Traditional Time-frequency Analysis Research Articles

Generalized Horizontal Synchrosqueezing Transform: Algorithm and Applications

Time-frequency analysis (TFA) is regarded as an efficient technique to reveal the hidden characteristics of the oscillatory signal. At present, the traditional TFA methods always construct the signal model in the time domain and assume the instantaneous features of the modes to be continuous. Thus, most of these approaches fail to tackle some specific kinds of impulselike signal, including shock and vibration waves, damped tones, or marine mammals. This article introduces a new method called generalized horizontal synchrosqueezing transform (GHST) to process the transient signal. A signal model defined in the frequency domain is used to deduce the GHST. Next, the new synchrosqueezing operator termed as group delay (GD) is proposed based on high-order Taylor expansions of the signal model. Finally, the modulus around ridge curves is rearranged from the original position to the estimated GD. Numerical results of a simulated signal demonstrate the precision of the GHST in terms of both readability of the time-frequency representation and reconstruction accuracy. Additionally, the proposed method is implemented to diagnose the fault in a rotary machine by analyzing the vibration signal. The validation demonstrates that the GHST performs better than other traditional TFA methods, and it is qualified for the online condition monitoring of the industrial mechanical system.

Parameter Optimization of Generalized S Transform Based on Improved Genetic Algorithm

Background: For the traditional Fourier Transform (FT), it cannot effectively detect the frequency of non-stationary signals with time. Analyzing the local characteristics of time-varying signal by using FT is hard to achieve. Therefore, many time-frequency analysis methods which can meet different needs have been proposed on the basis of the traditional Fourier transform, like the Short Time Fourier Transform (STFT), the widely used Continuous Wavelet Transform (CWT), Wigner-Ville Distribution (WVD) and so on. However, the best time and frequency resolution cannot be achieved at the same time due to the uncertainty criterion. Methods: From the point of view of optimizing time-frequency performance, a new Generalized S Transform (GST) window function optimization method is proposed by combining time frequency aggregation with an improved genetic algorithm in this paper. Results: In the noiseless condition, the Linear Frequency Modulation (LFM), Nonlinear Frequency Modulation (NLFM) and binary Frequency Shift Keying (2FSK) signals are simulated. The simulation results prove that the method can improve the time-frequency concentration and decreasing Rényi entropy effectively. Compared with other four traditional time-frequency analysis methods, the improved GST has more advantages. Conclusion: In this paper, a new method of optimizing the window function in GST based on improved GA is proposed in this paper. Experiments on LFM, NLFM and 2FSK signals show that the proposed method not only has the advantages of high resolution, but also determines the optimal parameters via the time frequency focusing criterion and the Rényi entropy. Compared with the other four kinds of time-frequency analysis methods, the optimized GST based on improved GA in this paper has the best time-frequency focusing.

A New Method of Two-stage Planetary Gearbox Fault Detection Based on Multi-Sensor Information Fusion

Due to their high transmission ratio, high load carrying capacity and small size, planetary gears are widely used in the transmission systems of wind turbines. The planetary gearbox is the core of the transmission system of a wind turbine, but because of its special structure and complex internal and external excitation, the vibration signal spectrum shows strong nonlinearity, asymmetry and time variation, which brings great trouble to planetary gear fault diagnosis. The traditional time-frequency analysis technology is insufficient in the condition monitoring and fault diagnosis of wind turbines. For this reason, we propose a new method of planetary gearbox fault diagnosis based on Compressive sensing, Two-dimensional variational mode decomposition (2D-VMD) and full-vector spectrum technology. Firstly, the nonlinear reconstruction and noise reduction of the signal is carried out by using compressed sensing, and then the signal with multiple degrees of freedom is adaptively decomposed into multiple sets of characteristic scale components by using 2D-VMD. Then, Rényi entropy is used as the optimization index of 2D-VMD analysis performance to extract the effective target intrinsic mode function (IMF) component, reconstruct the dynamics signal in the planetary gearbox, and improve the signal-to-noise ratio. Then, using the full-vector spectrum technique, the homologous information collected by numerous sensors is data layer fused in the spatial domain and the time domain to increase the comprehensiveness and certainty of the fault information. Finally, the Teager–Kaiser energy operator is used to demodulate the potential low-frequency dynamics frequency characteristics from the high-frequency domain and detect the fault characteristic frequency. Furthermore, the correctness and validity of the method are verified by the fault test signal of the planetary gearbox.

Phascope: Fine-Grained, Fast, Flexible Motion Profiling based on Phase Offset in Acoustic OFDM Signal

Acoustic Doppler shift estimation is a cost-effective way to implement Human-Computer Interaction applications across existing smart devices such as smart phones and smart spekaers. However, due to the inherent uncertainty principle in the traditional time-frequency analysis, it remains challenging to profile motions accurately and timely. In this paper, phase offset in acoustic OFDM signal is leveraged for developing Phascope, a fine-grained, fast and flexible motion profiling scheme. We evaluate Phascope using simulation and experiment on COTS devices. Sub-millisecond response time is achieved for Phascope in our experiment. Besides, with optimal subcarrier selection and SNR of 30 dB over all subcarriers, Phascope can estimate motion speed of 0.1 m/s with 6.75% root-mean-square error (RMSE) compared to optimized FFT method.

A Reservoir Information Extraction Method Based on Improved Hilbert-Huang Transform

Hilbert-Huang transform (HHT) is a nonlinear non-stationary signal processing technique, which is more effective than traditional time-frequency analysis methods in complex seismic signal processing. However, this method has problems such as modal aliasing and end effect. The problem causes the accuracy of signal processing to drop. Therefore, this paper introduces the method of combining the Ensemble Empirical Mode Decomposition (EEMD) and the Normalized Hilbert transform (NHT) to extract the instantaneous properties. The specific process is as follows: First, the EEMD method is used to decompose the seismic signal to a series of Intrinsic Mode Functions (IMF), and then The IMFs is screened by using the relevant properties, and finally the NHT is performed on the IMF to obtain the instantaneous properties.

Matching pursuit based on the rotated time-frequency atomic dictionary and its applications to seismic non-stationary data

AbstractThe time-frequency spectrum of an attenuated seismic wave rotates due to the influence of intrinsic quality factor. Traditional time-frequency analysis methods are either limited by time-frequency resolution or incapable of rotated time-frequency representation. To solve it, a matching pursuit (MP) method based on the rotated time-frequency atomic dictionary (MPFR) was proposed. By introducing a frequency rotation factor to the four-parameter dictionary in the conventional MP method, a five-parameter dictionary with frequency rotation characteristics was constructed, and the calculation process of each parameter was given. We tested the method on the synthetic traces and field data sets. The results showed that the proposed method can effectively realize rotated time-frequency characterization of attenuated seismic waves. Compared with the conventional atoms, the rotated time-frequency atoms are more compliant to the local features of non-stationary seismic data. Moreover, the effective description of rotated time-frequency characteristics can be used as an auxiliary technique to predict the reservoirs related to the attenuation. A care has to be taken when thin layers are encountered, since wavelet interference may cause rotated time-frequency characteristics independent of dispersion and attenuation in MPFR method.

Detection of remotely piloted aircraft using bio-acoustic techniques

This paper describes a biologically inspired approach for acoustically detecting and tracking small remotely piloted aircraft based on processing found in the insect visual system. Previous work has shown the insect visual system is excellent at enhancing and isolating signals in complex and noisy visual scenes. By constructing spectrograms of audio signals, we essentially converted audio data into images, which could then be processed in the same way as visual data sets. Traditional time-frequency analysis was used to characterise the signatures of remotely piloted aircraft observed by multiple sets of small microphone arrays located on the ground. A model based on multiple layers of non-linear dynamic adaptive components measured from responses of insect visual neurons was then applied to the observed spectrograms to enhance the related acoustic harmonics and suppress the unrelated noise. The result was crisp low-amplitude signal detection and classification of these difficult target sets. In contrast to traditional systems that operate uniformly across the entire spectrum—attempting to capture the world as faithfully as possible—the bio-inspired processing uses multiple time scales and operates independently on each time-frequency cell (pixel). This reveals unseen harmonics otherwise hidden by noise, thereby extending the maximum range at which even slow-moving, low amplitude targets are detected and tracked.This paper describes a biologically inspired approach for acoustically detecting and tracking small remotely piloted aircraft based on processing found in the insect visual system. Previous work has shown the insect visual system is excellent at enhancing and isolating signals in complex and noisy visual scenes. By constructing spectrograms of audio signals, we essentially converted audio data into images, which could then be processed in the same way as visual data sets. Traditional time-frequency analysis was used to characterise the signatures of remotely piloted aircraft observed by multiple sets of small microphone arrays located on the ground. A model based on multiple layers of non-linear dynamic adaptive components measured from responses of insect visual neurons was then applied to the observed spectrograms to enhance the related acoustic harmonics and suppress the unrelated noise. The result was crisp low-amplitude signal detection and classification of these difficult target sets. In contrast t...

Effect of sparsity‐aware time–frequency analysis on dynamic hand gesture classification with radar micro‐Doppler signatures

Dynamic hand gesture recognition is of great importance in human-computer interaction. In this study, the authors investigate the effect of sparsity-driven time-frequency analysis on hand gesture classification. The time-frequency spectrogram is first obtained by sparsity-driven time-frequency analysis. Then three empirical micro-Doppler features are extracted from the time-frequency spectrogram and a support vector machine is used to classify six kinds of dynamic hand gestures. The experimental results on measured data demonstrate that, compared to traditional time-frequency analysis techniques, sparsity-driven time-frequency analysis provides improved accuracy and robustness in dynamic hand gesture classification.

Dynamic Monitoring and Vibration Analysis of Ancient Bridges by Ground-Based Microwave Interferometry and the ESMD Method

In this paper, we propose to conduct a dynamic monitoring and vibration analysis of ancient bridges by means of ground-based microwave interferometry and the extreme-point symmetric mode decomposition (ESMD) method. Ground-based microwave interferometry, a novel non-contact technology with a high accuracy, is used to acquire dynamic time series displacements with environmental excitation factors and a transient load with a car, respectively. The ESMD method, a new alternative to the Hilbert-Huang transform (HHT), is adopted to conduct the instantaneous vibration analysis of Zhaozhou Bridge. Firstly, a series of intrinsic mode functions (IMFs) are obtained together with an optimal adaptive global mean (AGM) curve by using a mode symmetric about the maxima and minima points. Secondly, the instantaneous frequency of each IMF is obtained by the use of a direct interpolation algorithm, which can reconcile the conflict between the period and the frequency for the traditional time-frequency analysis methods. As a representative case, Zhaozhou Bridge, a well-known Chinese ancient bridge constructed more than 1400 years ago, is studied in detail. Four kinds of dynamic time series displacements—two of them acquired by considering only environmental excitation factors for the mid-span and 1/4-span points and the others obtained with the transient load of a car for the mid-span and 1/4-span points—are selected to pursue a comparison of the decomposed IMFs and the instantaneous frequencies to perform the instantaneous vibration analysis of Zhaozhou Bridge. By comparing the results obtained with HHT for the decomposed IMFs and the instantaneous frequencies, the results show that the proposed method has a powerful ability to evaluate the instantaneous dynamic response of ancient bridges.

IMF-Slices for GPR Data Processing Using Variational Mode Decomposition Method

Using traditional time-frequency analysis methods, it is possible to delineate the time-frequency structures of ground-penetrating radar (GPR) data. A series of applications based on time-frequency analysis were proposed for the GPR data processing and imaging. With respect to signal processing, GPR data are typically non-stationary, which limits the applications of these methods moving forward. Empirical mode decomposition (EMD) provides alternative solutions with a fresh perspective. With EMD, GPR data are decomposed into a set of sub-components, i.e., the intrinsic mode functions (IMFs). However, the mode-mixing effect may also bring some negatives. To utilize the IMFs’ benefits, and avoid the negatives of the EMD, we introduce a new decomposition scheme termed variational mode decomposition (VMD) for GPR data processing for imaging. Based on the decomposition results of the VMD, we propose a new method which we refer as “the IMF-slice”. In the proposed method, the IMFs are generated by the VMD trace by trace, and then each IMF is sorted and recorded into different profiles (i.e., the IMF-slices) according to its center frequency. Using IMF-slices, the GPR data can be divided into several IMF-slices, each of which delineates a main vibration mode, and some subsurface layers and geophysical events can be identified more clearly. The effectiveness of the proposed method is tested using synthetic benchmark signals, laboratory data and the field dataset.

Gear fault diagnosis based on the structured sparsity time-frequency analysis

Abstract Over the last decade, sparse representation has become a powerful paradigm in mechanical fault diagnosis due to its excellent capability and the high flexibility for complex signal description. The structured sparsity time-frequency analysis (SSTFA) is a novel signal processing method, which utilizes mixed-norm priors on time-frequency coefficients to obtain a fine match for the structure of signals. In order to extract the transient feature from gear vibration signals, a gear fault diagnosis method based on SSTFA is proposed in this work. The steady modulation components and impulsive components of the defective gear vibration signals can be extracted simultaneously by choosing different time-frequency neighborhood and generalized thresholding operators. Besides, the time-frequency distribution with high resolution is obtained by piling different components in the same diagram. The diagnostic conclusion can be made according to the envelope spectrum of the impulsive components or by the periodicity of impulses. The effectiveness of the method is verified by numerical simulations, and the vibration signals registered from a gearbox fault simulator and a wind turbine. To validate the efficiency of the presented methodology, comparisons are made among some state-of-the-art vibration separation methods and the traditional time-frequency analysis methods. The comparisons show that the proposed method possesses advantages in separating feature signals under strong noise and accounting for the inner time-frequency structure of the gear vibration signals.

A study on Gabor frame for estimating instantaneous dynamic characteristics of structures

A structure under damage normally exhibits nonlinear dynamic behaviors and time-dependent stiffness and damping. By estimating instantaneous dynamic characteristics of a structures is generally very useful when assessing structural damage in real application. This study presents a novel and effective approach that accurately estimating instantaneous dynamic characteristic of a structure using time-varying autoregressive exogenous (TVARX) model on Gabor frame. To evaluate the time-varying coefficient matrices of a time-series model, the proposed procedure applies Gaussian-based weighted function and Fourier transform on time series model, then the Gabor-transform-based time series formula could be obtained. The dynamic characteristics of a structure are determined from the coefficient matrices. Numerical analyses demonstrate that the proposed approach is superior to traditional time-frequency analysis in accurately estimating instantaneous dynamic characteristics of a structure. Finally, the proposed approach is applied to process measured data for a steel frame specimen subjected to a series of base excitations in shaking table tests.

Vibration signal analysis using parameterized time–frequency method for features extraction of varying-speed rotary machinery

In real application, when rotary machinery frequently involves variable-speed, unsteady load and defect, it will produce non-stationary vibration signal. Such signal can be characterized by mono- or multi-component frequency modulation (FM) and its internal instantaneous patterns are closely related to operation condition of the rotary machinery. For example, instantaneous frequency (IF) and instantaneous amplitude (IA) of a non-stationary signal are two important time–frequency features to be inspected. For vibration signal analysis of the rotary machinery, time–frequency analysis (TFA), known for analyzing the signal in the time and frequency domain simultaneously, has been accepted as a key signal processing tool. Particularly, parameterized TFA, among various TFAs, has shown great potential to investigate time–frequency features of non-stationary signals. It attracts more attention for improving time–frequency representation (TFR) with signal-dependent transform parameters. However, the parameter estimation and component separation are two problems to tackle with while using the parameterized TFA to extract time–frequency features from non-stationary vibration signal of varying-speed rotary machinery. In this paper, we propose a procedure for the parameterized TFA to analyze the non-stationary vibration signal of varying-speed rotary machinery. It basically includes four steps: initialization, estimation of transform parameter, component separation and parameterized TFA, as well as feature extraction. To demonstrate the effectiveness of the proposed method in analyzing mono- and multi-component signals, it is first used to analyze the vibration response of a laboratory rotor during a speed-up and run-down process, and then extract the instantaneous time–frequency signatures of a hydro-turbine rotor in a hydroelectric power station during a shut-down stage. In addition, the results are compared with several traditional TFAs and the proposed method outperforms others in accurate feature extraction, which is promising in applications of fault detection, system condition monitoring, parameter identification, etc.

Coning target micro‐motion feature extraction via scattering centre reconstruction

The issue of extracting micro-Doppler (mD) information of the coning target radar echoes with or without Doppler aliasing is considered using scattering centre reconstruction combined with the time-frequency analysis (TFA) method. The effectiveness of the presented method is investigated using real measured radar signal experiments. For radar echoes without Doppler aliasing, extraction of the mD information of the coning target using traditional TFA can be obtained. However, using the presented method the mD information is more precise. For radar echoes with Doppler aliasing, there are significant differences in precision between the traditional TFA and the presented methods, and the mD information is smeared using the traditional TFA. Nevertheless, the extraction of mD information can be achieved by the presented method.

A new wind turbine fault diagnosis method based on the local mean decomposition

This paper proposed a novel wind turbine fault diagnosis method based on the local mean decomposition (LMD) technology. Wind energy is a renewable power source that produces no atmospheric pollution. The condition monitoring and fault diagnosis in wind turbine system are important in avoiding serious damage. Vibration analysis is a normal and useful technology in wind turbine condition monitoring and fault diagnosis. However, the relatively slow speed of the wind turbine components set a limitation in early fault diagnosis using vibration monitoring method. The traditional time-frequency analysis techniques have some drawbacks which make them not suitable for the nonlinear, non-Gaussian signal analysis. LMD is a new iterative approach to demodulate amplitude and frequency modulated signals, which is suitable for obtaining instantaneous frequencies in wind turbine condition monitoring and fault diagnosis. The experiment analysis of the wind turbine vibration signal proves the validity and availability of the new method.

A Time-Frequency Filtering Method Based on Generalized S Transform and its Application in Machinery Fault Diagnosis

Aimed at the problem of low resolution and cross term interference of the traditional time-frequency analysis methods, a new time-frequency filtering method based on generalized S transform is proposed. The method is extended under the premise of the linearity, lossless invertibility, high time-frequency resolution of S transform. On the basis, a coefficient which is direct to the signal energy distribution is introduced. In this way, the resolution of the S transform can be adjust adaptively. Eventually, this method is applied to the time-frequency filtering. The results of simulation and faulty bearing show that the proposed methodology can achieve good effect of noise reduction, and be more suitable for the non-stationary characteristics of vibration signals.

Vibration Analysis of Rotor System by Combined Adaptive Time-Frequency Analysis and Independent Component Analysis

Traditional time-frequency analysis methods such as short-time Fourier transform (STFT) and Wigner-Ville distribution (WVD) cannot always work effectively for the complex rotor systems where the multiple faults are involved. A noise cancellation method for the rotor faults detection is proposed in this paper by combining the independent component analysis (ICA) scheme and the adaptive time-frequency analysis (ATFA) approach. In the proposed method, the raw picked data are first separated into different independent components (ICs) via the ICA according to the different vibration sources. Then the ICs are processed by the ATFA to obtain a clear vibration character for the fault diagnosis. Experiments on a rotor system with hybrid fault of the rotor imbalance and the bolt looseness are introduced to verify the feasibility and validity of the proposed scheme.

Application of Hilbert-Huang Transform Method on Fault Diagnosis for Wind Turbine Rotor

Many signals of wind turbine faults are non-stationary and have highly complex time-frequency characteristics. Traditional time-frequency analysis method, such as Windowed Fourier Transform method, has no noticeable effect in handing non-stationary signals. Hilbert-Huang Transform (HHT) is a new signal processing method for analyzing the non-stationary mechanical signals. Based on Empirical Mode Decomposition (EMD), the Intrinsic Mode Function (IMF) in HHT can reflect the intrinsic physical characteristics of original data. Moreover, it is a good way to identify the faults involving a breakdown change. First, the principles and advantages of the HHT are presented in detail in this paper. Then, three typical faults of wind turbine rotor, such as rotor imbalance, aerodynamic asymmetry due to blade surface roughness and yaw misalignment are discussed by the HHT. Last, reasonable conclusions are drawn by the comparison between this method and the Wavelet Transform (WT) method with the help of simulation fault signals. The results show the effectiveness of HHT method for diagnosing those faults of wind turbine rotor.