Time-frequency Energy Distribution Research Articles

A dynamics simulation-assisted transfer learning method for track condition diagnosis in urban rail transits

Track defects are gradually emerging with the development of urban rail transits. However, there is rare research implemented to diagnose track conditions in real time. Although some intelligent data-driven methods seem to have the potential to achieve the track condition diagnosis, it’s hard to acquire sufficient labeled data in actual applications. This study proposes a dynamics simulation-assisted transfer learning (TL) method for label-scarce track condition diagnosis. Firstly, a dynamics model of axle-box bearings considering the service environment is established. Based on this model, a large amount of axle-box vibration signals corresponding to healthy/defective track conditions is simulated. Wavelet transform is performed for these signals to characterize their time-frequency energy distribution modes in the format of time-frequency maps, which are considered source-domain data. Similarly, the time-frequency maps of the collected signals during vehicle operation are served as the target-domain data. Subsequently, a sub-domain alignment TL network is constructed to map the data from the source and target domain into a deep feature space. In this network, unlabeled target-domain data are classified to obtain their pseudo labels. Finally, Wasserstein distance measure and multiple domain discriminators are employed to achieve label alignment between two domains for each corresponding category. A feature centroid-driven loss function is applied to further reduce the intra-class variations, ultimately realizing accurate knowledge transfer from simulated signals to collected signals. A two-level sliding window algorithm is designed to detect abnormal axle-box vibration signal parts which are then diagnosed through the well-trained network. The proposed method is validated through a transfer diagnosis experiment using simulated signals and collected signals. This study provides a promising solution to diagnose different track conditions, which is of great significance for ensuring running safety in urban rail transits.

Dynamic response characteristics of shaking table model tests on the gabion reinforced retaining wall slope under seismic action

In the present study, a series of shaking table model tests were performed on a slope with a gabion reinforced retaining wall. Transfer functions were employed to compute the inherent frequencies of the slope. Furthermore, the investigation examined various aspects of the slope, including the peak acceleration amplification factor, incremental dynamic stresses, displacements, and tensile forces. Additionally, the study employed the Hilbert Huang transform (HHT) to analyze the slope's time-frequency characteristics and energy distribution. The findings of the study revealed that there is an inverse relationship between the amplitude of the input seismic wave and the natural frequency of the top of the gabion reinforced retaining wall slope. As the amplitude of the seismic wave increases, the natural frequency of the slope decreases. The amplification factors for peak acceleration were all found to be less than 1.9, suggesting a notable dissipation of seismic energy in comparison to typical slopes. The response of incremental dynamic stress was most pronounced in the middle section of the slope, followed by the top of the slope. The magnitude of the incremental displacement was found to be highest at layer 4, whereas the incremental tensile force exhibited its maximum value at layer 5. The dynamic response exhibited the least pronounced characteristics at the lower portion of the slope, demonstrating the most stable behavior. The peak frequencies observed in the Hilbert marginal spectrum displayed comparable characteristics to the natural frequencies.

A Dual-Stage-Recognition Network for Distributed Optical Fiber Sensing Perimeter Security System

Accurate intrusion recognition along the optical fiber is still an enormous challenge in the distributed acoustic sensing (DAS) based security system. Especially in the complex environments, various unknown disturbs such as the animal activities will lead to high false alarm rate of intrusion detection system. In this work, an accurate and effective intrusion pattern recognition using a dual-stage-recognition network is proposed and demonstrated for practical environments with various animal activities and mechanical movements. The dual-stage-recognition network consists of the pre-recognition stage for shallow classification and the sub-recognition stage for discriminating the similar events. In the pre-recognition stage, three target events of non-intrusion, human-animal activities and mechanical movements can be classified by the decision tree classifier based on the temporal energy and the frequency spectrum information. After that, in the sub-recognition stage, the target events of human and various animal activities can be further distinguished by the combination of the time-frequency analysis and BP neural network. Besides, in order to improve the computation efficiency of BP network model, the characteristics information of the time-frequency energy distribution is efficiently compressed by the proportion statistics of four energy-levels. The field test of a month proves that the proposed method can realize a high average recognition accuracy rate of 97.6% for five typical events with a fast average response time of 0.253 s, which is very promising in the intrusion events recognition in practical environments.

Deep auto-encoder network for mechanical fault diagnosis of high-voltage circuit breaker operating mechanism

Abstract To improve the accuracy of the mechanical fault diagnosis of the operating mechanism and fully exploit the characteristic information in the vibration signal of the high-voltage circuit breaker, a mechanical fault diagnosis method of the operating mechanism of the high-voltage circuit breaker based on the deep self-encoding network is proposed. First, the vibration signal of the switch operating mechanism is extracted, the wavelet packet conversion is performed, and the vibration signal of each frequency band is divided into equal times. The energy of the time–frequency subplane of the vibration signal is then calculated, and the time–frequency energy distribution is used as a switch. Finally, a breaker failure diagnostic model based on the deep self-coding network is established. Pretraining and tuning and a 126 kV high-voltage switch are used to simulate different types of faults and validate the method. Experimental results show that this method can acquire sample failure data and perform failure diagnosis, and the diagnosis accuracy rate reaches 97.5%. The deep self-coding network can fully pierce deep information on the switch vibration signal.

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.

Characterizing gas-liquid two-phase flow behavior using complex network and deep learning.

Gas-liquid two-phase flow is polymorphic and unstable, and characterizing its flow behavior is a major challenge in the study of multiphase flow. We first conduct dynamic experiments on gas-liquid two-phase flow in a vertical tube and obtain multi-channel signals using a self-designed four-sector distributed conductivity sensor. In order to characterize the evolution of gas-liquid two-phase flow, we transform the obtained signals using the adaptive optimal kernel time-frequency representation and build a complex network based on the time-frequency energy distribution. As quantitative indicators, global clustering coefficients of the complex network at various sparsity levels are computed to analyze the dynamic behavior of various flow structures. The results demonstrate that the proposed approach enables effective analysis of multi-channel measurement information for revealing the evolutionary mechanisms of gas-liquid two-phase flow. Furthermore, for the purpose of flow structure recognition, we propose a temporal-spatio convolutional neural network and achieve a classification accuracy of 95.83%.

Analysis of wave-induced vertical ship responses by Hilbert-Huang transform method

Time series of wave-induced ship responses are analysed by the Hilbert-Huang Transform (HHT) method. The results of the analysis of numerically simulated motions and loads on a chemical tanker in head waves are compared with the analysis of experimental data from laboratory model tests. The Empirical Mode Decomposition, which is a first part of HHT method is applied to the sea surface elevations of two sea states (high and low seas) and the wave-induced vertical motions and bending moments and the results are discussed. It is found that the decomposition of the experimental data into intrinsic components compares well with the decomposition of the numerically simulated ones for both high and low seas. The first two or three intrinsic mode functions carry the major part of the energy of both experimental and numerical simulated data. The time-frequency distribution of energy, called Hilbert spectrum, is calculated by the second part of HHT method. The Hilbert spectrum of the sea surface elevation is compared with Hilbert spectrum of wave-induced ship motions and moments in an attempt to study the time-frequency characteristics of ship response. The results of the present work provide confidence in the usage of numerical simulation data for the decomposition into intrinsic components of ship responses, avoiding the need for experimental data from laboratory model tests.

Attenuation characteristics of impact-induced seismic wave in deep tunnels: An in situ investigation based on pendulum impact test

The radiated seismic energy is an important index for the intensity assessment of microseismic (MS) events and the early warning of dynamic disasters. However, the energy of MS signals is significantly attenuated due to the heterogeneity and viscous damping of rock media. Therefore, the study on attenuation characteristics of MS signals in underground engineering has practical significance for the accurately estimation of radiated seismic energy. Based on a pendulum impact test facility and MS monitoring system, an in situ investigation was carried out to explore attenuation characteristics at a deep tunnel. The results show that the seismic energy and peak particle velocity (PPV) attenuation are exponentially related to the propagation distance. The attenuation coefficient of energy is larger than that of PPV. With the increase in the input impact-energy, the seismic energy attenuation coefficient decreases as a power function. An empirical relationship between energy attenuation coefficient and wave impedance of rock mass was established in this scenario. Moreover, the time-frequency characteristics and energy distribution laws of impact-induced signals were investigated by the continuous wavelet transform (CWT) and wavelet packet analyses, respectively. The dominant frequency of signals decreases gradually as the propagation distance increases. Based on the energy attenuation characteristics, a new method was proposed to calculate the released source energy of MS events in the field. This study can provide an insight into energy attenuation characteristics of seismic waves and references for attenuation correction in seismic energy calculation.

Instantaneous Frequency Estimation Method for the Vibration Signal of Rotating Machinery Based on STFTSC Algorithm

In this paper, an instantaneous frequency identification method known as STFTSC is developed by combining short-time Fourier transformation and the seam carving (SC) algorithm (widely used in image processing). In this method, the STFT is applied to analyze the time-frequency energy distribution of a vibration signal under variable-speed conditions. Subsequently, the energy gradient is calculated through the Sobel operator based on the time-frequency energy distribution. The energy gradient distribution contains multiple ridges, which are corresponding instantaneous frequencies of different orders. Finally, the targeted ridge extraction is transformed into an optimization problem, and the dynamic programming algorithm (DP) is used to search the targeted ridge with the minimum energy gradient to estimate the instantaneous frequency. The effectiveness of the proposed method is validated by a simulation experiment, moreover, a rotating machinery fault simulation test bench is employed to validate the method, which is then compared with polynomial chirplet transformation (PCT) and analyzed during the test process. The results show that the STFTSC instantaneous frequency estimation algorithm has a higher extraction accuracy and better application value in engineering problems than the PCT.

Signal Useful Information Recovery by Overlapping Supports of Time-Frequency Representations

This paper presents a novel method for automatic extraction of useful information from time-frequency distributions of noisy signals. Signals' features are examined through the combined analysis of their time-frequency energy distributions and inverse complexity maps. The inverse complexity approach gives a new entropy-based insight into the signal structure. These two approaches result in mostly disjoint time-frequency supports, overlapping only in the proximity of the signal components. Locations of the signal components (i.e., useful information) are thus identified by low complexity and high amplitude occurring together in the time-frequency plane. Compared to existing methods using only the time-frequency energy distribution, useful information extraction by the proposed method exhibits a significantly reduced error rate.

Research on electromagnetic radiation (EMR) waveform characteristics of coal failure process using Hilbert-Huang transform (HHT)

Electromagnetic radiation (EMR) waveforms contain rich information on coal fracture law, which is of great value to the refined study of their characteristics. In this paper, the Hilbert-Huang transform (HHT) method is used to analyze and process EMR waveform of coal failure process. The results show that HHT method can adapt well to the nonstationary and nonlinear characteristics of EMR waveform. It adaptively decomposes EMR waveforms by empirical mode decomposition (EMD), extracts the intrinsic mode function (IMF) characteristics of EMR waveforms, and obtains the law of instantaneous energy changes of EMR waveforms. At the same time, EMR waveform energy is quantitatively expressed on the three-dimensional Hilbert energy spectrum (time–frequency-energy distribution), and the refined features of EMR waveform signal are effectively extracted. The instantaneous energy of EMR and the three-dimensional Hilbert energy spectrum processed by HHT method more easily describe the fracture law of coal body. Compared with conventional characteristic parameters, such as EMR amplitude and dominant frequency, the identification degree of the precursor characteristics of coal body instability is greatly improved. Among the short-term Fourier transform (STFT), wavelet transform (WT) and HHT nonstationary signal processing methods, HHT method has an improved adaptability and superiority and can reveal the characteristics of coal deformation and failure more carefully and accurately, which provides a new means for better using and improving EMR method to monitor coal instability and failure.

Effect of beam oscillating pattern on laser welding of steel to PMMA

Laser welding of 1 mm-thick steel and PMMA was employed via beam oscillating. Three modes of beam oscillation, transverse, longitudinal and circular were explored. Due to the stirring effect, the beam oscillation improves the weld formation and promotes the flow of bubbles in the molten layer. The circular oscillation gives the strongest weld homogeneous without overheat discoloration defect. The bonding strength was 38% more than the weldment without beam oscillation. The weld strength improvement was attributed to the variation of the oscillating speed varies the time-frequency distribution of the beam energy. This technology reduces the morphological defects and increases the uniformity of the weld. The improvement mechanism of beam oscillation on bubble behavior and melt flow behavior is also discussed.

Study on Response Characteristics of Surrounding Rock Rupture Microseismic Events during Coal Roadway Excavation

In order to solve the problems such as coal burst and abnormal gas overrun caused by the fracture of surrounding rock in the process of mining in the coal roadway, the ESG microseismic monitoring system is built on the driving face of 8005 transportation roadway of Wuyang Coal Mine to carry out a real-time, continuous, and omnidirectional dynamic state monitoring. In this way, the characteristics of time-frequency evolution and energy distribution of the acquired signals are systematically analyzed, and the location of the roadway microseismic events is studied. The results show the following: (1) influenced by mining activities, the localized microseismic events are mostly distributed in front and on both sides of the working face. Due to mining activities and geological changes, the equilibrium of original stress in coal and rock mass is broken. The stress thus is released accompanied by fracture before reaching a new equilibrium. (2) By comparing the coal and rock fracture signals with the interference signals, it is found that the fracture signals have short duration and large amplitude with obvious abrupt change characteristics. The interference signals have long duration and relatively small amplitude with less obvious change. (3) Fourier transform analysis shows that the main frequency of coal rock fracture signals is 100–200 Hz with large total energy concentrated in the first frequency band, while that of interference signals is mostly less than 100 Hz with small total energy. The research results can effectively identify the coal and rock dynamic disasters, provide technical support for the prediction and early warning of hidden danger, and guide the safe and efficient production.

The smooth transition GARCH model for simulation of highly nonstationary earthquake ground motions

The aim of this paper is to extend a stochastic model for simulation of highly nonstationary ground motions (GMs). In this model, the dual-tree complex discrete wavelet transform (DT-CDWT) is applied to a recorded ground motion to extract its wavelet coefficients and then the Smooth Transition Generalized Autoregressive Conditional Heteroscedastic (ST-GARCH) model is used to simulate these coefficients. This model simulates nonstationary features of real GMs greatly, because the conditional variance estimated by this model changes compatibly with the amplitude nonstationary features of real GMs. Because of having asymmetric structure, this model also estimates sudden changes in the amplitude of ground motions. Some of the special capabilities of this model are the simulation of multiple increasing–decreasing cycles in the temporal amplitude of GMs, prediction of several peaks in the frequency spectrum of GMs, estimation of steps of their energy curve, and simultaneous simulation of all shocks of a GM sequence. Also, this model simulates the time–frequency energy distribution of both wide-frequency and narrow-frequency bandwidth GMs.

Modal Analysis of a Bridge During High-Speed Train Passages by Enhanced Variational Mode Decomposition

Modal analysis of bridge under high-speed trains is essential to the design and health monitoring of bridge, but it is difficult to be implemented since the vehicle–bridge interaction (VBI) effect is involved. In this paper, the time–frequency analysis technique is performed on the non-stationary train-induced bridge responses to estimate the frequency variations. To suppress the interference terms in time–frequency analysis but preserve the time-variant characteristics of responses, the enhanced variational mode decomposition (VMD) is proposed, which is used to decompose the train-induced dynamic response into many of envelope-normalized intrinsic mode functions (IMFs). Then the short-time Fourier transform is applied to observe the time–frequency energy distribution of each IMF. The train-induced bridge signals measured from a large-scale high-speed railway bridge are analyzed in this paper. The IMFs associated with the pseudo-frequencies caused by train or the resonant frequencies of bridge are distinguished. And, frequency variations are captured from the time–frequency energy distributions of envelope-normalized IMFs. The results show the proposed method can extract the frequency variations of low-energy IMFs effectively, which are hard to be observed from the time–frequency energy distribution of train-induced bridge response. The instantaneous frequency characteristics extracted from the train-induced bridge response could be the important support for investigating the VBI effect of train–bridge system.

Monitoring of material-removal mechanism in micro-electrical discharge machining by pulse classification and acoustic emission signals

Micro-electrical discharge machining is a stochastic process where the interaction between the materials and the process parameters are difficult to understand. Monitoring of the process becomes necessary to achieve the dimensional accuracy of the micro-featured components. Although thermo-mechanical erosion is the most accepted material-removal mechanism, it fails to explain the material removal with very short pulse duration. Alternative postulate like electrostatic force-induced stress yielding provides a stronger argument, rising ambiguity over the material-removal process in the micro-electrical discharge machining regime. In this work, it was found that the stress waves released from the material during micro-electrical discharge-machining process indicate material removal by mechanical deformation and fracture mechanism. These stress waves were captured using the acoustic emission sensor. The discharge pulses were captured by voltage measurement and classified using voltage gradient and machining time duration into three major categories, open pulse, normal pulse and arc pulse. The acoustic emission signal features were extracted and identified by time–frequency–energy distribution analysis. A feed-forward back-propagation neural network mapping of the pulse instances was performed with the obtained acoustic emission signature. The time–frequency–energy distribution analysis of the acoustic emission and the scanning electron microscope images of the craters provide conclusive evidence that the material is removed by mechanical stress and fracture. The feed-forward back-propagation network model was trained to predict the discharge categories of the pulse instances with AE signal inputs which can be used for monitoring the material-removal mechanism in micro-electrical discharge machining operation.

Building safety monitoring based on extreme gradient boosting in distributed optical fiber sensing

Abstract Aiming at the problem of the safety monitoring of the surrounding environment of the glass window on the building, a scheme of distributed optical fiber acoustic sensors based on the phase sensitive time-domain reflection is proposed. Firstly, Wigner bispectrum is used to analyze the time–frequency energy distribution of vibration signal, then the axially integrated bispectrum algorithm is used to extract the time–frequency characteristic components, and the method of sub-band division is used to avoid information loss and decrease the cost of computing. The eigenvectors of different vibration events are recognized by extreme gradient boosting tree algorithm. Based on the diversity of acoustic signal types in the environment, there are eight kinds of events including wind blowing, knocking, window opening, watering, hammering, dog barking, aircraft sound and no disturbance to be selected for vibration experiments. The experimental results show that the scheme can get better recognition effect, and the average recognition rate of eight kinds of events reaches 93.3%.

Fractional Synchrosqueezing Transformation and its Application in the Estimation of the Instantaneous Frequency of a Rolling Bearing

The time-frequency energy distribution processed by a short-time Fourier transform can be compressed to the real instantaneous frequency by the synchrosqueezing transformation (SST), which improves the time-frequency energy concentration of the signal. However, there is a large error in the instantaneous frequency estimation of a multicomponent nonpure harmonic signal by the SST. Therefore, a method for determining the instantaneous frequency (IF) of a rolling bearing based on a fractional synchrosqueezing transformation (FRSST) is proposed. First, the theoretical derivation of the FRSST algorithm as a signal processing technique is given and the steps of the IF estimation are presented. Second, the main advantages of the proposed FRSST algorithm are proved. In the comparison of simulation signals, it is verified that the FRSST algorithm has a high time-frequency concentration, is non-fragile to the frequency modulation rate, has noise robustness and has nonsensitivity to the cross-frequency signal. Finally, the FRSST algorithm is applied to the IF estimation of a rolling bearing under rising speed and fluctuated speed, and is compared with the SST based on variational mode decomposition (VMD-SST), the generalized parametric SST (PSST) and polynomial chirplet transform (PCT). The test results show that the estimation error of IF based on the FRSST method is the least for a rolling bearing with the four fault types under rising speed. On average, the estimation error is 2.2180 Hz less than the corresponding error of the VMD-SST and 1.1862 Hz less than the corresponding error of the PSST method.

Radar Signal Intra-Pulse Modulation Recognition Based on Convolutional Neural Network and Deep Q-Learning Network

Intra-pulse modulation recognition of radar signals is an important part of modern electronic intelligence reconnaissance and electronic support systems. With the increasing density of radar signals, the analysis and processing of multi-component radar signals have become an urgent problem in the current radar reconnaissance system. In this paper, an intra-pulse modulation recognition approach for single-component and dual-component radar signals is proposed. First, in order to adapt to the time-frequency energy distribution characteristics of various radar signals, we propose to extract the time-frequency images (TFIs) of received signals by Cohen class time-frequency distribution (CTFD) with multiple kernel functions. Besides, the image processing methods are used to suppress noise and adjust the size and amplitude of the TFIs. Second, we design and pre-train a TFI feature extraction network for radar signals based on a convolutional neural network (CNN). Finally, to improve the probability of successful recognition (PSR) of the recognition system in the pulse overlapping environment, a multi-label classification network based on a deep Q-learning network (DQN) is explored. Besides, two sub-networks take TFIs based on special kernel functions as input and re-judge the recognition results of some specific signals to further enhance the recognition effect of the recognition system. The proposed approach can identify 8 kinds of random overlapping radar signals. The simulation results show that the overall PSR of dual-component radar signals and single-component radar signals can reach 94.83% and 94.43%, respectively, when the signal-to-noise ratio (SNR) is −6 dB.

Sparsely Localized Time-Frequency Energy Distributions for Multi-Component LFM Signals

This letter presents a high resolution method which separates close components of a multi-component linear frequency modulated (LFM) signal and eliminates their Cross-Terms (CTs). We first investigate the energy distribution of the Auto-Terms (ATs) and CTs in ambiguity plane. This reveals that the energy of the CTs of parallel close components is significant around the origin. We propose to mask the samples in which the CTs may have interferences with the ATs. This mask is signal-dependent and its directions are determined using the relationship between the radial slices of ambiguity function (AF) and the fractional Fourier transform (FrFT). Exploiting sparsity in time-frequency (TF) domain and by solving an ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm minimization problem, the localized time-frequency distribution (TFD) is extracted from the acquired samples of the AF. Simulation results reveal significant improvements in the efficiency compared to previous works.