Time-frequency Spectrum Research Articles

A Novel Joint Time-Frequency Spectrum Resources Sustainable Risk Prediction Algorithm Based on TFBRL Network for the Electromagnetic Environment

To protect the electromagnetic environment and understand its current state in a timely manner, monitoring the electromagnetic environment has great practical significance, while massive amounts of data are generated. It is crucial to utilize data mining technology to extract valuable information from these massive amounts of data for effective spectrum management. Traditional spectrum prediction methods do not integrate the prior information of spectrum resource occupancy, so that the prediction of the channel state of a single frequency point is of limited significance. To address these issues, the paper describes a dynamic threshold algorithm which mines bottom noise and spectrum resource occupancy from massive electromagnetic environment data. Moreover, the paper describes a joint time-frequency spectrum resource prediction algorithm based on the time-frequency block residual LSTM (TFBRL) network, which utilizes hourly time closeness, daily period, and annual trend as prior knowledge of spectrum resources. The TFBRL network comprises three main parts: (1) a residual convolution network with a squeeze-and-excitation (SE) attention mechanism, (2) a long short term memory (LSTM) model with memory ability to capture sequence latent information, and (3) a feature fusion module based on a matrix to combine time closeness, daily period, and annual trend feature components. Experimental results demonstrate that the TFBRL network outperforms the baseline networks, improving by 31.37%, 16.00% and 13.06% compared with the best baseline for MSE, RMSE and MAE, respectively. Thus, the TFBRL network has good risk prediction performance and lays the foundation for subsequent frequency scheduling.

The W transform with a chirp-modulated window

A high-resolution time–frequency spectrum is desirable for processing and interpreting seismic data. The W transform is a method that effectively preserves the resolution in the low-frequency region of the time–frequency spectrum of nonstationary seismic signals. To further increase the energy concentration of the time–frequency spectrum estimated with the W transform, we propose to combine the W transform with a chirp-modulated window. The chirp rate in the chirp-modulated window can control the rotation of the window in the time–frequency plane to achieve a better match with the time–frequency spectrum. The chirp rate in the modified W transform can be directly determined with the estimated instantaneous frequency. It has been shown that the W transform with a chirp-modulated window maintains the resolution of the time–frequency spectrum and improves the energy concentration around the dominant frequency against noise. To speed up the computational process of the W transform with a chirp-modulated window, we formulate the transform as a matrix-vector multiplication, which can be accelerated by using graphics processing unit computations. The application of the modified algorithm to synthetic and field data indicates that the frequency anomalies can be easily identified with the modified W transform.

A neuro-fuzzy network modeling method for uncovering the dynamic properties of time-varying systems

Nonstationary signals are commonly encountered in various fields and applications. Modeling nonstationary signals with time-varying systems is of vital importance in understanding the underlying information and revealing the dynamic properties. In this paper, a neuro-fuzzy network-based method is proposed for the time-varying autoregressive (TVAR) system with multiple degrees of freedom. By expressing the time-varying parameters as a set of local linear models and validity functions, the TVAR system is transformed into an equivalent neural fuzzy network. The model structure and the time-varying parameters of the TVAR system correspond to the architecture and the weights of the equivalent neural network, respectively, and can be determined by training the equivalent neural network. Fundamentally, the new architecture is generated via growing and pruning the tree branches/neurons in a decision tree algorithm. Followed by a weights training process with Least Square optimization, the neural networks are finally evaluated with the target nonstationary signals. The optimal architecture and weights lie in the one with the least disparity. Several nonstationary signals, including the electroencephalogram and the radar wave that are qualitatively different in the time–frequency characteristics, are utilized to verify the effectiveness of the proposed method. Furthermore, we show that the proposed method is applicable not only to time-varying systems with complete measurements but also to incomplete measurable cases. Applying this method to the vibration signals output from a time-varying origami-tube structure under external excitations, the high time–frequency resolution of the proposed method is demonstrated via the time–frequency spectrum, from which the inherent mechanical properties and the underlying dynamic characteristics of the time-varying origami-tube structure are revealed.

A Dynamic Self-Attention-Based Fault Diagnosis Method for Belt Conveyor Idlers

Idlers are typical rotating parts of a belt conveyor carrying the conveyor belt and materials. The complex operating noise and unstable features lead to poor accuracy of sound-based idler fault diagnosis. This paper proposes a fault diagnosis method for belt conveyor idlers based on Transformer’s dynamic self-attention (DSA). Firstly, the A-weighted time-frequency spectrum of the idler sound is extracted as the input. Secondly, based on the DSA block, the multi-frequency cross-correlation DSA algorithm is designed to extract the cross-correlation features between different frequency bands in the input feature map, and the global DSA algorithm is applied to perceive and enhance the global correlation features in parallel. Finally, the cross-correlation and global correlation features are concatenated and linearly projected into a fault-type space to diagnose typical bearing and roller faults of idlers. The method makes full use of the relevant information scattered in different frequency bands of the idler running sound under complex working conditions and reduces the negative effect of the strong running noise on the extraction of weak fault features. Experimental results show that the fault diagnosis accuracy is 94.6% and the latency is 27.8 ms.

Application of Feature Extraction Method Based on Empirical Fourier Decomposition in Rotor Rub-impact Fault

This paper provides a feature extraction technique primarily by using empirical Fourier decomposition (EFD) to reveal the time-frequency features of rotor rub-impact fault. The Hilbert transform estimates the instantaneous frequency (IF) and instantaneous amplitude (IA) of the signal generated by EFD. Finally, high-quality time-frequency representation (TFR) is reconstructed by the adaptive time-frequency spectrum (ATFS). An example of the rotor rub-impact fault is utilized to demonstrate efficiency of this technique, and the results are contrasted with those of empirical mode decomposition (EMD). EFD performs better in the modal mixing problem than EMD and has excellent decomposition efficiency. It realizes IF feature extraction and offers a more precise TFR.

Multi-spectra synchrosqueezing transform

The synchrosqueezing transform (SST) is an effective method to obtain a clear time-frequency representation (TFR). Unfortunately, it suffers from low time-frequency (TF) resolution faced with strongly frequency-modulated signals, such as chirp signals. In this paper, we propose the generalized synchrosqueezing fractional S-transform (GSSFrST) to address this deficiency. In addition, we have also considered its second-order version to further enhance the TFR. They combine the advantages of fractional Fourier transform and synchrosqueezing generalized S-transform to improve the TF concentration. To further improve the TF resolution, we propose the multi-spectra synchrosqueezing transform (MSST) based on the GSSFrST and Hough transform. Inspired by the idea of image fusion, the MSST uses multiple TF spectra to fuse into a novel TF spectrum to represent each component of the signal in more detail. The experimental results show that MSST is a promising TF analysis tool for cross chirp signal separation and instantaneous frequency estimation.

Recognition of penetration states based on arc sound of interest using VGG-SE network during pulsed GTAW process

Real-time welding monitoring is of great importance for intelligent welding, and the recognition of penetration states based on acoustic signal has been a hot topic. However, previous studies have relied on expert knowledge to extract sound features and ignored that acoustic features have distinct effects on the penetration state. In this paper, based on convolution neuron networks (CNNs), an adaptively feature extraction model for arc sound has been proposed. The time-frequency spectrum of arc sound was obtained by short-time Fourier transform (STFT) and served as the input of proposed model. The fully connected layers are replaced with global average pooling (GAP) or global maximum pooling (GMP) to alleviate the overfitting. To research the interest of arc sound during GTAW process, the squeeze and excitation network (SE-Net) is embedded into CNNs to pay more attention to the region of interest in the time-frequency spectrum. The experimental results have demonstrated that the proposed model outperforms the conventional methods and yield high accuracy of 98.25 %. Furthermore, the interested region of arc sound under different penetration states is visualized by Grad-CAM and guided Grad-CAM. This study extends the application of attention mechanism in intelligent welding and achieved remarkable performance.

Time-frequency characteristics of microwaves generated by hypervelocity impact

When space debris impinges upon a spacecraft shield structure at an ultra-high speed, part of the debris’ kinetic energy is converted into electromagnetic energy, which radiates outward in the form of electromagnetic waves and can interfere with the spacecraft's normal communication. To investigate the radiation characteristics of the emitted electromagnetic waves, a series of experiments were conducted using a two-stage light gas gun, in which a spherical aluminum alloy (diameter:6.4 mm) projectile impinges on a 23-mm-thick target of the same material at velocities of 3.3–6.3 km/s. A real-time spectrum analyzer and super-heterodyne receiver were used to measure the microwaves in the frequency and time domains, respectively. Then, the time–frequency spectrum of the microwaves was obtained by Hilbert-Huang Transform. Further, two mechanisms of microwave generation—plasma expansion and material destruction—in an aluminum–aluminum impact are proposed, and the radiation powers of the two mechanisms are estimated based on the theoretical analysis and experimental results. Finally, the effect of the plasma cutoff frequency on the microwave propagation is explained, and the relationship between the radiation mechanism and the impact velocity is obtained. When the impact velocity is less than 5.2 km/s, material destruction is the main mechanism of microwave radiation, whereas at impact velocities > 5.2 km/s, plasma expansion dominates.

Damage Detection in Reinforced Concrete Member Using Local Time-Frequency Transform Applied to Vibration Measurements

Signal processing and analysis of structural vibration measurements are key components of structural damage detection (SDD) in structural health monitoring (SHM). The goal of signal processing is to extract subtle changes in the measured signals, which can be used to infer changes in structural parameters and damage. Time-frequency analysis is one of the most popular characterization methods for studying non-stationary vibration signals. In this article, the local time-frequency transform (LTFT) is applied and evaluated to calculate the time-domain signals because of its excellent time-frequency energy distribution properties. The LTFT matches the input data by the Fourier basis in an inverse problem framework and uses the least squares method to solve the time-varying Fourier coefficients. Subsequently, it defines the time-frequency spectrum as the calculated time-varying Fourier coefficients. While the LTFT has been used in the field of geophysics for seismic data processing, its application to structural vibration signals is novel. Both synthetic signals as well as signals collected from a large-scale laboratory test of a reinforced concrete girder were processed with the LTFT and compared with Rényi entropy for quantifying the time-frequency spectrum, the time-frequency resolution abilities of short time Fourier transform (STFT), and S transform (ST). The results show that the LTFT is superior to the traditional time-frequency analysis schemes, in that it is more effective in identifying the energy changes in the time-frequency spectrum before and after structural damage in the form of cracking has occurred. At the same time, it provides high-precision time-frequency resolution and excellent noise suppression abilities. The effectiveness and feasibility of the LTFT applied to the synthetic and experimental signals are verified.

Frequency hopping signal detection based on optimized generalized S transform and ResNet.

The performance of traditional frequency hopping signal detection methods based on time frequency analysis is limited by the tradeoff of time-frequency resolution and spectrum leakage. Machine learning-based frequency hopping signal detection techniques have a high level of complexity. Therefore, this paper proposes a residual network and the optimized generalized S transform to detect frequency hopping signals. First, based on the time-frequency aggregation measure, the generalized S transform parameters $ \lambda $ and $ p $ are optimized using a multi-population genetic algorithm. Second, the optimized generalized S transform is used to determine a signal's time-frequency spectrum, which is then normalized to make this robust to noise power uncertainty. Finally, a residual network structure is designed which receives the time-frequency spectrum. To detect frequency hopping signals, the network automatically learns the time-frequency properties of signals and noise. Simulated findings indicate that the multi-population genetic algorithm not only increases optimization efficiency when compared to a regular genetic algorithm, but also has faster convergence and more stable optimization results. Compared with a hybrid convolutional network/recurrent neural network algorithm, the proposed technique is better at detection and has less computational and storage complexity.

Time-Delay Estimation of Microseismic DAS Data Using Band-Limited Phase-Only Correlation

Time-delay estimation is a critical step in many geophysical applications. Conventional approaches are mainly based on the cross correlation of waveforms in time domain but show strong distortions with multiple oscillations and side lobes. We propose a band-limited phase-only correlation (POC) algorithm for time-delay estimation. The algorithm involves the following key steps: 1) transforming 1-D waveform into 2-D time–frequency spectra using S-transform; 2) calculating the band-limited POC function of the transformed spectra; and 3) measuring time delays by analyzing POC coefficient. We demonstrate the effectiveness of the proposed algorithm using synthetic and real microseismic fiber-optic distributed acoustic sensing (DAS) datasets. Results show that POC can effectively and accurately estimate the time delays of waveforms. Compared with the performance of the conventional cross correlation method in time domain, the proposed method has three main advantages: 1) better identification of event and noise waveforms; 2) lower uncertainty of narrow correlation peaks; and 3) weaker distortions with small oscillations and side lobes.

Synchrosqueezing-Based Short-Time Fractional Fourier Transform

A novel synchrosqueezing transform to the time-frequency representation based on short-time fractional Fourier transform for strong time-varying signals is proposed in this paper. To finely describe the local characteristics of nonstationary signal in the short-time fractional Fourier transform domain, a new instantaneous frequency estimator, a new instantaneous fractional frequency estimator and the corresponding energy reassignment operators are given by time-fractional frequency basis. The discrete implementation and signal reconstruction of the proposed method are investigated. Furthermore, the calculation of the optimal fractional order, computational complexity and limitation of the proposed method are discussed. Various strong time-varying signal experiments and time-frequency spectrum energy attenuation gradient extraction experiments of real synthetic aperture radar (SAR) images are conducted to verify the effectiveness and superiority of the proposed method over some advanced time-frequency analysis methods in energy concentration, time-frequency localization, signal reconstruction and clutter suppression.

VLSI Architecture of DCT-Based Harmonic Wavelet Transform for Time–Frequency Analysis

The complex harmonic wavelet(CHW) is being used to directly compute frequency content with respect to time by employing discrete Fourier transform(DFT) and inverse discrete Fourier transform. However, DFT coefficients suffer severe leakage of energy from one band to another band of frequency. The leakage between bands is minimized by employing discrete cosine transform(DCT) in the harmonic wavelet transform, which leads to a better representation of the time-frequency spectrum. This paper introduces a new VLSI architecture for DCT-based harmonic wavelet for hardware implementation and prototyped on a commercially available virtex5 field-programmable gate array(xc5vlx110t). To validate the proposed implementation, its real-time captured results in the logic analyzer are verified with simulation results. The maximum operating frequency targeting the FPGA mentioned above device is reported as 114.34 MHz. The total On-Chip power of the above implementation is 1.102W, out of which 68mW is the dynamic power dissipation at a toggle rate of 12%. Finally, for the area utilization of the above implementation, its resource utilization targeting the above FPGA device is reported.

Multitype Noise Suppression in Magnetic Resonance Sounding Data Based on a Time–Frequency Fully Convolutional Neural Network

Magnetic resonance sounding (MRS) is one of the technical applications of nuclear magnetic resonance (NMR) used to directly detect and quantify groundwater content. MRS suffers from a low signal-to-noise ratio (SNR) due to the low amplitude of free induction decay (FID) signals and an inability to shield environmental noise. In this paper, a time-frequency fully convolutional neural network (TFCN) was proposed to suppress random, harmonic, and spike noise from MRS data. The TFCN parameters were trained with the time-frequency spectrum obtained by the short-time Fourier transform (STFT) of the MRS datasets as the input and the noise-free FID signals as the output. Based on the results of synthetic and field data experiments, the TFCN was compared with existing denoising methods. The results showed that the TFCN extracted the envelope of the FID signals from low-SNR random noise with higher accuracy than other methods. Moreover, the TFCN simultaneously suppressed multiple types of noise and exhibited high computational efficiency.

Few-Shot Radar Jamming Recognition Network via Time-Frequency Self-Attention and Global Knowledge Distillation

Radar jamming recognition aims to accurately recognize the type of jamming to provide guidance for radar countermeasures. Although previous deep learning-based methods have made promising performance, they mainly rely on convolutional neural network (CNN) based on local processing, which ignore the global information in the time-frequency domain data of the jamming signal and also require much inference time to obtain the final recognition results. In this paper, a novel few-shot jamming recognition network via time-frequency self-attention and global knowledge distillation (JR-TFSAD) is proposed by jointly considering the global information in the time-frequency spectrum of the jamming signal and the real-time performance of the recognition network. A time-frequency self-attention model (TFSA) is proposed to extract the global deep features of radar jamming signals by learning the correlation between two arbitrary points in the time-frequency spectrum of the jamming signal, thus improving the recognition accuracy. Moreover, to effectively reduce the inference time of the method while preserving the recognition accuracy, a global knowledge distillation model (GKD) is further constructed to perform jamming recognition by distilling the global knowledge from the TFSA model. The experimental results on the simulated and measured mixed dataset verify that the proposed method has higher recognition accuracy and shorter inference time compared to the state-of-the-art methods.

Deconvolutive Frequency Corrected Three-Parameter S-Transform and Its Application in Tight Sandstone Reservoir

As an effective time-frequency (TF) analysis method, S transform (ST) has an extensive application in signal processing. However, for broad-band seismic signals, the peaks of the frequency distribution in the TF spectrum of ST biases the actual Fourier spectrum. Besides, the TF resolution of ST is affected by the relatively fixed window function and the Heisenberg uncertainty principle. In order to correct the frequency bias and improve the TF resolution of ST, and at the same time, to increase the flexibility of the window function, we propose a new TF analysis method, called the deconvolutive frequency corrected three-parameter S transform (DFC-TPST). The DFC-TPST includes two steps: modifying the window function to achieve the frequency corrected three-parameter S transform (FC-TPST) and deconvoluting FC-TPST to achieve DFC-TPST. The synthetic example proves the superiority of the method in characterizing seismic signals. Through comparison of field data testing, we find that the proposed method can be well applied to the hydrocarbon detection in tight sandstone reservoir.

Variational time–frequency adaptive decomposition of machine multi-impact vibration signals

The vibration signal of a mechanical equipment shell displays multi-impact coupling characteristics, when reciprocating mechanical vibration signals of large marine diesel engines and petrochemical reciprocating compressors, which exhibits the characteristics of nonstationarity, strong coupling, and strong interference in the time–frequency domain. Signal decomposition and multi-source impact identification have great significance for early fault diagnosis. However, existing decomposition methods for extracting fault frequency bands cannot satisfy demands for extracting impacts from the multi-source impact signals of reciprocating machinery. In this study, variational time–frequency adaptive decomposition (VTFAD) for multi-impact vibration signals is established to decompose and extract single-impact components. A variational model based on the minimization of a spectral center moment is proposed based on the two-dimensional morphological characteristics of energy concentration and discrete distribution in the time–frequency spectrum of the impact signal. An iterative solution is obtained using the alternating direction multiplier method; the time–frequency center and effective time–frequency domain components of the impact are calculated adaptively. A parameter optimization selection scheme is designed for selecting the number of time–frequency domain decompositions and quadratic penalty factor in the optimization process. The test of simulated mechanical multi-impact signals demonstrated that the proposed method can adaptively and accurately identify the time–frequency centers and time–frequency domain characteristics of the impacts in multi-impact vibration signals. VTFAD was applied to a diesel engine connecting the rod-bearing wear-fault vibration signal. The results show that VTFAD can effectively identify the new impacts caused by the fault and accurately extract the key characteristics of the impacts.

A GPR 2D Teager-Kaiser energy operator based on the multivariate variational mode decomposition

ABSTRACT To delineate the anomalies related to subsurface target bodies and the geophysical events, a novel method based on the effective combination of the multivariate variational mode decomposition (MVMD) and 2D Teager-Kaiser operator (2D-TKEO) is proposed for ground-penetrating radar (GPR) data processing in this letter. The proposed method takes advantage of the multi-channel decomposition scheme of MVMD and the multi-directional localization of 2D-TKEO for tracking energy attributes. The time-frequency spectrum can be generated based on the IMF-slices decomposed by the MVMD, on which the 2D-TKEO is introduced to focus the spectrum energy, then the common frequency slices are extracted to reveal the energy components of different frequency ranges. The forward model and GPR field data are applied here to demonstrate that the time-frequency spectrum and the subsequent common-frequency slices based on the proposed MVMD-2DTKEO approach can depict the subsurface target bodies (e.g., voids and pipes) and subsurface layers with higher resolution and better stratigraphic continuity, compared with that of the S-transform and the VMD-1DTKEO.

Research on Vibration Data-Driven Fault Diagnosis for Iron Core Looseness of Saturable Reactor in UHVDC Thyristor Valve Based on CVAE-GAN and Multimodal Feature Integrated CNN

The imbalance of data samples and fluctuating operating conditions are the two main challenges faced by vibration data-driven fault diagnosis for the iron core looseness of saturable reactors in UHVDC thyristor valves. This paper proposes a vibration data-driven saturable reactor iron core looseness fault diagnosis strategy named CVG-MFICNN based on CVAE-GAN and MFICNN to overcome the two challenges. This strategy uses a novel 1-D CVAE-GAN model to produce generated samples and expand the training set based on imbalanced training samples. An MFICNN model structure is designed to allow the simultaneous processing of multimodal features such as the SST time-frequency spectrum, time-domain vibration sequence, frequency-domain power spectrum sequence, and time-domain statistics. Using these multimodal features and the MFICNN model, the hidden fault information in vibration data can be effectively mined. An experiment is conducted to collect vibration data of saturable reactors with different faults. Models based on the proposed strategy and other methods are trained and tested using the collected data. The comparison results show that the performance of the proposed CVG-MFICNN approach is significantly superior to that of single-feature CNNs, traditional machine learning methods, and classical image classification CNNs in the application of UHVDC thyristor valve saturable reactor iron core looseness fault diagnosis.

Research on recognition algorithm of impact vibration based on HOG feature of time–frequency spectrum

The time–frequency spectrum of the vibration signal obtained based on the time–frequency transformation algorithm can fully reflect the energy distribution at any time–frequency coordinate. But this characteristic is not easy to be insight and generalized by the human eye, especially in the era of big data, in the face of massive data and rapid processing. During the research, we found that this information can be clearly expressed in the histogram of oriented gradient (HOG) feature of the time–frequency spectrum. Therefore, the time–frequency spectrum support vector machine classifier based on the HOG feature of the vibration signal has considerable feasibility. This article had conducted in-depth research on this idea, determined the advantages of wavelet time–frequency spectrum for signal recognition, and further selected wavelet basis and kernel function. A comprehensive test of the HOG parameters had finally achieved a good recognition effect. The comprehensive recognition accuracy of the algorithm for the impact and vibration signals collected in this paper was stable at about 96%. The research results will be applied to the future smart city vibration monitoring system. On the other hand, it may provide a new idea to improve the accuracy of the current battlefield target recognition system.