Concentrated Time-frequency Research Articles

Synchrosqueezing extracting transform and its application in bearing fault diagnosis under non-stationary conditions

The measured vibration signals of mechanical equipment with defects are generally non-stationary. Time–frequency analysis is an effective tool in processing non-stationary signals. However, the concentration of time–frequency representation will greatly affect the performance of feature extraction. Thus, a more concentrated time–frequency analysis method plays an important role in mechanical signal processing and fault diagnosis. A novel time–frequency analysis method, called synchrosqueezing extracting transform has been proposed in this study. The proposed method can not only well extract the time-varying information of the nonstationary signal then achieve a better-concentrated time–frequency representation, but also have better noise robustness and lower time-consuming than the traditional time–frequency analysis methods. The analysis of numerical signals verified the great performance of this method. Finally, synchrosqueezing extracting transform is used to process the bearing vibration signals under variable speed conditions. It has been demonstrated that the proposed method achieves better results than other state-of-art time–frequency analysis methods.

Gas Reservoir Characterization Using Lp-Norm Constrained High-Resolution Seismic Spectral Attributes

Reservoir prediction is often a primary objective in seismic exploration, especially for deep hydrocarbon detection with its potential for assessing oil and gas resources. Time–frequency analysis has become a successful method for detecting subsurface features and can also be used to identify potential hydrocarbon reservoirs. However, current applications for hydrocarbon detection often occur at low resolution, due to the influence of the windowing functions and lack of prior constraints, thereby affecting gas prediction for thin reservoirs. To rectify this issue, we investigate the use of sparse inverse spectral decomposition (SISD) based on the wavelet transform, which adopts an lp norm to constrain the time–frequency spectra, and thereby provides a more highly concentrated time–frequency representation than conventional spectral decomposition techniques. The main objective of this paper is to investigate the performance of spectral attributes derived from lp-norm constrained SISD and its application to the characterization of deep-marine dolomite reservoirs in southwest China. The gas-bearing zones in target reservoir are predicted well by extracting and analyzing the spectral amplitude responses of different frequency components. The predicted favorable gas-bearing areas are closely related to local structures in the target reservoir, which are also in good agreement with gas-testing results at three well locations and may be used to guide subsequent exploration well development in this region.

On the Use of Concentrated Time-Frequency Representations as Input to a Deep Convolutional Neural Network: Application to Non Intrusive Load Monitoring.

Since decades past, time–frequency (TF) analysis has demonstrated its capability to efficiently handle non-stationary multi-component signals which are ubiquitous in a large number of applications. TF analysis us allows to estimate physics-related meaningful parameters (e.g., , group delay, etc.) and can provide sparse signal representations when a suitable tuning of the method parameters is used. On another hand, deep learning with Convolutional Neural Networks (CNN) is the current state-of-the-art approach for pattern recognition and allows us to automatically extract relevant signal features despite the fact that the trained models can suffer from a lack of interpretability. Hence, this paper proposes to combine together these two approaches to take benefit of their respective advantages and addresses non-intrusive load monitoring (NILM) which consists of identifying a home electrical appliance (HEA) from its measured energy consumption signal as a “toy” problem. This study investigates the role of the TF representation when synchrosqueezed or not, used as the input of a 2D CNN applied to a pattern recognition task. We also propose a solution for interpreting the information conveyed by the trained CNN through different neural architecture by establishing a link with our previously proposed “handcrafted” interpretable features thanks to the layer-wise relevant propagation (LRP) method. Our experiments on the publicly available PLAID dataset show excellent appliance recognition results (accuracy above 97%) using the suitable TF representation and allow an interpretation of the trained model.

Non-Stationary Power System Forced Oscillation Analysis Using Synchrosqueezing Transform

Non-stationary forced oscillations (FOs) have been observed in power system operations. However, most detection methods assume that the frequency of FOs is stationary. In this paper, we present a methodology for the analysis of non-stationary FOs. Firstly, Fourier synchrosqueezing transform (FSST) is used to provide a concentrated time-frequency representation of the signals that allows identification and retrieval of non-stationary signal components. To continue, the Dissipating Energy Flow (DEF) method is applied to the extracted components to locate the source of forced oscillations. The methodology is tested using simulated as well as real PMU data. The results show that the proposed FSST-based signal decomposition provides a systematic framework for the application of DEF Method to non-stationary FOs.

Time-Reassigned Multisynchrosqueezing Transform for Bearing Fault Diagnosis of Rotating Machinery

The impulse features in a condition monitoring (CM) signal usually imply the occurrence of a defect in a rotating machine. To accurately capture the impulse components in a CM signal, a concentrated time-frequency analysis (TFA) method based on time-reassigned synchrosqueezing transform (TSST) is proposed. First, the limitation of the TSST method in dealing with strong frequency-varying signals is explored. Second, an iteration procedure is introduced to address the blurry time frequency representation problem of TSST. The convergence of the iteration algorithm is also analyzed. Finally, an algorithm is proposed to extract the impulse features for signal reconstructions, which are also useful for an accurate diagnosis of the fault type. A simulated noise-contaminated signal and three sets of experimental data are employed in this article to evaluate the performance of the proposed method. Results obtained from this article confirm that the proposed method has a better performance in dealing with impulsive-like signals than other TFA methods.

Chatter detection in robotic drilling operations combining multi-synchrosqueezing transform and energy entropy

Robotic drilling shows higher efficiency and precision than the manual drilling, which has great application prospects in the aviation manufacturing. Nevertheless, due to the detrimental effects on surface quality, tool wear, the safety of the robot and machining efficiency, chatter vibration has been a major obstacle to achieve stable and efficient robotic drilling. Therefore, it is particularly significant to detect and manage to suppress the chatter as early as possible. This paper presents a novel approach to identify the chatter in robotic drilling process based on multi-synchrosqueezing transform (MSST) and energy entropy. To begin with, matrix notch filters are designed to effectively eliminate the interference of spindle rotating frequency and its harmonics to the measured vibration signal. Subsequently, the filtered signal is processed by the MSST to obtain concentrated time-frequency representation. Then, the signal is divided equally into finite frequency bands and the subcomponent corresponding to each frequency band is reconstructed through the reverse MSST. Finally, in consideration of the change of the vibration signal in frequency and energy distribution when chatter occurs, the energy entropy is computed as the chatter detection indicator. The proposed chatter detection method was validated by robotic drilling experiments with different tools, machining parameters, and workpiece material, and the results indicate that the proposed method can effectively detect the chatter before it is fully developed and recognize the chatter earlier than the synchroextracting-based method.

Determination of Lamb wave phase velocity dispersion using time–frequency analysis

Accurate knowledge of dispersion relations is of vital importance for Lamb wave-based damage detection. In this paper, an experimental technique is proposed to obtain the Lamb waves phase velocity dispersion without prior knowledge of material properties. It requires measurements at only two neighboring positions, and can evaluate phase velocity dispersion over a wide frequency range. In that technique, the short-time chirp-Fourier transform is first applied to the Lamb wave signals to achieve a concentrated time–frequency representation. On this basis, ridge tracking is completed and the group delay (GD) of the interested modes is estimated accurately. Subsequently, the Vold–Kalman filter is introduced to extract these wave modes, and the instantaneous phase is estimated from each individual wave mode via Hilbert transform. Lastly, the phase velocity is obtained as a function of the propagation distance, GD and phase shift. The proposed technique is investigated in two different mediums: simulated signals as Lamb wave propagating in an aluminum plate and experimental signals as that in a carbon fiber-reinforced polymer laminate. The results demonstrate its effectiveness and efficiency.

Time-frequency characteristics estimation of underwater moving objects using memory-dependent derivative method

The line-spectra changes of the radiated noise of underwater moving object is observed as the form of narrow-band time varying signal due to the Doppler effect. The modulation law of the time varying signal contains a large number of feature information of moving targets, which can be used for detection and classification. The goal of time-frequency analysis is to extract subtle changes the function relationship of frequency over time. In this research, a memory-dependent derivative methodology is proposed to deal with accurate time–frequency representation of time varying signals under strong background noise. Memory-dependent derivative is a convolution of a common derivative by the time-varying signals with a dynamic weighted function in the past period time. Considering the stated methodology, it is derived that the discrete data from previous times to estimate signal value at current time and reduce the effects of the noise. Using the Fourier transformation with different scales and delays transformation as the kernel function, the energy concentrated time-frequency curve is obtained with higher resolution and without frequency leakage. The simulated results demonstrate that given method is immune to background noise and estimate the main frequencies with high accuracy, specially the rapid change of the modulated frequency.

A Concentrated Time–Frequency Analysis Tool for Bearing Fault Diagnosis

In industrial rotating machinery, the transient signal usually corresponds to the failure of a primary element, such as a bearing or gear. However, faced with the complexity and diversity of practical engineering, extracting the transient signal is a highly challenging task. In this paper, we propose a novel time–frequency analysis method termed the transient-extracting transform, which can effectively characterize and extract the transient components in the fault signals. This method is based on the short-time Fourier transform and does not require extended parameters or a priori information. Quantized indicators, such as Renyi entropy and kurtosis, are employed to compare the performance of the proposed method with other classical and advanced methods. The comparisons show that the proposed method can provide a much more energy-concentrated time–frequency representation, and the transient components can be extracted with a significantly larger kurtosis. The numerical and experimental signals are used to show the effectiveness of our method.

Seismic data analysis using synchrosqueezing short time Fourier transform

The synchrosqueezing wavelet transform (SWT) reallocates the wavelet transform values to different points, hence produces a sharp spectral decomposition for the input signal. The SWT method was widely used for de-noising, spectral decomposition, etc. In this paper, a new synchrosqueezing method was proposed based on short time Fourier transform. The proposed method reassigns the short time Fourier transform values to different points, thus produces a concentrated time–frequency map. Furthermore, the proposed method has an inverse formula, which allows the reconstruction of the input signal from its spectral decomposition. Examples showed that the proposed method is effective for revealing the time–frequency characterizations of non-stationary signals.

Multisensor signal denoising based on matching synchrosqueezing wavelet transform for mechanical fault condition assessment

Since it is difficult to obtain the accurate running status of mechanical equipment with only one sensor, multisensor measurement technology has attracted extensive attention. In the field of mechanical fault diagnosis and condition assessment based on vibration signal analysis, multisensor signal denoising has emerged as an important tool to improve the reliability of the measurement result. A reassignment technique termed the synchrosqueezing wavelet transform (SWT) has obvious superiority in slow time-varying signal representation and denoising for fault diagnosis applications. The SWT uses the time–frequency reassignment scheme, which can provide signal properties in 2D domains (time and frequency). However, when the measured signal contains strong noise components and fast varying instantaneous frequency, the performance of SWT-based analysis still depends on the accuracy of instantaneous frequency estimation. In this paper, a matching synchrosqueezing wavelet transform (MSWT) is investigated as a potential candidate to replace the conventional synchrosqueezing transform for the applications of denoising and fault feature extraction. The improved technology utilizes the comprehensive instantaneous frequency estimation by chirp rate estimation to achieve a highly concentrated time–frequency representation so that the signal resolution can be significantly improved. To exploit inter-channel dependencies, the multisensor denoising strategy is performed by using a modulated multivariate oscillation model to partition the time–frequency domain; then, the common characteristics of the multivariate data can be effectively identified. Furthermore, a modified universal threshold is utilized to remove noise components, while the signal components of interest can be retained. Thus, a novel MSWT-based multisensor signal denoising algorithm is proposed in this paper. The validity of this method is verified by numerical simulation, and experiments including a rolling bearing system and a gear system. The results show that the proposed multisensor matching synchronous squeezing wavelet transform (MMSWT) is superior to existing methods.

Noncontact Physiological Dynamics Detection Using Low-power Digital-IF Doppler Radar

The instantaneous vital sign rates, which are related to physiological dynamics, are important indicators of human health condition. This paper presents a noncontact way to measure the human instantaneous vital signs using digital-intermediate frequency (IF) Doppler radar. The synchrosqueezing transform-based algorithm has been proposed to get a concentrated time-frequency (TF) distribution, so that the high-resolution instantaneous heartbeat and respiratory rates and the time-domain signals can be acquired. Moreover, the developed radar with customized radio frequency module employs the direct IF sampling technique to achieve high sensitivity to capture the tiny vital sign variations. Experiments with different human subjects and physiological conditions have been carried out. Compared with the landmark-based method and traditional TF algorithms, the results show that instantaneous vital signs can be acquired more accurately within 3 m at a -13 dBm transmit power by the proposed method. Therefore, the radar can be used for evaluating the physiological dynamics and assessing health condition.

High-Order Synchrosqueezing Transform for Multicomponent Signals Analysis—With an Application to Gravitational-Wave Signal

This study puts forward a generalization of the short-time Fourier-based Synchrosqueezing Transform using a new local estimate of instantaneous frequency. Such a technique enables not only to achieve a highly concentrated time-frequency representation for a wide variety of AM-FM multicomponent signals but also to reconstruct their modes with a high accuracy. Numerical investigation on synthetic and gravitational-wave signals shows the efficiency of this new approach.

AE Signal Processing for Propagating Crack of Wind Turbine Blade Based on Optimized Morlet Wavelet

. Because the AE (Acoustic Emission, AE) characteristics of crack propagating of wind turbine blade is sudden and impactive, Shannon entropy is adopted to optimize the Morlet wavelet basis function by bandwidth parameters. Experimental results show that wavelet scale has relatively concentrated time-frequency characteristics when optimal bandwidth spectral parameter is 5.1. Compared with situation without optimization, it improves the noise interference phenomenon and be able to clearly show the impact characteristics of spectrum, which indicates that optimized wavelet scale is suitable for the extraction of the AE signal characteristic in wind turbine blade crack propagation.

The identification of multi-cave combinations in carbonate reservoirs based on sparsity constraint inverse spectral decomposition

Sparsity constraint inverse spectral decomposition (SCISD) is a time-frequency analysis method based on the convolution model, in which minimizing the l1 norm of the time-frequency spectrum of the seismic signal is adopted as a sparsity constraint term. The SCISD method has higher time-frequency resolution and more concentrated time-frequency distribution than the conventional spectral decomposition methods, such as short-time Fourier transformation (STFT), continuous-wavelet transform (CWT) and S-transform. Due to these good features, the SCISD method has gradually been used in low-frequency anomaly detection, horizon identification and random noise reduction for sandstone and shale reservoirs. However, it has not yet been used in carbonate reservoir prediction. The carbonate fractured-vuggy reservoir is the major hydrocarbon reservoir in the Halahatang area of the Tarim Basin, north-west China. If reasonable predictions for the type of multi-cave combinations are not made, it may lead to an incorrect explanation for seismic responses of the multi-cave combinations. Furthermore, it will result in large errors in reserves estimation of the carbonate reservoir. In this paper, the energy and phase spectra of the SCISD are applied to identify the multi-cave combinations in carbonate reservoirs. The examples of physical model data and real seismic data illustrate that the SCISD method can detect the combination types and the number of caves of multi-cave combinations and can provide a favourable basis for the subsequent reservoir prediction and quantitative estimation of the cave-type carbonate reservoir volume.

Phase space localized functions in the Dunkl setting

Time–frequency analysis plays a central role in signal analysis, because signals that have highly concentrated time–frequency content are used in many applications. The uncertainty principle in Fourier analysis sets a limit to the possible simultaneous concentration of a function and its Dunkl transform. To localize signals in the time–frequency plane we use time–frequency localization operators in the Dunkl setting to measure their time–frequency content on some subset of finite measure. Then, using eigenfunctions of these operators, which are maximally time–frequency concentrated, we prove a characterization of functions that are time–frequency concentrated in the region of interest, and we obtain approximation inequalities for such functions using a finite linear combination of eigenfunctions.

Zoom Synchrosqueezing Transform for Instantaneous Speed Estimation of High Speed Spindle

Instantaneous speed (IS) is of great significance of fault diagnosis and condition monitoring of the high speed spindle. In this paper, we propose a novel zoom synchrosqueezing transform (ZST) for IS estimation of the high speed spindle. Due to the limitation of the Heisenberg uncertainty principle, the conventional time-frequency analysis (TFA) methods cannot provide both good time and frequency resolution at the whole frequency region. Moreover, in most cases, the interested frequency component of a signal only locates in a narrow frequency region, so there is no need to analyze the signal in the whole frequency region. Different from conventional TFA methods, the proposed method arms to analyze the signal in a specific frequency region with both excellent time and frequency resolution so as to obtain accurate instantaneous frequency (IF) estimation results. The proposed ZST is an improvement of the synchrosqueezing wavelet transform (SWT) and consists of two steps, i.e., the frequency-shift operation and the partial zoom synchrosqueezing operation. The frequency-shift operation is to shift the interested frequency component from the lower frequency region to the higher frequency to obtain better time resolution. The partial zoom synchrosqueezing operation is conducted to analyze the shifted signal with excellent frequency resolution in a considered frequency region. Compared with SWT, the proposed method can provide satisfactory energy concentrated time-frequency representation (TFR) and accurate IF estimation results. Additionally, an application of the proposed ZST to the IS fluctuation estimation of a motorized spindle was conducted, and the result showed that the IS estimated by the proposed ZST can be used to detect the quality of the finished workpiece surface.

Reduced Interference Sparse Time-Frequency Distributions for Compressed Observations

Traditional quadratic time-frequency distributions are not designed to deal with randomly undersampled signals or data with missing samples. The compressed data measurements introduce noise-like artifacts in the ambiguity domain, compounding the problem of separating the signal auto-terms and cross-terms. In this paper, we propose a multi-task kernel design for suppressing both the artifacts and the cross-terms, while preserving the signal desirable auto-terms. The proposed approach results in highly concentrated time-frequency signature. We evaluate our approach using various polynomial phase signals and show its benefits, especially in the case of strong artifacts.

General Parameterized Time-Frequency Transform

Interest in parameterized time-frequency analysis for non-stationary signal processing is increasing steadily. An important advantage of such analysis is to provide highly concentrated time-frequency representation with signal-dependent resolution. In this paper, a general scheme, named as general parameterized time-frequency transform (GPTF transform), is proposed for carrying out parameterized time-frequency analysis. The GPTF transform is defined by applying generalized kernel based rotation operator and shift operator. It provides the availability of a single generalized time-frequency transform for applications on signals of different natures. Furthermore, by replacing kernel function, it facilitates the implementation of various parameterized time - frequency transforms from the same standpoint. The desirable properties and the dual definition in the frequency domain of GPTF transform are also described in this paper. One of the advantages of the GPTF transform is that the generalized kernel can be customized to characterize the time - frequency signature of non-stationary signal. As different kernel formulation has bias toward the signal to be analyzed, a proper kernel is vital to the GPTF. Thus, several potential kernels are provided and discussed in this paper to develop the desired parameterized time - frequency transforms. In real applications, it is desired to identify proper kernel with respect to the considered signal. This motivates us to propose an effective method to identify the kernel for the GPTF.

Computing Deblurred Time-Frequency Distributions Using Artificial Neural Networks

This paper presents an effective correlation vectored taxonomy algorithm to compute highly concentrated time-frequency distributions (TFDs) using localized neural networks (LNNs). Spectrograms and pre-processed Wigner–Ville distributions of known signals are vectorized and clustered as per the elbow criterion to constitute the training data for multiple artificial neural networks. The best trained networks become part of the LNNs. Test TFDs of unknown signals are then processed through the algorithm and presented to the LNNs. Experimental results demonstrate that appropriately vectored and clustered data once processed through the LNNs produce high resolution TFDs. Examples are presented to show the effectiveness of the proposed algorithm via analysis based on entropy and visual interpretation.