Conventional Time-frequency Analysis Research Articles

A seismic thin‐layer detection factor calculated by integrated S transform with non‐negative matrix factorization

AbstractTime–frequency analysis is one of the effective methods for seismic thin‐layer detection. Conventional time–frequency analysis technology for seismic thin‐layer detection is interfered by the energy of adjacent frequency signals, and there is information redundancy in the frequency‐domain analysis. Therefore, an S transform with improved window factor, which is based on the constrained non‐negative matrix factorization, is constructed to realize seismic thin‐layer detection. First, the seismic data is processed by the S transform of the improved window factor, and then we can obtain the frequency‐domain information with strong time–frequency focus by changing the adjustment factor and attenuation factor in the window function. Furthermore, the key frequency of the seismic data spectrum, which can also be called the key frequency characteristic factor, can be calculated by the non‐negative matrix factorization algorithm. Fortunately, the overthrust model shows a good correspondence between the key frequency characteristic factor and the thin‐layer interface. The field data example shows that this approach provides a new approach for thin‐layer detection.

Time-frequency enhanced characterization method based on asymmetric image reconstruction autoencoder

The vibration signals of mechanical equipment are subject to the influence of complex and variable working conditions, often exhibiting non-smooth and non-linear characteristics. The conventional time-frequency (TF) analysis (TFA) method, which relies on energy concentration, is susceptible to noise and impact, making it challenging to accurately extract fault characteristics. To overcome these limitations, this paper proposes an innovative approach. In this paper, we introduce an asymmetric image reconstruction autoencoder model, which is based on two well-known TFA methods, namely, short-time Fourier transform (STFT) and synchroextracting transform (SET), effectively reducing noise and improving the TF energy concentration process through learning the mapping relationship between STFT and SET. To address the clarity issue in the reconstructed TF images, the paper incorporates a channel attention mechanism known as SE Block into the encoding-decoding structure. Additionally, a skip connection structure is introduced to aid in restoring the structural details of the reconstructed TF images. Moreover, an improved weighted joint loss function is proposed to adaptively enhance various types of TF distribution features. This enhancement ensures that different characteristics of TF distribution are adequately addressed during the reconstruction process. The proposed method is put to the test using both simulated signals and experimental signals from gearbox rolling bearing faults. The results demonstrate that compared to traditional TFA and post-processing methods, the proposed model exhibits superior capabilities in enhancing the TF characterization of multi-source time-varying signals. Furthermore, it demonstrates remarkable robustness to noise and can accurately extract instantaneous frequency. These findings point to the promising potential of this method for mechanical fault identification and diagnosis applications.

A Novel GNSS Sweep Interference Detection and Mitigation Method Based on Radon–Wigner Transform

In this paper, a novel Radon-Wigner transform (RWT) based sweep interference detection and mitigation method has been proposed for global navigation satellite system (GNSS) receivers working in the disturbing scenarios. The proposed GNSS sweep interference detection and mitigation method has been tested using real GPS L1-C/A data disturbed by the sweep interference in a controlled test bench experiment. The results have shown that the proposed method can effectively deal with the cross-term problems with the conventional time-frequency (TF) analysis techniques and provide much improved GNSS interference detection performance in comparison to the existed Wigner-Ville distribution (WVD) and Wigner-Hough transform (WHT) approaches; and the characteristic parameters of the GNSS sweep interfering signal can be efficiently estimated according to the peak position of the RWT computed in the parameter space. In order to excite the GNSS sweep interfering signal, the dechirping and notch filtering techniques have been suggested to realize the GNSS anti-interference functionality, providing satisfactory anti-interference performance for GNSS receivers, this has been further verified by the GNSS signal acquisition experiment in the interfering environment.

Classification of underwater soundscapes using raw hydroacoustic signals

Automatic classification of underwater soundscapes remains an open problem, mainly due to the challenges posed by multi-source interferences. Accurately classifying anthropogenic sounds in the marine environment, specifically those emanating from surface-ships, is concerned in this study. To achieve this, the convolutional neural network (CNN) with sine-cardinal-likeconstrained convolutional kernels is proposed, where kernels represent unsolved filter coefficients. Raw signals of sound pressures passively received by the hydrophone are used directly in this method without the need for the routine time-frequency analysis (TFA) beforehand. The convolutional layer with constrained kernels plays a crucial role in extracting features from hydroacoustic signals, effectively acting as a learnable extension of the bandpass filter groups with flexible bandwidth. One significant advantage of the proposed approach is its adaptive filtering capability based on the real-world data, which makes it effectively filter out irrelevant interference sounds. Such heterogeneous interferences often exhibit diverse unknown spectral ranges, making them challenging for conventional TFA with fixed parameters. By leveraging this adaptability, the output of the convolutional layer serves as a task-specific spectrogram, customized to the classifier after being trained on hydroacoustic data. The experiments on the ShipsEar dataset demonstrate the promising results of our solution than TFA and vanilla CNN.

Synchroextracting frequency synchronous chirplet transform for fault diagnosis of rotating machinery under varying speed conditions

The fault diagnosis of rotating machine is essential to maintain its operational safety and avoid catastrophic accidents. The vibration signals collected from the varying speed rotating machinery are non-stationary, and time–frequency analysis (TFA) is a feasible method for varying speed fault diagnosis by revealing time-varying instantaneous frequency (IF) information in signals. However, most conventional TFA methods are not specifically designed for rotating machinery vibration signals and may not be able to handle these signals, especially in the presence of noise. Therefore, this paper develops a unique TFA method designated as synchroextracting frequency synchronous chirplet transform (SEFSCT) for vibration signal analysis and fault diagnosis of rotating machinery. In the proposed method, the frequency synchronous chirplet transform (FSCT) that utilizes the frequency synchronous chirp rate is first introduced, which takes fully into account the intrinsic proportional relationship of time-varying IFs of the signal. Then, to further concentrate the time–frequency representation (TFR) of FSCT, the synchroextracting operator is constructed based on the Gaussian modulated linear chirp model and the SEFSCT is naturally developed by integrating the FSCT and synchroextracting operator. With the proposed SEFSCT, a high-quality TFR can be generated, thus the time-varying IFs and mechanical failure can be accurately identified. The SEFSCT is employed to deal with synthetic and actual signals, and the results illustrate its efficacy in handling non-stationary signals and diagnosing the mechanical failure.

Wind Turbine Planetary Gearbox Fault Diagnosis via Proportion-Extracting Synchrosqueezing Chirplet Transform

Wind turbine planetary gearboxes usually work under time-varying conditions, leading to nonstationary vibration signals. These signals often consist of multiple time-varying components with close instantaneous frequencies. Therefore, high-quality time-frequency analysis (TFA) is needed to extract the time-frequency feature from such nonstationary signals for fault diagnosis. However, it is difficult to obtain high-quality time-frequency representations (TFRs) through conventional TFA methods due to low resolution and time-frequency blurs. To address this issue, we propose a new TFA method termed the proportion-extracting synchrosqueezing chirplet transform (PESCT). Firstly, the proportion-extracting chirplet transform (PECT) is employed to generate high-resolution underlying TFRs. Then, the energy concentration of the underlying TFRs is enhanced via the synchrosqueezing transform. Finally, wind turbine planetary gearbox fault can be diagnosed by analysis of the dominant time-varying components revealed by the concentrated TFRs with high resolution. The proposed PESCT is suitable for achieving high-quality TFRs for complicated nonstationary signals. Numerical and experimental analyses validate the effectiveness of the PESCT in characterizing the nonstationary signals from wind turbine planetary gearboxes.

Feature Extraction of a Non-Stationary Seismic–Acoustic Signal Using a High-Resolution Dyadic Spectrogram

Using a novel mathematical tool called the Te-gram, researchers analyzed the energy distribution of frequency components in the scale–frequency plane. Through this analysis, a frequency band of approximately 12 Hz is identified, which can be isolated without distorting its constituent frequencies. This band, along with others, remained inseparable through conventional time–frequency analysis methods. The Te-gram successfully addresses this knowledge gap, providing multi-sensitivity in the frequency domain and effectively attenuating cross-term energy. The Daubechies 45 wavelet function was employed due to its exceptional 150 dB attenuation in the rejection band. The validation process encompassed three stages: pre-, during-, and post-seismic activity. The utilized signal corresponds to the 19 September 2017 earthquake, occurring between the states of Morelos and Puebla, Mexico. The results showcased the impressive ability of the Te-gram to surpass expectations in terms of sensitivity and energy distribution within the frequency domain. The Te-gram outperformed the procedures documented in the existing literature. On the other hand, the results show a frequency band between 0.7 Hz and 1.75 Hz, which is named the planet Earth noise.

Hilbert–Huang Transform Incorporating Analytical Mode Decomposition and Its Application in Fractured-Vuggy Carbonate Reservoir Prediction

High-precision time-frequency (TF) analysis (TFA) can accurately detect anomalies in oil and gas reservoirs. However, conventional TFA methods cannot effectively identify fractured-vuggy carbonate reservoirs, which are deep and strongly heterogeneous. In this paper, a TFA method based on analytical mode decomposition (AMD) and the Hilbert-Huang transform (HHT) is proposed. Specifically, seismic signals are decomposed by empirical mode decomposition (EMD) and then by AMD. Finally, the TF distribution of the seismic signals is obtained after Hilbert spectrum analysis (HSA). Synthetic seismic data demonstrate that the AMD-HHT method can effectively eliminate mode mixing and provide higher time and frequency resolutions and energy focus than conventional TFA methods. In addition, model and field seismic data also verify that the AMD-HHT method can effectively detect hydrocarbon-related energy anomalies hidden in broadband seismic data.

A non-linear time–frequency tool for machinery fault diagnosis under varying speed condition

Vibration signals acquired from rotating machines operating under varying speed condition often exhibit strong frequency modulation. Conventional time–frequency analysis techniques cannot accurately capture the rapid changing dynamic of such signals where the time–frequency representation often suffers from the diffused energy problem. A new technique binding the demodulation technique and synchroextracting transform (SET) is thus proposed in this paper to overcome this problem. A theoretical analysis is also presented in the study to show the underlying mechanism that the SET technique has certain limitations in dealing with strong time-varying signals, whereas the proposed technique can effectively overcome such limitations. Several numerical examples and two sets of bearing experimental data are used to verify the effectiveness of the proposed technique in the analysis of time-varying signals and for bearing fault diagnosis.

Reassignment-enable reweighted sparse time-frequency analysis for sparsity-assisted aeroengine rub-impact fault diagnosis

Time-frequency analysis (TFA) is an effective tool for the feature extraction of nonstationary signals. However, the energy concentration of the TF representation (TFR) obtained by conventional TFA is weakened when the instantaneous frequency (IF) of signals varies fast, which adversely affects the feature extraction and reconstruction. In this paper, a reassignment-enable reweighted sparse TF method (Re2STF) is proposed to achieve high energy concentration as well as highly accurate reconstruction when analyzing signals with fast-varying IF, and thus is effective to the vibration analysis of aeroengine rub-impact fault. A reweighted sparse TF model is constructed, which iteratively employs the TF reassignment representation into the reweighted strategy to suppress noise and match the fast-varying TF structure better. In particular, the reassignment-enable weight can highlight the TF ridge and suppress the TF coefficients elsewhere. Furthermore, an effective acceleration strategy for the fast iterative shrinkage threshold algorithm is proposed to speed up the model solving. The simulation study and the application in the vibration analysis of a dual-rotor turbofan engine show the improvement of Re2STF in denoising, TF energy concentration and reconstruction, thus proving the effectiveness in aeroengine rub-impact fault diagnosis.

Demodulated time-direction synchrosqueezing transform and its applications in mechanical fault diagnosis

Time-frequency analysis is recognized as a dynamic tool to analyze the nonstationary signal. The synchrosqueezing transform is usually applied as a post-processing method to further improve the readability of the time-frequency representation. Synchrosqueezing transform is related to the reassignment method and can be performed in two directions, namely time direction and frequency direction. Frequency-direction reassignment helps to squeeze the slowly changing ridge. However, the time-direction reassignment is efficient to process the signal with rapid variation in instantaneous frequency. Thus, there exists a conflict in most of the time-frequency analysis methods while dealing with a signal containing both of these two components. In this study, a new method called demodulated time-direction synchrosqueezing transform is introduced, which is not only capable of achieving a higher compact TFR but also allow reconstructing the mode. In order to explain demodulated time-direction synchrosqueezing transform, a signal model is established in frequency domain. Then, a demodulated procedure is implemented to eliminate time-frequency analysis diffusion. Finally, time-direction reassignment is carried out to further enhance the energy concentration of the time-frequency analysis. The proposed demodulated time-direction synchrosqueezing transform method is evaluated by both simulation and experimental research. The results reveal that the performance of demodulated time-direction synchrosqueezing transform is better than the conventional time-frequency analysis methods, and it can be applied to the fault diagnosis in a machine.

Evaluating the Different Stages of Parkinson's Disease Using Electroencephalography With Holo-Hilbert Spectral Analysis.

Electroencephalography (EEG) can reveal the abnormalities of dopaminergic subcortico-cortical circuits in patients with Parkinson’s disease (PD). However, conventional time-frequency analysis of EEG signals cannot fully reveal the non-linear processes of neural activities and interactions. A novel Holo-Hilbert Spectral Analysis (HHSA) was applied to reveal non-linear features of resting state EEG in 99 PD patients and 59 healthy controls (HCs). PD patients demonstrated a reduction of β bands in frontal and central regions, and reduction of γ bands in central, parietal, and temporal regions. Compared with early-stage PD patients, late-stage PD patients demonstrated reduction of β bands in the posterior central region, and increased θ and δ2 bands in the left parietal region. θ and β bands in all brain regions were positively correlated with Hamilton depression rating scale scores. Machine learning algorithms using three prioritized HHSA features demonstrated “Bag” with the best accuracy of 0.90, followed by “LogitBoost” with an accuracy of 0.89. Our findings strengthen the application of HHSA to reveal high-dimensional frequency features in EEG signals of PD patients. The EEG characteristics extracted by HHSA are important markers for the identification of depression severity and diagnosis of PD.

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.

EEG Motor Imagery Classification With Sparse Spectrotemporal Decomposition and Deep Learning

Classification of electroencephalogram-based motor imagery (MI-EEG) tasks raises a big challenge in the design and development of brain-computer interfaces (BCIs). In view of the characteristics of nonstationarity, time-variability, and individual diversity of EEG signals, a deep learning framework termed SSD-SE-convolutional neural network (CNN) is proposed for MI-EEG classification. The framework consists of three parts: 1) the sparse spectrotemporal decomposition (SSD) algorithm is proposed for feature extraction, overcoming the drawbacks of conventional time-frequency analysis methods and enhancing the robustness to noise; 2) a CNN is constructed to fully exploit the time-frequency features, thus outperforming traditional classification methods both in terms of accuracy and kappa value; and 3) the squeeze-and-excitation (SE) blocks are adopted to adaptively recalibrate channelwise feature responses, which further improves the overall performance and offers a compelling classification solution for MI-EEG applications. Experimental results on two datasets reveal that the proposed framework outperforms state-of-the-art methods in terms of both classification quality and robustness. The advantages of SSD-SE-CNN include high accuracy, high efficiency, and robustness to cross-trial and cross-session variations, making it an ideal candidate for long-term MI-EEG applications.

Objective Extraction of Evoked Event-Related Oscillation from Time-Frequency Representation of Event-Related Potentials

Evoked event-related oscillations (EROs) have been widely used to explore the mechanisms of brain activities for both normal people and neuropsychiatric disease patients. In most previous studies, the calculation of the regions of evoked EROs of interest is commonly based on a predefined time window and a frequency range given by the experimenter, which tends to be subjective. Additionally, evoked EROs sometimes cannot be fully extracted using the conventional time-frequency analysis (TFA) because they may be overlapped with each other or with artifacts in time, frequency, and space domains. To further investigate the related neuronal processes, a novel approach was proposed including three steps: (1) extract the temporal and spatial components of interest simultaneously by temporal principal component analysis (PCA) and Promax rotation and project them to the electrode fields for correcting their variance and polarity indeterminacies, (2) calculate the time-frequency representations (TFRs) of the back-projected components, and (3) compute the regions of evoked EROs of interest on TFRs objectively using the edge detection algorithm. We performed this novel approach, conventional TFA, and TFA-PCA to analyse both the synthetic datasets with different levels of SNR and an actual ERP dataset in a two-factor paradigm of waiting time (short/long) and feedback (loss/gain) separately. Synthetic datasets results indicated that N2-theta and P3-delta oscillations can be stably detected from different SNR-simulated datasets using the proposed approach, but, by comparison, only one oscillation was obtained via the last two approaches. Furthermore, regarding the actual dataset, the statistical results for the proposed approach revealed that P3-delta was sensitive to the waiting time but not for that of the other approaches. This study manifested that the proposed approach could objectively extract evoked EROs of interest, which allows a better understanding of the modulations of the oscillatory responses.

Boosts in brain signal variability track liberal shifts in decision bias.

Adopting particular decision biases allows organisms to tailor their choices to environmental demands. For example, a liberal response strategy pays off when target detection is crucial, whereas a conservative strategy is optimal for avoiding false alarms. Using conventional time-frequency analysis of human electroencephalographic (EEG) activity, we previously showed that bias setting entails adjustment of evidence accumulation in sensory regions (Kloosterman et al., 2019), but the presumed prefrontal signature of a conservative-to-liberal bias shift has remained elusive. Here, we show that a liberal bias shift is reflected in a more unconstrained neural regime (boosted entropy) in frontal regions that is suited to the detection of unpredictable events. Overall EEG variation, spectral power and event-related potentials could not explain this relationship, highlighting that moment-to-moment neural variability uniquely tracks bias shifts. Neural variability modulation through prefrontal cortex appears instrumental for permitting an organism to adapt its biases to environmental demands.

Simultaneous Measurement of Radial and Transversal Velocities Using Interferometric Radar

The linear velocity of an arbitrary moving object comprises two orthogonal components with reference to the observing radar, which are radial velocity and transversal velocity. Simultaneous measurement of both the radial and transversal velocities can provide a complete 2-D movement information for further target detection, tracking, and classification. The interferometric radar is capable of measuring the 2-D velocity of an arbitrary moving object simultaneously, regardless of the trajectory. However, the radial velocities and transversal velocities are coupled in the interferometric measurement due to the nonlinear processing when there are multiple moving objects in the radar field of view (FoV), thus the conventional time-frequency analysis fails to measure the transversal velocities. In this article, we first derive and analyze the signal distortion caused by the nonlinear interferometric operation. We then propose two new methods of combining the inverse Radon transform (IRT) and short-time Fourier transform (STFT), which can concentrate a sinusoidally frequency-modulated waveform from time-frequency domain into a point in the parameter domain, thus separating the transversal velocity measurements of different objects with rigid-body rotations. Simulation and experimental results are provided to validate the effectiveness of the proposed methods.

Seismic time–frequency spectrum analysis based on local polynomial Fourier transform

Time–frequency analysis technology is widely used in non-stationary seismic data analysis. The energy concentration of the spectrum depends on the consistency of the kernel function of the time–frequency analysis method and the instantaneous frequency variation of the signals. The conventional time–frequency analysis methods usually require that the local instantaneous frequency of the signals remains unchanged or linearly changed. So it is difficult to accurately characterize the instantaneous frequency nonlinear variation of the non-stationary signal. The local polynomial Fourier transform (LPFT) method can effectively describe the instantaneous frequency variation by local high-order polynomial fitting and obtain the results with high spectral and energy concentration. The numerical simulations and field seismic data applications show that the time–frequency spectrum results obtained by LPFT can reflect the instantaneous frequency variation characteristics of the seismic data, while ensuring the concentration of time–frequency energy.

Air compressor fault diagnosis based on lifting wavelet transform and probabilistic neural network

Due to the wide variety of faults, the components of air compressor fault condition vibration signal are complex. Fault features extracted by conventional time-frequency analysis and multi-resolution analysis are not comprehensive enough to reflect the fault condition of air compressor. To overcome this deficiency, this paper proposes an air compressor fault diagnosis algorithm based on lifting wavelet. Firstly, the vibration signal of the air compressor is decomposed by lifting wavelet; then the statistic such as the peak value and Kurtosis of the decomposition layer is calculated as the fault features. Finally, Probabilistic Neural Network is utilized to classify the fault state. In the experiment, the fault extraction methods such as Wavelet Packet Decomposition and Continuous Wavelet Transform are compared. The results indicate that the fault features extracted by lifting wavelet are more comprehensively to reflect the fault condition of air compressor while other fault character extraction methods need more fault characteristics; the fault diagnosis accuracy by utilizing proposed method is high and the training time is short, which is more suitable for the online fault diagnosis of the actual air compressor.

Time-Frequency Squeezing and Generalized Demodulation Combined for Variable Speed Bearing Fault Diagnosis

High-resolution time-frequency representation (TFR) method is effective for signal analysis and feature detection. However, for variable speed bearing vibration signal, conventional TFR method is prone to blur and affect the accuracy of the instantaneous frequency estimation. Moreover, the traditional order tracking, relying on equi-angular resampling, usually suffers from interpolation error. To solve such problems, we propose a joint time-frequency (TF) squeezing method and generalized demodulation (GD) to realize variable speed bearing fault diagnosis. The method can represent the time-varying fault characteristic frequency precisely and be free from resampling. First, using fast spectral kurtosis to select the optimal-frequency band which is sensitive to rolling bearing fault, and extracting envelope by Hilbert transform within the selected optimal frequency band. Next, a high-quality TF clustering method based on short-time Fourier transform is applied to the TF analysis of the envelope to get a clear TFR, from which the frequency information for GD is obtained. Finally, processing the basic demodulator via the peak search through the TF analysis results in the TFR for GD to gain a resampling-free-order spectrum. Based on the more precise TF information from the clearer TFR, the bearing fault can be diagnosed via GD without tachometer or any resampling involved, avoiding the amplitude error and low computational efficiency of resampling. Simulation study and experimental signal analysis validate that the proposed method has better performance than those methods based on conventional TF analysis and resampling.