Complex Nonstationary Signals Research Articles

Time–Frequency-Multisqueezing Transform

In the real world, most signals encountered are nonstationary. It is essential to extract a time-frequency (TF) characteristics in such signals for an accurate description. Two parameters are usually applied to quantify the TF characteristics of a nonstationary signal, i.e., instantaneous frequency (IF) and group delay (GD). A post-processing strategy was adopted by two recently developed techniques, the synchrosqueezing transform (SST) and the time-reassigned SST (TSST) to accurately capture the change rules of IF and GD respectively. However, due to the diversity of modes in complex nonstationary signals, no existing technique has been used to effectively estimate both IF and GD simultaneously. To solve this problem, a post-processing analysis technique termed as time-frequency-multisqueezing transform (TFMST) is proposed in this paper where a so-called chirp rate (CR) discrimination criterion is established by considering the Gaussian window in the short-time Fourier transform. The proposed method can accurately categorize nonstationary signals containing harmonic- and impulsive-like components to achieve a concurrent description and ensure the recovery of original signals. The proposed method is validated by numerical simulation and real signal analyses.

An adaptive cepstrum feature representation method with variable frame length and variable filter banks for acoustic emission signals

Acoustic emission technology is widely employed in defect detection, structural health monitoring, fault diagnosis, and other applications due to its benefits of non-contact, real-time, sensitivity, and flexibility. To implement efficient and timely intelligent monitoring, it is crucial to promptly and precisely gather the time-varying properties in the non-stationary acoustic emission signals. The current work proposes an adaptive cepstrum feature representation method that combines variable frame length and variable filter bank. The variable frame length is implemented based on the spectral distribution correlation, and the optimal frame length and frame rate are selected by iterative operations. The variable filter bank, on the other hand, characterizes the local measure features of variable frame length signals by setting dynamic weight distributions. The proposed adaptive cepstrum algorithm can be used as an auxiliary tool to initially analyze complex non-stationary signals, and thus effectively identify the time-varying and frequency components in acoustic emission signals. The superiority of the proposed method has been confirmed on simulation data. Furthermore, the practical performance of the proposed method is evaluated and illustrated based on the burst signal from laser shock peening processing and the mixed signal from pipeline leakage. The proposed method can be extended to other broadband signals and can be used for feature pre-processing before deep learning network modeling to improve recognition accuracy due to its high time–frequency resolution.

Research on Aging State Detection Method of Rubber O-ring Sealing Structure

The rubber seal structure is used extensively in mechanical devices, long-term use may bring major safety hazards and economic losses. In order to ensure the healthy operation of machinery and equipment, it is necessary to test the aging condition of the rubber sealing structure nondestructive online. In order to address the problem of unsteady vibration signals, a complex nonstationary signal is degraded into the sum of multiple product functions by means of global local mean decomposition, and then the energy features in these PF components are extracted, and the first three components with the largest energy eigenvalues are selected to form a sensitive feature vector set. Overall, the results of the search data show that the proposed method can efficiently extract energy features from a large set of original features, and the first three largest energy features can be selected to form a sensitive feature set, which can provide effective data information for the detection of the aging state of Rubber O-ring Sealing Structure (ROSS) in the next step.

An Improved Method to Enhance SNR of Non-Stationary Signal Based on Nonuniform Windows Adaptive Modulation for Measurement

It is very important for non-stationary signal processing, signal measurement, and signal enhancement to improve signal-to-noise ratio (SNR) and suppress noise. For complex non-stationary signals measurement, there is still a lack of effective methods to improve the signal-to-noise ratio without damaging original signal. Therefore, it is vital to develop signal processing method to improve SNR of non-stationary signal in many actual industrial measurement. This paper proposes a new method to enhance the SNR for non-stationary signal processing. First, a self-adapting mathematic model is presented to describe the short-time impulse with board spectrum, judge the non-stationary part of the signal, and determine the length of time window based on itself. Then, for the non-stationary signals in this short time window, the improved self-adaptive modulation is used to remove the non-stationary components and retain the stationary components. Third, the stationary component of the short-time window and the normal part of the original signal are connected via cubic spline interpolation algorithm. Finally, this paper analyzes the range of SNR improvement and measurement accuracy of the new method. Based on the results of experiment, the proposed method can effectively improve the signal-to-noise ratio of non-stationary signals and suppress noise, which is of great significance for measurement.

A New De-Noising Method Based on Enhanced Time-Frequency Manifold and Kurtosis-Wavelet Dictionary for Rolling Bearing Fault Vibration Signal.

The transient pulses caused by local faults of rolling bearings are an important measurement information for fault diagnosis. However, extracting transient pulses from complex nonstationary vibration signals with a large amount of background noise is challenging, especially in the early stage. To improve the anti-noise ability and detect incipient faults, a novel signal de-noising method based on enhanced time-frequency manifold (ETFM) and kurtosis-wavelet dictionary is proposed. First, to mine the high-dimensional features, the C-C method and Cao’s method are combined to determine the embedding dimension and delay time of phase space reconstruction. Second, the input parameters of the liner local tangent space arrangement (LLTSA) algorithm are determined by the grid search method based on Renyi entropy, and the dimension is reduced by manifold learning to obtain the ETFM with the highest time-frequency aggregation. Finally, a kurtosis-wavelet dictionary is constructed for selecting the best atom and eliminating the noise and reconstruct the defective signal. Actual simulations showed that the proposed method is more effective in noise suppression than traditional algorithms and that it can accurately reproduce the amplitude and phase information of the raw signal.

CFs-focused intelligent diagnosis scheme via alternative kernels networks with soft squeeze-and-excitation attention for fast-precise fault detection under slow & sharp speed variations

The evolution of deep learning-based intelligent fault diagnosis is mainly confronted with challenges on the analysis of complex non-stationary signals and the design of strong robust models. The causal relationship between the two promotes the development of better models, among them, convolution frameworks (CFs) are regarded as one of the most versatile structures. In standard CFs, the receptive fields of the kernels in each layer are designed to share the same scale, which easily leads to model performance degradation in non-stationary data analysis. Consequently, we propose a dynamically selective mechanism in CFs that allows every kernel to adaptively adjust its receptive field by multi-scale information, which is named as alternative kernels networks (AkNets). Combining with specially designed squeeze-and-excitation (SE) attention, the AkNets utilize information-guided soft attention to fuse multiple branches with different kernel scales, which generates different effective receptive fields of kernels in fusion layer. Five bearing vibration data collected under slow & sharp speed variations verify the effectiveness of proposed approach. The results indicate that the AkNets greatly improve the efficiency on the premise of high recognition accuracy. Moreover, the extended application of the AkNets’ unit can assist various state-of-art CFs-based models improve the recognition accuracy by 3%–12%.

Intelligent spectrogram – A tool for analysis of complex non-stationary signals

The paper introduces the concept of Intelligent Spectrogram as a general tool for analysis of non-stationary signals. The method is based on a self-tuning mechanism, which automatically provides optimum window length of the spectrogram. The method calculates coefficients of variation (also known as relative standard deviation) for time and frequency scales and finds extremum value of their product. The proposed Intelligent Spectrogram might serve as an auxiliary tool for initial analysis of complex non-stationary signals, for which selection of particular window length might be beneficial for one class of signal components, but highly detrimental to others. The idea of the method is presented on a simulated signal, while its practical performance is illustrated on a real signal from a wind turbine run-down.

Modified wavelet analysis of ECoG-pattern as promising tool for detection of the blood\u2013brain barrier leakage

A new approach for detection oscillatory patterns and estimation of their dynamics based by a modified CWT skeleton method is presented. The method opens up additional perspectives for the analysis of subtle changes in the oscillatory activity of complex nonstationary signals. The method was applied to analyze unique experimental signals obtained in usual conditions and after the non-invasive increase in the blood–brain barrier (BBB) permeability in 10 male Wistar rats. The results of the wavelet-analysis of electrocorticography (ECoG) recorded in a normal physiological state and after an increase in the BBB permeability of animals demonstrate significant changes between these states during wakefulness of animals and an essential smoothing of these differences during sleep. Sleep is closely related to the processes of observed changes in the BBB permeability.

Enhancement of time-frequency post-processing readability for nonstationary signal analysis of rotating machinery: Principle and validation

Rotating machinery signals are often composed of multiple components and are nonstationary under practical time-varying conditions. In most cases, the constituent frequency components are close to each other on time–frequency plane. As such, better time–frequency readability is necessary to discover the underlying physical nature of such complex nonstationary signals. Nevertheless, conventional time–frequency analysis methods suffer from limited time–frequency resolution and/or cross-term interferences, thus cannot achieve desirable time–frequency readability. In recent decades, some time–frequency post-processing methods (such as time–frequency reassignment, synchrosqueezing transform, multi-tapering, concentration of frequency and time, and higher-order synchrosqueezing transform) have been proposed to improve the time–frequency readability from two aspects: reducing cross-term interferences and enhancing time–frequency energy concentration. However, they still surfer from time-frequency blurs for the signal whose time–frequency ridges are close to each other on time–frequency plane. To address this issue, we propose a framework to improve the post-processing methods. Firstly, the Vold-Kalman filter is employed to extract constituent frequency components, by exploiting its capability to separate mono-components. Then, the time–frequency representation (TFR) of each mono-component is obtained via time–frequency post-processing method separately. Finally, the TFR of raw signal is constructed by superposing the TFR of all mono-components. This framework achieves a TFR of high time–frequency resolution, free from cross-term interferences, and therefore better time–frequency readability. As such, it extends time–frequency post-processing methods to analyze complex nonstationary signals. The proposed framework is illustrated through numerical simulation, and validated using typical rotating machine vibration data (including the experimental signals of a planetary gearbox and an induction motor, ground test data of a civil aircraft engine and in-situ measurement of a hydraulic turbine rotor). The analysis results show the good capability of proposed framework to reveal the frequency contents and their time-varying features of complex nonstationary signals.

Order spectrum analysis enhanced by surrogate test and Vold-Kalman filtering for rotating machinery fault diagnosis under time-varying speed conditions

Rotating machinery signals are usually dominated by rotating frequency harmonics, and the presence of these frequency components or change in their magnitudes indicate health condition. Order spectrum is widely applied in rotating machinery fault feature extraction, because of its capability in intuitive spectral representation of rotating frequency harmonics in order domain. However, some speed non-synchronous components are often present. They show wide-band features in order spectra, and hinder accurate identification of rotating frequency harmonic orders. To address this issue, a scheme is proposed to identify and remove speed non-synchronous components of either constant or time-varying frequency. To this end, surrogate test is generalized through new candidate construction method and nonstationarity based indicator for test criterion, to identify true nonstationary signal components adaptively and eliminate subjective influences. Vold-Kalman filter is used to separate signal components by exploiting its capability in mono-component decomposition of complex nonstationary signals. The proposed method is validated through analyses of both induction motor stator current signals and hydraulic turbine rotor vibration signal. The results demonstrate its advantages over conventional computed order spectrum analysis.

An adjustable envelope based EMD method for rolling bearing fault diagnosis

Empirical mode decomposition (EMD) can decompose complex non-stationary signals into the sum of several intrinsic mode functions (IMF), and it is widely used in fault diagnosis of mechanical devices. In order to solve the mode mixing problem and enhance the fault feature extraction ability, an adjustable envelope based EMD (AE-EMD) method was proposed. Firstly, the envelope fitting method is replaced by rational Hermite interpolation, which can effectively avoid the outstanding over and undershoot problem in the conventional fitting curve. Secondly, the optimal parameter in the AE-EMD is searched by grey wolf optimizer (GWO) using the maximum Kurtosis index as the objective function. Then, the AE-EMD method combined with the Hilbert envelope spectrum is employed to extract the fault characteristic frequency. Case study demonstrates that AE-EMD can restrain the mode mixing effectively, and it also has better fault feature extraction ability compared with the conventional EMD. This proposed method has potential significance to the fault diagnosis and condition-based maintenance (CBM) of rolling bearings in the large and complex equipment.

An Improved Multi-Ridge Extraction Method Based on Differential Synchro-Squeezing Wavelet Transform

It is very important to accurately extract the instantaneous frequency (IF) of complex non-stationary signals, so the signal processing methods based on IF are widely used in engineering. However, in non-stationary complex vibration signals, it is difficult to extract the instantaneous frequency under strong noise because the frequency changes rapidly. This paper proposes an improved multi-ridge extraction method based on differential synchro-squeezing wavelet transform (DSWT). First, an improved method DSWT is proposed to reduce the computation time and image noise of synchro-squeezing wavelet transform (SWT). The running time of the algorithm can be further reduced by segmenting the signal and compressing the time-frequency matrix. The image noise can be significantly reduced by differentiating SWT time-frequency matrix. It lays a good foundation for the extraction of the time-frequency ridge line. Secondly, an improved multi-ridge extraction method is proposed. The ridge jump due to end effect can be eliminated adaptively in segmented extraction. It further improves the time-frequency aggregation and extraction effect of the wavelet ridgeline image. Finally, the improved multi-ridge extraction method based on DSWT (DSWT-IMRE) is verified by the simulation data and experimental data under different conditions. Compared with the method proposed in previous study, the results show that DSWT-IMRE has higher extraction accuracy.

Real-time Measurement of Projectile Velocity in a Ballistic Fabric with a High-frequency Doppler Radar

Because of technical limitations, most experimental studies on the energy-absorbing properties of ballistic fabrics are limited to discrete evaluations based on impact and residual velocities. Consequently, the continuous interaction between a projectile and a target material is still commonly assessed with analytical models or numerical simulations, the validation of which is based on the aforementioned discrete values. The present document aims at describing and validating a new experimental method to make it possible to evaluate the continuous evolution of the projectile velocity during penetration into a fabric material. The method is based on the Doppler effect and a specific and complex nonstationary signal treatment. A high-frequency continuous-wave Doppler radar was adapted to assess the continuous evolution of the velocity of a projectile penetrating a fabric material. Based on two ballistic-grade fabric configurations, a perforating and a nonperforating case were described and evaluated. The instantaneous Doppler frequency was extracted based on the Hilbert-Huang transform. A validation of the proposed method was performed based on high-speed camera images, giving the displacement of the apex of the deformation pyramid of the fabric with time. Additionally, a Weibel® Doppler radar was used to measure the impact velocity. Based on instantaneous frequencies deduced from the high-frequency radar signal analysis, Doppler theory and high-speed camera images, velocity–time and displacement–time plots were obtained. Additionally, the evolution of the fabric deformation (pyramid morphology) was recorded from the high-speed camera images. Comparisons between the data assessed with the high-frequency Doppler radar and those deduced from the high-speed camera indicated that good agreement exists between the two methods. The new Doppler radar method seems to be a promising complementary tool for measuring the continuous interaction between a projectile and a fabric target material.

Application of an improved variational mode decomposition algorithm in leakage location detection of water supply pipeline

In the research of pipeline leak location, signal decomposition can be used to extract effective leak signal components. Variational mode decomposition (VMD) can decompose a complex non-stationary signals into several simple band-limited intrinsic mode functions (BLIMFs). However, the number of modes K and the quadratic penalty item α need to be preset before using VMD, which brings limitations to VMD. Therefore, an improved adaptive VMD (IAVMD) is proposed in this paper. This method can adaptively determine the quadratic penalty item α for each BLIMF according to the frequency characteristics of the signal. Meanwhile, the energy loss coefficient and the correlation of adjacent BLIMFs is regarded as an evaluation index to determine the best number of modes K. Finally, this method is used to locate the leak location of water pipelines, which can significantly improve the positioning accuracy.

A novel signal feature extraction technology based on empirical wavelet transform and reverse dispersion entropy

Feature extraction is an important part of signal processing, which is significant for signal detection, classification, and recognition. The nonlinear dynamic analysis method can extract the nonlinear characteristics of signals and is widely used in different fields. Reverse dispersion entropy (RDE) proposed by us recently, as a nonlinear dynamic analysis method, has the advantages of fast computing speed and strong anti-noise ability, which is more suitable for measuring the complexity of signal than traditional permutation entropy (PE) and dispersion entropy (DE). Empirical wavelet transform (EWT), based on the theory of wavelet analysis, can decompose a complex non-stationary signal into a number of empirical wavelet functions (EWFs) with compact support set spectrum, which has better decomposition performance than empirical mode decomposition (EMD) and its improved algorithms. Considering the advantages of RDE and EWT, on the one hand, we introduce EWT into the field of underwater acoustic signal processing and fault diagnosis to improve the signal decomposition accuracy; on the other hand, we use RDE as the features of EWFs to improve the signal separability and stability. Finally, we propose a novel signal feature extraction technology based on EWT and RDE in this paper. Experimental results show that the proposed feature extraction technology can effectively extract the complexity features of actual signals. Moreover, it also has higher distinguishing ability for different types of signals than five latest feature extraction technologies.

Solution of the Problem of Classification of Hydroacoustic Signals Based on Harmonious Wavelets and Machine Learning

Two types of real hydroacoustic signals of whales are classified based on the harmonic wavelet transform (HWT) coefficients (fast implementation), windowed Fourier transform (FT) (spectrogram), and conventional FT using the k-NN algorithm. The accuracy of the classification is estimated for various signal-to-noise ratios (SNRs). In order to reduce the dimension of the feature space during classification using the k-NN algorithm, the use of the modulo N reduction method is proposed. The efficiency of the use of harmonic wavelets in the classification of complex nonstationary signals is experimentally proved. The applicability of speech processing methods for the classification of underwater bioacoustic signals is confirmed. The discussed methods are initially developed taking into account the characteristics of human speech, but, nevertheless, showed good results even without being tuned to the characteristics of the classified signals. The problem of classifying two types of whales by the sounds they make using a neural network is solved.

Classification of Hydroacoustic Signals Based on Harmonic Wavelets and a Deep Learning Artificial Intelligence System

This paper considers two approaches to hydroacoustic signal classification, taking the sounds made by whales as an example: a method based on harmonic wavelets and a technique involving deep learning neural networks. The study deals with the classification of hydroacoustic signals using coefficients of the harmonic wavelet transform (fast computation), short-time Fourier transform (spectrogram) and Fourier transform using a kNN-algorithm. Classification quality metrics (precision, recall and accuracy) are given for different signal-to-noise ratios. ROC curves were also obtained. The use of the deep neural network for classification of whales’ sounds is considered. The effectiveness of using harmonic wavelets for the classification of complex non-stationary signals is proved. A technique to reduce the feature space dimension using a ‘modulo N reduction’ method is proposed. A classification of 26 individual whales from the Whale FM Project dataset is presented. It is shown that the deep-learning-based approach provides the best result for the Whale FM Project dataset both for whale types and individuals.

Atomic-Force Microscopy of Resistive Nonstationary Signal Switching in ZrO2(Y) Films

Local resistive switching by complex nonstationary signals in zirconium-dioxide-stabilized films on conducting substrates has been studied by atomic-force microscopy with a conducting probe. Film resistance was switched by triangular voltage pulses on which a high-frequency sinusoidal signal was superimposed. It is found that the ratio of currents through the junction between the probe and film surface in high-resistance and low-resistance states increases after the superposition of a sinusoidal signal (as compared to switching by simple triangular pulses). An increase in the temporal stability of the current strength in these states was also found when switching with a sinusoidal signal. This effect is associated with resonant activation of oxygen ion migration over vacancies in an external ac electric field.

Broadband Mode Decomposition and Its Application to the Quality Evaluation of Welding Inverter Power Source Signals

This article proposes a novel data-driven adaptive decomposition method named broadband mode decomposition (BMD) for analyzing complex signals containing broadband components, such as square signals and sawtooth signals. For effective broadband signals with “sharp corners,” an unavoidable error occurs when applying former methods, such as variational mode decomposition (VMD) and ensemble empirical mode decomposition (EEMD), due to the Gibbs phenomenon and the interpolation of extreme points. Therefore, we propose BMD for separating the broadband modes, narrowband modes, and noise in a complex nonstationary signal. First, an associative dictionary library consisting of typical broadband signals and narrowband signals is established. Second, a smoothness function is employed as the optimization objective function, and the amplitude, frequency, and phase of the broadband signals and the filter parameters of the narrowband signals are applied as optimization parameters. Third, the sparsest decomposition results are obtained by searching the dictionary using an artificial chemical reaction optimization algorithm. The simulation and experimental signal analyses indicate that BMD is more accurate than EEMD and VMD in extracting broadband components from a noisy signal and that BMD is suitable for quality evaluations of welding inverter power source signals.

Traction Inverter Open Switch Fault Diagnosis Based on Choi–Williams Distribution Spectral Kurtosis and Wavelet-Packet Energy Shannon Entropy

In this paper, a new approach for fault detection and location of open switch faults in the closed-loop inverter fed vector controlled drives of Electric Multiple Units is proposed. Spectral kurtosis (SK) based on Choi–Williams distribution (CWD) as a statistical tool can effectively indicate the presence of transients and locations in the frequency domain. Wavelet-packet energy Shannon entropy (WPESE) is appropriate for the transient changes detection of complex non-linear and non-stationary signals. Based on the analyses of currents in normal and fault conditions, SK based on CWD and WPESE are combined with the DC component method. SK based on CWD and WPESE are used for the fault detection, and the DC component method is used for the fault localization. This approach can diagnose the specific locations of faulty Insulated Gate Bipolar Transistors (IGBTs) with high accuracy, and it requires no additional devices. Experiments on the RT-LAB platform are carried out and the experimental results verify the feasibility and effectiveness of the diagnosis method.