High-resolution Time-frequency Research Articles

An Adaptive Chirp Mode Decomposition-Based Method for Modal Identification of Time-Varying Structures

Modal parameters are inherent characteristics of civil structures. Due to the effect of environmental factors and ambient loads, the physical and modal characteristics of a structure tend to change over time. Therefore, the effective identification of time-varying modal parameters has become an essential topic. In this study, an instantaneous modal identification method based on an adaptive chirp mode decomposition (ACMD) technique was proposed. The ACMD technique is highly adaptable and can accurately estimate the instantaneous frequencies of a structure. However, it is important to highlight that an initial frequency value must be selected beforehand in ACMD. If the initial frequency is set incorrectly, the resulting instantaneous frequencies may lack accuracy. To address the aforementioned problem, the Welch power spectrum was initially developed to extract a high-resolution time–frequency distribution from the measured signals. Subsequently, the time–frequency ridge was identified based on the maximum energy position in the time–frequency distribution plot, with the frequencies associated with the time–frequency ridge serving as the initial frequencies. Based on the initial frequencies, the measured signals with multiple degrees of freedom could be decomposed into individual time-varying components with a single degree of freedom. Following that, the instantaneous frequencies of each time-varying component could be calculated directly. Subsequently, a sliding window principal component analysis (PCA) method was introduced to derive instantaneous mode shapes. Finally, vibration data collected under various operational scenarios were used to validate the proposed method. The results demonstrated the effective identification of time-varying modal parameters in real-world civil structures, without missing modes.

CTNet: A data-driven time-frequency technique for wind turbines fault diagnosis under time-varying speeds

Nonstationary fault signals collected from wind turbine planetary gearboxes and bearings often exhibit close-spaced instantaneous frequencies (IFs), or even crossed IFs, bringing challenges for existing time-frequency analysis (TFA) methods. To address the issue, a data-driven TFA technique, termed CTNet is developed. The CTNet is a novel model that combines a fully convolutional auto-encoder network with the convolutional block attention module (CBAM). In the CTNet, the encoder layer is first designed to extract coarse features of the time-frequency representation (TFR) calculated by the general linear Chirplet transform (GLCT); second, the decoder layer is combined to restore and conserve details of the key time-frequency features; third, the skip connections are designed to accelerate training by linking extracted and reconstructed features; finally, the CBAM is introduced to adaptively explore channel and spatial relationships of the TFR, focusing more on close-spaced or crossed frequency features, and effectively reconstruct the TFR. The effectiveness of the CTNet is validated by numerical signals with close-spaced or crossed IFs, and real-world signals of wind turbine planetary gearbox and bearings. Comparison analysis with state-of-the-art TFA methods shows that the CTNet has high time-frequency resolution in characterizing nonstationary signals and a much better ability to detect wind turbine faults.

Application of Generalized S-Transform in the Measurement of Dynamic Elastic Modulus

Resonance is commonly used for in situ measurement of the dynamic elastic modulus to evaluate the strength of concrete samples. Many researchers are also exploring the application of this convenient measurement technology for safety monitoring. Nevertheless, the presence of cracks and variations in curing conditions within samples can impact the resonance frequency range, potentially leading to potential inaccuracies in measurements. In order to improve the measurement accuracy of resonance frequency, this study introduces the Generalized S-Transform (GST) algorithm for measuring the dynamic elastic modulus, which utilizes its high time-frequency resolution to scan the power peak-point in non-stationary and transient excitation signals to determine the resonance frequency. For concrete materials with lower consistency, the experimental results verify the high accuracy of this algorithm in measuring resonance frequency compared with Fast Fourier Transform (FFT). This provides a reference for using the algorithm to measure the dynamic elastic modulus in civil engineering applications, such as buildings and bridges.

Joint extraction-based multivariate chirp mode decomposition and its application to fault diagnosis of rotating machinery under variable speed conditions

Vibration signals from rotating machinery during variable speed conditions exhibits non-stationary characteristics, posing a challenge for fault diagnosis. When a machine fails, the vibration signal of any component connected to the bearing carries valuable information about the equipment’s status. Processing multichannel variable speed signals at the same time avoids losing part of information and improves fault diagnosis. Therefore, this study put up a novel approach called joint extraction-based multivariate chirp mode decomposition (JMCMD) to analyze multichannel signals of rotating machinery with varying speeds. The approach comprises the joint extraction framework and the multichannel signal instantaneous frequency initialization (MSIFI). First, JMCMD employs a joint component extraction framework, which can precisely and simultaneously extract complicated characteristic components close to each other in multiple channels. Second, this study extends the parameterized demodulation (PD) technique to multiple channels to find the initialized instantaneous frequency of multichannel signals. Through the joint extraction strategy’s integration with MSIFI, JMCMD is capable of efficaciously extracting all significant characteristic components of multichannel signals. Additionally, the high-resolution time–frequency representation (TFR) constructed from JMCMD’s output can clearly reveal the time-varying fault characteristic frequency of the rotor-bearing system. Simulation analysis and actual cases demonstrate that the suggested approach is an effective way to identify fault feature components, making it highly applicable in signal decomposition and fault detection.

A novel multi-feature fusion attention neural network for the recognition of epileptic EEG signals.

Epilepsy is a common chronic brain disorder. Detecting epilepsy by observing electroencephalography (EEG) is the main method neurologists use, but this method is time-consuming. EEG signals are non-stationary, nonlinear, and often highly noisy, so it remains challenging to recognize epileptic EEG signals more accurately and automatically. This paper proposes a novel classification system of epileptic EEG signals for single-channel EEG based on the attention network that integrates time-frequency and nonlinear dynamic features. The proposed system has three novel modules. The first module constructs the Hilbert spectrum (HS) with high time-frequency resolution into a two-channel parallel convolutional network. The time-frequency features are fully extracted by complementing the high-dimensional features of the two branches. The second module constructs a grayscale recurrence plot (GRP) that contains more nonlinear dynamic features than traditional RP, fed into the residual-connected convolution module for effective learning of nonlinear dynamic features. The third module is the feature fusion module based on a self-attention mechanism to assign optimal weights to different types of features and further enhance the information extraction capability of the system. Therefore, the system is named HG-SANet. The results of several classification tasks on the Bonn EEG database and the Bern-Barcelona EEG database show that the HG-SANet can effectively capture the contribution degree of the extracted features from different domains, significantly enhance the expression ability of the model, and improve the accuracy of the recognition of epileptic EEG signals. The HG-SANet can improve the diagnosis and treatment efficiency of epilepsy and has broad application prospects in the fields of brain disease diagnosis.

Multiple enhanced synchrosqueezing in the time–frequency–chirprate space

It is challenging to analyze multi-component signals with crossover instantaneous frequencies (IFs), both in producing high-resolution time–frequency representations and disentangling intrinsic modes. One of the most promising attempts is lifting the two-dimensional TFRs to three-dimensional time–frequency–chirprate (TFC) representations. However, the strong “blurring” effect in the chirp rate (CR) axis makes it rather challenging to estimate accurate IF and CR trajectories. Driven by this need, a method to provide highly energy-concentrated TFC representation, called multiple enhanced synchrosqueezing chirplet transform (MESCT), is proposed in this paper. MESCT is an enhanced iterative framework that combines multi-synchrosqueezing and multi-taper techniques. MESCT estimates IF and CR using phase information from different chirplet transform results with different windows, which provides more accurate estimates for reassignment. Then, three-dimensional multi-synchrosqueezing operations subsequently concentrate the ambiguous energy. As a result, MESCT accurately sharpens the TFC representations, even around the crossing points. Thus, accurate IF and CR trajectories can be jointly estimated by the three-dimensional ridge detection algorithm. Finally, crossover modes can be retrieved with high precision based on accurate trajectory estimation. A series of numerical experiments, both simulations and real-world cases, are considered to demonstrate the effectiveness and advantages of the proposed method.

Interference mitigation for FMCW radar via chirp rate estimation and signal separation

As a prevalent system in radar technology, the Frequency modulated continuous wave (FMCW) radar faces significant challenges in interference. This paper proposes a three-step interference mitigation strategy considering the time–frequency (TF) features of interference and time-domain properties of beat signals. Initially, the process involves statistical analysis of chirp rates from high-energy TF points, estimating the matched chirp rates of interference signals. Subsequently, the improved multisynchrosqueezing chirplet transform (IMSSCPT) is suggested for high-resolution TF characterization of interference signals. Utilizing the ridge extraction method, we accurately detect the TF region of interference signals. This precise localization enables the gradual separation of the reconstructed interference from the received signals. Finally, we perform parallel singular value decomposition on Hankel matrices, which are stacked from the mitigated subsequences to obtain the beat subspace and reconstruct the beat signal to reduce the negative effect of noise. A series of experimental comparisons of the proposed algorithm with existing methods have validated its exceptional performance, particularly under conditions of high-level noise.

Spectral analysis of seismic data based on a combined generalized S transform

The S transform is widely used to delineate seismic spectral anomalies associated with hydrocarbons during reservoir characterization. To overcome the relatively poor time-frequency resolution due to the fixed varying pattern of the window used in the S transform, we present a combined generalized S transform (CGST) for the spectral analysis of seismic data. First, the CGST decomposes the signal into a series of intrinsic mode functions (IMFs) using a complete ensemble empirical mode decomposition (CEEMD). An objective function is defined to quantitatively determine the spectral energy concentration criteria for optimal parameter selection of the improved Gaussian windows. Then, the time-frequency spectra for all the IMFs within narrower frequency bands are calculated using the respective Gaussian windows with normalized energy and individual optimal controlling parameters. We applied the CGST to spectral analyses of both synthetic signals and seismic field data. The results indicate that the CGST exhibits good performance with a higher time-frequency resolution. Field examples illustrate that the CGST can be used to characterize the spectral behavior of thin beds and indicate low-frequency shadows associated with hydrocarbon reservoirs.

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.

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.

Classification of Motor Imagery EEG signals using high resolution time-frequency representations and convolutional neural network

A Motor Imagery (MI) based Brain Computer Interface (BCI) system aims to provide neuro-rehabilitation for the motor disabled people and patients with brain injuries (e.g., stroke patients) etc. The aim of this work is to classify the left and right hand MI tasks by utilizing the occurrence of event related desynchronization and synchronization (ERD\\ERS) in the Electroencephalogram (EEG) during these tasks. This study proposes to use a set of Complex Morlet Wavelets (CMW) having frequency dependent widths to generate high-resolution time-frequency representations (TFR) of the MI EEG signals present in the channels C3 and C4. A novel method for the selection of the value of number of cycles relative to the center frequency of the CMW is studied here for extracting the MI task features. The generated TFRs are given as input to a Convolutional neural network (CNN) for classifying them into left or right hand MI tasks. The proposed framework attains a classification accuracy of 82.2% on the BCI Competition IV dataset 2a, showing that the TFRs generated in this work give a higher classification accuracy than the baseline methods and other existing algorithms.

Adaptive radial basis functions based Time-Varying model for EEG analysis in patients with cervical dystonia

Precise time–frequency (TF) analysis of electroencephalogram (EEG) signals is critical in evaluating cortical responses of patients with cervical dystonia (CD). Traditional methods are faced with challenges of constrained time–frequency resolution and accuracy, limiting the application of EEG in CD patients. This study introduces a novel adaptive basis function-based for TF representation method to meet the challenge. The methodology begins by identifying the kernel function center through an adaptive clustering technique. Then, the optimum structures and scales of the kernel function are determined by the improved genetic algorithm, which enable more precise tracking of EEG signals. Finally, accurately estimated parameters are converted to high-resolution TF images using a parameter spectrum estimation method, providing more detailed information of the EEG data. Leveraging the insights from the TF images, a regression model correlating TF features with clinical scores was developed to assess severity of CD patients. Simulation results show that the proposed method has superior tracking capabilities and a higher time–frequency resolution than current state-of-the-art methods. In the analysis of real EEG signals, we observed a notable elevation in gamma band power within the C3 and P3 channels, significantly differing from healthy individuals (p < 0.05), however, which cannot be found by other methods. This indicates distinctive high-frequency cortical activation associated with CD. Moreover, the regression model reaches a correlation coefficient above 0.82, suggesting its potential for objectively assessing severity of CD patients. Collectively, this study provides a robust tool for EEG signal analysis, and the analysis result will contribute to clinic treatment.

A transformer acoustic signal analysis method based on matrix pencil and hybrid deep neural network

Acoustic signal analysis is an important component of transformer online monitoring. Currently, traditional methods have problems such as low spectral resolution, imbalanced sample distribution, and unsatisfactory classification performance. This article first introduces the matrix pencil algorithm for time-frequency spectrum analysis of acoustic signals, and then uses the SMOTE algorithm to expand the imbalanced samples. Then, an ACmix hybrid deep neural network model is constructed to classify 11 types of transformer operation and environmental acoustic signals. Finally, detailed experiments were conducted on the method proposed in this paper, and the experimental results showed that the matrix pencil algorithm has high time-frequency resolution and good noise resistance performance. The SMOTE sample expansion method can significantly improve the recognition accuracy by more than 2%. Overall accuracy of the proposed method in acoustic signal classification tasks reaches 91.81%.

A high-resolution time-frequency analysis technique based on bi-directional squeezing and its application in fault diagnosis of rotating machinery

Most of the signals in the field of industrial engineering are nonstationary signals, and the accurate description of the time-frequency (TF) characteristics of nonstationary signals is important for the advancement of industrial engineering. Instantaneous frequency (IF) and group delay (GD) are common TF features used to describe nonstationary signals. Time-reassigned synchrosqueezing transform and synchrosqueezing transform are two TF analysis tools that can accurately characterize the GD and IF of nonstationary signals by squeezing the TF coefficients in the time direction and frequency direction, respectively. However, it is difficult for such two techniques to accurately characterize IF and GD simultaneously. A novel method called time-frequency squeezing transform is introduced in this paper to conquer this drawback. The technique first uses the short-time Fourier transform to calculate the time-frequency representation (TFR) of a signal, and then divides the TFR into two parts according to a chirp rate estimator. The subdivided TFR parts are then squeezed in the frequency and time directions to accurately characterize the IF and GD, respectively, and the two squeezed results are added to form a high-resolution result. The effectiveness of the proposed technique is demonstrated with numerical and experimental signals.

Localization method of subsynchronous oscillation source based on high-resolution time-frequency distribution image and CNN

The penetration of new energy sources such as wind power is increasing, which consequently increases the occurrence rate of subsynchronous oscillation events. However, existing subsynchronous oscillation source-identification methods primarily analyze fixed-mode oscillations and rarely consider time-varying features, such as frequency drift, caused by the random volatility of wind farms when oscillations occur. This paper proposes a subsynchronous oscillation source-localization method that involves an enhanced short-time Fourier transform and a convolutional neural network (CNN). First, an enhanced STFT is performed to secure high-resolution time-frequency distribution (TFD) images from the measured data of the generation unit ports. Next, these TFD images are amalgamated to form a subsynchronous oscillation feature map that serves as input to the CNN to train the localization model. Ultimately, the trained CNN model realizes the online localization of subsynchronous oscillation sources. The effectiveness and accuracy of the proposed method are validated via multimachine system models simulating forced and natural oscillation events using the Power Systems Computer Aided Design platform. Test results show that the proposed method can localize subsynchronous oscillation sources online while considering unpredictable fluctuations in wind farms, thus providing a foundation for oscillation suppression in practical engineering scenarios.

Synchronous odd symmetric transform for rolling bearing fault diagnosis

Time-frequency analysis (TFA) is an important tool to process non-stationary signals and detect bearing faults. For considering energy concentration, computational efficiency, and computational accuracy, a novel TFA technique, termed synchronous odd symmetric transform (SOST) is proposed in this paper. In the SOST, the odd symmetry extraction operator (OSEO) is defined according to the odd symmetric window based short-time Fourier transform (OSTFT). The main idea of OSEO is to obtain accurate instantaneous frequency (IF) ridges in a satisfactory computation time. Meanwhile, the STFT result is retained at the IF ridges, and the time–frequency representation (TFR) with high energy concentration is calculated. The performance of the developed technique is verified by a multi-component signal with strong frequency-modulated and amplitude-modulated (FM-AM) laws. Experimental analysis results show that the proposed SOST can display bearing fault-related time–frequency trajectories with high time–frequency resolution.

A promising method for breaking the logjam of time-frequency analysis in astronomy

Abstract Time-frequency analysis could provide detailed dynamic information of celestial bodies and is critical for comprehension of astronomical phenomena. However, it is far from being well-developed in astronomy. Hilbert–Huang transform (HHT) is an advanced time-frequency method but has two problems in analysing astronomical signals. One is that many astronomical signals may be composed of multiple components with various amplitudes and frequencies, while HHT uses assisted noises with the same amplitude to extract all components. The other is that HHT is an empirical method requiring tunable parameters to be optimized using experimental results or known facts, which are challenging to obtain in astronomy and it is therefore hard to determine whether the signal decomposition is right or not. In this study, we adjust the noise amplitude to optimize the decomposition based on the orthogonality of the obtained components and discard the decompositions with non-physical results. Three experiments show that this new extension of HHT is an effective method suitable for high-resolution time-frequency analysis in astronomy. It can be used to dig out valuable pieces of information which are inaccessible with other methods, and thus has the potential to open up new avenues for astronomy research.

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.

Comparative analysis of fixed-pitch and variable-pitch control systems for multirotor drones: Acoustic characteristics and rotor phase control

In this study, the aerodynamic and aeroacoustic characteristics of multirotor electric vertical take-off and landing aircraft in hovering and forward flight are compared using two representative control methods: fixed-pitch control and variable-pitch control (i.e., revolution per minute (RPM) control and collective pitch control). To this end, a comprehensive multirotor noise assessment framework is used to predict the aerodynamics and noise of multirotors controlled by RPM and collective pitch. High-resolution time–frequency analysis is used to clarify the differences in noise spectral characteristics. The findings indicate that blade passage frequency characteristics vary significantly depending on the control method. The phase differences between the rotors of variable-pitch control remain constant irrespective of disturbances or attitude control. In other words, the frequencies of the tone noise do not exhibit short-periodic modulation, unlike those of RPM-controlled multirotor. Additionally, the aeroacoustic characteristics of fixed-pitch and variable-pitch controlled multirotor in response to wind velocity fluctuation are investigated by considering the direction of noise radiation and interference effects. The impact of the turbulent kinetic energy of wind on the noise characteristics is examined by quantifying the noise components associated with aerodynamic unsteadiness in flight. Furthermore, the rotor phase control method can be applied to reduce noise in both control methods. The optimization of rotor phases reduces tone noise significantly at the target observer point without causing aerodynamic losses in variable-pitch controlled multirotor. In contrast, the reduction in tone noise remains relatively limited for fixed-pitch controlled multirotor, as the rotor phase differences are not maintained.

EEG-Based Seizure Detection Using Variable-Frequency Complex Demodulation and Convolutional Neural Networks

Epilepsy is a complex neurological disorder characterized by recurrent and unpredictable seizures that affect millions of people around the world. Early and accurate epilepsy detection is critical for timely medical intervention and improved patient outcomes. Several methods and classifiers for automated epilepsy detection have been developed in previous research. However, the existing research landscape requires innovative approaches that can further improve the accuracy of diagnosing and managing patients. This study investigates the application of variable-frequency complex demodulation (VFCDM) and convolutional neural networks (CNN) to discriminate between healthy, interictal, and ictal states using electroencephalogram (EEG) data. For testing this approach, the EEG signals were collected from the publicly available Bonn dataset. A high-resolution time–frequency spectrum (TFS) of each EEG signal was obtained using the VFCDM. The TFS images were fed to the CNN classifier for the classification of the signals. The performance of CNN was evaluated using leave-one-subject-out cross-validation (LOSO CV). The TFS shows variations in its frequency for different states that correspond to variation in the neural activity. The LOSO CV approach yields a consistently high performance, ranging from 90% to 99% between different combinations of healthy and epilepsy states (interictal and ictal). The extensive LOSO CV validation approach ensures the reliability and robustness of the proposed method. As a result, the research contributes to advancing the field of epilepsy detection and brings us one step closer to developing practical, reliable, and efficient diagnostic tools for clinical applications.