Time-frequency Spectrum Research Articles

Fracture mode classification of UHPC based on deep learning and wavelet time–frequency spectrum derived from acoustic emission waveform

Fracture mode categorization is essential in identifying the failure stage, evaluating the damage characteristics, and providing references for structural maintenance. Acoustic emission (AE), as a passive nondestructive technique, presents great potential in damage characterization of cementitious materials and structures. In this study, a convolutional neural network (CNN) and gated recurrent unit (GRU) integrated model for tensile, shear, and mixed cracking mode classification of ultra-high-performance concrete (UHPC) was proposed and verified based on AE waveform features. First, four-point bending and direct shear tests for UHPC specimens were carried out, respectively, to generate AE waveform signals corresponding to different cracking modes (tensile, shear, and mixed ones). Subsequently, the collected one-dimensional AE signals were converted into two-dimensional time–frequency spectrum by continuous wavelet transform. And an AE dataset was constructed after manual labeling based on the corresponding relationships between cracking modes and wavelet time–frequency spectra. Then, an automatic CNN-GRU automatic classification model was established using wavelet time–frequency spectrum images as input variables, where the CNN extracts spatial image features, and the GRU screens time dependencies and realizes final classification. The proposed CNN-GRU model achieves an accuracy of 96.17% for cracking mode classification of UHPC, which is superior both in computational accuracy and efficiency to lightweight CNN and AlexNet. Classification outcomes for UHPC specimen under four-point bending and direct shear tests revealed the proportion of tensile cracks progressively decreased with the increase of damage, while shear cracks exhibited the opposite trend. The percentage of mixed mode cracks maintained relatively stable throughout the failure stages. The model proposed in this study presents favorable performance to reveal the underlying damage evolution mechanism during UHPC fracture, which can also provide references for the cracking mode classification of other cementitious materials and structures.

Simulation of spatially varying non-stationary seismic waves using random frequencies and non-uniform fast fourier transform

The simulation of spatially varying non-stationary seismic waves is a crucial consideration for the seismic analysis of engineering structures. The traditional approach often incurs substantial computational expenses and suffers from low efficiency due to the extensive implementation of large-scale matrix factorizations at numerous sampling points in both time and frequency domains. In this study, an enhanced approach is developed for the efficient simulation of non-stationary seismic waves. The core of this approach lies in the utilization of random frequency sampling coupled with time-domain interpolation to reduce matrix factorizations, and non-uniform fast Fourier transform for expediting the summation of trigonometric functions. A parametric analysis is conducted to investigate the effect of vital parameters, including the decoupling strategy of time-frequency spectrum, the number of random frequencies, and the number of interpolation knots over time, on both the efficiency and accuracy of the enhanced approach. Consequently, the preferred values for these parameters are determined. By considering the simulation of seismic waves acting on a group of bridges, the enhanced approach is validated in the view of correlation functions. The results demonstrate a high level of fidelity of the simulated seismic waves and proves the effectiveness of the enhanced approach in the efficient simulation of spatially varying non-stationary earthquake ground motions. The developed approach can be used for the simulation of non-stationary seismic waves for a wide range of engineering structures.

Deep learning-based acoustic emission source localization in heterogeneous rock media without prior wave velocity information

Abstract Acoustic emission (AE) source localization is crucial for monitoring but often relies on prior information, such as wave velocity and arrival time. This study introduces a novel method for locating AE sources in rocks without such information, addressing challenges posed by heterogeneous sensor arrays. Experiments involving pencil led break (PLB) tests on sandstone cubes collected AE waveforms and their coordinates. A ResNet-50 based deep learning model was developed to correlate the time-frequency spectra of AE with PLB locations, expressed as spatial Gaussian distributions. The model, achieved a 79% prediction accuracy for AE localization in complex environments. While there is room for improvement in training data quantity and diversity, the results validate the model’s effectiveness, particularly in coal mines and tunnel engineering.

Quantification of nonlinear effect in seismic signal using Holo-Hilbert spectral analysis

Affected by excitation conditions, absorption, and attenuation of stratum and receiving instruments, the seismic signal is non-stationary and nonlinear. Time-frequency spectral analysis methods are effective and widely used in describing the time-varying features of seismic signals. However, these methods are all based on additive expansions, and cannot represent the nonlinearity of signal, which is achieved through a multiplicative process. Therefore, the information provided by the time-frequency spectrum is incomplete. To show the nonlinearity of seismic signal, that is, the modulation effect of low-frequency components on high-frequency components, the Holo-Hilbert spectral analysis method is introduced in this paper. Holo-Hilbert spectral analysis (HHSA) contains nested empirical mode decomposition and Hilbert transform to achieve a full informational spectrum represented by two frequency dimensions. In the Holo-Hilbert spectrum, one dimension represents frequency-modulated (FM) frequency, which characterizes the non-stationarity of the signal, and the other dimension represents the amplitude-modulated (AM) frequency, which indicates the nonlinear effect in the signal. Synthetic and field data examples verify the feasibility of HHSA in characterizing the cross-frequency interaction of non-stationary seismic signals as a potential tool to detect reservoirs.

IMST-based identification of time-varying cable forces in cable-supported bridges: Numerical, experimental, and field test validation

Accurately assessing the structural integrity of cable-supported bridges hinges upon the precise determination of time-varying cable forces. In this study, a novel method is proposed for identifying these forces, even with the challenge of having only a single accelerometer available. Leveraging an improved Multisynchrosqueezing Transform (IMST) with an efficient ridge extraction algorithm, this method offers a robust solution. The IMST is employed to construct a clearer time-frequency spectrum based on the monitored acceleration response of a cable. Subsequently, the time-frequency ridge extraction algorithm enables the derivation of the cable's instantaneous frequency. Ultimately, the time-varying cable forces are computed by using the axially loaded beam theory and considering the influence of bending stiffness. Validations through a numerical benchmark model and a scaled cable testing confirm the efficacy of this approach. Result indicates that the average error in identifying cable forces is less than 2.50% in the numerical simulation. Moreover, the method is successfully applied to a real-world bridge scenario, demonstrating its ability to accurately evaluate cable forces despite having access to only a single-point noisy acceleration response.

Interaction of a UWB impulse with a layer of sandy soil, having a rough upper boundary

ABSTRACT In this paper, the changes in the character of time shapes, amplitudes, frequency spectra, and time delay of ultra-wideband (UWB) impulses (duration of 0.33 ns) reflected from the layer of wet sand with a rough upper boundary were investigated. It was shown that the attenuation of UWB impulse amplitude, which is reflected from the upper rough boundary of the sand layer, can be described by the model of Fresnel reflection coefficient for a smooth surface using the Gaussian correction factor (FRGC). At this root-mean-square (RMS), height of soil surface roughness was in the range of ~0–21 mm, but the determination coefficient and RMS error (RMSE) were found to be equal to 0.94 and 0.02, respectively. An experiment close to linear increase/decrease in the propagation time of impulses reflected from the upper/lower boundary of the layer, respectively, was found with increasing the RMS heights of upper boundary. It is shown that the propagation time of such impulses can be described by the modified FRGC model with an error from RMSE = 0.09 ns to RMSE = 0.15 ns. The results of these findings are of practical importance for the interpretation of remote sensing data for precise soil moisture measurements from unmanned aerial vehicle platforms using UWB impulses.

Multi-fault diagnosis of industrial rotating machines using advanced sliding window and WSST-CNN

Accurate fault diagnosis of rotating machines is the most important part of industries, as it helps manage the workforce and inventory within the stipulated time. In industries, when the fault occurs at one component, that may propagate to other components due to excessive speed and load, leading to the occurrence of a simultaneous fault condition. Identification of multi-component faults is relatively more difficult than single-component faults due to the possibility of characteristic frequency overlapping that is observed during signal processing. This work considered various single and complex multi-component fault conditions of a rotating machine, and data is acquired at different speed and load conditions using a standard acoustic array setup. The signals are then converted into signal segments using a continuously moving advanced sliding window. From the extracted segments time-frequency spectrums are generated by using Wavelet Synchrosqueezed Transform (WSST) followed by the training of deep neural networks. The performance analysis of the model is carried out, and it is found that the proposed methodology helped diagnose multi-faults at different speed and load conditions. It mitigates the complexity of high-end signal processing techniques for distinguishing the fault characteristics. This study will be beneficial for industries to diagnose multi-faults in incipiently.

Unsteady numerical study on the effects of inlet distortion parameters on the aerodynamic instability of the centrifugal compressor

Total pressure inlet distortion significantly impairs the aerodynamic performance and flow stability of centrifugal compressors. This paper presents a full annulus unsteady numerical simulation to investigate the flow mechanisms under varying inlet distortion parameters. First, the flow characteristics of a uniform inflow is studied as a baseline for comparison with distorted inlet conditions. Results indicate that the interaction between shock waves and tip leakage flow is a primary factor leading to aerodynamic instability. The instability signal in this region is detected through fast Fourier transform and frequency slice wavelet transform (FSWT). Under near stall condition, different distortion parameters are set to research the effects on aerodynamic performance, flow mechanisms, and instability characteristics. The results reveal that distortion intensity has the most significant impact, causing a maximum stall margin loss of 55.43%, followed by distortion angle with a maximum stall margin loss of 43.02%. Total pressure inlet distortion leads to a deterioration in aerodynamic performance, primarily due to premature occurrences of unstable flow phenomena such as leading-edge spillage and trailing-edge backflow. The onset key features triggering aerodynamic instability are identified as leading-edge spillage vortex, tip leakage vortex, and passage vortex. The continuous disintegration of the tip leakage vortex results in low-frequency fluctuating energy exhibiting multipeak characteristics, with pulsation peaks centered around 0.5 BPF, related to the spike stall of the compressor. The high-energy frequency band dissipates over time in the time–frequency spectrum, as shown by FSWT results, indicating the characteristics of instability in the flow.

Asymmetric instability of flow-induced vibration for elastically mounted cube at moderate Reynolds numbers

The asymmetric instability in two streamwise orthogonal planes for three-dimensional flow-induced vibration (FIV) of an elastically mounted cube at a moderate Reynolds number of 300 is numerically investigated in this paper. The full-order computational fluid dynamics method, data-driven stability analysis via the eigensystem realization algorithm and the selective frequency damping method and total dynamic mode decomposition (TDMD) are applied here to explore this problem. Due to the unsteady non-axisymmetric wakefield formed for flow passing a stationary cube, the FIV response was found to exhibit separate structural stability and oscillations (including lock-in and galloping behaviour) in the two different streamwise orthogonal planes while the body is released. The initial kinetic energy accompanying the release of the cube could destabilize the above-mentioned structural stability. The observed FIV asymmetric instability is verified by the root trajectory of the structural mode obtained via data-driven stability analysis. The stability of the structural modes dominates regardless of whether the structural response oscillates significantly in various (reduced) velocity ranges. Further TDMD analysis on the wake structure, accompanied by the time–frequency spectrum of time-history structural displacements, suggested that the present FIV unit with galloping behaviour is dominated by the combination of the shifted base-flow mode, structure modes and several harmonics of the wake mode.

Characterization of Seismic Signal Patterns and Dynamic Pore Pressure Fluctuations Due to Wave-Induced Erosion on Non-Cohesive Slopes

Wave erosion of slopes can easily trigger landslides into marine environments and pose severe threats to both the ecological environment and human activities. Therefore, near-shore slope monitoring becomes crucial for preventing and alerting people to these potential disasters. To achieve a comprehensive understanding, it is imperative to conduct a detailed investigation into the dynamics of wave erosion processes acting on slopes. This research is conducted through flume tests, using a wave maker to create waves of various heights and frequencies to erode the slope models. During the tests, seismic signals, acoustic signals, and pore pressure generated by wave erosion and slope failure are recorded. Seismic and acoustic signals are analyzed, and time-frequency spectra are calculated using the Hilbert–Huang Transform to identify the erosion events and signal frequency ranges. Arias Intensity is used to assess seismic energy and explore the relationship between the amount of erosion and energy. The results show that wave height has a more decisive influence on erosion behavior and retreat than wave frequency. Rapid drawdown may potentially cause the slope to slide during cyclic swash and backwash wave action. As wave erosion changes from swash to impact, there is a significant increase in the spectral magnitude and Power Spectral Density (PSD) of both seismic and acoustic signals. An increase in pore pressure is observed due to the rise in the run-up height of waves. The amplitude of pore pressure will increase as the slope undergoes further erosion. Understanding the results of this study can aid in predicting erosion and in planning effective management strategies for slopes subject to wave action.

Radio Frequency Signal-Based Drone Classification with Frequency Domain Gramian Angular Field and Convolutional Neural Network

Over the past few years, drones have been utilized in a wide range of applications. However, the illegal operation of drones may pose a series of security risks to sensitive areas such as airports and military bases. Hence, it is vital to develop an effective method of identifying drones to address the above issues. Existing drone classification methods based on radio frequency (RF) signals have low accuracy or a high computational cost. In this paper, we propose a novel RF signal image representation scheme that incorporates a convolutional neural network (CNN), named the frequency domain Gramian Angular Field with a CNN (FDGAF-CNN), to perform drone classification. Specifically, we first compute the time–frequency spectrum of raw RF signals based on short-time Fourier transform (STFT). Then, the 1D frequency spectrum series is encoded as 2D images using a modified GAF transform. Moreover, to further improve the recognition performance, the images obtained from different channels are fused to serve as the input of a CNN classifier. Finally, numerous experiments were conducted on the two available open-source DroneRF and DroneRFa datasets. The experimental results show that the proposed FDGAF-CNN can achieve a relatively high classification accuracy of 98.72% and 98.67% on the above two datasets, respectively, confirming the effectiveness and generalization ability of the proposed method.

Fast and Lightweight Voice Replay Attack Detection via Time-Frequency Spectrum Difference

Fast and Lightweight Voice Replay Attack Detection via Time-Frequency Spectrum Difference

The linear canonical W-transform

The time-frequency spectrum of seismic data is commonly used as an attribute in the analysis and interpretation of nonstationary seismic signals. To improve the capability of the W-transform to analyze nonstationary data, we introduce the linear canonical W-transform (LCWT) by implementing an affine matrix along with scaling parameters to generate high resolution and energy-concentrated time-frequency spectra. More features of nonstationary signals can be explored in the time-linear canonical frequency domain by transforming the time-frequency plane, which makes the algorithm more applicable to seismic signals. For the completeness of the LCWT, we also develop the inverse LCWT to extend its applications. Examples of synthetic and field seismic data show that a highly resolved and energy-concentrated time-frequency spectrum can be estimated with the LCWT with negligible additional computational burden. In addition, our algorithm is promising for several seismic data processing and interpretation techniques, such as reservoir characterization and thin layer identification.

Incipient instability real-time warning via adaptive wavelet synchrosqueezed transform: Onboard applications from compressors to gas turbine engines

To address the limitations of existing stall/surge warning methods—including variations in research subjects, sensor configurations, computational complexity, and the universality of thresholds—this study proposes a novel incipient instability warning approach utilizing adaptive wavelet synchrosqueezed transform. Each detection cycle begins with the acquisition of a low-pass filtered and downsampled total pressure signal from the compressor outlet, captured via a sliding window to represent the pressure sample. Then, the adaptive wavelet synchrosqueezed transform (AWSST), employing dynamic discretization with scales and synchrosqueezing technology, analyzes the real-time pressure sample to extract precise instantaneous frequency changes at low computational costs. Features of instability severity are derived from the amplitude, phase, and pressure drop within the time-frequency spectrum, leading to the formulation of a warning logic. The proposed method's effectiveness and universality are validated through hardware-in-loop (HIL) tests using multiple surge test data. Results show that the proposed method outperforms traditional real-time warning methods, which rely on the pressure change rate, by enhancing accuracy and advancing warning times by 15 ms–50 ms. Notably, the threshold is universal for compressors or engines of the same model. By increasing the acceptable performance decline criteria, compressors, turbofan engines, and turboshaft engines can employ a common set of thresholds.

Motion Clutter Suppression for Non-Cooperative Target Identification Based on Frequency Correlation Dual-SVD Reconstruction.

Non-cooperative targets, such as birds and unmanned aerial vehicles (UAVs), are typical low-altitude, slow, and small (LSS) targets with low observability. Radar observations in such scenarios are often complicated by strong motion clutter originating from sources like airplanes and cars. Hence, distinguishing between birds and UAVs in environments with strong motion clutter is crucial for improving target monitoring performance and ensuring flight safety. To address the impact of strong motion clutter on discriminating between UAVs and birds, we propose a frequency correlation dual-SVD (singular value decomposition) reconstruction method. This method exploits the strong power and spectral correlation characteristics of motion clutter, contrasted with the weak scattering characteristics of bird and UAV targets, to effectively suppress clutter. Unlike traditional clutter suppression methods based on SVD, our method avoids residual clutter or target loss while preserving the micro-motion characteristics of the targets. Based on the distinct micro-motion characteristics of birds and UAVs, we extract two key features: the sum of normalized large eigenvalues of the target's micro-motion component and the energy entropy of the time-frequency spectrum of the radar echoes. Subsequently, the kernel fuzzy c-means algorithm is applied to classify bird and UAV targets. The effectiveness of our proposed method is validated through results using both simulation and experimental data.

Comparative study of earthquake effects on the Canton Tower based on full-scale measurements

From 2011 to 2023, the monitoring system of a super high-rise structure, the Canton Tower, recorded many earthquakes. This study categorizes 11 earthquakes over these 13 years based on the distances between the epicenters and the tower for investigation. Firstly, the acceleration time histories and frequency spectra of these earthquakes are compared. Secondly, different system identification techniques, i.e., automated frequency domain decomposition (AFDD) and covariance-driven stochastic subspace identification (SSI-COV), are applied to the acceleration records to study the dynamic characteristics of the tower under earthquakes. Thirdly, three time-domain indexes based on the singular value decomposition (SVD) are proposed to measure and compare the impact of these earthquakes on the tower. The proposed indexes show good performance in assessing the impact of earthquakes and the structural condition. This study on the dynamic characteristics of Canton Tower under earthquakes at different distances can serve as a benchmark for further structural health monitoring and structural dynamic analysis.

A Novel Time-Frequency Parameterization Method for Oscillations in Specific Frequency Bands and Its Application on OPM-MEG.

Time-frequency parameterization for oscillations in specific frequency bands reflects the dynamic changes in the brain. It is related to cognitive behavior and diseases and has received significant attention in neuroscience. However, many studies do not consider the impact of the aperiodic noise and neural activity, including their time-varying fluctuations. Some studies are limited by the low resolution of the time-frequency spectrum and parameter-solved operation. Therefore, this paper proposes super-resolution time-frequency periodic parameterization of (transient) oscillation (STPPTO). STPPTO obtains a super-resolution time-frequency spectrum with Superlet transform. Then, the time-frequency representation of oscillations is obtained by removing the aperiodic component fitted in a time-resolved way. Finally, the definition of transient events is used to parameterize oscillations. The performance of this method is validated on simulated data and its reliability is demonstrated on magnetoencephalography. We show how it can be used to explore and analyze oscillatory activity under rhythmic stimulation.

Modulation recognition for underwater acoustic communication based on hybrid neural network and feature fusion

It is a huge challenge for underwater acoustic receivers to correctly identify modulation methods due to the complex underwater channel environment and severe noise interference. Combined with the lightweight network (SqueezeNet) and attention mechanism (SENet), a multi-attribute and multi-scale feature fusion model based on a hybrid neural network is proposed, which achieves efficient and accurate recognition for modulation modes. First, the wavelet time-frequency (WTF) spectrum, square power spectrum, and contour maps of cyclic spectrum are extracted as multi-attribute inputs for the network to reduce the impact of inherent defects in single attribute feature. Second, shallow and deep features based on the SqueezeNet model are obtained as multi-scale features, of which the key feature expression ability is enhanced by the SENet model to provide sufficient feature information for modulation recognition. The simulation experiments and sea trial data confirm that the suggested method demonstrates strong generalization capabilities and effectiveness when applied to underwater acoustic channels and environmental noise. In contrast to algorithms in existence, the method verifies superior recognition abilities.

Synchrosqueezing voices through deep neural networks for horizon interpretation

Horizon picking is a crucial element in reservoir characterization, but it remains a labor-intensive process. Manually interpreting horizons across thousands of vertical seismic slices in a 3D seismic survey significantly increases the time and labor required for this task. Although several automated methods for extracting the horizons in seismic images have been developed, their effectiveness can be hampered by interruptions in lateral continuity, such as faults and noise. In addition, closely spaced horizons pose a challenge, making it even more difficult to recognize their exact position. To track the horizons through a 3D seismic volume, other seismic attributes extracted from the 3D seismic data must be used. We suggest using spectral voice components together with the original seismic amplitudes to track the surfaces of the target horizons. We generate the time-frequency spectrum using a high-resolution method, namely the synchrosqueezing wavelet transform (SWT), and the real part of the complex SWT spectrum is the voice component. We import the spectral voice component and the seismic amplitude into a neural network. A deep convolutional neural network is used to track the horizon surfaces within a 3D seismic volume. We evaluate this application on a field seismic data set where closely spaced thin layers are located within a complex faulted formation with noisy seismic data with a low signal-to-noise ratio. The integration of the amplitude and phase within the attribute of the voice component indicates that it improves the quality of the generated horizons, especially compared with using the seismic amplitude only for this task. An example from field data demonstrates the ability of our method to accurately delineate the horizons across fault surfaces and in the immediate vicinity of unconformities. This exceeds the current limits of the existing methods for horizon detection.

Nonlinear analysis and recognition of epileptic EEG signals in different stages.

It is a hot problem in epilepsy research to detect and predict seizures by EEG signals. Clinically, it is generally observed that there are only sudden abnormal signals during the ictal stage, but there is no significant difference in the EEG signal between the interictal and preictal stages. To solve the problem that preictal signals are difficult to recognize clinically, and then effectively improve the recognition efficiency of epileptic seizures, so, in this paper, some nonlinear methods are comprehensively used to extract the hidden information in the EEG signals in different stages, namely, phase space reconstruction (PSR), Poincaré section (PS), synchroextracting transform (SET), and machine learning for EEG signal analysis. First, PSR based on C-C method is used, and the results show that there are different diffuse attractor trajectories of the signals in different stages. Second, the confidence ellipse (CE) is constructed by using the scatter diagram of the corresponding trajectory on PS, and the aspect ratio and area of the ellipse are calculated. The results show that there is an interesting transitional phenomenon in preictal stage. To recognize ictal and preictal signals, time-frequency (TF) spectrums, which are processed by SET, are fed into the convolutional neural network (CNN) classifier. The accuracy of recognizing ictal and preictal signals reaches 99.7% and 93.7%, respectively. To summarize, our results based on nonlinear method provide new research ideas for seizure detection and prediction.NEW & NOTEWORTHY Our results based on nonlinear method have better practical significance and clinical application value and improved the prediction efficiency of epileptic EEG signals effectively. This work provides direct insight into the application of these biomarkers for seizure detection and prediction.