CN105954031B - A kind of envelope Analysis Method based on unusual spectral factorization filtering - Google Patents
A kind of envelope Analysis Method based on unusual spectral factorization filtering 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
- G01M13/02—Gearings; Transmission mechanisms
- G01M13/028—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
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Abstract
The invention discloses a kind of envelope Analysis Method based on unusual spectral factorization filtering, this method is decomposed first with singular spectrum decomposition method to primary signal, then the noise component(s) and trend term in decomposition result are excluded using the rearrangement and replacement operation of data, then filtered signal for the first time is analyzed using spectrum kurtosis method again, obtain the centre frequency and bandwidth of optimal filter, then second of filtering is carried out again to filtered signal for the first time using the wave filter, then Envelope Analysis is carried out to second of filtered signal using rational spline iteration smoothed envelope analysis method, the fault type of rotating machinery is finally determined according to envelope spectrum.The present invention is suitable for the complicated rotating machinery fault signal of processing, can determine the fault type of rotating machinery exactly, have good noise immunity and robustness, be easy to engineer applied.
Description
Technical field
The present invention relates to condition monitoring for rotating machinery and fault diagnosis field, and in particular to one kind is filtered based on unusual spectral factorization
The envelope Analysis Method of ripple.
Background technology
Envelope Analysis technology is widely used in the fault diagnosis of gear and rolling bearing.Existing Envelope Analysis technology has
Three defects below：（1）Existing Envelope Analysis technology is either directly analyzed primary signal, or only to original
Signal analyzed again after simply filtering, therefore existing method is easily done by noise, trend and other compositions
Disturb, so as to cause the analysis precision of prior art relatively low；（2）Existing Envelope Analysis technology be based on Hilbert is converted,
And Hilbert conversion requires that analyzed signal must be the narrow band signal of simple component, otherwise the frequency modulating section of signal will
The amplitude envelope analysis result of signal is polluted, but signal to be analyzed at present does not meet the bar of simple component and arrowband strictly
Part, it so may result in prior art and erroneous judgement problem easily occur because precision is not high；（3）The envelope spectrum obtained by conventional method
End effect be present.
The content of the invention
The problem to be solved in the present invention is the deficiency for more than, proposes a kind of Envelope Analysis based on unusual spectral factorization filtering
Method, after envelope Analysis Method of the invention, there is analysis result accuracy and accuracy height, and can detect exactly
The advantages of rotating machinery fault type.
To solve above technical problem, the technical scheme that the present invention takes is as follows：It is a kind of based on unusual spectral factorization filtering
Envelope Analysis Method, it is characterised in that comprise the following steps：
Step 1：The vibration signal x of rotating machinery is measured with sample frequency fs using acceleration transducer（k）, （k=1,
2, …,N）, N is the length of sampled signal；
Step 2：Using unusual spectral factorization (Singular Spectrum Decomposition) algorithm by signal x（k）
N component sum is resolved into, i.e.,, wherein, ci（k）Represent i-th point obtained by singular spectrum decomposition algorithm
Amount, unusual spectral factorization is it is well known that be shown in document
P. Bonizzi, J.M. KAREL, O. Meste, R.L. Peeters, Singular spectrum
decomposition: A new method for time series decomposition, Advances in
Adaptive Data Analysis, 2014,6 (4): 1-29；
Step 3：To ci（k）Perform reordering operations and substitute and operate, it is rearranged to operate obtained data ci shuffle（k）Table
Show, data c is obtained after substituting operationi FTran（k）Represent；
Step 4：To ci（k）、ci shuffle（k）And ci FTran（k）Multi-fractal is performed respectively removes trend fluction analysis
（Multifractal Detrended Fluctuation Analysis, MFDFA）, obtain generalized Hurst index curve, ci
（k）Generalized Hurst index curve Hi（q）Represent；ci shuffle（k）Generalized Hurst index curve Hi shuffle（q）Table
Show；ci FTran（k）Generalized Hurst index curve Hi FTran（q）Represent；
Step 5：If Hi（q）With Hi shuffle（q）Or Hi（q）With Hi FTran（q）Between relative error be less than 5%, or
Person Hi（q） 、Hi shuffle（q）And Hi FTran（q）Three does not change with q, then abandons corresponding ci（k）Component；
Step 6：To remaining ci（k）Component is summed, and by this and to be designated as signal rearranged and substitute filtered result xf1
（k）；
Step 7：To xf1（k）Spectrum kurtosis analysis is performed, obtains the centre frequency f corresponding to signal kurtosis maximum0And band
Wide B；
Step 8：According to centre frequency f0With bandwidth B to xf1（k）Bandpass filtering is carried out, obtains xf2（k）；
Step 9：To signal xf2（k）The analysis of rational spline iteration smoothed envelope is performed, obtains signal envelope eov（k）；
Step 10：To obtained signal envelope eov（k）Perform discrete Fourier transform and obtain envelope spectrum, according to envelope spectrum
Characteristic frequency judges the fault type of machine.
A kind of prioritization scheme, in the step 3 data rearrangement operation comprise the following steps：
Upset component c at randomi（k）Put in order.
Further, the operation of data replacement comprises the following steps in the step 3：
1）To component ci（k）Discrete Fourier transform is performed, obtains component ci（k）Phase；
2）Component c is replaced with one group of pseudo- independent same distribution number in (- π, π) sectioni（k）Original phase；
3）Inverse discrete Fourier transform is performed to the frequency domain data after phase substitutes and obtains data ci IFFT（k）, ask for
Data ci IFFT（k）Real part.
Further, MFDFA methods comprise the following steps in the step 4：
1）Constructionx(k)(k=1,2,…,N) profileY(i)：
；
x(k) represent c in step 4 described in claim 1i（k）Or ci shuffle（k）Or ci FTran（k）；
2）By signal profileY(i) be divided into it is nonoverlappingN s Segment length issData, due to data lengthNGenerally can not be whole
Removes, so the remaining one piece of data of meeting can not utilize；
In order to make full use of the length of data, then it is obtained with identical length segmentation, such one from the opposite direction of data
2N s Segment data；
3）Using polynomial trend of the least square fitting per segment data, the variance per segment data is then calculated：
；
y v (i) for the of fittingvThe trend of segment data, if the polynomial trend of fitting ismRank, then remember that this goes trend process
For（MF-）DFAm；In this example, m=1；
4）Calculate theqThe average value of rank wave function：
；
5）Ifx(k) self-similarity characteristics be present, thenqThe average value of rank wave functionF q (s) and time scalesBetween
Power law relation be present：
F q (s)~s H(q)；
WhenqWhen=0, step 4）In formula diverging, at this momentH(0) by logarithmic mean process defined in following formula come really
It is fixed：
；
6）To step 5）In formula both sides take the logarithm can obtain ln [F q (s)]=H(q)ln(s)+c (cFor constant), thus
The slope of straight line can be obtainedH(q)。
Further, the spectrum kurtosis method in the step 7 comprises the following steps：
1）Constructing a cut-off frequency isf c =0.125+εLow pass filterh(n)；ε>0, in this examplef c =0.3；
2）It is based onh(n) passband is constructed as [0;0.25] quasi- low pass filterh 0(n) and passband be [0.25;0.5]
Quasi- high-pass filterh 1 (n),
；
3）SignalThroughh 0(n)、h 1 (n) filter and resolve into low frequency part after down-sampledAnd radio-frequency head
Point, the down-sampled factor is 2, then the shaping filter tree after successive ignition filters, kth layer have 2 k Individual frequency band, its
InRepresent the in wave filter treekOn layeriThe output signal of individual wave filter,i=0,…,2k- 1,0≤k≤K-1, this
K=8 in example；c 0(n) represent x in step 7 described in claim 1f1（k）；
4）In decomposition treekOn layeriThe centre frequency of individual wave filterf ki And bandwidthB k Respectively
f ki =(i+2-1)2-k-1
B k =2-k-1
5）Calculate each filter results( i=0,…,2k- 1) kurtosis；
6）All spectrum kurtosis are collected, obtain the total spectrum kurtosis of signal.
Further, the rational spline iteration smoothed envelope analysis method in the step 9 comprises the following steps：
1）Calculate signalz(k) Jue Dui Zhi ∣z(k) ∣ local extremum；In the 1st iteration,z(k) represent claim
X in 1 step 9f2（k）；
2）Envelope eov is obtained using rational spline curve fitting Local Extremum1（k）；
3）It is rightz(k) be normalized to obtain；
4）2nd iteration：z 1(k) new data is used as again, repeat above-mentioned steps 1）~3）, obtain
；
5）Ith iteration：z i-1(k) new data is used as again, repeat above-mentioned steps 1）~ 3), obtain
；
If 6)nWhat secondary iteration obtainedz n (k) amplitude be less than or equal to 1, then iterative process stop, finally obtaining
Signalz(k) envelope be。
The present invention uses above technical scheme, and compared with prior art, the present invention has advantages below：
1) primary signal is decomposed using unusual spectral factorization, then excludes it using the rearrangement and replacement operation of data
In noise and trend component, the only useful component in stick signal component, so as to avoid noise and trend component to bag
The influence of network analysis result, analysis result accuracy and accuracy are high.
2) signal envelope and frequency modulating section are kept completely separate using rational spline iteration smoothed envelope analysis method, energy
Influence of the frequency modulating section to signal envelope analysis result is enough avoided, so as to improve the precision of Envelope Analysis.
3) fault type of rotating machinery can be detected exactly.
4) there is end effect in the envelope spectrum obtained by conventional method, and the envelope spectrum obtained by the present invention can avoid
End effect.
The present invention will be further described with reference to the accompanying drawings and examples.
Brief description of the drawings
Accompanying drawing 1 is the flow chart of the inventive method in the embodiment of the present invention；
Accompanying drawing 2 is to carry out preliminary exposition to signal using low pass filter and high-pass filter in the embodiment of the present invention to show
It is intended to；
Accompanying drawing 3 is the schematic diagram for quickly calculating spectrum kurtosis in the embodiment of the present invention using tree-shaped filter construction；
Accompanying drawing 4 is the bearing vibration signal for having in the embodiment of the present invention inner ring failure；
Accompanying drawing 5 is to inner ring faulty bearing vibration signal in the embodiment of the present invention using traditional envelope Analysis Method
Analysis result；
Analysis result of the accompanying drawing 6 for the present invention in the embodiment of the present invention to inner ring faulty bearing vibration signal；
Accompanying drawing 7 is the bearing vibration signal for having in the embodiment of the present invention outer ring failure；
Accompanying drawing 8 is to outer ring faulty bearing vibration signal in the embodiment of the present invention using traditional envelope Analysis Method
Analysis result；
Analysis result of the accompanying drawing 9 for the present invention in the embodiment of the present invention to outer ring faulty bearing vibration signal.
Embodiment
Embodiment, as shown in Figure 1, Figure 2, Figure 3 shows, a kind of envelope Analysis Method based on unusual spectral factorization filtering, including with
Lower step：
Step 1：The vibration signal x of rotating machinery is measured with sample frequency fs using acceleration transducer（k）, （k=1,
2, …,N）, N is the length of sampled signal；
Step 2：Using unusual spectral factorization (Singular Spectrum Decomposition) algorithm by signal x（k）
N component sum is resolved into, i.e.,, wherein, ci（k）Represent i-th obtained by singular spectrum decomposition algorithm
Component, unusual spectral factorization is it is well known that be shown in document
P. Bonizzi, J.M. KAREL, O. Meste, R.L. Peeters, Singular spectrum
decomposition: A new method for time series decomposition, Advances in
Adaptive Data Analysis, 2014,6 (4): 1-29；
Step 3：To ci（k）Perform reordering operations and substitute and operate, it is rearranged to operate obtained data ci shuffle（k）Table
Show, data c is obtained after substituting operationi FTran（k）Represent；
Step 4：To ci（k）、ci shuffle（k）And ci FTran（k）Multi-fractal is performed respectively removes trend fluction analysis
（Multifractal Detrended Fluctuation Analysis, MFDFA）, obtain generalized Hurst index curve, ci
（k）Generalized Hurst index curve Hi（q）Represent；ci shuffle（k）Generalized Hurst index curve Hi shuffle（q）Table
Show；ci FTran（k）Generalized Hurst index curve Hi FTran（q）Represent；
Step 5：If Hi（q）With Hi shuffle（q）Or Hi（q）With Hi FTran（q）Between relative error be less than 5%, or
Person Hi（q） 、Hi shuffle（q）And Hi FTran（q）Three does not change with q, then abandons corresponding ci（k）Component；
Step 6：To remaining ci（k）Component is summed, and by this and to be designated as signal rearranged and substitute filtered result xf1
（k）；
Step 7：To xf1（k）Spectrum kurtosis analysis is performed, obtains the centre frequency f corresponding to signal kurtosis maximum0And band
Wide B；
Step 8：According to centre frequency f0With bandwidth B to xf1（k）Bandpass filtering is carried out, obtains xf2（k）；
Step 9：To signal xf2（k）The analysis of rational spline iteration smoothed envelope is performed, obtains signal envelope eov（k）；
Step 10：To obtained signal envelope eov（k）Perform discrete Fourier transform and obtain envelope spectrum, according to envelope spectrum
Characteristic frequency judges the fault type of machine.
Data rearrangement operation comprises the following steps in step 3：
Upset component c at randomi（k）Put in order.
Data substitute operation and comprised the following steps in step 3：
1）To component ci（k）Discrete Fourier transform is performed, obtains component ci（k）Phase；
2）Component c is replaced with one group of pseudo- independent same distribution number in (- π, π) sectioni（k）Original phase；
3）Inverse discrete Fourier transform is performed to the frequency domain data after phase substitutes and obtains data ci IFFT（k）, ask for
Data ci IFFT（k）Real part.
MFDFA methods comprise the following steps in step 4：
1）Constructionx(k)(k=1,2,…,N) profileY(i)：
；
x(k) represent c in step 4 described in claim 1i（k）Or ci shuffle（k）Or ci FTran（k）；
2）By signal profileY(i) be divided into it is nonoverlappingN s Segment length issData, due to data lengthNGenerally can not be whole
Removes, so the remaining one piece of data of meeting can not utilize；
In order to make full use of the length of data, then it is obtained with identical length segmentation, such one from the opposite direction of data
2N s Segment data；
3）Using polynomial trend of the least square fitting per segment data, the variance per segment data is then calculated：
；
y v (i) for the of fittingvThe trend of segment data, if the polynomial trend of fitting ismRank, then remember that this goes trend process
For（MF-）DFAm；In this example, m=1；
4）Calculate theqThe average value of rank wave function：
；
5）Ifx(k) self-similarity characteristics be present, thenqThe average value of rank wave functionF q (s) and time scalesBetween
Power law relation be present：
F q (s)~s H(q)；
WhenqWhen=0, step 4）In formula diverging, at this momentH(0) by logarithmic mean process defined in following formula come really
It is fixed：
；
6）To step 5）In formula both sides take the logarithm can obtain ln [F q (s)]=H(q)ln(s)+c (cFor constant), thus
The slope of straight line can be obtainedH(q)。
Spectrum kurtosis method in step 7 comprises the following steps：
1）Constructing a cut-off frequency isf c =0.125+εLow pass filterh(n)；ε>0, in this examplef c =0.3；
2）It is based onh(n) passband is constructed as [0;0.25] quasi- low pass filterh 0(n) and passband be [0.25;0.5]
Quasi- high-pass filterh 1 (n),
；
3）SignalThroughh 0(n)、h 1 (n) filter and resolve into low frequency part after down-sampledAnd high frequency
Part, the down-sampled factor is 2, then the shaping filter tree after successive ignition filters, kth layer have 2 k Individual frequency band,
WhereinRepresent the in wave filter treekOn layeriThe output signal of individual wave filter,i=0,…,2k- 1,0≤k≤K-
1, K=8 in this example；c 0(n) represent x in step 7 described in claim 1f1（k）；
4）In decomposition treekOn layeriThe centre frequency of individual wave filterf ki And bandwidthB k Respectively
f ki =(i+2-1)2-k-1
B k =2-k-1
5）Calculate each filter results( i=0,…,2k- 1) kurtosis；
6）All spectrum kurtosis are collected, obtain the total spectrum kurtosis of signal.
Rational spline iteration smoothed envelope analysis method in step 9 comprises the following steps：
1）Calculate signalz(k) Jue Dui Zhi ∣z(k) ∣ local extremum；In the 1st iteration,z(k) represent claim
X in 1 step 9f2（k）；
2）Envelope eov is obtained using rational spline curve fitting Local Extremum1（k）；
3）It is rightz(k) be normalized to obtain；
4）2nd iteration：z 1(k) new data is used as again, repeat above-mentioned steps 1）~3）, obtain
；
5）Ith iteration：z i-1(k) new data is used as again, repeat above-mentioned steps 1）~ 3), obtain
；
If 6)nWhat secondary iteration obtainedz n (k) amplitude be less than or equal to 1, then iterative process stop, finally obtaining
Signalz(k) envelope be。
Experiment 1, is tested the performance of algorithm of the present invention using the bearing vibration data with inner ring failure
Card.
Bearing used in experiment is 6205-2RS JEM SKF, using electric discharge machining method on bearing inner race working depth
The groove for being 0.3556mm for 0.2794mm, width simulates bearing inner race failure, and this experiment load is about 0.7457kW, driving
It is about 29.5Hz that motor, which turns frequency, and bearing inner race fault characteristic frequency is about 160Hz, sample frequency 4.8KHz, during signal sampling
A length of 1s.
The inner ring fault-signal collected is as shown in Figure 4.
The signal shown in Fig. 4 is analyzed using traditional envelope Analysis Method first, obtained analysis result such as Fig. 5
It is shown.From fig. 5, it can be seen that the fault signature of bearing is blanked completely, therefore traditional envelope Analysis Method can not be effectively
Extract the fault signature of bearing；In addition, from fig. 5, it can be seen that the left end point of envelope spectrum there is abnormal high level, this explanation is by passing
There is end effect for the envelope spectrum that system method obtains.
Signal shown in Fig. 4 is analyzed using method proposed by the invention, obtained analysis result such as Fig. 6 institutes
Show.From fig. 6, it can be seen that the spectral line corresponding to 160Hz and 320Hz corresponds to respectively apparently higher than other spectral lines, the two frequencies
1 frequency multiplication and 2 frequencys multiplication of bearing inner race fault characteristic frequency, may determine that bearing has inner ring failure accordingly；Can from Fig. 6
Go out, the envelope spectrum obtained by the present invention does not have end effect.
Show through many experiments, in the case where loading and failure dimensional depth being constant, the present invention is capable of reliable recognition
Minimum inner ring failure dimension width is about 0.21 mm, and conventional method is capable of the minimum inner ring failure dimension width of reliable recognition
About 0.53mm, precision improve 60.4%.
Experiment 2, is tested the performance of algorithm of the present invention using the bearing vibration data with outer ring failure
Card.
Bearing used in experiment is 6205-2RS JEM SKF, using electric discharge machining method on bearing outer ring working depth
The groove for being 0.5334mm for 0.2794mm, width simulates bearing outer ring failure, and this experiment load is about 2.237 kW, driving
It is about 28.7Hz that motor, which turns frequency, and bearing outer ring fault characteristic frequency is about 103Hz, sample frequency 4.8KHz, during signal sampling
A length of 1s.
The outer ring fault-signal collected is as shown in Figure 7.
The signal shown in Fig. 7 is analyzed using traditional envelope Analysis Method first, obtained analysis result such as Fig. 8
It is shown.From figure 8, it is seen that the fault signature of bearing is blanked completely, therefore traditional envelope Analysis Method can not be effectively
Extract the fault signature of bearing；In addition, from figure 8, it is seen that the left end point of envelope spectrum there is abnormal high level, this explanation is by passing
There is end effect for the envelope spectrum that system method obtains.
Signal shown in Fig. 7 is analyzed using method proposed by the invention, obtained analysis result such as Fig. 9 institutes
Show.From fig. 9, it can be seen that the spectral line corresponding to 103Hz and 206Hz corresponds to respectively apparently higher than other spectral lines, the two frequencies
1 frequency multiplication and 2 frequencys multiplication of bearing outer ring fault characteristic frequency, may determine that bearing has outer ring failure accordingly；Can from Fig. 9
Go out, the envelope spectrum obtained by the present invention does not have end effect..
Show through many experiments, in the case where loading and failure dimensional depth being constant, the present invention is capable of reliable recognition
Minimum outer ring failure dimension width is about 0.31mm, and conventional method is capable of the minimum outer ring failure dimension width of reliable recognition about
For 0.68mm, precision improves 54.4%.
According to result of the test, think after analysis：
1) traditional envelope Analysis Method directly carries out Envelope Analysis to primary signal, or to merely through simple process
Primary signal afterwards carries out Envelope Analysis, different from traditional envelope Analysis Method, and the present invention is first with unusual spectral factorization pair
Primary signal is decomposed, and then excludes noise and trend component therein, Jin Jinbao using the rearrangement and replacement operation of data
The useful component in component of signal is stayed, so as to avoid the influence of noise and trend component to Envelope Analysis result, improves standard
Exactness and accuracy.
2) traditional envelope Analysis Method is based on Hilbert is converted, and Hilbert conversion requires analyzed letter
Number must be the narrow band signal of simple component, otherwise the frequency modulating section of signal will pollute the Envelope Analysis result of signal, but
It is the condition that signal to be analyzed does not meet simple component and arrowband strictly at present, so may result in prior art because of precision not
High and erroneous judgement problem easily occur, different from traditional envelope Analysis Method, the present invention is divided using rational spline iteration smoothed envelope
Signal envelope and frequency modulating section are kept completely separate by analysis method, can avoid frequency modulating section to signal envelope analysis result
Influence, so as to improve the precision of Envelope Analysis.
3) fault type of rotating machinery can be detected exactly.
4) there is end effect in the envelope spectrum obtained by conventional method, and the envelope spectrum obtained by the present invention can avoid
End effect.
5）Each step effect：
1) step：Gather vibration signal；
2) step：Primary signal is resolved into the form of different component sums, some of which component corresponds to noise and trend term,
Some components correspond to useful signal；
3) ~ 5) step：The signal obtained to above-mentioned decomposition performs reordering operations and substituted and operates, and rejects noise therein point
Amount and trend term, only retain useful signal；
6) step：Remaining useful signal is summed, using this and it is rearranged as signal and substitute filtered result xf1
(k)；
7) step：To filtered signal xf1(k) spectrum kurtosis analysis is performed, obtains center corresponding at signal maximum kurtosis
Frequency f0And bandwidth B；
8) step：According to centre frequency f0With bandwidth B to xf1(k) bandpass filtering is carried out, obtains signal xf2(k)；
9) step：Calculate signal xf2(k) envelope eov (k)；
10) step：Discrete Fourier transform is performed to eov (k) and obtains envelope spectrum, the failure of bearing is judged according to envelope spectrum
Type.
One skilled in the art would recognize that above-mentioned embodiment is exemplary, it is in order that ability
Field technique personnel can be better understood from present invention, should not be understood as limiting the scope of the invention, as long as
According to technical solution of the present invention improvements introduced, protection scope of the present invention is each fallen within.
Claims (4)
1. a kind of envelope Analysis Method based on unusual spectral factorization filtering, it is characterised in that comprise the following steps：
Step 1：The vibration signal x of rotating machinery is measured with sample frequency fs using acceleration transducer（k）, k=1, 2, …,
N, N are the length of sampled signal；
Step 2：Using unusual spectral factorization (Singular Spectrum Decomposition) algorithm by signal x（k）Decompose
Into n component sum, i.e.,, wherein, ci（k）I-th of the component obtained by singular spectrum decomposition algorithm is represented,
Unusual spectral factorization is known；
Step 3：To ci（k）Perform reordering operations and substitute and operate, it is rearranged to operate obtained data ci shuffle（k）Represent,
Data c is obtained after substituting operationi FTran（k）Represent；
Step 4：To ci（k）、ci shuffle（k）And ci FTran（k）Multi-fractal is performed respectively removes trend fluction analysis
（Multifractal Detrended Fluctuation Analysis, MFDFA）, obtain generalized Hurst index curve, ci
（k）Generalized Hurst index curve Hi（q）Represent；ci shuffle（k）Generalized Hurst index curve Hi shuffle（q）Table
Show；ci FTran（k）Generalized Hurst index curve Hi FTran（q）Represent；
Step 5：If Hi（q）With Hi shuffle（q）Or Hi（q）With Hi FTran（q）Between relative error be less than 5%, or Hi
（q） 、Hi shuffle（q）And Hi FTran（q）Three does not change with q, then abandons corresponding ci（k）Component；
Step 6：To remaining ci（k）Component is summed, and by this and to be designated as signal rearranged and substitute filtered result xf1（k）；
Step 7：To xf1（k）Spectrum kurtosis analysis is performed, obtains the centre frequency f corresponding to signal kurtosis maximum0And bandwidth B；
Step 8：According to centre frequency f0With bandwidth B to xf1（k）Bandpass filtering is carried out, obtains xf2（k）；
Step 9：To signal xf2（k）The analysis of rational spline iteration smoothed envelope is performed, obtains signal envelope eov（k）；
Step 10：To obtained signal envelope eov（k）Perform discrete Fourier transform and obtain envelope spectrum, according to envelope spectrum signature
Frequency judges the fault type of machine.
2. a kind of envelope Analysis Method based on unusual spectral factorization filtering according to claim 1, it is characterised in that described
Data rearrangement operation comprises the following steps in step 3：
Upset component c at randomi（k）Put in order.
A kind of 3. envelope Analysis Method based on unusual spectral factorization filtering according to claim 1, it is characterised in that：It is described
Data substitute operation and comprised the following steps in step 3：
1）To component ci（k）Discrete Fourier transform is performed, obtains component ci（k）Phase；
2）Component c is replaced with one group of pseudo- independent same distribution number in (- π, π) sectioni（k）Original phase；
3）Inverse discrete Fourier transform is performed to the frequency domain data after phase substitutes and obtains data ci IFFT（k）, ask for data
ci IFFT（k）Real part.
4. a kind of envelope Analysis Method based on unusual spectral factorization filtering according to claim 1, it is characterised in that described
Rational spline iteration smoothed envelope analysis method in step 9 comprises the following steps：
1）Calculate signalz(k) Jue Dui Zhi ∣z(k) ∣ local extremum；In the 1st iteration,z(k) represent claim 1 institute
State x in step 9f2（k）；
2）Envelope eov is obtained using rational spline curve fitting Local Extremum1（k）；
3）It is rightz(k) be normalized to obtain；
4）2nd iteration：z 1(k) new data is used as again, repeat above-mentioned steps 1）~3）, obtain
；
5）Ith iteration：z i-1(k) new data is used as again, repeat above-mentioned steps 1）~ 3), obtain
；
If 6)nWhat secondary iteration obtainedz n (k) amplitude be less than or equal to 1, then iterative process stop, finally obtaining signalz
(k) envelope be。
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| CN108801634B (en) * | 2018-03-21 | 2019-12-03 | 昆明理工大学 | The method and its application of bearing fault characteristics frequency are extracted based on singular value decomposition and the frequency band entropy of optimization |
| CN108880506B (en) * | 2018-06-07 | 2020-07-31 | 西安电子科技大学 | Method for realizing polynomial fitting digital filter |
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