Short-Time/-Angle Spectral Analysis for Vibration Monitoring of Bearing Failures under Variable Speed

Vibration-condition monitoring aims to detect bearing damages of rotating machinery’s incipient failures mainly through time–frequency methods because of their efficient analysis of nonstationary signals. However, by having failures with impulse behavior, short-term events have a tendency to be diluted under variable-speed conditions, while information on frequency changes tends to be lost. Here, we introduce an approach to highlighting bearing impulsive failures by measuring short-term spectral components to deal with variable-speed vibrations. The short-term estimator employs two sliding windows: a small one that measures the instantaneous amplitude level and tracks impulsive components and a large interval that evaluates the average background amplitude. Aiming to characterize cyclo-non-stationary processes with impulsive behavior, the emphasizing high-order-based estimator based on the principle of spectral entropy is introduced. For evaluation, both visual inspection and classifier performance are assessed, contrasting the spectral-entropy estimator with the widely used spectral-kurtosis approach for dealing with impulsive signals. The validation of short-time/-angle spectral analysis performed on three datasets at variable speed showed that the proposed spectral-entropy estimator is a promising indicator for emphasizing bearing failures with impulse behavior.

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A combined generalized Warblet transform and second order synchroextracting transform for analyzing nonstationary signals of rotating machinery

Scientific Reports ◽

10.1038/s41598-021-96343-2 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Kai Wei ◽

Xuwen Jing ◽

Bingqiang Li ◽

Chao Kang ◽

Zhenhuan Dou ◽

...

Keyword(s):

Vibration Signal ◽

Rotating Machinery ◽

Second Order ◽

Variable Speed ◽

Short Time Fourier Transform ◽

Stationary Characteristic ◽

Nonstationary Signals ◽

Time Frequency ◽

Effective Technology ◽

Short Time

AbstractIn recent years, considerable attention has been paid in time–frequency analysis (TFA) methods, which is an effective technology in processing the vibration signal of rotating machinery. However, TFA techniques are not sufficient to handle signals having a strong non-stationary characteristic. To overcome this drawback, taking short-time Fourier transform as a link, a TFA methods that using the generalized Warblet transform (GWT) in combination with the second order synchroextracting transform (SSET) is proposed in this study. Firstly, based on the GWT and SSET theories, this paper proposes a method combining the two TFA methods to improve the TFA concentration, named GWT–SSET. Secondly, the method is verified numerically with single-component and multi-component signals, respectively. Quantized indicators, Rényi entropy and mean relative error (MRE) are used to analyze the concentration of TFA and accuracy of instantly frequency (IF) estimation, respectively. Finally, the proposed method is applied to analyze nonstationary signals in variable speed. The numerical and experimental results illustrate the effectiveness of the GWT–SSET method.

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Variable Speed Estimation for Wheel-Bearings with STFT and BP Neural Network

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.945-949.1112 ◽

2014 ◽

Vol 945-949 ◽

pp. 1112-1115

Author(s):

Yuan Zhou ◽

Bin Chen ◽

Bao Cheng Gao ◽

Si Jie Zhang

Keyword(s):

Neural Network ◽

Bp Neural Network ◽

Background Noise ◽

Speed Estimation ◽

Variable Speed ◽

Short Time Fourier Transform ◽

Time Frequency ◽

Novel Method ◽

Instantaneous Frequencies ◽

Short Time

For the variable speed estimation of wheel-bearings in strong background noise, a novel method with the short-time Fourier transform and BP neural network (STFT-BPNN) is proposed. In the method, it calculates the time-frequency spectrum with STFT technique. Then the instantaneous frequency is estimated by peak detection. Taking the instantaneous frequencies as the input vectors, the BP neural network is trained to fit the discrete instantaneous frequencies. The effectiveness of proposed method is demonstrated by simulation. Experimental results show that proposed method provides better performance on variable speed estimation for wheel-bearings.

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Investigation on Impact Response Feature of Railway Vehicles With Wheel Flat Fault Under Variable Speed Conditions

Journal of Vibration and Acoustics ◽

10.1115/1.4046126 ◽

2020 ◽

Vol 142 (3) ◽

Cited By ~ 5

Author(s):

Yang Jianwei ◽

Yue Zhao ◽

Jinhai Wang ◽

Yongliang Bai ◽

Chuan Liu

Keyword(s):

Fourier Transform ◽

Variable Speed ◽

Dynamic Features ◽

Modeling And Analysis ◽

Railway Vehicles ◽

Safety Issues ◽

Time Frequency ◽

Wheel Flat ◽

Short Time ◽

Response Feature

Abstract Wheel faults are the main causes of safety issues in railway vehicles. The modeling and analysis of wheel faults is crucial for determining and studying the dynamic characteristics of railway vehicles under variable speed conditions. Hence, a vehicle–track coupled dynamics model was established for analysis and calculations. The results showed that the dynamic features of the wheel with a flat fault were more pronounced under traction and braking conditions, whereas the variations in the features under coasting conditions were insignificant. In this paper, a short-time fast Fourier transform and reassignment method was used to process the signals, because the results were unclear when the time–frequency graph was processed only by short time Fourier transform, especially under braking conditions. The variation in the fault frequency under variable speed conditions was determined. Finally, statistical indicators were used to describe the vibration behaviors caused by the wheel flat fault.

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Time-Local Spectral Analysis for Non-Stationary Time Series: The S-Transform for Noisy Signals

Fluctuation and Noise Letters ◽

10.1142/s0219477503001439 ◽

2003 ◽

Vol 03 (03) ◽

pp. L357-L364 ◽

Cited By ~ 35

Author(s):

C. R. Pinnegar ◽

L. Mansinha

Keyword(s):

Time Series ◽

Spectral Analysis ◽

Wavelet Transforms ◽

Gaussian White Noise ◽

Stationary Time Series ◽

Time Frequency ◽

S Transform ◽

Undesirable Characteristic ◽

Noisy Signals ◽

Short Time

The S-transform is a method of time-local spectral analysis (also known as time-frequency analysis), a modified short-time Fourier Transform, in which the width of the analyzing window scales inversely with frequency, in analogy with continuous wavelet transforms. If the time series is non-stationary and consists of a mix of Gaussian white noise and a deterministic signal, though, this type of scaling leads to larger apparent noise amplitudes at higher frequencies. In this paper, we introduce a modified S-transform window with a different scaling function that addresses this undesirable characteristic.

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A Study of Parameters Setting of the STADZT

Acta Polytechnica ◽

10.14311/1654 ◽

2012 ◽

Vol 52 (5) ◽

Author(s):

Václav Turoň

Keyword(s):

Spectral Analysis ◽

Fourier Transform ◽

Frequency Resolution ◽

Short Time Fourier Transform ◽

Time Frequency ◽

Stationary Signals ◽

Zolotarev Polynomials ◽

Non Stationary Signal ◽

Short Time ◽

Main Influence

This paper deals with the new time-frequency Short-Time Approximated Discrete Zolotarev Transform (STADZT), which is based on symmetrical Zolotarev polynomials. Due to the special properties of these polynomials, STADZT can be used for spectral analysis of stationary and non-stationary signals with the better time and frequency resolution than the widely used Short-Time Fourier Transform (STFT). This paper describes the parameters of STADZT that have the main influence on its properties and behaviour. The selected parameters include the shape and length of the segmentation window, and the segmentation overlap. Because STADZT is very similar to STFT, the paper includes a comparison of the spectral analysis of a non-stationary signal created by STADZT and by STFT with various settings of the parameters.

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VARIABILITY OF ARTERIAL PRESSURE AT SHORT-TERM TIME INTERVALS

Issues of radio electronics ◽

10.21778/2218-5453-2019-1-72-77 ◽

2019 ◽

pp. 72-77

Author(s):

S. M. Zakharov

Keyword(s):

Blood Pressure ◽

Heart Rate ◽

Heart Rate Variability ◽

Spectral Analysis ◽

Arterial Pressure ◽

Real Time ◽

Time Interval ◽

Short Term ◽

Time Intervals ◽

Short Time

The time and spectral analysis of blood pressure signals (BP of systolic, diastolic, pulse) obtained in real time and reflecting the work of the heart at short time intervals is presented. As a time interval, a sequence of one hundred cardiac cycles was chosen. The main parameters of variability are determined. The proposed method of analysis is an analogue of heart rate variability (HRV), based on the study of RR cardiointervals. Spectral analysis of blood pressure signals shows differences in the degree of orderliness or disorder of individual frequencies or the spectrum as a whole. The presented methodology will allow to reveal further features for use in the diagnosis of various pathologies.

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Time-Frequency Representation of Inspiratory Motor Output in Anesthetized C57BL/6 Mice In Vivo

Journal of Neurophysiology ◽

10.1152/jn.00646.2004 ◽

2005 ◽

Vol 93 (3) ◽

pp. 1762-1775 ◽

Cited By ~ 15

Author(s):

Marvin H. O'Neal ◽

Evan T. Spiegel ◽

Ki H. Chon ◽

Irene C. Solomon

Keyword(s):

Spectral Analysis ◽

Time Scale ◽

Spectral Power ◽

Short Time Scale ◽

Time Varying ◽

Spectral Activity ◽

Time Frequency ◽

Inspiratory Motor ◽

Short Time ◽

Time Invariant

Inspiratory motor discharges, in addition to long-time-scale rhythmic oscillatory bursting, exhibit short-time-scale rhythmic oscillations that have been identified, and subsequently characterized, using power spectral analyses [predominantly fast-Fourier transforms (FFT)]. These analyses assume that the signal being analyzed is stationary; however, this is not the case for most biological signals, which exhibit varying degrees of nonstationarity. To overcome this limitation, time-frequency methods, which provide not only the frequency content but also information regarding the timing of these fast rhythmic oscillations (i.e., dynamics of spectral activity), should be used. Thus this study was performed to investigate the dynamic or time-varying features of spectral activity in inspiratory motor output. Both conventional time-invariant and time-frequency (time-varying) spectral analysis methods were performed on recordings of diaphragm EMG, phrenic nerve, and hypoglossal nerve discharges obtained from spontaneously breathing urethan-anesthetized adult C57BL/6 mice. Conventional time-invariant spectral analysis using a FFT algorithm revealed three dominant peaks in the power spectrum, which were located at 1) 20–46, 2) 83–149, and 3) 177–227 Hz. Time-frequency spectral analysis using a generalized time-frequency representation (TFR) with the smoothed pseudo-Wigner-Ville distribution (SPWD) kernel confirmed the general location of these spectral peaks, identified additional spectral peaks within the frequency ranges described above, and revealed a time-dependent expression of spectral activity within the inspiratory burst for each of the frequency ranges. Furthermore, this method revealed that 1) little or no spectral activity occurs during the initial portion of the inspiratory burst in any of the frequency ranges identified, 2) transient oscillations in the magnitude of spectral power exist where spectral activity occurs, and 3) total spectral power exhibits an augmenting pattern over the course of the inspiratory burst. These data, which provide the first description of spectral content in inspiratory motor discharges in adult mice, show that both time-invariant and time-varying spectral analysis methods are capable of identifying short-time-scale rhythmic oscillations in inspiratory motor discharge (as expected); however, the dynamic (i.e., timing) features of this oscillatory activity can only be obtained using the time-frequency method. We suggest that time-frequency methods, such as the SPWD, should be used in future studies examining short-time-scale (fast) rhythmic oscillations in inspiratory motor discharges, because additional insight into the neural control mechanisms that participate in inspiratory-phase neuronal and motoneuronal synchronization may be obtained.

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Enhancement of Maternal ECG Using Short-Term Fourier Transform for Foetal Electrocardiogram Extraction

International Journal of Advanced Research in Science, Communication and Technology ◽

10.48175/ijarsct-2312 ◽

2021 ◽

pp. 84-91

Author(s):

Prof. M. Senthil Vadivu ◽

Saranya H ◽

Vijay Kumar K S

Keyword(s):

Fourier Transform ◽

Wave Structure ◽

Well Being ◽

Short Term ◽

Morphological Examination ◽

Time Frequency ◽

Non Invasive ◽

Frequency Representation ◽

Short Time

The objective of the project is to improve maternal abdomen recording for better prediction of foetal Electrocardiogram (FECG). One of the most difficult tasks in observing foetal well-being is obtaining a clean foetal Electrocardiogram (FECG) using non-invasive abdominal recordings. The foetal graph's low signal quality, on the other hand, makes morphological examination of its wave structure in clinical follow-up difficult. The signal contains precise information that can help doctors to monitor fetal health during pregnancy and labor. The abdominal signal is normalized and separated in the pre-processing stage for wave shape analysis in clinical follow-up. The Kaiser window is used for spectral analysis and segmenting the signal. The two-dimensional (2D) time-frequency representation is obtained by short-time Fourier transform (STFT). The STFT enhances the abdominal recordings of maternal Electrocardiogram (MECG) for efficient separation of foetal electrocardiogram (FECG) to monitor the foetus well-being.

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Constrained least-squares spectral analysis: Application to seismic data

Geophysics ◽

10.1190/geo2011-0210.1 ◽

2012 ◽

Vol 77 (5) ◽

pp. V143-V167 ◽

Cited By ~ 53

Author(s):

Charles I. Puryear ◽

Oleg N. Portniaguine ◽

Carlos M. Cobos ◽

John P. Castagna

Keyword(s):

Spectral Analysis ◽

Fourier Transform ◽

Wavelet Transform ◽

Seismic Data ◽

Continuous Wavelet ◽

Window Length ◽

Short Time Fourier Transform ◽

Constrained Least Squares ◽

Time Frequency ◽

Short Time

An inversion-based algorithm for computing the time-frequency analysis of reflection seismograms using constrained least-squares spectral analysis is formulated and applied to modeled seismic waveforms and real seismic data. The Fourier series coefficients are computed as a function of time directly by inverting a basis of truncated sinusoidal kernels for a moving time window. The method resulted in spectra that have reduced window smearing for a given window length relative to the discrete Fourier transform irrespective of window shape, and a time-frequency analysis with a combination of time and frequency resolution that is superior to the short time Fourier transform and the continuous wavelet transform. The reduction in spectral smoothing enables better determination of the spectral characteristics of interfering reflections within a short window. The degree of resolution improvement relative to the short time Fourier transform increases as window length decreases. As compared with the continuous wavelet transform, the method has greatly improved temporal resolution, particularly at low frequencies.

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The Use of Time-Frequency Moments as Inputs of LSTM Network for ECG Signal Classification

Electronics ◽

10.3390/electronics9091452 ◽

2020 ◽

Vol 9 (9) ◽

pp. 1452

Author(s):

Grzegorz Kłosowski ◽

Tomasz Rymarczyk ◽

Dariusz Wójcik ◽

Stanisław Skowron ◽

Tomasz Cieplak ◽

...

Keyword(s):

Instantaneous Frequency ◽

Short Term Memory ◽

Signal Classification ◽

Ecg Signal ◽

Spectral Entropy ◽

Short Term ◽

Data Set ◽

Time Frequency ◽

Frequency Moments ◽

Lstm Network

This paper refers to the method of using the deep neural long-short-term memory (LSTM) network for the problem of electrocardiogram (ECG) signal classification. ECG signals contain a lot of subtle information analyzed by doctors to determine the type of heart dysfunction. Due to the large number of signal features that are difficult to identify, raw ECG data is usually not suitable for use in machine learning. The article presents how to transform individual ECG time series into spectral images for which two characteristics are determined, which are instantaneous frequency and spectral entropy. Feature extraction consists of converting the ECG signal into a series of spectral images using short-term Fourier transformation. Then the images were converted using Fourier transform again to two signals, which includes instantaneous frequency and spectral entropy. The data set transformed in this way was used to train the LSTM network. During the experiments, the LSTM networks were trained for both raw and spectrally transformed data. Then, the LSTM networks trained in this way were compared with each other. The obtained results prove that the transformation of input signals into images can be an effective method of improving the quality of classifiers based on deep learning.

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