Time-frequency Energy Research Articles

A new method of harmonic time-frequency decomposition: The K-S decomposition

S transform and its improved algorithms are limited by the Gaussian window, which cannot realize high time-frequency energy concentration and exact identification of harmonic time-frequency parameters. A significant improvement has done in this paper: K-S decomposition is built based on the idea of FFT + Kaiser window + IFFT. The Each column vector of the two-dimensional time-frequency complex matrix obtained by K-S decomposition represents the frequency of the signal and each row is instantaneous magnitude in each selected frequency in time domain. Thus the parameter of amplitude, spectrum, time and phase can be achieved and adaptive time-frequency analysis is realized. The simulation experiments of the complex power system harmonic verify the feasibility and adaptive ability of K-S decomposition.

Analysis of Magnetic Field Waveforms of Different Launching Stages of Rail Gun Based on Wavelet Transform

Electromagnetic disturbance in the course of rail-gun launching has great influence on the launching process and staff. Based on the magnetic force measured at the startup acceleration and separation stages, the corresponding magnetic field can be calculated. The magnetic field at different positions and heights near the rail gun is analyzed and compared. The results show that the position of the armature has great influence on the magnetic field. The maximum value of the instantaneous magnetic field should be located in the middle of the rail gun. At the same position, the magnetic field decays rapidly with the increase of height. The electromotive force waveforms are analyzed by using the wavelet transform; the analysis shows that the wavelet transform can reveal the time-frequency energy distribution of the electromotive force more accurately and clearly. The research of this paper has a guiding significance to the shielding design of magnetic field of the electromagnetic rail gun, and will promote the development of rail guns.

Characteristics of non–linear dynamics and energy transfer in a vibration gas–solid fluidized bed by using Hilbert–Huang transform

The study explores the characteristics of non–linear fluidization of vibration gas–solid fluidized bed (VGFB) and the laws of wave energy transfer. A VGFB (Φ 110 mm × 180 mm) with the −0.3 + 0.074 mm magnetite particle was adopted in the experiment. The Hilbert–Huang transform (HHT) analysis of the pressure signal was used to obtain the time–frequency–energy two–dimensional Hilbert–Huang spectrum of pressure fluctuation signals under different fluidized states, and this revealed that the pressure fluctuation signal was composed of complex inter- and intra– wave frequency modulation components, this verified the non–linearity and randomness of the pressure signal. The distribution of the empirical mode decompositions (IMFs) energy of pressure fluctuation signal under different operation conditions was analyzed, and the results indicated that the IMF4 energy increased with increases in the bubble size. Conversely, with decreases in the bubble size, the energy was gradually transferred from IMF4 to IMF3, this revealed that the energy distribution of IMF3 and IMF4 exhibited a good correspondence with the bubble phase behavior and was a quantitative reflection of the non–linear bed fluidization. Finally, the main frequency and energy of the pressure signal were used to describe the dynamic behavior of the VGFB under different fluidized states. The results indicated that the pressure fluctuation frequency of quasi–dispersive fluidization and bubbling fluidization were both lower than that of the frequency of turbulent fluidization. Additionally, the pressure signal energy of quasi–dispersive fluidization was the lowest, bubbling fluidization was intermediary, and turbulent fluidization was the highest.

A bearing vibration data analysis based on spectral kurtosis and ConvNet

Today’s modern industry has accepted condition monitoring based on intelligent fault diagnosis of rotating machinery systems to provide precision and sustainability. The conventional signal processing methods are less productive due to the involvement of various noises from different sources in the vibration signal, and therefore, recently fault diagnosis approaches use the artificial intelligent techniques along with the signal processing methods. Thus, motivated by the kurtogram and convolutional neural network (CNN), a novel efficient method for the fault classification of rotating machines is proposed in this paper. Kurtogram is a measure of dispersion for time–frequency energy density which provides additional frequency contents information and as an effect represents a pattern of each fault uniquely. Thus, it inspires to utilize the kurtogram as an input feature vector, and it helps in reducing the task of identifying dominant features to represent the different faults. Hence, this 2D distinct feature vector presented to CNN for fault classification. The various levels of kurtogram are examined by tuning different hyperparameters of CNN to achieve a good feature set for decent performance. The experimental results demonstrate that the proposed method effectively classifies the bearing faults under different operating conditions in comparison to other methods.

Fast classification for rail defect depths using a hybrid intelligent method

In view of the fact that the traditional laser ultrasonic imaging test takes a long time and cannot achieve large area scanning of rail. This paper explores the possibility of combing the laser-ultrasonic technology and a hybrid intelligent method to fast achieve classification and evaluation of artificial rolling contact fatigue (RCF) defect in different depths. The laser ultrasonic scanning detection system is used to collect data samples from different locations of the defects quickly, and the signals are detected by an interferometer. Once the characteristic information of different rail defects is acquired and trained by Support Vector Machine (SVM), the high efficient and high-precision rail detection can be realized through the input of the feature in the detection process. The hybrid method is composed by Wavelet Packet Transform (WPT), Kernel Principal Component Analysis (KPCA) and SVM. The WPT is used to decompose the signal of surface defect in different frequency bands. The KPCA is used to eliminate the redundancy of the original feature set, thereby reducing the correlation among all the defect features. Wavelet packet time-frequency coefficient (X), energy (E) and local entropy (F) are generated and a new feature (Ynew) is created by fusing X, E and F, as a result of WPT and KPCA. Finally, a support vector machine (SVM) method is used to classify RCF defect in different depths. It implements a fast classification of small data. Compared with single features, fusion feature has the highest accuracy rate up to 98.73%.

Zoom synchrosqueezing transform-based chatter identification in the milling process

Self-excited chatter vibration is one of the most unexpected phenomena during the milling operation, which is always combined with time-varying and non-stationary characteristics. This paper presents a milling chatter detection approach combined with the time-frequency analysis (TFA) method and instantaneous frequency and energy aggregation characteristics of the chatter vibration in the milling process. A zoom synchrosqueezing transform (ZST)-based chatter identification approach and several chatter identification indicators are constructed for milling chatter identification. The TFA method ZST is used to characterize the time-varying and non-stationary characteristics of the chatter vibration. The zoom strategy is used to improve the time-frequency resolution and energy concentration of the obtained time-frequency distribution. From an energy aggregation characteristic perspective, 13 instantaneous frequency domain statistic indicators and an instantaneous energy ratio indicator based on the time-frequency distribution obtained by ZST are developed for milling chatter identification. Four groups of cutting tests with both end milling and peripheral milling are conducted to validate the effectiveness of the developed chatter identification indicators, and results show that the developed chatter identification indicators can effectively identify chatter in the milling process and are insensitive to the cutting parameters.

An automatic optimal excitation frequency tracking method based on digital tracking filters for sandwiched piezoelectric transducers used in broken rail detection

Based on digital tracking filters and wireless communication technology, an automatic optimal excitation frequency tracking method for sandwiched piezoelectric ultrasonic transducers (SPUTs) is proposed. The proposed frequency tracking method uses a variable-step frequency search strategy and the optimal excitation frequency is determined by analyzing the receiving signals in time and frequency domains. Then the field test is carried out by the pitch-catch setup under different test distances: 50 m, 100 m, and 150 m. It is proved that compared with SPUTs excited at series resonance frequency, the FFT (Fast Fourier Transformation) amplitude, power spectrum density and Peak-to-Peak value are greatly improved and the maximum time-frequency energy becomes more concentrated when SPUTs are actuated at the optimal excitation frequency. Specially, the FFT amplitude, power spectrum density and Peak-to-Peak value can achieve the largest increase by 104.42%, 31.54%, 71.36%, respectively when the test distance is equal to 50 m. It can be concluded that the proposed frequency tracking method can efficiently track the optimal excitation frequency and be easy to achieve integration and automation.

Lesion localization algorithm of high-frequency epileptic signal based on Teager energy operator

Abstract High-frequency oscillations reflect the abnormal brain electrical activity in patients with epilepsy. It is significant to research the relationship between high-frequency oscillation and epilepsy originating area for the diagnosis and treatment of epilepsy. In view of the identification of epileptic EEG and the location of epileptic foci, a localization algorithm based on Teager operator is proposed. Firstly, the original epileptic EEG data are preprocessed, the wavelet weighted threshold and the frequency notch method are used to denoise the original epileptic high frequency oscillation signal. Taking into account the frequency characteristics of the high frequency oscillating signal itself, the FIR (Finite Impulse Response) digital filter is used to filter the epileptic high-frequency oscillation signal. Secondly, because the high frequency oscillation rhythm has the characteristics of high frequency, high energy and low amplitude, the Teager energy operator and curve length method are used to extract the characteristics. The PSD (Power Spectral Density) method is applied to qualitative analysis of epileptic lesion location. Finally, the EMD (Empirical Mode Decomposition) algorithm is used to decompose the high-frequency oscillation signal. Combined with Teager energy operator, Teager-huang transform is used to analyze the signal by time-frequency energy analysis. Quantitative analysis of epileptic lesion location is made by using EMD energy entropy method for different lead epileptic signals. The algorithm can effectively locate the location of the focus, independent of individual parameters and high degree of automation. It has good clinical application prospects.

Research on signal processing of segment-grout defect in tunnel based on impact-echo method

In shield tunneling construction, grout of precast concrete segments is widely applied to various geological conditions. However, the connection performance between the grout and segments after the grout cannot be determined by destructive means, such as coring. The impact-echo method is used extensively in nondestructive testing of civil engineering structures. Nevertheless, there are inadequate researches on determining defects in segment-grout structure. In this paper, the segment-grout structure was simulated experimentally and artificial defects were introduced in the grout. The Short-time Fourier Transform (STFT) and Wavelet Transform (WT) of signals obtained by the impact-echo method were carried out to analyze the time-frequency domain features of the impact-echo signals with and without defects in the grout. On this basis, defects in the grout layer were determined. Finally, energies of wavelet packet were calculated and characteristic relative energy indexes of wavelet packet at different positions were detained. It’s found that the values at positions without defects are relatively low. It’s demonstrated that the signal analysis of impact-echo method has to combine time-frequency domain information and energy distribution for detection of defects in the grout layer. Wavelet transform and energy analysis methods are effective means to detect defects in the grout layer.

Time-Frequency Energy Sensing of Communication Signals and Its Application in Co-Channel Interference Suppression.

As the number of mobile users and video traffics grow explosively, the data rate demands increase tremendously. To improve the spectral efficiency, the spectrum are reused inter cell or intra cell, such as the ultra dense network with multi-cell or the cellular network with Device-to-Device communications, where the co-channel interferences are brought and needs to be suppressed. According to the time-frequency energy sensing to the communication signals, the desired signal and the interference signal have different energy concentration areas on the time frequency plane, which provide opportunities to suppress the co-channel interference with time varying filter. This paper analyzes the time-frequency distributions of the Gaussian pulse shaping signals, discusses the effect of the analyzing window length on the time-frequency resolution, exploits the equivalence between the time frequency analysis at the baseband and at the radio front end, and finally reveals the advantages of the proposed masking threshold constrained time varying filter based co-channel interference mitigation method. The pass region for the linear time varying filter is generated according to the time-varying energy characteristics of the I/Q separated 4-QAM pulse shaping signals, where the optimum masking threshold is obtained by the optimum-BER criterion. The proposed co-channel interference suppression method is evaluated in aspect of BER performance, and simulation results show that the proposed method outperforms existing methods with low-pass or band-pass filters.

State variable technique islanding detection using time-frequency energy analysis for DFIG wind turbine in microgrid system

This paper introduces a new combined technique for wind turbine islanding detection using the trajectory of state variables and wavelet transform in microgrid system. The proposed relay is utilized of energy variation state of time-frequency transform coefficients of local signals in two-dimensional space. In order to improve of the proposed relay performance, a signal selection method based on the correlation concept between islanding and non-islanding signals. From of all patterns, the best of them with high correlation in islanding status is selected for the proposed relay learning. A neuro-fuzzy machine is used as learning of selected patterns to avoid threshold selection. The proposed technique is utilized to wind turbine islanding detection in a microgrid system contains various types of distributed generation including wind turbine, Combined Heat and Power (CHP) and photovoltaic system. Many islanding and non-islanding situation including motor starting, various load and capacitor switching in various operation conditions in the studied microgrid are simulated. Millstone characteristics of the proposed technique are included passive-based technique, negligible None Detection Zone (NDZ), suitable for microgrid application, performance increment in detection and fast detection time. Operation results of the proposed relay in various conditions confirm the performance of the proposed detection relay.

Intelligent Fault Diagnosis of HVCB with Feature Space Optimization-Based Random Forest

Mechanical faults of high-voltage circuit breakers (HVCBs) always happen over long-term operation, so extracting the fault features and identifying the fault type have become a key issue for ensuring the security and reliability of power supply. Based on wavelet packet decomposition technology and random forest algorithm, an effective identification system was developed in this paper. First, compared with the incomplete description of Shannon entropy, the wavelet packet time-frequency energy rate (WTFER) was adopted as the input vector for the classifier model in the feature selection procedure. Then, a random forest classifier was used to diagnose the HVCB fault, assess the importance of the feature variable and optimize the feature space. Finally, the approach was verified based on actual HVCB vibration signals by considering six typical fault classes. The comparative experiment results show that the classification accuracy of the proposed method with the origin feature space reached 93.33% and reached up to 95.56% with optimized input feature vector of classifier. This indicates that feature optimization procedure is successful, and the proposed diagnosis algorithm has higher efficiency and robustness than traditional methods.

Time Frequency analysis of Non-Stationary signals by Differential frequency window S –Transform

The S transform is an extension of Short Time Fourier Transform and Wavelet transform, has a time frequency resolution which is far from ideal. A differential frequency window is proposed in this paper to enhance the time frequency energy localization. When a non stationary signal consists of abrupt amplitude variation equal to peak of Gaussian function at initial intervals of chosen guassian window, then some part of the signal amplitude will be nullified during transform projection. The major function of differential frequency window is to track all abrupt amplitude-frequency variations which exploits in non – stationary signals. A mathematical method namely Newton Raphson method is adopted for this trace. The proposed scheme is tested for ECG data in presence of noise environment and results shows that proposed algorithm produces better enhanced energy localization in comparison to the standard S – Transform, STFT, and CWT. Furthermore the above algorithm is implemented on FPGA for real time applications.

Vertex-Frequency Energy Distributions

A vertex-varying spectral content on graphs challenges the assumption of vertex invariance and requires vertex-frequency representations for an adequate analysis. In this letter, we introduce a class of vertex-frequency energy distributions inspired by traditional time-frequency energy distributions. These newly introduced distributions do not use localization windows. Their efficiency in energy concentration is illustrated through examples.

Research on Earthquake Information Based on ENPEMF Signal Time-Frequency Analysis

Based on the study of earthquake information surface Yao natural electromagnetic field has become an important method to study earthquake precursors. This paper studies the relationship between ENPEMF and the occurrence of earthquakes, and discusses the characteristics of electromagnetic precursors that can be observed before the earthquake. In this paper, the definition of Hilbert Huang transform (HHT) is studied and applied to the two dimensional and H dimensions of the data of the earth's natural pulsed electric field analysis of time-frequency energy spectrum. It is concluded that, according to different functions, it is necessary to adjust the noise coefficient to adapt to the signal in order to obtain good results.

Breaking the Limits: Redefining the Instantaneous Frequency

The Carson and Fry (1937) introduced the concept of variable frequency as a generalization of the constant frequency. The instantaneous frequency (IF) is the time derivative of the instantaneous phase and it is well-defined only when this derivative is positive. If this derivative is negative, the IF creates problem because it does not provide any physical significance. This study proposes a mathematical solution and eliminate this problem by redefining the IF such that it is valid for all monocomponent and multicomponent signals which can be nonlinear and nonstationary in nature. This is achieved by using the property of the multivalued inverse tangent function. The efforts and understanding of all the methods based on the IF would improve significantly by using this proposed definition of the IF. We also demonstrate that the decomposition of a signal, using zero-phase filtering based on the well established Fourier and filter theory, into a set of desired frequency bands with proposed IF produces accurate time-frequency-energy (TFE) distribution that reveals true nature of signal. Simulation results demonstrate the efficacy of the proposed IF that makes zero-phase filter based decomposition most powerful, for the TFE analysis of a signal, as compared to other existing methods in the literature.

Time-frequency analysis of surface EMG signals for maximum energy localization during gait

The purpose of this work is to assess the maximum energy localization in time-frequency domain of the surface EMG signal of the main lower-limb muscles usually involved in able-bodied walking. The maximum energy localization in time-frequency domain has been identified by means of Continuous Wavelet Transform (CWT), a time-scale analysis method for multiresolution decomposition of continuous-time signals. WT coefficients allowed to reconstruct the scalogram function, providing an estimate of the local time-frequency energy density of a signal. Then, localization of maximum energy density has been identified as the interval in time-frequency where the scalogram is exceeding the 72% of the peak value of energy density in both time and frequency domain. Results showed that the localization of maximum signal energy in time coincided with the region of maximum muscle recruitment during walking. A common frequency band of maximum information content was identified for all muscles between 70 and 160 Hz. These findings could be suitable for both supporting the use of WT for sEMG analysis and providing clinical indications on muscle recruitment during walking.

Feature extraction and fault diagnosis of wind power generator vibration signals based on empirical wavelet transform

Given the nonlinear and nonstationary characteristics of wind power generator vibration signals, the empirical wavelet transform (EWT)-based method is proposed to analyze the vibration signal characteristics and to diagnose faults. The adaptive Fourier spectrum segmentation of EWT is analyzed, and an appropriate wavelet filter is constructed to extract different AM-FM mode functions. The Hilbert transform is conducted, and the signal modal component energy is normalized to obtain vibration feature quantities. A probabilistic neural network (PNN) is used to perform the classification and diagnosis of wind power generator vibration faults. The experiments are constructed based on simulation signals and vibration signals before the proposed method and Hilbert-Huang transform (HHT) are used to perform mode decomposition and to analyze the time-frequency energy spectrum. The experimental results showed that the obtained resolution modes by EWT are within the corresponding time domain signal characteristics. The number of mode decomposition layers is less than that of empirical mode decomposition. No characteristics of false modal are observed. The time-frequency energy spectrum diagram can better reflect the characteristics of original vibration signal than the spectrum based on HHT. The PNN-based vibration fault judgment can achieve an accuracy rate of 90 % with limited training samples.

Gear fault diagnosis based on time–frequency domain de-noising using the generalized S transform

Gears are the most important transmission modes used in mining machinery, and gear faults can cause serious damage and even accidents. In the work process, vibration signals are influenced not only by friction, nonlinear stiffness, and nonstationary loads, but also by strong noise. It is difficult to separate the useful information from the noise, which brings some trouble to the fault diagnosis of mining machinery gears. The generalized S transform has the advantages of the short time Fourier transform and wavelet transform and is reversible. The time–frequency energy distribution of the gear vibration signal can be accurately presented by the generalized S transform, and a time–frequency filter factor can be constructed to filter the vibration signal in the time–frequency domain. These characteristics play an important role when the generalized S transform is used to remove the noise in the time–frequency domain. In this paper, a new gear fault diagnosis based on the time–frequency domain de-noising is proposed that uses the generalized S transform. The application principle, method steps, and evaluation index of the method are presented, and a wavelet soft-threshold filtering method is implemented for comparison with the proposed approach. The effectiveness of the proposed method is demonstrated by numerical simulation and experimental investigation of a gear with a tooth crack. Our analyses also indicate that the proposed method can be used for fault diagnosis of mining machinery gears.

The Fourier decomposition method for nonlinear and non-stationary time series analysis.

for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.