot effectively decompose the modulation components which are inherent in vibration signals. To alleviate this issue, MSB based on the modulation characteristics of the signals is developed for demodulation and noise reduction. Still, the direct application of MSB has some interfering frequency components when extracting fault features from non-stationary signals. Ensemble empirical mode decomposition (EEMD) is an advanced nonlinear and non-stationary signal processing approach that can decompose the signal into a list of stationary intrinsic mode functions (IMFs). The proposed method takes advantage of WAEEMD and MSB for bearing fault diagnosis based on vibration signature analysis. Firstly, the vibration signal is decomposed into IMFs with a different frequency band using EEMD. Then, the IMFs are reconstructed into a new signal by the weighted average method, called WAEEMD, based on Teager energy kurtosis (TEK). Finally, MSB is applied to decompose the modulated components in the reconstructed signal and extract the fault characteristic frequencies for fault detection. Furthermore, the efficiency and performance of the proposed WAEEMD-MSB approach is demonstrated on the fault diagnosis for a motor bearing outer race fault and a gearbox bearing inner race fault. The experimental results verify that the WAEEMD-MSB has superior performance over conventional MSB and EEMD-MSB in extracting fault features and has precise and effective advantages for rolling element bearing fault detection.

Optimal Estimation of Wavelet Decomposition Level for a Matching Pursuit Algorithm

In this paper, we consider the application of the matching pursuit algorithm (MPA) for spectral analysis of non-stationary signals. First, we estimate the approximation error and the performance time for various MPA modifications and parameters using central processor unit and graphics processing unit (GPU) to identify possible ways to improve the algorithm. Next, we propose the modifications of discrete wavelet transform (DWT) and package wavelet decomposition (PWD) for further use in MPA. We explicitly show that the optimal decomposition level, defined as a level with minimum entropy, in DWT and PWD provides the minimum approximation error and the smallest execution time when applied in MPA as a rough estimate in the case of using wavelets as basis functions (atoms). We provide an example of entropy-based estimation for optimal decomposition level in spectral analysis of seismic signals. The proposed modification of the algorithm significantly reduces its computational costs. Results of spectral analysis obtained with MPA can be used for various signal processing applications, including denoising, clustering, classification, and parameter estimation.