Time-frequency Analysis Method Research Articles

Research on the Motion Features Model for Underwater Targets with Multiple Highlights and Multiple Micro-Motion Forms

Motion characterization, including Doppler and micro-Doppler, is crucial for the detection and identification of high-speed underwater targets. Under high-frequency and short-range conditions, underwater targets cannot be simply regarded as single highlight targets as they exhibit a complex structure with multiple scattering centers accompanied by distinct micro-motions. To address this multi-highlight and multi-micro-motion scenario, a model is proposed to characterize the motion features of underwater targets. Firstly, a mathematical model is established to represent the micro-Doppler features based on the single-highlight model. Subsequently, considering the overlap of multiple highlight echoes caused by the high-speed translation of the target and the long pulse detection signal, precise representation is achieved by setting motion positions and calculating time delays within the model. The results represent the echoes of moving targets with multiple highlights and micromotions. Finally, a time-frequency analysis method is employed to extract motion features and estimate target parameters, thereby validating the accuracy and effectiveness of the proposed model. This research provides a theoretical foundation for the modeling of underwater moving targets.

Recursive demodulated synchro spline-kernelled chirplet extracting transform: a useful tool for non-linear behavior estimation of non-stationary signal and application to wind turbine fault detection

Non-linear behavior is widespread in many kinds of signals from nature and engineering fields. Although the high energy-concentration level of various advanced time-frequency (TF) analysis (TFA) techniques currently developed ensure a fine representation of non-linear behavior of time-varying component (TVC) of the signal, it is far from sufficient to solely consider the single aspect of energy-concentration level, because the actual signal composition is always more complicated, especially for some thorny difficulties such as strong noise interference and the early weak TVC, etc., these negative factors bring significant challenges to reveal the non-linear behavior of TVC of practical signals. A new TFA method aimed at this issue, called recursive demodulated synchro spline-kernelled chirplet extracting transform (RDSSCET), is proposed in this paper. The proposed RDSSCET is developed on the frame of synchro spline-kernelled chirplet extracting transform (SSCET) and a newly designed external-internal nested double iteration mechanism, which effectively addresses the limitation of SSCET in handling multicomponent signals while also exhibiting superior high energy concentration and noise robustness. As such, the proposed RDSSCET can yield a more favorable outcome when revealing the non-linear behavior of TVC, particularly for weak TVC with strong noise interference. Comparison analysis results in numerical simulations verified the performance of RDSSCET. Its effectiveness in real applications is fully tested via two real-world sound signals and a practical case of wind turbine fault detection.

Heart Signal Analysis Using Multistage Classification Denoising Model

Cardiovascular disease is a major cause of death worldwide, and the COVID-19 pandemic has only made the situation worse. The purpose of this work is to explore various time-frequency analysis methods that can be used to classify heart sound signals and identify multiple abnormalities in the heart, such as aortic stenosis, mitral stenosis, and mitral valve prolapse. The signal has been modified using three techniques—tunable quality wavelet transform (TQWT), discrete wavelet transform (DWT), and empirical mode decomposition—to detect heart signal abnormality. The proposed model detects heart signal abnormality at two stages, the user end and the clinical end. At the user end, binary classification of signals is performed, and if signals are abnormal then further classification is done at the clinic. The approach starts with signal preprocessing and uses the discrete wavelet transform (DWT) coefficients to train the hybrid model, which consists of one long short-term memory (LSTM) network layer and three convolutional neural network (CNN) layers. This method produced comparable results, with a 98.9% classification accuracy for signals, through the utilization of the CNN and LSTM model. Combining the CNN’s skill in feature extraction with the LSTM’s capacity to record time-dependent features improves the efficacy of the model. Identifying issues early and initiating appropriate medication can alleviate the burden associated with heart valve diseases.

Weight extracting transform for instantaneous frequency estimation and signal reconstruction

This paper introduces a novel time–frequency analysis method called the Weight Extracting Transform (WET). The primary objective of WET is to enhance the energy concentration in linear time–frequency representations for time-varying signals. By aggregating the time–frequency blur produced by the short-time Fourier transform onto the actual instantaneous frequency, WET improves the readability and accuracy of the time–frequency representation. Additionally, the algorithm is extended to a more general linear time–frequency transform known as the chirplet transform, which effectively handles fast-varying signals. The WET method excels at distinguishing components with closely spaced instantaneous frequencies and can reconstruct the original signal from its time–frequency representation. Experimental results using simulated and real-world signals demonstrate that WET achieves superior energy concentration and noise robustness compared to existing methods.

Research on Feature Extraction and Fault Diagnosis Method for Rolling Bearing Vibration Signals Based on Improved FDM-SVD and CYCBD

In mechanical equipment, rolling bearing components are constantly exposed to intricate and diverse environmental conditions, rendering them vulnerable to wear, performance degradation, and potential malfunctions. To precisely extract and discern rolling bearing vibration signals amidst intricate noise interference, this paper introduces a fault feature extraction and diagnosis methodology that seamlessly integrates an improved Fourier decomposition method (FDM), singular value decomposition (SVD), and maximum second-order cyclostationary blind convolution (CYCBD). Initially, the FDM is employed to meticulously decompose the bearing fault signals into numerous signal components. Subsequently, a comprehensive weighted screening criterion is formulated, aiming to strike a balance between multiple indicators, thereby enabling the selective screening and reconstruction of pertinent signal components. Furthermore, SVD and CYCBD techniques are introduced to carry out intricate processing and envelope demodulation analysis of the reconstructed signals. Through rigorous simulation experiments and practical rolling bearing fault diagnosis tests, the method’s noteworthy effectiveness in suppressing noise interference, enhancing fault feature information, and efficiently extracting fault features is unequivocally demonstrated. Furthermore, compared to traditional time–frequency analysis methods such as EMD, EEMD, ITD, and VMD, as well as traditional deconvolution methods like MED, OMEDA, and MCKD, this method exhibits significant advantages, providing an effective solution for diagnosing rolling bearing faults in environments with strong background noise.

Seismic noise in South China Sea: High-quality time-frequency analysis from 0.01 to 125 Hz.

An efficient and precise time-frequency analysis method for real-time ocean bottom seismometer (RTOBS) data in the South China Sea (SCS) is presented. Overcoming the limitations of conventional methods, the method involves temporal segmentation, unique frequency octaves, and Fourier transforms to generate power spectral density (PSD) and probability density function profiles. The method demonstrates superior precision, computational efficiency, and full-bandwidth (0 to Nyquist) capability compared to traditional techniques, as validated through theoretical and empirical evaluations. Applied to SCS RTOBS data, it unveils temporal PSD variations, shedding light on underwater noise sources like earthquakes, offshore blasting, ship-induced disturbances, and tidal effects. Establishing background noise levels in the SCS supports noise source categorization and ocean environment monitoring. Furthermore, comparing onshore and offshore seismic stations advances interdisciplinary research, fostering a comprehensive understanding of acoustics and seismology in the region.

Research on inter-shaft bearing fault diagnosis method based on STFT-CNN modeling

Inter-shaft bearings are an essential component of aircraft engines, and their operational status determines the safety of aircraft engine operation. Therefore, to improve the accuracy of fault type prediction and enrich the feature information in vibration signals of aircraft engine inter-shaft bearings, this paper proposes an STFT-CNN model based on the AlexNet architecture, extending its application to the research of aircraft engine inter-shaft bearing fault diagnosis. This approach addresses the common reliance on personnel experience for fault type diagnosis in traditional aircraft engine inter-shaft bearing fault diagnosis. Firstly, real vibration fault signals from inter-shaft bearings are collected through experiments to enrich feature information in non-stationary signals using STFT time-frequency methods. Secondly, utilizing the high interpretability of the STFT-CNN model, fault feature data from inter-shaft bearings under various operating conditions are extracted to refine our understanding of fault feature information. Finally, leveraging the robustness of the STFT-CNN model, fault types are classified and predicted. The training process involves comparative analysis using different pooling algorithms, time-frequency analysis methods, and various deep learning network models. The results demonstrate that the STFT-CNN model, employing the maximum pooling algorithm, outperforms other models in predicting inter-shaft bearing faults, achieving an average fault prediction accuracy of 98.8% .

High-order iterative rearrangement transform for time–frequency characterization of bearing fault impact

Time–frequency analysis (TFA) can effectively characterize features of non-stationary signals. Traditional TFA algorithms construct signal models in the time domain and make the assumption that the instantaneous characteristics of each component are continuous. However, the instantaneous frequency (IF) of the transient signal is discontinuous in the time domain and exhibits a multifaceted relationship with time, such as shock, vibration wave, damped sound wave, etc. Additionally, in most existing TFA methods, low-order group delay (GD) is used to describe transient signals, which leads to unsatisfactory energy concentration and calculation accuracy. To address about issues, a novel TFA technique, termed high-order iterative rearrangement transform (HOIRT), is developed in this research. First, the signal model is defined within the frequency domain, and the frequency ridge of the transient signal is described by a high-order GD (HOGD), which is similar to the IF. Second, a HOGD-based iterative synchrosqueezing operator is defined to reassign time–frequency coefficients into the GD trajectories along the time direction. Finally, the HOGD-based frequency extraction operator is constructed to only retain the target time–frequency information of the transient signal from the rearranged results, such that the noise interference is eliminated and the energy-concentrated TFR is obtained. A simulation signal with nonlinear GDs is employed to illustrate the effectiveness of the HOIRT. Compared with the other seven typical TFA algorithms, the developed technique has the smallest calculation error and Rényi entropy, showing that the HOIRT has the highest accuracy and energy concentration. Analysis result of the bearing fault impact signal shows that the proposed HOIRT can display the time when pulses occur while ensuring high time–frequency resolution, making it suitable for detecting bearing faults.

On a Closer Look of a Doppler Tolerant Noise Radar Waveform in Surveillance Applications.

The prevalence of Low Probability of Interception (LPI) and Low Probability of Exploitation (LPE) radars in contemporary Electronic Warfare (EW) presents an ongoing challenge to defense mechanisms, compelling constant advances in protective strategies. Noise radars are examples of LPI and LPE systems that gained substantial prominence in the past decade despite exhibiting a common drawback of limited Doppler tolerance. The Advanced Pulse Compression Noise (APCN) waveform is a stochastic radar signal proposed to amalgamate the LPI and LPE attributes of a random waveform with the Doppler tolerance feature inherent to a linear frequency modulation. In the present work, we derive closed-form expressions describing the APCN signal's ambiguity function and spectral containment that allow for a proper analysis of its detection performance and ability to remove range ambiguities as a function of its stochastic parameters. This paper also presents a more detailed address of the LPI/LPE characteristic of APCN signals claimed in previous works. We show that sophisticated Electronic Intelligence (ELINT) systems that employ Time Frequency Analysis (TFA) and image processing methods may intercept APCN and estimate important parameters of APCN waveforms, such as bandwidth, operating frequency, time duration, and pulse repetition interval. We also present a method designed to intercept and exploit the unique characteristics of the APCN waveform. Its performance is evaluated based on the probability of such an ELINT system detecting an APCN radar signal as a function of the Signal-to-Noise Ratio (SNR) in the ELINT system. We evaluated the accuracy and precision of the random variables characterizing the proposed estimators as a function of the SNR. Results indicate a probability of detection close to 1 and show good performance, even for scenarios with a SNR slightly less than -10 dB. The contributions in this work offer enhancements to noise radar capabilities while facilitating improvements in ESM systems.

A Synchrosqueezed Transform Method Based on Fast Kurtogram and Demodulation and Piecewise Aggregate Approximation for Bearing Fault Diagnosis.

Synchrosqueezed transform (SST) is a time-frequency analysis method that can improve energy aggregation and reconstruct signals, which has been applied in the fields of medical treatment, fault diagnosis, and seismic wave processing. However, when dealing with time-varying signals, SST suffers from poor time-frequency resolution and is unable to deal with long signals. In order to accurately extract the characteristic frequency of variable speed rolling bearing faults, this paper proposes a synchrosqueezed transform method based on fast kurtogram and demodulation and piecewise aggregate approximation (PAA). The method firstly filters and demodulates the original signal using fast kurtogram and Hilbert transform to reduce the influence of background noise and improve the time-frequency resolution. Then, it compresses the signal by using piecewise aggregate approximation, so that the SST can deal with long signals and, thus, extract the fault characteristic frequency. The experimental data verification results indicate that the method can effectively identify the fault characteristic frequency of variable-speed rolling bearings.

Angle-dependent seismic attenuation-based gas-bearing detection of a sandstone river channel reservoir in the western Sichuan Basin

Abstract The shallow river channel sandstone reservoirs of Jurassic in the western Sichuan Basin are rich in natural gas. The gas-bearing sweet-spot has a ‘sausage-like’ distribution feature, with complex gas water distribution. Analyses of seismic data at different angles show that gas-bearing reservoir formation has different seismic attenuation features from the water-bearing formations, and such differences have a certain correlation with gas production. Accordingly, a gas-bearing detection technology based on angle-dependent seismic attenuation feature is proposed. First, the matching-pursuit time-frequency analysis method is used to extract high-resolution time-frequency spectra from seismic data at different incidence angles. Then, the angle-dependent seismic attenuation attribute is estimated using the extracted time-frequency spectra. Finally, the attribute is combined with the inverted impedance for gas-bearing detection. With the advantages of lower uncertainty and being less affected by reservoir porosity, the application results of the developed method have a high coincidence rate with the drilled wells, and the drilling wells deployed based on the detection results have achieved high production.

Vehicle Response-Based Bridge Modal Identification Using Different Time–Frequency Analysis Methods

Modal identification of bridges based on the responses of moving vehicles, termed as the indirect method, has drawn much attention in recent years. This indirect method has been proven to be capable of identifying bridge frequencies and mode shapes in the feasibility research. However, in the presence of additional factors such as vehicle speed and road surface roughness, it is difficult to identify high-order frequencies and high-resolution mode shapes of the bridge. The authors previously proposed a tractor-double-trailers model and the time–domain subtraction method to obtain the relative displacement of two trailers for bridge modal identification. In this study, the authors develop a methodology to improve the identification performance by combining the EMD technique and the time–frequency analysis method. The EMD technique is applied to separate the multi-source response signals of the trailers to obtain the signal component that contains only the bridge vibration. Then, different time–frequency analysis methods such as the short-time Fourier transform (STFT), Wigner–Ville distribution (WVD), and continuous wavelet transform (CWT) are adopted to construct the high-resolution bridge mode shapes. Numerical studies with one-dimensional and three-dimensional bridge models are conducted to verify the proposed method and investigate the effects of different factors. Finally, a laboratory test is implemented on a scaled bridge to verify the performance of the proposed method. The results show that the proposed method is able to separate the vehicle frequency and bridge frequencies, which facilitates the identification of bridge frequencies from the dynamic response of moving vehicles. Meanwhile, the CWT method performs the best in the identification of modal shapes among the three time–frequency analysis methods.

Local maximum synchrosqueezing reassigning chirplet transform and its application to gearbox fault diagnosis

Abstract Aiming at the problems of poor time-frequency aggregation and severe noise interference when traditional time-frequency analysis methods deal with complex multi-component signals, this paper proposes a new time-frequency analysis method – local maximum synchrosqueezing reassigning chirplet transform (LMSRCT). The core idea of the method is to introduce the principle of general linear chirplet transform (GLCT) into synchro-reassigning transform (SRT), followed by reassigning the results of local maximum synchrosqueezing chirplet transform (LMSSCT), and then introducing the innovative synchro-reassigning operator (SRO). This results to a novel three-step method for extracting instantaneous frequency, which ultimately yields the final time-frequency representation. This method ensures the integrity of each instantaneous frequency, solves the problem of energy divergence problems, and improves aggregation. Simulation and experimental results show that the LMSRCT can provide better characterization results compared to other methods and can effectively solve the different situations that occur between the instantaneous frequencies of complex signals. The proposed method can effectively estimate transmission speed, which achieves fault diagnosis under tacholess conditions, and the order analysis results are more accurate and reliable.

Improved empirical mode decomposition method based on amplitude-frequency characteristic of vortex signals.

The vortex flowmeter occupies a vital position in flow measurement with its unique advantages. It is essentially a fluid vibration instrument, and its measurement process is susceptible to interference, which seriously affects measurement accuracy. In particular, at low flow rates, it is an urgent problem to extract vortex signals from the complex noise. Among many signal processing methods, Empirical Mode Decomposition (EMD) is a time-frequency analysis method suitable for nonlinear, non-stationary signals. EMD can adaptively decompose noisy signals into noise and useful signal components arranged from high frequency to low frequency. For the above problems, an innovative, improved EMD method is proposed in this paper. The digital filter is designed according to the amplitude-frequency characteristic of vortex signals. After filtering, the vortex signal is adjusted to a fixed value, and high-frequency noise is filtered. According to the consistency of the filtered signal's amplitude, we design a decomposition stop criterion for EMD to process the output signal of the vortex sensor. This method not only maintains the characteristic of adaptive decomposition in EMD but also completes the automatic extraction of the vortex signal under complex noise. It provides a new comprehensive method for realizing high-precision and anti-interference vortex flowmeters.

Decoupling and Parameter Extraction Methods for Conical Micro-Motion Object Based on FMCW Lidar.

Micro-Doppler time-frequency analysis has been regarded as an important parameter extraction method for conical micro-motion objects. However, the micro-Doppler effect caused by micro-motion can modulate the frequency of lidar echo, leading to coupling between structure and micro-motion parameters. Therefore, it is difficult to extract parameters for micro-motion cones. We propose a new method for parameter extraction by combining the range profile of a micro-motion cone and the micro-Doppler time-frequency spectrum. This method can effectively decouple and accurately extract the structure and the micro-motion parameters of cones. Compared with traditional time-frequency analysis methods, the accuracy of parameter extraction is higher, and the information is richer. Firstly, the range profile of the micro-motion cone was obtained by using an FMCW (Frequency Modulated Continuous Wave) lidar based on simulation. Secondly, quantitative analysis was conducted on the edge features of the range profile and the micro-Doppler time-frequency spectrum. Finally, the parameters of the micro-motion cone were extracted based on the proposed decoupling parameter extraction method. The results show that our method can effectively extract the cone height, the base radius, the precession angle, the spin frequency, and the gravity center height within the range of a lidar LOS (line of sight) angle from 20° to 65°. The average absolute percentage error can reach below 10%. The method proposed in this paper not only enriches the detection information regarding micro-motion cones, but also improves the accuracy of parameter extraction and establishes a foundation for classification and recognition. It provides a new technical approach for laser micro-Doppler detection in accurate recognition.

EEG rhythm separation and time-frequency analysis of fast multivariate empirical mode decomposition for motor imagery BCI.

Motor imagery electroencephalogram (EEG) is widely employed in brain-computer interface (BCI) systems. As a time-frequency analysis method for nonlinear and non-stationary signals, multivariate empirical mode decomposition (MEMD) and its noise-assisted version (NA-MEMD) has been widely used in the preprocessing step of BCI systems for separating EEG rhythms corresponding to specific brain activities. However, when applied to multichannel EEG signals, MEMD or NA-MEMD often demonstrate low robustness to noise and high computational complexity. To address these issues, we have explored the advantages of our recently proposed fast multivariate empirical mode decomposition (FMEMD) and its noise-assisted version (NA-FMEMD) for analyzing motor imagery data. We emphasize that FMEMD enables a more accurate estimation of EEG frequency information and exhibits a more noise-robust decomposition performance with improved computational efficiency. Comparative analysis with MEMD on simulation data and real-world EEG validates the above assertions. The joint average frequency measure is employed to automatically select intrinsic mode functions that correspond to specific frequency bands. Thus, FMEMD-based classification architecture is proposed. Using FMEMD as a preprocessing algorithm instead of MEMD can improve the classification accuracy by 2.3% on the BCI Competition IV dataset. On the Physiobank Motor/Mental Imagery dataset and BCI Competition IV Dataset 2a, FMEMD-based architecture also attained a comparable performance to complex algorithms. The results indicate that FMEMD proficiently extracts feature information from small benchmark datasets while mitigating dimensionality constraints resulting from computational complexity. Hence, FMEMD or NA-FMEMD can be a powerful time-frequency preprocessing method for BCI.

Time-Frequency Analysis Method of Seismic Data Based on Sparse Constraints for Road Detection

Time-Frequency Analysis Method of Seismic Data Based on Sparse Constraints for Road Detection

Application of sparse S transform network with knowledge distillation in seismic attenuation delineation

Time-frequency analysis is a successfully used tool for analyzing the local features of seismic data. However, it suffers from several inevitable limitations, such as the restricted time-frequency resolution, the difficulty in selecting parameters, and the low computational efficiency. Inspired by deep learning, we suggest a deep learning-based workflow for seismic time-frequency analysis. The sparse S transform network (SSTNet) is first built to map the relationship between synthetic traces and sparse S transform spectra, which can be easily pre-trained by using synthetic traces and training labels. Next, we introduce knowledge distillation (KD) based transfer learning to re-train SSTNet by using a field data set without training labels, which is named the sparse S transform network with knowledge distillation (KD-SSTNet). In this way, we can effectively calculate the sparse time-frequency spectra of field data and avoid the use of field training labels. To test the availability of the suggested KD-SSTNet, we apply it to field data to estimate seismic attenuation for reservoir characterization and make detailed comparisons with the traditional time-frequency analysis methods.

Instantaneous frequency identification for nonstationary signals of time-varying structures using enhanced synchroextracting wavelet transform and dynamic optimization

Civil engineering structures under ambient excitations are essentially time-varying and nonlinear structural systems and the resultant response signals exhibit non-stationarity. To reveal the time-varying characteristics of non-stationary signals, time frequency analysis methods with high resolutions are required. Although synchroextracting short time Fourier transform (SESTFT) is able to generate more energy concentrated time frequency representations and allow signal reconstruction, its major disadvantage is the window function is fixed. To address this issue, an enhanced synchroextracting wavelet transform (ESEWT) method is proposed to refine frequency bands by combing synchroextracting and continuous wavelet transform. After that, dynamic optimization (DO) is used to extract instantaneous frequency (IF) curves within the refined frequency bands. Two numerical examples and an experimental study case are investigated to illustrate the effectiveness and accuracy of the proposed method. The results demonstrate that the proposed ESEWT is capable of extracting frequency bands more accurately and its combination with DO identifies IFs of non-stationary signals better than current time frequency analysis methods such as SESTFT.

Toward efficient and accurate extraction of instantaneous frequency with chirplet transform and its applications in bearing fault diagnosis

In many engineering applications, the instantaneous frequency (IF) needs to be identified rapidly and precisely, especially in rotating machinery condition monitoring, where quasi-real-time analysis is a favorable option, and any error in shaft speed (identified from the instantaneous frequency) needs to be reduced to prevent it from accumulating with time. The modern time–frequency analysis (TFA) method provides a way for IF identification; however, sometimes, it still suffers from energy smearing and closely spaced frequency interference. In addition, many TFA methods based on the chirplet transform also present the problem of excessive computation when searching for the optimal parameters. To overcome these limitations, we propose the multi-extracting velocity-synchronous chirplet transform (MEVCT), an enhanced TFA method, in this paper. In the MEVCT, a refined chirp parameter search is developed first to reduce the computational cost while increasing time–frequency accuracy. Then, an iterative high-order IF estimator is constructed to allow the IF to achieve or approach the actual values even in highly nonlinear situations. After that, the obtained IF estimate is substituted into the simultaneous extraction operator to reduce energy dispersion further and eliminate non-reassigned points (NRPs). Simulated and experimental signal analyses demonstrate that MEVCT is able to eliminate NRPs completely. Furthermore, when handling synchronous multicomponent signals, the proposed method has higher IF accuracy with less computational cost and better anti-noise capability.