CN110146291A - A kind of Rolling Bearing Fault Character extracting method based on CEEMD and FastICA - Google Patents
A kind of Rolling Bearing Fault Character extracting method based on CEEMD and FastICA Download PDFInfo
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Abstract
The present invention relates to a kind of Rolling Bearing Fault Character extracting methods based on CEEMD and FastICA, belong to fault diagnosis technology and signal processing analysis technical field.Vibration signal is decomposed the IMF component at several different frequencies first with CEEMD algorithm by this method, is then chosen corresponding IMF component according to kurtosis criterion and is reconstructed to obtain observation signal, remaining IMF component reconstructs to obtain virtual noise channel signal；It carries out observation signal and virtual noise channel signal to solve mixed denoising using FastICA algorithm；Teager energy operator is recycled to carry out demodulation process to the signal after denoising；FFT transform finally is carried out to the signal after demodulation, the spectrum signature of the signal after analytic transformation extracts the fault characteristic frequency of signal, obtains fault diagnosis result.The method of the present invention not only can effectively solve the problem of losing fault message and causing noise that cannot completely remove due to modal overlap during denoising, but also can extract be out of order fundamental frequency and frequency multiplication information clear and accurately, obtain fault diagnosis result.
Description
Technical field
The present invention relates to a kind of Rolling Bearing Fault Character extracting methods based on CEEMD and FastICA, belong to failure and examine
Disconnected technology and signal processing analysis technical field.
Background technique
Rolling bearing important role of performer in our production and living is important zero in mechanical manufacturing field
One of part and the higher machine components of spoilage, the operating status of rolling bearing largely decides industrial system
Working efficiency, industrial huge economic losses and casualties are resulted even in when serious, thus monitor its run shape
State is extremely important to ensure industrial normal production.But monitoring and collected vibration signal are not in Practical Project practice
With being only linear character as theory illusion, the actual vibration signal of rolling bearing usually has two kinds of spies of linear and nonlinear
Sign, bearing fault signal energy is small, frequency band distribution is wide, vulnerable to other noise jammings, and useful fault message is easily submerged, therefore
How to extract fault signature from complex industrial ambient noise becomes the hot spot of current research.Therefore it needs to utilize effective signal
Processing method extracts bearing fault characteristics information, determines fault type.
HUANG proposes a kind of event for being based on empirical mode decomposition (Empirical Mode Decomposition, EMD)
The features such as barrier diagnostic method, this method is adaptable strong, easy to operate in engineering practice, this method is applied into the axis of rolling
Preferable effect can be obtained in the fault-signal diagnosis held, but this method will appear during noise signal analysis and demodulation etc.
Modal overlap and end effect problem.
Field crystalline substance etc. proposes a kind of by integrated empirical mode decomposition (Ensemble Empirical Mode
Decomposition, EEMD) Fault Diagnosis of Roller Bearings that combines of related to airspace noise reduction.Although this method can be with
Solves the problems such as modal overlap existing for EEMD and end effect, but not can effectively solve white noise cannot be disappeared completely
Except the problems such as, and the noise added in the signal will affect the discomposing effect of signal.This method is for rolling bearing fault diagnosis
Noise reduction effect is not good enough, and fault signature extraction efficiency is not high.
Etc. proposing a kind of Fast Independent Component Analysis (Fast Independent Component
Analysis, FastICA) algorithm, which is applied in Practical Project when acquiring and handling signal is not in distortion,
FastICA algorithm is showed the independence of separating resulting by non-Gaussian system metric form, when the more big then explanation point of negentropy
Measurer has stronger non-Gaussian system, more preferable than (Independent Component Analysis, ICA) algorithm separating effect.
But this method needs to meet the condition that observation signal number is greater than source signal number, needs that other signals decomposition method is combined to carry out
Analysis.
Summary of the invention
In view of the above-mentioned problems, having the present invention provides a kind of Method for Bearing Fault Diagnosis based on CEEMD and FastICA
Effect extracts bearing fault characteristics information, accurately determines fault type.
The technical scheme is that gathering empirical mode decomposition (CEEMD) algorithm for vibration signal first with complementation
The intrinsic modal components (Intrinsic Mode Function, IMF) of several different frequencies are resolved into, it is then quasi- according to kurtosis
It then chooses corresponding IMF component to be reconstructed to obtain observation signal, remaining IMF component reconstructs to obtain virtual noise channel signal；Benefit
It carries out observation signal and virtual noise channel signal to solve mixed denoising with quick ICA (FastICA) algorithm；It recycles
Teager energy operator (Teager-Kaiser Energy Operator, TKEO) carries out demodulation process to the signal after denoising；
FFT transform finally is carried out to the signal after demodulation, the spectrum signature of the signal after analytic transformation extracts the failure spy of vibration signal
Sign.
Specific step is as follows for the method:
1, CEEMD decomposition is carried out to primary fault vibration signal x (t) first
1.1 by a pair of of amplitude size is identical and the standard white noise of carrier phase shift 1800 is added to primary fault vibration letter
In number x (t), two new signal x are obtained1(t) and x2(t)
Wherein n (t) is standard white noise；
1.2 couples of new signal x1(t) and x2(t) EMD resolution process is done, is obtained
x1(t) n IMF component I is obtainedi1(t) and a residual components rn1(t), x2(t) n IMF component I is obtainedi2(t)
With a residual components rn2(t)；
Wherein specific step is as follows for EMD decomposition:
(1) it is defined according to IMF, the Local Extremum of the determination vibration signal s (t) to be decomposed passes through cubic spline interpolation
Method curve connects extreme point, and obtained upper and lower envelope calculates upper and lower envelope curve m1(t), s (t) and local extremum
Between difference h1(t) it is denoted as:
h1(t)=s (t)-m1(t)
Wherein intrinsic mode functions IMF must satisfy following two standard conditions:
1) former vibration signal passes through the IMF component that EMD is decomposed, if aliasing occurs for component signal, will form multiple
Close signal.
2) each IMF can be linear or nonlinear, but the extreme point number of each IMF component and zero passage points
Must be identical, and upper and lower envelope is about time shaft Local Symmetric.
(2) if h1(t) 2 conditions of IMF are unsatisfactory for, then repeatedly step 1；If h1(t) meet IMF condition, h1(t) then it is
Single order IMF, is denoted as:
c1(t)=h1(t)
(3) s (t) is subtracted into c1(t), then remaining r is obtained1(t), it is denoted as:
r1(t)=s (t)-c1(t)
(4) by r1(t) signal new as one constantly repeats the above steps to obtain n rank IMF, until can not be to s (t)
It decomposes again, x (t) decomposition is finally obtained into n IMF component and 1 residual components rn(t), it may be assumed that
1.3 seek x1(t) and x2(t) average value of the IMF component after decomposing obtains primary fault vibration signal x (t) decomposition
IMF component I afterwardsi(t), x is sought1(t) and x2(t) average value of the residual components after decomposition after decomposing obtains primary fault
Residual components r after vibration signal x (t) decompositionn(t):
rn(t)=(rn1(t)+rn2(t))/2。
2, according to kurtosis criterion, the IMF component that kurtosis value is greater than 3 is chosen, and it is overlapped to obtain observation signal G1
(t), it is superimposed to obtain virtual noise channel signal G with remaining IMF component2(t), kurtosis value K is the number of vibration signal information distribution
Word statistic, size can be used for describing included in vibration signal impact ingredient number
Wherein IrmsRepresent IMF component Ii(t) root-mean-square value, N represent sampling number, N≤n.
The kurtosis effect of signals that is hit is larger, is a kind of dimensionless group, so being relatively specific for the event of mechanical damage class
Barrier diagnosis.When bearing is under normal operating conditions, kurtosis value is about 3, and when rolling bearing breaks down, which can be corresponding
Increase, i.e., kurtosis value can be greater than 3, deviate normal distribution.The kurtosis value of IMF component signal is bigger, show it includes failure punching
It hits that ingredient is more, then chooses the IMF component that kurtosis value is greater than 3.
3, using FastICA algorithm to observation signal G1(t) and virtual noise channel signal G2(t) it is mixed to carry out solution, it is right respectively
Signal Z after should obtaining noise reduction1(t) and Z2(t), choosing in the two signals becomes joint comprising the more signal of fault message
Signal Z (t) after noise reduction, carrying out solution using FastICA algorithm, mixed specific step is as follows:
(1) it treats the mixed signal of solution and carries out centralization processing, make its mean value 0；
(2) whitening processing is carried out to the centralization data that treated, obtains signal U；
(3) number m, the m=n for the component that selection needs to estimate randomly chooses an initial weight vector Wp；
(4) it is randomly provided the number of iterations p；
(5) it is iterated calculating: Wp=E { Ug (Wp TU)}-E{g′(Wp TU) } W, wherein the norm of constraint W is 1, g (Wp TU)
=tanh (Wp TU), g ' (Wp TU) for g (Wp TU it) differentiates, E { Ug (Wp TIt U is) } to Ug (Wp TU desired value, W) are askedp TFor Wp's
Transposition；
(6)Wherein constrain WjNorm be 1；
(7) W is enabledp=Wp/||Wp| |, | | Wp| | it is WpNorm；
(8) if WpIt does not restrain, return step (5), until WpConvergence；
(9) p=p+1 is enabled, if p≤m, return step (4), otherwise iteration terminates；
(10) iteration terminates result Wp, WpAs signal after noise reduction.
4, signal Z (t) row Teager-Kaiser energy operator after joint noise reduction is demodulated, the signal W after being demodulated
(n).It is as follows to demodulate calculation formula:
W (n)=Z2(n)-Z(n-1)Z(n+1)
Z (n) is the discrete form of Z (t), and Z (n-1) and Z (n+1) are the discrete form of Z (t-1) and Z (t+1), Z respectively
(t-1) and Z (t+1) respectively indicates the signal at t-1 moment and t+1 moment.
5, to the signal W (n) after demodulation into fast Fourier FFT transform, the spectrum signature of signal Y (t) after analytic transformation,
Identify fault characteristic frequency.
The working principle of the invention: it is identical, positive and negative pairs of that CEEMD method adds one group of amplitude in decomposing to original signal
Standard white noise carries out EMD decomposition to it respectively, obtains new IMF to the IMF component averaged of every group of positive and negative white noise
Component, this method can be completely counterbalanced by white noise, solve the problems, such as modal overlap, reduce reconstruction signal caused by residual white noise and miss
Difference improves signal decomposition computational efficiency.But still there is noise after the processing of CEEMD method, and noise can be effectively reduced in ICA method
Influence, FastICA algorithm is a kind of quick optimizing iterative algorithm, by the way of batch processing, it using negentropy maximum as
One search direction may be implemented sequentially to extract independent source, which uses the optimization algorithm of fixed point iteration, so that noise reduction
Effect is more preferable.
The beneficial effects of the present invention are:
(1) signal is decomposed by CEEMD, it is logical to choose corresponding IMF component composition virtual noise according to kurtosis criterion
Road had not only solved the problems, such as that blindly introducing virtual noise channel caused processing result bad, but also has solved ICA algorithm and owe to ask surely
Topic.
(2) by kurtosis value select respective component reconstruct, solve because blindness selection component reconstruct observation signal cause therefore
Hinder the problem of characteristic information is lost, reconstruction signal and virtual channel signal are subjected to FsatICA and solve mixed noise reduction process, is then utilized
TKEO method carries out demodulation process to the signal after noise reduction, can more protrude the shock characteristic of fault-signal.
(3) modal overlap that the method for the present invention not only can solve during decomposing denoising causes noise that cannot completely remove
Problem can also improve fractionation efficiency.CEEMD combines noise-reduction method with FastICA's, passes through experimental contrast analysis, CEEMD-
FastICA method can efficiently extract out the failure fundamental frequency and frequency multiplication characteristic information of rolling bearing, for bearing fault type
Method of discrimination research have better application value.
Detailed description of the invention
Fig. 1 is the flow chart of the method for the present invention；
Fig. 2 is the IMF component map that inner ring fault-signal CEEMD is decomposed；
Fig. 3 is reconstruct observation signal time domain waveform；
Fig. 4 is virtual channel time domain plethysmographic signal figure；
Fig. 5 is time domain plethysmographic signal figure after CEEMD-FastICA noise reduction；
Fig. 6 is CEEMD-FastICA inventive method treated bearing inner race spectrogram；
Fig. 7 is CEEMD-FastICA inventive method treated bearing outer ring spectrogram；
Fig. 8 is CEEMD-TKEO method treated bearing inner race spectrogram；
Fig. 9 is CEEMD-TKEO method treated bearing outer ring spectrogram；
Figure 10 is EEMD-FastICA inventive method treated bearing inner race spectrogram；
Figure 11 is EEMD-FastICA inventive method treated bearing outer ring spectrogram.
Specific embodiment
In the following with reference to the drawings and specific embodiments, the invention will be further described.
Embodiment 1: as shown in Figure 1, a kind of Rolling Bearing Fault Character extracting method based on CEEMD and FastICA, first
Primary fault vibration signal x (t) is resolved into the IMF component of several different frequencies first with CEEMD algorithm, then according to kurtosis
Criterion chooses corresponding IMF component and is reconstructed to obtain observation signal G1(t), remaining IMF component reconstructs to obtain virtual noise channel
Signal G2(t)；Using FastICA algorithm by observation signal G1(t) and virtual noise channel signal G2(t) it carries out solving at mixed denoising
Reason obtains signal Z (t) after joint noise reduction；Teager energy operator is recycled to carry out demodulation process to signal Z (t) after joint noise reduction
Signal W (n) after being demodulated；FFT transform finally is carried out to the signal W (n) after demodulation, the signal Y's (t) after analytic transformation
Spectrum signature extracts the fault characteristic frequency of signal, obtains fault diagnosis result.
Rolling bearing inner ring fault-signal is analyzed using the above method in the present embodiment, with CEEMD in bearing
Circle fault-signal x (t) is decomposed, and obtains 6 IMF components as shown in Fig. 2, calculating the kurtosis value of each IMF component, as a result such as
Shown in table 1:
Each IMF component kurtosis value that 1 inner ring fault-signal CEEMD of table is decomposed
| IMF component signal | IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 |
| Kurtosis value | 6.478 | 8.528 | 5.134 | 2.822 | 2.683 | 2.563 |
Directly find out that the corresponding kurtosis value of IMF1~IMF3 is greater than 3 from table 1, so choosing preceding 3 IMF components carries out letter
Number reconstruct obtains observation signal G1(t), observation signal time domain waveform is as shown in figure 3, remaining 3 IMF component combinations construct
Virtual channel signal G2(t) time domain waveform is as shown in Figure 4, it can be seen that single signal decomposition simultaneously reconstructs time domain plethysmographic signal figure
Display needs to be further processed there are still noise；Using FastICA algorithm to observation signal G1(t) (shown in Fig. 5 (a)) and empty
Quasi- channel signal G2(t) it is mixed that solution is carried out (shown in Fig. 5 (b)), obtains signal Z after joint noise reduction1(t) and Z2(t), such as Fig. 5 (c) and
Shown in Fig. 5 (d)；It can be seen that solving mixed signal Z2(t) fault characteristic information having is more apparent, then to signal Z2(t) TKEO is carried out
Energy operator demodulation, the signal W (n) after being demodulated；FFT transform finally is carried out to signal W (n), obtains signal Y (t) frequency spectrum
Figure is as shown in fig. 6, can clearly obtain rolling bearing inner ring failure fundamental frequency by Fig. 6 is 152.3Hz (close to optimum value
156.14Hz), while in figure 6 frequencys multiplication can be clearly navigated to, are thus determined, bearing is in inner ring malfunction.
It, will in order to further verify the superiority of the Rolling Bearing Fault Character extracting method based on CEEMD-FastICA
The method compares experiment with the fault signature extracting method based on CEEMD-TKEO and based on EEMD-FastICA.It rolls
Bearing fault inner ring fault vibration signal is after the processing of CEEMD-TKEO fault signature extracting method, and bearing inner race frequency spectrum is as schemed
Shown in 8.As seen from Figure 8, it is out of order although can be extracted from CEEMD-TKEO method treated bearing inner race frequency spectrum
Fundamental frequency (frequency multiplication) characteristic information, but bearing fault frequency multiplication characteristic information is unobvious, and characteristic frequency spectral line peak value is also not
It is very prominent.
Same rolling bearing fault inner ring vibration signal is after the processing of EEMD-FastICA method, bearing inner race frequency spectrum
As shown in Figure 10.Failure base can only be extracted after the processing of bearing inner race fault-signal EEMD-FastICA method as can be seen from Figure 10
Frequency and 2 frequency multiplication information.
Embodiment 2: analyzing housing washer fault-signal in the present embodiment, with CEEMD to bearing inner race event
Hinder signal decomposition, arrives several IMF components；The kurtosis value of each IMF component signal is calculated separately, before selection kurtosis value is biggish
Two component signals are reconstructed, and obtain observation signal, remaining IMF component construction virtual noise channel signal；Utilize FastICA
Algorithm carries out solution to observation signal and virtual channel signal and mixes, and obtains signal after joint noise reduction；Signal after noise reduction is carried out
The demodulation of Teager-Kaiser energy operator, the signal after being demodulated；FFT transform is carried out to the signal after demodulation, obtains signal
Spectrogram is as shown in fig. 7, can clearly obtain rolling bearing inner ring failure fundamental frequency by Fig. 7 is 105.5Hz (close to most preferably
Value 103.36Hz), while 5 frequencys multiplication can be clearly navigated in figure, thus determine, bearing is in outer ring malfunction.
With embodiment 1, by housing washer fault vibration signal by the event of CEEMD-TKEO and EEMD-FastICA
Hinder feature extracting method processing, respectively obtain spectrogram as shown in figs. 9 and 11, it can be seen from the figure that event can only can be extracted
Hinder fundamental frequency and 2 frequency multiplication information.And CEEMD-FastICA method can extract 8 frequency multiplication feature of housing washer clear and accurately
Information enables to Rolling Bearing Fault Character frequency shock characteristic more prominent, so that bearing fault characteristics frequency is more effective
It extracts on ground.To prove that CEEMD-FastICA method effect is more preferable.
Above in conjunction with attached drawing, the embodiment of the present invention is explained in detail, but the present invention is not limited to above-mentioned
Embodiment within the knowledge of a person skilled in the art can also be before not departing from present inventive concept
Put that various changes can be made.
Claims (5)
1. a kind of Rolling Bearing Fault Character extracting method based on CEEMD and ICA, it is characterised in that:
Primary fault vibration signal x (t) is resolved into the IMF component of several different frequencies first with CEEMD algorithm, then according to
Corresponding IMF component is chosen according to kurtosis criterion to be reconstructed to obtain observation signal G1(t), remaining IMF component, which reconstructs, is virtually made an uproar
Sound channel signal G2(t)；Using FastICA algorithm by observation signal G1(t) and virtual noise channel signal G2(t) it is mixed to carry out solution
Denoising obtains signal Z (t) after joint noise reduction；Teager energy operator is recycled to solve signal Z (t) after joint noise reduction
Mediate the signal W (n) after reason is demodulated；FFT transform finally is carried out to the signal W (n) after demodulation, the signal after analytic transformation
The spectrum signature of Y (t) extracts the fault characteristic frequency of signal, obtains fault diagnosis result.
2. the Rolling Bearing Fault Character extracting method according to claim 1 based on CEEMD and FastICA, feature
Be: it is described using CEEMD algorithm by primary fault vibration signal x (t) resolve into several different frequencies IMF component it is specific
Steps are as follows:
(1) a pair of of amplitude size is identical and 180 ° of carrier phase shift of standard white noise is added to primary fault vibration signal x
(t) in, two new signal x are obtained1(t) and x2(t)
Wherein n (t) is standard white noise；
(2) to new signal x1(t) and x2(t) EMD resolution process is done
x1(t) n IMF component I is obtainedi1(t) and a residual components rn1(t), x2(t) n IMF component I is obtainedi2(t) and one
A residual components rn2(t)；
(3) x is sought1(t) and x2(t) after the average value of the IMF component after decomposing obtains primary fault vibration signal x (t) decomposition
IMF component Ii(t), x is sought1(t) and x2(t) average value of the residual components after decomposition after decomposing obtains primary fault vibration
Residual components r after signal x (t) decompositionn(t):
rn(t)=(rn1(t)+rn2(t))/2。
3. the Rolling Bearing Fault Character extracting method according to claim 1 based on CEEMD and FastICA, feature
Be: the foundation kurtosis criterion chooses corresponding IMF component and refers to IMF component of the selection kurtosis value greater than 3 and fold to it
Add to obtain observation signal G1(t), it is superimposed to obtain virtual noise channel signal G with remaining IMF component2(t), kurtosis value K is vibration letter
The statistics amount of number information distribution,
Wherein IrmsRepresent IMF component Ii(t) root-mean-square value, N represent sampling number, N≤n.
4. the Rolling Bearing Fault Character extracting method according to claim 1 based on CEEMD and FastICA, feature
It is: described to utilize FastICA algorithm by observation signal G1(t) and virtual noise channel signal G2(t) it carries out solving mixed denoising
The detailed process for obtaining signal Z (t) after joint noise reduction is, using FastICA algorithm to observation signal G1(t) and virtual noise is logical
Road signal G2(t) it is mixed to carry out solution, respectively corresponds to obtain the signal Z after noise reduction1(t) and Z2(t), it chooses in the two signals and includes
The more signal of fault message becomes signal Z (t) after joint noise reduction, carries out the mixed specific steps of solution such as using FastICA algorithm
Under:
(1) it treats the mixed signal of solution and carries out centralization processing, make its mean value 0；
(2) whitening processing is carried out to the centralization data that treated, obtains signal U；
(3) number m, the m=n for the component that selection needs to estimate randomly chooses an initial weight vector Wp；
(4) it is randomly provided the number of iterations p；
(5) it is iterated calculating: Wp=E { Ug (Wp TU)}-E{g′(Wp TU) } W, wherein the norm of constraint W is 1, g (Wp TU)=
tanh(Wp TU), E { Ug (Wp TIt U is) } to Ug (Wp TU desired value) is sought；
(6)Wherein constrain WjNorm be 1；
(7) W is enabledp=Wp/||Wp| |, | | Wp| | it is WpNorm；
(8) if WpIt does not restrain, return step (5), until WpConvergence；
(9) p=p+1 is enabled, if p≤m, return step (4), otherwise iteration terminates；
(10) iteration terminates result Wp, WpSignal as after noise reduction.
5. the Rolling Bearing Fault Character extracting method according to claim 1 based on CEEMD and FastICA, feature
It is: signal W (n)=Z after the demodulation2(n)-Z (n-1) Z (n+1), Z (n) are the discrete form of Z (t), Z (n-1) and Z
It (n+1) is the discrete form of Z (t-1) and Z (t+1) respectively, Z (t-1) and Z (t+1) respectively indicate t-1 moment and t+1 moment
Signal.
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| CN111079710A (en) * | 2019-12-31 | 2020-04-28 | 江苏理工学院 | Multilayer noise reduction method based on improved CEEMD rolling bearing signal |
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| CN113361205A (en) * | 2021-06-23 | 2021-09-07 | 合肥工业大学 | Bearing vibration signal fault diagnosis optimization design method based on genetic algorithm and CEEMD |
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| CN113567129A (en) * | 2021-07-28 | 2021-10-29 | 大连海天兴业科技有限公司 | CEEMD-based noise reduction method for train bearing vibration signal |
| CN114486263A (en) * | 2022-02-15 | 2022-05-13 | 浙江大学 | Noise reduction and demodulation method for vibration signal of rolling bearing of rotary machine |
| CN115452377A (en) * | 2022-08-15 | 2022-12-09 | 盐城工学院 | Rolling bearing fault diagnosis method based on CEEMDAN and self-adaptive denoising |
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| CN111079706A (en) * | 2019-12-31 | 2020-04-28 | 辽宁石油化工大学 | Structural modal parameter identification method for improving EEMD (ensemble empirical mode decomposition) based on wavelet and ICA (independent component analysis) |
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| CN113567129A (en) * | 2021-07-28 | 2021-10-29 | 大连海天兴业科技有限公司 | CEEMD-based noise reduction method for train bearing vibration signal |
| CN114486263A (en) * | 2022-02-15 | 2022-05-13 | 浙江大学 | Noise reduction and demodulation method for vibration signal of rolling bearing of rotary machine |
| CN115452377A (en) * | 2022-08-15 | 2022-12-09 | 盐城工学院 | Rolling bearing fault diagnosis method based on CEEMDAN and self-adaptive denoising |
| CN115452377B (en) * | 2022-08-15 | 2024-01-12 | 盐城工学院 | Rolling bearing fault diagnosis method based on CEEMDAN and adaptive denoising |
| CN116699319A (en) * | 2023-08-07 | 2023-09-05 | 湖南大学 | Fault positioning method for grid type submarine observation network direct current power supply system |
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