Zoom Synchrosqueezing Transform for Instantaneous Speed Estimation of High Speed Spindle

2016 ◽  
Vol 836-837 ◽  
pp. 310-317 ◽  
Author(s):  
Song Tao Xi ◽  
Hong Rui Cao ◽  
Xue Feng Chen
Keyword(s):  
Frequency Shift ◽  
High Speed ◽  
Frequency Component ◽  
Frequency Region ◽  
Frequency Resolution ◽  
Good Time ◽  
Heisenberg Uncertainty Principle ◽  
Time Frequency ◽  
Synchrosqueezing Transform ◽  
Instantaneous Speed

Instantaneous speed (IS) is of great significance of fault diagnosis and condition monitoring of the high speed spindle. In this paper, we propose a novel zoom synchrosqueezing transform (ZST) for IS estimation of the high speed spindle. Due to the limitation of the Heisenberg uncertainty principle, the conventional time-frequency analysis (TFA) methods cannot provide both good time and frequency resolution at the whole frequency region. Moreover, in most cases, the interested frequency component of a signal only locates in a narrow frequency region, so there is no need to analyze the signal in the whole frequency region. Different from conventional TFA methods, the proposed method arms to analyze the signal in a specific frequency region with both excellent time and frequency resolution so as to obtain accurate instantaneous frequency (IF) estimation results. The proposed ZST is an improvement of the synchrosqueezing wavelet transform (SWT) and consists of two steps, i.e., the frequency-shift operation and the partial zoom synchrosqueezing operation. The frequency-shift operation is to shift the interested frequency component from the lower frequency region to the higher frequency to obtain better time resolution. The partial zoom synchrosqueezing operation is conducted to analyze the shifted signal with excellent frequency resolution in a considered frequency region. Compared with SWT, the proposed method can provide satisfactory energy concentrated time-frequency representation (TFR) and accurate IF estimation results. Additionally, an application of the proposed ZST to the IS fluctuation estimation of a motorized spindle was conducted, and the result showed that the IS estimated by the proposed ZST can be used to detect the quality of the finished workpiece surface.

Sparse time-frequency representation based on multiwindow discrete Gabor transform

2018 ◽  
Vol 16 (05) ◽  
pp. 1850041
Author(s):  
Rui Li ◽  
Jian Zhou
Keyword(s):  
Frequency Spectrum ◽  
Frequency Resolution ◽  
Good Time ◽  
Gabor Transform ◽  
Analysis Tool ◽  
Sparse Regularization ◽  
Heisenberg Uncertainty Principle ◽  
Arithmetic Average ◽  
Time Frequency ◽  
Frequency Representation

The multiwindow discrete Gabor transform (M-DGT) is an important time-frequency analysis tool in many applications. In this paper, sparse time-frequency representation (TFR) based on M-DGT with sparse regularization theory is presented. The M-DGT is first formulated as a convex constrained optimization model by minimizing the objective function with a mixed [Formula: see text]–[Formula: see text] norm of the M-DGT coefficients. Then, an iterative algorithm based on the split Bergman method is utilized to compute the sparse Gabor time-frequency spectrum of the analyzed signal. According to the Heisenberg uncertainty principle, using an analysis window with good time resolution in M-DGT will lead to the Gabor TFR with high frequency resolution and vice versa. To obtain the sparse TFR with good time-frequency resolution (or concentration), the sparse spectra of M-DGT can be combined by the arithmetic average or the geometric average. Numerical experiments clearly show that the proposed method is an effective and powerful tool for analyzing nonstationary signals, by which the high time-frequency concentration (or resolution) of the Gabor time-frequency spectrum can be obtained as compared to traditional M-DGT.

High-resolution characterization of geologic structures using the synchrosqueezing transform

2017 ◽  
Vol 5 (1) ◽  
pp. T75-T85 ◽  
Author(s):  
Naihao Liu ◽  
Jinghuai Gao ◽  
Zhuosheng Zhang ◽  
Xiudi Jiang ◽  
Qi Lv
Keyword(s):  
High Resolution ◽  
Frequency Analysis ◽  
Seismic Data ◽  
Proper Time ◽  
Frequency Resolution ◽  
Heisenberg Uncertainty Principle ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Basic Wavelet ◽  
Synchrosqueezing Transform

The main factors responsible for the nonstationarity of seismic signals are the nonstationarity of the geologic structural sequences and the complex pore structure. Time-frequency analysis can identify various frequency components of seismic data and reveal their time-variant features. Choosing a proper time-frequency decomposition algorithm is the key to analyze these nonstationarity signals and reveal the geologic information contained in the seismic data. According to the Heisenberg uncertainty principle, we cannot obtain the finest time location and the best frequency resolution at the same time, which results in the trade-off between the time resolution and the frequency resolution. For instance, the most commonly used approach is the short-time Fourier transform, in which the predefined window length limits the flexibility to adjust the temporal and spectral resolution at the same time. The continuous wavelet transform (CWT) produces an “adjustable” resolution of time-frequency map using dilation and translation of a basic wavelet. However, the CWT has limitations in dealing with fast varying instantaneous frequencies. The synchrosqueezing transform (SST) can improve the quality and readability of the time-frequency representation. We have developed a high-resolution and effective time-frequency analysis method to characterize geologic bodies contained in the seismic data. We named this method the SST, and the basic wavelet is the three-parameter wavelet (SST-TPW). The TPW is superior in time-frequency resolution than those of the Morlet and Ricker wavelets. Experiments on synthetic and field data determined its validity and effectiveness, which can be used in assisting in oil/gas reservoir identification.

A Frequency-Shift Synchrosqueezing Method for Instantaneous Speed Estimation of Rotating Machinery

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Songtao Xi ◽  
Hongrui Cao ◽  
Xuefeng Chen ◽  
Xingwu Zhang ◽  
Xiaoliang Jin
Keyword(s):  
Frequency Shift ◽  
Viterbi Algorithm ◽  
Vibration Signal ◽  
Rotating Machinery ◽  
Vibration Measurement ◽  
Frequency Resolution ◽  
Estimation Methods ◽  
Real Time Control ◽  
Time Frequency ◽  
Instantaneous Speed

Instantaneous speed (IS) measurement is crucial in condition monitoring and real-time control of rotating machinery. Since the direct measurement of instantaneous rotating speed is not always available, the vibration measurement has been used for indirect estimation methods. In this paper, a novel indirect method is proposed to estimate the IS of rotating machinery. First, a frequency-shift synchrosqueezing transform is proposed to process the vibration signal to obtain the time–frequency (TF) representation. Second, the Viterbi algorithm is employed to extract the shifted instantaneous frequency (IF) from the TF representation. Finally, the extracted IF is used to recover the IF of the measured vibration signal. The IS of rotating machinery can be calculated from the estimated IF. The proposed method is validated with both numerical simulations and experiments. The results show that the proposed method could provide much higher frequency resolution, better TF concentration results, and more accurate IF estimation of the considered signal compared with the synchrosqueezing method. Furthermore, the proposed method was confirmed to be less sensitive to noise, especially for high-frequency components.

scholarly journals Analysis of time-varying signals using continuous wavelet and synchrosqueezed transforms

2018 ◽  
Vol 376 (2126) ◽  
pp. 20170254 ◽  
Author(s):  
Jean Baptiste Tary ◽  
Roberto Henry Herrera ◽  
Mirko van der Baan
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Seismic Signal ◽  
American Football ◽  
Frequency Resolution ◽  
Time Varying ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Frequency Information ◽  
Synchrosqueezing Transform

The continuous wavelet transform (CWT) has played a key role in the analysis of time-frequency information in many different fields of science and engineering. It builds on the classical short-time Fourier transform but allows for variable time-frequency resolution. Yet, interpretation of the resulting spectral decomposition is often hindered by smearing and leakage of individual frequency components. Computation of instantaneous frequencies, combined by frequency reassignment, may then be applied by highly localized techniques, such as the synchrosqueezing transform and ConceFT, in order to reduce these effects. In this paper, we present the synchrosqueezing transform together with the CWT and illustrate their relative performances using four signals from different fields, namely the LIGO signal showing gravitational waves, a ‘FanQuake’ signal displaying observed vibrations during an American football game, a seismic recording of the M w 8.2 Chiapas earthquake, Mexico, of 8 September 2017, followed by the Irma hurricane, and a volcano-seismic signal recorded at the Popocatépetl volcano showing a tremor followed by harmonic resonances. These examples illustrate how high-localization techniques improve analysis of the time-frequency information of time-varying signals. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

The Time-Frequency Resolution of Short Time Fourier Transform Based on Multi-Window Functions

2011 ◽  
Vol 214 ◽  
pp. 122-127 ◽  
Author(s):  
Li Hua Wang ◽  
Qi Dong Zhang ◽  
Yong Hong Zhang ◽  
Kai Zhang
Keyword(s):  
Fourier Transform ◽  
Time Resolution ◽  
High Performance ◽  
Frequency Resolution ◽  
Good Time ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Window Functions ◽  
Short Time ◽  
Good Time Resolution

The short-time Fourier transform has the disadvantage that is does not localize time and frequency phenomena very well. Instead the time-frequency information is scattered which depends on the length of the window. It is not possible to have arbitrarily good time resolution simultaneously with good frequency resolution. In this paper, a new method that uses the short-time Fourier transform based on multi-window functions to enhance time-frequency resolution of signals has been proposed. Simulation and experimental results present the high performance of the proposed method.

scholarly journals Multi-Band Frequency Window for Time-Frequency Fault Diagnosis of Induction Machines

2019 ◽  
Author(s):  
Jordi Burriel-Valencia ◽  
Ruben Puche-Panadero ◽  
Javier Martinez-Roman ◽  
Angel Sapena-Bano ◽  
Martin Riera-Guasp ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Time Window ◽  
Early Stage ◽  
Induction Machines ◽  
Frequency Domain Analysis ◽  
Frequency Resolution ◽  
Good Time ◽  
Band Frequency ◽  
Time Frequency ◽  
Multi Band

Induction machines drive many industrial processes, and their unexpected failure can cause heavy production losses. The analysis of the current spectrum can identify online the characteristic fault signatures at an early stage, avoiding unexpected breakdowns. Nevertheless, frequency domain analysis requires stable working conditions, which is not the case for wind generators, motors driving varying loads, etc. In these cases an analysis in the time-frequency domain -such as a spectrogram- is required for detecting faults signatures. The spectrogram is built using the short frequency Fourier transform, but its resolution depends critically on the time window used to generate it: short windows provide good time resolution, but poor frequency resolution, just the opposite than long windows. Therefore, the window must be adapted at each time to the shape of the expected fault harmonics, by highly skilled maintenance personnel. In this paper, this problem is solved with the design of a new multi-band window, which generates simultaneously many different narrow-band current spectrograms, and combines them into a single, high resolution one, without the need of manual adjustments. The proposed method is validated with the diagnosis of bar breakages during the start-up of a commercial induction motor.

Generalized wavelet-based synchrosqueezing transform: Algorithm and applications

2020 ◽  
Vol 19 (6) ◽  
pp. 2051-2062
Author(s):  
Xiaotong Tu ◽  
Yue Hu ◽  
Saqlain Abbas ◽  
Fucai Li
Keyword(s):  
Frequency Estimation ◽  
Research Work ◽  
Frequency Resolution ◽  
Noise Robustness ◽  
Practical Implementation ◽  
Instantaneous Frequency Estimation ◽  
Mapping Procedure ◽  
Time Frequency ◽  
Synthetic Signal ◽  
Synchrosqueezing Transform

Time–frequency analysis is recognized as an efficient tool to characterize the time-varying feature from the oscillatory signal by transforming it into an identifiable form. Some traditional time–frequency transforms are subjected to poor time–frequency resolution or do not allow for mode reconstruction. As a postprocessing method, the synchrosqueezing transform has been utilized to tackle these problems. In this framework, a new method termed as generalized wavelet-based synchrosqueezing transform is developed in the current research work to deal with a strong modulated signal. The proposed method is capable to theoretically generate unbiased instantaneous frequency estimation at any order by defining a higher-order Taylor expansion signal model. The signal mapping procedure is also embedded in the algorithm to further improve the anti-noise robustness of the presented method. Numerical investigation of synthetic signal verifies the feasibility of the generalized wavelet-based synchrosqueezing transform as compared to previously developed approaches. Moreover, the practical implementation of the proposed method for the detection of the rotor rub-impact fault demonstrates that the generalized wavelet-based synchrosqueezing transform is qualified for machine fault diagnosis under the variable speed conditions.

Adaptive Signal Analysis Based on Radial Parabola Kernel

2007 ◽  
Vol 10-12 ◽  
pp. 737-741 ◽  
Author(s):  
S.C. Wang ◽  
J. Han ◽  
Jian Feng Li ◽  
Zhi Nong Li
Keyword(s):  
Kernel Functions ◽  
Frequency Resolution ◽  
Good Time ◽  
Signal Distribution ◽  
Time Frequency ◽  
Frequency Representation ◽  
Fixed Kernel ◽  
Limited Class ◽  
Adaptive Kernel ◽  
Adaptive Signal

Because of the deficiency of fixed kernel in bilinear time-frequency distribution (TFD), i.e. for each mapping, the resulting time-frequency representation is satisfactory only for a limited class of signals, a new adaptive kernel function named the radial parabola kernel (RPK), is proposed. The RPK can adopt the optimizing method to filter cross-terms adaptively according to the signal distribution, obtain good time-frequency resolution, and offer improved TFD for a large class of signals. Compared with traditional fixed -kernel functions, such as Wigner-Ville distribution, Choi-Willams distribution and Cone-kernel distribution, the superiority of the RPK function is obvious. At last, the RPK function is applied to the analysis of vibration signals of bearing, and the result proves the RPK function an effective method in analyzing signals.

Gabor time–frequency representation for transient signals using multiwindow discrete Gabor transform

2017 ◽  
Vol 15 (04) ◽  
pp. 1750036 ◽  
Author(s):  
Xian-He Gao ◽  
Liang Tao
Keyword(s):  
Frequency Spectrum ◽  
Time Resolution ◽  
Time Domain ◽  
Frequency Resolution ◽  
Gabor Transform ◽  
Transient Signals ◽  
Heisenberg Uncertainty Principle ◽  
Time Frequency ◽  
Frequency Representation ◽  
Analysis Window

Multiwindow discrete Gabor transform (M-DGT) is applied to present the Gabor time–frequency representation for transient signals (exponentially damped sinusoidal signals) with high time–frequency resolution. Due to the limitation of the constrained time–frequency localization governed by the Heisenberg uncertainty principle, using a wider analysis window in time domain will lead to the Gabor time–frequency spectrum (or representation) with higher frequency resolution but poor time resolution for the transient signals, and using a narrower analysis window in time domain will result in the Gabor time–frequency spectrum (or representation) with higher time resolution but poor frequency resolution for the transient signals. To obtain the Gabor time–frequency representation with both higher frequency resolution and higher time resolution, the above two spectra can be combined by geometric average. The experimental results show that the combined Gabor time–frequency representation for the transient signals has higher time–frequency resolution than that obtained when only the single analysis window is used in the traditional discrete Gabor transform.

A velocity synchrosqueezing transform for fault diagnosis of planetary gearboxes under nonstationary conditions

2016 ◽  
Vol 231 (15) ◽  
pp. 2868-2884 ◽  
Author(s):  
Yunpeng Guan ◽  
Ming Liang ◽  
Dan-Sorin Necsulescu
Keyword(s):  
Fault Diagnosis ◽  
Vibration Signal ◽  
Frequency Resolution ◽  
Time Frequency ◽  
Machinery Condition Monitoring ◽  
Frequency Representation ◽  
Nonstationary Vibration ◽  
Synchrosqueezing Transform ◽  
Fine Resolution ◽  
Nonstationary Conditions

Time–frequency analysis is widely used in the field of machinery condition monitoring and fault diagnosis under nonstationary conditions. Among the time–frequency methods synchrosqueezing transform outperforms others in providing fine-resolution time–frequency representation. However, it suffers from time–frequency smear when analysing nonstationary signals. To address this issue, this paper proposes a new synchrosqueezing-transform-based method which works by (1) mapping the raw nonstationary vibration signal into a corresponding stationary angle domain signal to meet the stationarity requirement of the synchrosqueezing transform, (2) performing the synchrosqueezing transform of the corresponding signal and (3) restoring the time–frequency representation of the raw signal from the synchrosqueezing transform result of the corresponding signal. As the synchrosqueezing transform is applied to the stationary corresponding signal, the time–frequency smear is eliminated in the synchrosqueezing transform result of the corresponding signal and the final signal time–frequency representation. As such the proposed method can generate a smear-free time–frequency representation with fine time–frequency resolution and thus provide more reliable diagnosis decisions. A fast implementation algorithm is also developed to simplify the implementation of the proposed method. The effectiveness of the proposed method is validated using both simulated and experimental vibration signals of planetary gearboxes.

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