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.

Adaptive radial sinc kernel distribution and its application in mechanical fault diagnosis

2016 ◽  
Vol 231 (3) ◽  
pp. 485-493 ◽  
Author(s):  
Zhinong Li ◽  
Ming Zhu ◽  
Fulei Chu ◽  
Xuping He
Keyword(s):  
Fault Diagnosis ◽  
Frequency Distribution ◽  
Kernel Function ◽  
Rolling Bearing ◽  
Kernel Functions ◽  
Frequency Resolution ◽  
Good Time ◽  
Time Frequency ◽  
Fixed Kernel ◽  
Time Frequency Distribution

Based on the deficiency of fixed-kernel in the traditional time–frequency distribution, which is lack of adaptability, a new adaptive kernel function, which is named as the adaptive radial sinc kernel, is proposed according to design criteria of adaptive optimal kernel. The definition and algorithm of radial sinc kernel are given, and the proposed method is compared with the tradition time–frequency distribution. The simulation results show that the proposed method is superior to the traditional fixed-kernel functions, such as Wigner–Ville distribution, Choi–Williams distribution, cone-kernel distribution and continuous wavelet transform. The adaptive radial sinc kernel can overcome the deficiency of fixed-kernel function in traditional time–frequency distribution, adopt the optimizing method to filter the cross-terms adaptively according to the signal distribution, obtain good time–frequency resolution and has extensive adaptability for an arbitrary signal. Finally, the proposed method has been applied to the fault diagnosis of rolling bearing, and the experiment result shows that the proposed method is very effective.

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.

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.

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.

Design of Adaptive Filter for Health Monitoring on a Gearbox

2006 ◽  
Vol 321-323 ◽  
pp. 1237-1240
Author(s):  
Sang Kwon Lee ◽  
Jung Soo Lee
Keyword(s):  
Signal Processing ◽  
Frequency Domain ◽  
Adaptive Filter ◽  
Health Monitoring ◽  
Background Noise ◽  
Adaptive Signal Processing ◽  
Vibration Signals ◽  
Time Frequency ◽  
Frequency Representation ◽  
Adaptive Signal

Impulsive vibration signals in gearbox are often associated with faults, which lead to due to irregular impacting. Thus these impulsive vibration signals can be used as indicators of machinery faults. However it is often difficult to make objective measurement of impulsive signals because of background noise signals. In order to ease the measurement of impulsive signal embedded in background noise, we enhance the impulsive signals using adaptive signal processing and then analyze them in time and frequency domain by using time-frequency representation. This technique is applied to the diagnosis of faults within laboratory gearbox.

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.

Fault Identification for Rotating Machinery Using Adaptive Signal Processing and Time-Frequency Analysis

1997 ◽  
Author(s):  
Sang-Kwon Lee ◽  
Paul R. White
Keyword(s):  
Signal Processing ◽  
Background Noise ◽  
Combustion Engine ◽  
Adaptive Signal Processing ◽  
Rotating Machinery ◽  
Fault Identification ◽  
Vibration Signals ◽  
Time Frequency ◽  
Frequency Representation ◽  
Adaptive Signal

Abstract Impulsive sound and vibration signals in rotating machinery are often associated with faults which lead to due to irregular impacting. Thus these impulsive sound and vibration signals can be used as indicators of machinery faults. However it is often difficult to make objective measurement of impulsive signals because of background noise signals. In order to ease the measurement of impulsive sounds embedded in background noise, we enhance the impulsive signals using adaptive signal processing and then analyze them in time and frequency domain by using time-frequency representation. This technique is applied to the diagnosis of faults within internal combustion engine and industrial gear.

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.

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

2019 ◽  
Vol 16 (5) ◽  
pp. 822-841
Author(s):  
Pengfei Qi ◽  
Yanchun Wang
Keyword(s):  
Seismic Waves ◽  
Matching Pursuit ◽  
Frequency Characteristics ◽  
Thin Layers ◽  
Frequency Resolution ◽  
Data Sets ◽  
Time Frequency ◽  
Frequency Representation ◽  
Intrinsic Quality ◽  
Mp Method

Abstract The 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.

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