Time-frequency Distribution Method Research Articles

Short-time adaptive compact kernel distribution for fault diagnosis under variable working condition bearing

Time-frequency distribution (TFD) methods are extensively employed in the diagnosis of bearings operating under variable working conditions. However, these methods often face high computational complexity, limited time-frequency resolution, and cross-terms. To address these issues, this paper presents a new approach called Short-Time Adaptive Compact Kernel Distribution (STACKD). Based on the characteristics of the vibration signals, we designed Chirp-modulated Gaussian Window and used them to segment the overall signal into small segments. Then, we used a two-step Bayesian optimization method to obtain adaptive compact kernel distributions (ACKD) for these small segments of the signal. Finally, we recombined the ACKD of these small segments into a global STACKD. Results from simulations and experiments demonstrate that STACKD offers improved robustness against interference signals, lower computational complexity, and higher time-frequency resolution without cross-term effects. This method is tailored for diagnosing rolling bearings under variable working conditions, providing enhanced visualization of diagnostic processes with superior time-frequency resolution.

Beam-forming of broadband QFM signals using generalized time–frequency transform

ABSTRACTDetection and localisation of contacts using sensor array play a significant role in the area of array signal processing. In this paper, a new beam-forming analysis for broad-banded quadratic frequency modulated (QFM) signals using generalised time–frequency transform (GTFT) is presented by extending the conventional fractional Fourier transform (FrFT). As FrFT is constrained to the analysis of linear chirps, detection using GTFT is found to be the appropriate selection for higher-order chirps with the suitable choice of the kernel. The parameters of the QFM signal is extracted using the polynomial chirplet transform time–frequency distribution method. Subsequently, the direction of arrival (DoA) estimation algorithms viz. conventional beam-former (CBF), minimum variance distortionless response (MVDR), multiple signal classification (MUSIC) and minimum norm (MN) are re-cast using the quadratic steering vector derived for QFM chirps and hence renamed as GTFT-CBF, GTFT-MVDR, GTFT-MUSIC and GTFT-MN, respectively. The efficacy of the algorithm is validated through various signals including practical sonar array data. It is seen from the theoretical analysis as well as simulations that GTFT-MUSIC excels other DoA (bearing) estimation techniques. The GTFT analysis on back propagated signals using sonar array aided in effective underwater channel modelling.

Applications of fractional lower order time-frequency representation to machine bearing fault diagnosis

The machinery fault signal is a typical non-Gaussian and non-stationary process. The fault signal can be described by S U+03B1 S distribution model because of the presence of impulses. Time-frequency distribution is a useful tool to extract helpful information of the machinery fault signal. Various fractional lower order U+0028 FLO U+0029 time-frequency distribution methods have been proposed based on fractional lower order statistics, which include fractional lower order short time Fourier transform U+0028 FLO-STFT U+0029, fractional lower order Wigner-Ville distributions U+0028 FLO-WVDs U+0029, fractional lower order Cohen class time-frequency distributions U+0028 FLO-CDs U+0029, fractional lower order adaptive kernel time-frequency distributions U+0028 FLO-AKDs U+0029 and adaptive fractional lower order time-frequency auto-regressive moving average U+0028 FLO-TFARMA U+0029 model time-frequency representation method. The methods and the exiting methods based on second order statistics in S U+03B1 S distribution environments are compared, simulation results show that the new methods have better performances than the existing methods. The advantages and disadvantages of the improved time-frequency methods have been summarized. Last, the new methods are applied to analyze the outer race fault signals, the results illustrate their good performances.

Analysis of Power Quality Signals Using an Adaptive Time-Frequency Distribution

Spikes frequently occur in power quality (PQ) disturbance signals due to various causes such as switching of the inductive loads and the energization of the capacitor bank. Such signals are difficult to analyze using existing time-frequency (TF) methods as these signals have two orthogonal directions in a TF plane. To address this issue, this paper proposes an adaptive TF distribution (TFD) for the analysis of PQ signals. In the proposed adaptive method, the smoothing kernel’s direction is locally adapted based on the direction of energy in the joint TF domain, and hence an improved TF resolution can be obtained. Furthermore, the performance of the proposed adaptive technique in analyzing electrical PQ is thoroughly studied for both synthetic and real world electrical power signals with the help of extensive simulations. The simulation results (specially for empirical data) indicate that the adaptive TFD method achieves high energy concentration in the TF domain for signals composed of tones and spikes. Moreover, the local adaptation of the smoothing kernel in the adaptive TFD enables the extraction of TF signature of spikes from TF images, which further helps in measuring the energy of spikes in a given signal. This new measure can be used to both detect the spikes as well as to quantify the extent of distortion caused by the spikes in a given signal.

Analysis about Effect of Hollow on Time-Frequency Characteristic of Surface Vibration Signal

In blasting excavation of shallow tunnel, the surface vibration of excavated tunnel can be amplified due to effect of hollow. This effect is an important factor for safety of surface buildings. Based on the measured data of one tunnel excavation project, combining wavelet analysis and AOK time-frequency distribution method, the surface vibration signals in front and rear position of working face are processed into different frequency bands. Taking PPV, dominant frequency, d7 (7.8125-15.625 Hz) band energy ratio and d7 (7.8125-15.625 Hz) band energy duration as indexes, the effect of hollow on time-frequency characteristics of surface vibration signal is studied in this article. The results show that, affected by the hollow in excavated region, the PPV and dominant frequency increase, and the d7 (7.8125-15.625 Hz) band energy shows fluctuant ratio of total energy and an increase of band energy duration. The results show that the hollow influence on the frequency characteristics of the surface vibration signals comprehensively, and also provide an analytical basis for anti-vibration and vibration reduction study from the angle of energy.

A Cascaded Approach for Correcting Ionospheric Contamination with Large Amplitude in HF Skywave Radars

Ionospheric phase perturbation with large amplitude causes broadening sea clutter's Bragg peaks to overlap each other; the performance of traditional decontamination methods about filtering Bragg peak is poor, which greatly limits the detection performance of HF skywave radars. In view of the ionospheric phase perturbation with large amplitude, this paper proposes a cascaded approach based on improved S-method to correct the ionospheric phase contamination. This approach consists of two correction steps. At the first step, a time-frequency distribution method based on improved S-method is adopted and an optimal detection method is designed to obtain a coarse ionospheric modulation estimation from the time-frequency distribution. At the second correction step, based on the phase gradient algorithm (PGA) is exploited to eliminate the residual contamination. Finally, use the measured data to verify the effectiveness of the method. Simulation results show the time-frequency resolution of this method is high and is not affected by the interference of the cross term; ionospheric phase perturbation with large amplitude can be corrected in low signal-to-noise (SNR); such a cascade correction method has a good effect.

Time-Frequency Processing of Nonstationary Signals: Advanced TFD Design to Aid Diagnosis with Highlights from Medical Applications

This article presents a methodical approach for improving quadratic time-frequency distribution (QTFD) methods by designing adapted time-frequency (T-F) kernels for diagnosis applications with illustrations on three selected medical applications using the electroencephalogram (EEG), heart rate variability (HRV), and pathological speech signals. Manual and visual inspection of such nonstationary multicomponent signals is laborious especially for long recordings, requiring skilled interpreters with possible subjective judgments and errors. Automated assessment is therefore preferred for objective diagnosis by using T-F distributions (TFDs) to extract more information. This requires designing advanced high-resolution TFDs for automating classification and interpretation. As QTFD methods are general and their coverage is very broad, this article concentrates on methodologies using only a few selected medical problems studied by the authors.

Multicomponent Signal Analysis Based on Polynomial Chirplet Transform

Chirplet transform (CT) is effective in characterization of instantaneous frequency (IF) for monocomponent linear-frequency-modulated signal. However, the CT is not suitable to analyze multicomponent signal with nonlinear-frequency-modulated component. In this paper, a time–frequency fusion technique based on polynomial CT (PCT) (TFPCT) is proposed to characterize the time–frequency structure of such signals. The TFPCT relies on the fact that the PCT is able to concentrate the energy closely along the IF of the monocomponent signal in time–frequency distribution (TFD). For multicomponent signal, the TFPCT first estimates the proper coefficients with respect to individual component and, second, produces a series of the TFD using the PCT. Each TFD has better energy concentration along the IF of one component. Then, in order to reduce the interference of unwanted component and preserve the component of interest, each TFD is filtered and grouped as an image. At last, the TFPCT combines these TFDs to be an eventual fused TFD, which has the energy concentrating closely along the IF of all components. Comparison with several conventional TFD methods on both numerical multicomponent signal and bat echolocation signal validates the potential and the effectiveness of the proposed method.

Time-frequency analysis of nonlinear and non-stationary weak signals of corona discharge

It is very useful to study the signals radiated from corona discharges for the purposes of high-voltage line monitoring. Time-frequency analysis can clearly reveal the time-varying spectrum characteristics of such signals, which is very useful for analyzing and processing the non-linear and non-stationary weak signals, such as the signals radiated from corona discharges. Several time-frequency analysis methods, such as the Short-Time Fourier Transform (STFT), Wigner-Ville distribution and the Hilbert-Huang Transform (HHT) and so on, are used in this paper. The simulation data with the same and different amplitudes are comparatively analyzed by these time-frequency distribution methods. It can be concluded that the time-frequency analysis method based on HHT is more efficient to identify and suitable for the non-linear and non-stationary weak signals.

Seismic spectral decomposition using deconvolutive short-time Fourier transform spectrogram

The spectral decomposition technique plays an important role in reservoir characterization, for which the time-frequency distribution method is essential. The deconvolutive short-time Fourier transform (DSTFT) method achieves a superior time-frequency resolution by applying a 2D deconvolution operation on the short-time Fourier transform (STFT) spectrogram. For seismic spectral decomposition, to reduce the computation burden caused by the 2D deconvolution operation in the DSTFT, the 2D STFT spectrogram is cropped into a smaller area, which includes the positive frequencies fallen in the seismic signal bandwidth only. In general, because the low-frequency components of a seismic signal are dominant, the removal of the negative frequencies may introduce a sharp edge at the zero frequency, which would produce artifacts in the DSTFT spectrogram. To avoid this problem, we used the analytic signal, which is obtained by applying the Hilbert transform on the original real seismic signal, to calculate the STFT spectrogram in our method. Synthetic and real seismic data examples were evaluated to demonstrate the performance of the proposed method.

Joint space‐time–frequency method based on fractional Fourier transform to estimate moving target parameters for multistatic synthetic aperture radar

In practice, the configuration of spaceborne multistatic synthetic aperture radar (MSAR) is generally three-dimensional (3D) stereo geometry, under which condition most current algorithms of motion parameter estimation are invalid. In this study, a joint space-time-frequency method is presented to estimate motion parameters of ground moving target for MSAR of 3D geometry. First, the array expression for azimuth echo named extended space-time model (ESTM) is derived; then on the basis of ESTM, a spatial time-frequency distribution method based on fractional Fourier transform algorithm is derived; finally the performance of the presented method is analysed, and the advantages comparing with velocity synthetic aperture radar are discussed via some computer simulations. The work provides a feasible method of multi-channel processing for the 3D MSAR.

Marine Diesel Engine Fault Diagnosis by Using an Improved Hilbert Spectrum

Vibration signal analysis is a useful method for recognizing the pattern of a machine's working condition. However, it is difficult to recognize nonstationary and nonlinear vibration signal patterns satisfactorily with the traditional Fourier spectrum method. This paper introduces a novel time-frequency distribution method: an improved Hilbert spectrum (HS) for nonstationary vibration signal analysis, that is, applying a wavelet packet de-noise method as a preprocess of the HS. The HS is developed according to instantaneous frequency analysis by using a new kind of signal analysis method called empirical mode decomposition (EMD), which is highly accurate in analyzing various nonstationary and nonlinear signals. Due to a self-adaptive decomposition process, noise has a great effect on the accuracy of the EMD process and the corresponding HS. This has limited the application of the HS on real vibration analysis. In this study, a wavelet packet de-noising technique is employed as a preprocessing to improve the signal-to-noise ratio and the accuracy of the HS. Experimental data of a marine diesel fuel injection system are used to evaluate the improved methodology for system pattern recognition and fault diagnosis.

Smoothed pseudo Wigner–Ville distribution as an alternative to Fourier transform in rats

Techniques for examining signals in the time and frequency domains are well-established tools. These tools have their limitations; they tell us in a broad sense where the signal component exists in the frequency domain, but they do not tell us how its frequency characteristics change over time. The time-frequency has become a powerful alternative for the analysis of signals. Among various time-frequency distribution methods, one of the most studied is the Wigner–Ville distribution. The aim of this study was to evaluate in conscious rats smoothed pseudo Wigner–Ville distribution (SPWVD) as an alternative to the fast Fourier transform (FFT) in RR intervals and in systolic blood pressure (SBP), before and after adrenergic and cholinergic receptor blockade. Fourteen Wistar rats equipped with telemetry probe were evaluated: (1) under control conditions; (2) after injection of saline (100 μl kg −1 i.v.); (3) after atenolol (1 mg kg −1 i.v.); (4) after atropine methyl nitrate (0.5 mg kg −1 i.v.); and (5) after phentolamine (5 mg kg −1 i.v.). FFT and SPWVD were applied to RR intervals and SBP time series. Six-minute time series of RR intervals, systolic and diastolic pressures were analysed. The bias and distribution of differences between FFT and SPWVD methods in RR intervals under base conditions were 1.4±0.4% ( r 2=0.94; P<0.01) in LF/LF+HF; 1.5±0.5% ( r 2=0.92; P<0.01) in HF/LF+HF and 4.8±1.9% ( r 2=0.92; P<0.01) in LF/HF. In SBP the bias and distribution were 1.5±0.8% ( r 2=0.90; P<0.05) in LF/LF+HF and 1.7±0.6% ( r 2=0.92; P<0.01) in HF/LF+HF. In the frequency domain analysis of RR intervals and SBP there was no difference between FFT and SPWVD. The agreement between the methods demonstrates that in stationary signals both methods can be used interchangeably. SPWVD may be an interesting tool to analyse biomedical signals; it provides a good resolution at high frequency and a good frequency resolution at low frequencies independently if signals remain stationary.

Time-frequency distribution methods for the analysis of click-evoked otoacoustic emissions

Click-evoked otoacoustic emissions (CEOAEs) are time-varying signals with a clear frequency dispersion along with the time axis. Analysis of CEOAEs is of considerable interest due to their close relation with cochlear mechanisms. The particular structure of CEOAEs requires a time-frequency method with both a satisfactory time and frequency resolution. In this paper, several basic time-frequency distribution methods are considered and compared on the basis of both simulated signals and real CEOAEs. Results from simulations and real CEOAEs revealed that the wavelet approach is highly suitable for the analysis of such signals. Some examples of the application of the Wavelet Transform to CEOAEs are provided here. Applications range from the extraction of normative data from adult OAEs to the extraction of quantitative parameters for clinical purposes.

Performance analysis of instantaneous frequency-based interference excision techniques in spread spectrum communications

Jammers characterized by their instantaneous frequencies can be effectively mitigated in direct sequence spread spectrum communications by using open-loop adaptive excision filters. The primary requirement for these filters is that they must possess a notch in tune with the jammer instantaneous frequency (IF) to annihilate the interference power at every time sample. The interference time-varying frequency can be obtained using existing IF estimators, including quadratic time-frequency distribution methods. Without focusing on any specific estimator, we develop expressions for the receiver performance using a general class of multiple-zero FIR excision filters and show the dependence of the bit error rate (BER) on the filter order and its group delay. The effect of inaccuracies in the jammer instantaneous frequency information on the receiver performance is considered and evaluated as a function of the filter notch bandwidth. The latter is defined by the filter zero multiplicity, which is shown to be an important factor in the analysis of the correlator signal-to-noise ratio (SNR).

Time-frequency distribution of evoked otoacoustic emissions.

Otoacoustic emissions (OAE) are non-stationary signals that vary in time depending on the characteristics of the stimulus. Traditional spectral analysis using Fourier methods ignores the effects of time and can miss important temporal information. Therefore, a better form of spectral analysis requires the use of time-frequency distribution methods. Traditionally, short time Fourier transforms (STFT), commonly known as spectrograms, are used to provide such time-frequency representations. STFT however, suffer from poor resolution and do not provide enough detail about the characteristics of the emissions. In this study, recently developed time-frequency distributions, the Wigner Distribution (WD) and the Choi-Williams Distribution (CWD) are investigated to provide high resolution representations of transient evoked OAEs. Although WD has excellent properties for time-frequency analysis, it suffers from cross-term artefacts generated when multiple sinusoids are present. CWD provides a solution to this problem at the expense of poor time and frequency support. In this study, we use both distributions to estimate the cross-products and provide a relatively artefact-free time-frequency distribution of OAEs. This method is applied to both click and tone burst evoked OAE and shows a more detailed time-frequency representation with as many crests and valleys as different latencies.