CN107941511A - A kind of implementation method of the frequency based on signal Time-frequency Decomposition-kurtosis figure - Google Patents
A kind of implementation method of the frequency based on signal Time-frequency Decomposition-kurtosis figure Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
- G01M13/04—Bearings
- G01M13/045—Acoustic or vibration analysis
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
- G01M13/02—Gearings; Transmission mechanisms
- G01M13/021—Gearings
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
- G01M13/02—Gearings; Transmission mechanisms
- G01M13/028—Acoustic or vibration analysis
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Abstract
The invention discloses a kind of implementation method of the frequency based on signal Time-frequency Decomposition-kurtosis figure, frequency slice wavelet transformation is carried out to signal to ask for its Time-frequency Decomposition result first, based on this, the bandwidth of one signal component reconstruct of selection, with certain frequency at intervals of step-length, time-frequency subspace is spatially chosen in Time-frequency Decomposition, the time frequency space of signal, which is divided into, a series of has same band and overlapped subspace.Then, time domain component of the signal in these subspaces is extracted using frequency slice wavelet transformation inverse transformation, and calculates the kurtosis value of the time domain component of these subspaces, and then obtain kurtosis value sequence of the signal in entirely analysis frequency band；Using the centre frequency of each time-frequency subspace as abscissa value, the kurtosis of corresponding signal component be used as ordinate value, you can obtain frequency-kurtosis curve of the signal, the corresponding frequency of peak value on frequency-kurtosis curve is the resonant frequency of mechanism or component.
Description
Technical Field
The invention belongs to the field of signal processing of mechanical equipment, and particularly relates to a frequency-kurtosis graph implementation method based on signal time-frequency decomposition.
Background
Bearings, gears, etc. are the most commonly used components in mechanical equipment, and more than 30% of mechanical equipment failures are associated with them. When the parts are damaged or failed, the structural parts can be excited to resonate in the rotating process of the parts, the amplitude modulation phenomenon occurs to the vibration signals along with repeated impact due to repeated occurrence of impact response, and the frequency of the amplitude modulation is related to the failure characteristics. These features are buried in noise at the beginning of a fault, and therefore, selecting a resonance frequency band separates out repetitive shock features, which can effectively determine the type of fault.
The kurtosis is a common dimensionless index in fault diagnosis of mechanical equipment, and can be used for measuring the strength of an impact component in a signal. It is a statistical quantity index, and if it is calculated based on the sampling signal of a certain time period, the kurtosis is a time domain index. In the case of a working machine, when a component failure occurs, the dynamic performance thereof changes and vibration is intensified, and therefore, kurtosis is often used to evaluate the state of the machine or the component in the field of machine state monitoring and failure diagnosis.
Document [1] uses a short-time fourier transform as a basis, filters a vibration signal with a certain bandwidth after selecting a window function, then calculates the kurtosis of the envelope of each frequency band filtering signal, and determines a resonance frequency band by using the maximum kurtosis value to extract the damage characteristic of a bearing. Document [2] filters a signal by using a narrow-band filtering method to obtain a series of signal components, and determines a resonance frequency band to extract damage characteristics of a bearing by calculating kurtosis of a frequency spectrum amplitude sequence on the basis of obtaining a frequency spectrum enveloped by the signal components. Document [3] performs time-frequency decomposition on a vibration signal by using frequency slice wavelet transform to obtain time-frequency energy distribution of the signal, then divides a time-frequency space of the signal by a given frequency bandwidth, calculates time-frequency kurtosis indexes of the time-frequency subspaces on the basis of the time-frequency energy distribution, and determines a resonance frequency band to extract damage characteristics of a bearing.
The above method has the following problems in the application process:
(1) by adopting short-time Fourier transform filtering and narrow-band filtering methods, the bandwidth and the center frequency of a window function need to be set in advance, and prior knowledge is needed.
(2) Dividing a frequency band or time-frequency space of a signal in a non-overlapping, equal-width fashion with a given bandwidth tends to miss the best frequency band, since the characteristic frequency bands do not necessarily fall exactly within the artificially divided frequency bands or time-frequency intervals.
(3) The width selection of the filtering frequency band has a large influence on the calculation of the kurtosis values of a time domain and a frequency domain based on signal envelopes, the bandwidth selection is too large, the envelope components of the filtering signals are complex, the kurtosis values cannot well reflect the impact characteristics of the signals, the bandwidth selection is too small, the envelope components of the filtering signals are single, the envelope changes slowly, and the impact characteristics cannot be displayed.
The following are relevant references retrieved by the applicant:
[1]J.Antoni and R.B.Randall，The spectral kurtosis：application to thevibratorysurveillance and diagnostics of rotating machines[J].MechanicalSystems and SignalProcessing，2006，20：308-331。
[2]T.Barszcz，A.Jabtoński.A novel method for the optimal bandselection for vibration signal demodulation and comparison with the Kurtogram[J].Mechanical Systems and Signal Processing，2011，25：431–451。
[3] chendong, high-peng, high-strength, a rolling bearing damage diagnosis method based on time-frequency kurtosis spectrum, mechanical engineering report 2015, 51 (11): 78-83.
Disclosure of Invention
In view of the above-mentioned drawbacks and disadvantages of the prior art, an object of the present invention is to provide a method for implementing a frequency-kurtosis curve based on a frequency slice wavelet transform method of a signal.
In order to realize the task, the invention adopts the following technical solution:
a method for realizing frequency-kurtosis diagram based on signal time-frequency decomposition includes carrying out frequency slice wavelet transform on signal to obtain its time-frequency decomposition result, selecting a bandwidth for signal component reconstruction based on said result, selecting time-frequency sub-space on time-frequency decomposition space by using a certain frequency interval as step length, and dividing time-frequency space of signal into a series of mutually overlapped sub-spaces with same bandwidth. Then, extracting time domain components of the signal in the subspaces by adopting inverse transformation of frequency slice wavelet transform, and calculating kurtosis values of the time domain components of the subspaces so as to obtain a kurtosis value sequence of the signal in the whole analysis frequency band; the central frequency of each time-frequency subspace is taken as an abscissa value, and the kurtosis of the corresponding signal component is taken as an ordinate value, so that a frequency-kurtosis curve of the signal can be obtained, and the frequency corresponding to the peak value on the frequency-kurtosis curve is taken as the resonance frequency of the mechanism or the component; wherein:
the frequency slice wavelet transform is a signal time-frequency decomposition method, before signal transform, a frequency slice function is selected, and the transform result is the energy mapping of signals in a time-frequency space;
the analysis frequency band is the Nyquist frequency band of the signal, the lower limit frequency of the analysis frequency band is 0Hz, and the upper line frequency is half of the sampling frequency of the signal.
The specific implementation method comprises the following steps:
(1) selecting a frequency slicing function;
(2) and determining the bandwidth of the reconstructed signal component, wherein the bandwidth is preferably 3-5 times of the maximum damage characteristic frequency for bearing or gear vibration signal analysis.
(3) A frequency step is determined that is no greater than its gyration frequency for bearing or gear vibration signal analysis.
(4) Removing a direct current component in the acquired vibration signal;
(5) performing frequency slice wavelet transform on the signal without the direct current component;
(6) extracting signal components of subspaces through inverse transformation, and calculating kurtosis values of time domain components of the subspaces so as to obtain a kurtosis value sequence of the signal in the whole analysis frequency band;
(7) calculating a center frequency of each subspace;
(8) drawing a frequency-kurtosis curve of the signal by taking the central frequency of the subspace as a horizontal coordinate and taking the kurtosis of the corresponding signal component as a vertical coordinate; the peak on the frequency-kurtosis curve corresponds to the resonant frequency of the mechanism or component.
According to the invention, the signal reconstruction refers to a process of performing frequency slice wavelet inverse transformation or Fourier transformation on the selected frequency band to separate out the signal components of the frequency band.
The method for realizing the frequency-kurtosis graph based on the signal time-frequency decomposition has the advantages that the method for dividing the time-frequency space of the analyzed signal into a series of subspaces which have the same bandwidth and are mutually overlapped is adopted, so that the original signal information is redundantly applied, the impact characteristic information contained in the vibration signal can be fully and effectively extracted, the kurtosis change trend in the whole analysis frequency band of the signal can be reflected, the extraction of fault characteristics is facilitated, and the neighborhood region of the frequency corresponding to the peak value can be selected as the frequency band for demodulation and analysis when the engineering is applied.
Drawings
FIG. 1 is a flow chart of a frequency-kurtosis curve based on signal time-frequency decomposition according to the present invention.
FIG. 2 is a time domain waveform diagram of signal y (t);
FIG. 3 is a waveform diagram of sinusoidal signal components;
FIG. 4 is a repeating impulse component waveform;
FIG. 5 is a waveform diagram of an amplitude modulation component;
FIG. 6 is a graph of the resulting frequency-kurtosis based on signal time-frequency decomposition;
the present invention will be described in further detail with reference to the following drawings and examples.
Detailed Description
This embodiment provides a method for implementing a frequency-kurtosis curve based on signal time-frequency decomposition, which aims to find a resonance frequency in a signal, and to determine a resonance frequency band to extract amplitude modulation characteristics in the signal.
Firstly, the signal is processed with frequency slice wavelet transform to obtain its time-frequency decomposition result, on the basis of this, a bandwidth for signal component reconstruction is selected, a certain frequency interval is used as step length, a time-frequency subspace is selected on the time-frequency decomposition space, and the time-frequency space of the signal is divided into a series of mutually overlapped subspaces with same bandwidth. Then, extracting time domain components of the signal in the subspaces by adopting inverse transformation of frequency slice wavelet transform, and calculating kurtosis values of the time domain components of the subspaces so as to obtain a kurtosis value sequence of the signal in the whole analysis frequency band; the central frequency of each time-frequency subspace is taken as an abscissa value, and the kurtosis of the corresponding signal component is taken as an ordinate value, so that a frequency-kurtosis curve of the signal can be obtained, and the frequency corresponding to the peak value on the frequency-kurtosis curve is taken as the resonance frequency of the mechanism or the component; wherein:
the frequency slice wavelet transform is a signal time-frequency decomposition method, before signal transform, a frequency slice function is selected, and the transform result is the energy mapping of signals in a time-frequency space;
the analysis frequency band is the Nyquist frequency band of the signal, the lower limit frequency of the analysis frequency band is 0Hz, and the upper line frequency is half of the sampling frequency of the signal.
In this embodiment:
the frequency slice wavelet transform is a signal time-frequency decomposition method, before signal transformation, a frequency slice function needs to be selected, and the transformation result is the energy mapping of signals in a time-frequency space.
The kurtosis is a dimensionless statistical index describing the signal in the time domain and is sensitive to the impulsive component in the signal.
The frequency-kurtosis curve is a trend graph representing the time-domain kurtosis of the signal component of the sub-band (sub-time-frequency space) of the analysis frequency band along with the frequency change.
When the method is applied to engineering, the neighborhood region of the frequency corresponding to the peak value can be selected as the frequency band of demodulation analysis.
The specific implementation method comprises the following steps:
(1) selecting a frequency slicing function;
(2) and determining the bandwidth of the reconstructed signal component, wherein the bandwidth is preferably 3-5 times of the maximum damage characteristic frequency for bearing or gear vibration signal analysis.
(3) A frequency step is determined that is no greater than its gyration frequency for bearing or gear vibration signal analysis.
(4) Removing a direct current component in the acquired vibration signal;
(5) performing frequency slice wavelet transform on the signal without the direct current component;
(6) extracting signal components of subspaces through inverse transformation, and calculating kurtosis values of time domain components of the subspaces so as to obtain a kurtosis value sequence of the signal in the whole analysis frequency band;
(7) calculating a center frequency of each subspace;
(8) and drawing a frequency-kurtosis curve of the signal by taking the central frequency of the subspace as an abscissa and taking the kurtosis of the corresponding signal component as an ordinate.
The signal reconstruction refers to a process of performing frequency slice wavelet inverse transformation or fourier transformation on the selected frequency band to separate out signal components of the frequency band.
Specific implementation procedures are given below.
For the time domain signal f (t), its Fourier transform is setIf the frequency slicing function is p (t), then the frequency sliced wavelet transform of the signal is:
in the formula, κ>0，Is composed ofThe function of the conjugate of (a) to (b),is the Fourier transform of p (t).
Since ω is 2 pi f, when k is constant, the transformation result W (t, ω, κ) can be written as W (t, f), which is an energy mapping of the signal on the time-frequency space.
In the time-frequency subspace [ t ]1,t2,f1,f2]May be inverse transformed to obtain:
let the vibration signal s (t) be fsFor sampling the sampling frequency, a signal sequence S ═ S of length N is obtainediI is 1 to N, which corresponds to a time interval of [0j,...,tN-1]Wherein, tj＝j/fs,j＝0～N-1。
Removing a direct current component in the vibration signal:
wherein,is s (t) in the time interval [0, tN-1]Is measured.
Transforming the signal x (t) by formula (1) to obtain x (t) in the time-frequency interval [0, tN-1,0,fs/2]The transformation result of (c) is: w (t, f)＝{W(tk,fk),tk＝0～tN-1,fk＝0～fs/2}。
Defining the frequency bandwidth as delta W and the step length as f on the time-frequency space of the signalpThen, in step i, the signal component y reconstructed from the time-frequency subspacei(t) is:
1,2s/2fpThe integer part of (2).
Calculating the signal component yiKurtosis of (t):
l is yi(t) the length of the (t),is yi(t) mean value.
When i 1, 2.. said., M, a signal s (t) is obtained in the frequency band [0, f ]s/2]The kurtosis value sequence of (a):
KR＝{Kr(i),i＝1,2,......,M}
order:then:
Fc＝{fc(i),i＝1,2,......,M}
by KR＝{Kr(i) 1,2,.. ere, M } as ordinate, Fc＝{fc(i) I 1,2, a. The peak value of which can characterize the junctionThe resonant frequency of the structure or component.
Engineering application example:
a time domain signal y (t) is shown in FIG. 2, with a sampling frequency of 20kHz and a sampling length of 2048. It is constructed by adding 3 components of fig. 2, fig. 3 and fig. 4 and then superposing a certain amount of white noise. The frequency of the sinusoidal signal component of fig. 3 is f1The repetition frequency of the repetitive shock component of fig. 4 is 100Hz, the resonance frequency of the structure is 3000Hz, the amplitude modulation frequency of the amplitude modulation component of fig. 5 is 100Hz, and the carrier frequency is 1500 Hz.
FIG. 6 is a frequency-kurtosis curve for signal y (t) with a bandwidth of 300Hz, step size of 100Hz, and 2 peaks in the curve indicating 1500Hz and 3000Hz, which are the carrier frequency and the structural resonance frequency, respectively.
Claims (3)
1. A method for realizing frequency-kurtosis diagram based on signal time-frequency decomposition includes carrying out frequency slice wavelet transform on signal to obtain its time-frequency decomposition result, selecting a bandwidth for signal component reconstruction based on said result, selecting time-frequency sub-space on time-frequency decomposition space by using a certain frequency interval as step length, and dividing time-frequency space of signal into a series of mutually overlapped sub-spaces with same bandwidth. Then, extracting time domain components of the signal in the subspaces by adopting inverse transformation of frequency slice wavelet transform, and calculating kurtosis values of the time domain components of the subspaces so as to obtain a kurtosis value sequence of the signal in the whole analysis frequency band; the central frequency of each time-frequency subspace is taken as an abscissa value, and the kurtosis of the corresponding signal component is taken as an ordinate value, so that a frequency-kurtosis curve of the signal can be obtained, and the frequency corresponding to the peak value on the frequency-kurtosis curve is taken as the resonance frequency of the mechanism or the component; wherein:
the frequency slice wavelet transform is a signal time-frequency decomposition method, before signal transform, a frequency slice function is selected, and the transform result is the energy mapping of signals in a time-frequency space;
the analysis frequency band is the Nyquist frequency band of the signal, the lower limit frequency of the analysis frequency band is 0Hz, and the upper line frequency is half of the sampling frequency of the signal.
2. The method of claim 1, wherein the specific implementation method is as follows:
(1) selecting a frequency slicing function;
(2) and determining the bandwidth of the reconstructed signal component, wherein the bandwidth is preferably 3-5 times of the maximum damage characteristic frequency for bearing or gear vibration signal analysis.
(3) A frequency step is determined that is no greater than its gyration frequency for bearing or gear vibration signal analysis.
(4) Removing a direct current component in the acquired vibration signal;
(5) performing frequency slice wavelet transform on the signal without the direct current component;
(6) extracting signal components of subspaces through inverse transformation, and calculating kurtosis values of time domain components of the subspaces so as to obtain a kurtosis value sequence of the signal in the whole analysis frequency band;
(7) calculating a center frequency of each subspace;
(8) drawing a frequency-kurtosis curve of the signal by taking the central frequency of the subspace as a horizontal coordinate and taking the kurtosis of the corresponding signal component as a vertical coordinate; the peak on the frequency-kurtosis curve corresponds to the resonant frequency of the mechanism or component.
3. The method of claim 1 or 2, wherein the signal reconstruction refers to a process of performing a frequency slice inverse wavelet transform or a fourier transform on the selected frequency band to separate out signal components of the frequency band.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108955871A (en) * | 2018-08-27 | 2018-12-07 | 河海大学 | A kind of tap switch vibration signal noise-reduction method based on quick kurtogram algorithm |
| CN109525215A (en) * | 2018-09-29 | 2019-03-26 | 长安大学 | It is a kind of to compose the experience small wave converting method for determining sub-band boundary using kurtosis |
| CN111637964A (en) * | 2020-05-12 | 2020-09-08 | 西南交通大学 | Rail corrugation identification method |
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| US4536086A (en) * | 1982-11-18 | 1985-08-20 | The Perkin-Elmer Corporation | Holographic figure sensor |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108955871A (en) * | 2018-08-27 | 2018-12-07 | 河海大学 | A kind of tap switch vibration signal noise-reduction method based on quick kurtogram algorithm |
| CN109525215A (en) * | 2018-09-29 | 2019-03-26 | 长安大学 | It is a kind of to compose the experience small wave converting method for determining sub-band boundary using kurtosis |
| CN109525215B (en) * | 2018-09-29 | 2023-02-28 | 长安大学 | Empirical wavelet transform method for determining subband boundary by using kurtosis spectrum |
| CN111637964A (en) * | 2020-05-12 | 2020-09-08 | 西南交通大学 | Rail corrugation identification method |
| CN111637964B (en) * | 2020-05-12 | 2021-10-26 | 西南交通大学 | Rail corrugation identification method |
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