CN106053061B - A kind of envelope Analysis Method for decomposing and composing kurtosis based on nonlinear model - Google Patents
A kind of envelope Analysis Method for decomposing and composing kurtosis based on nonlinear model Download PDFInfo
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- CN106053061B CN106053061B CN201610492088.2A CN201610492088A CN106053061B CN 106053061 B CN106053061 B CN 106053061B CN 201610492088 A CN201610492088 A CN 201610492088A CN 106053061 B CN106053061 B CN 106053061B
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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 for being decomposed and being composed kurtosis based on nonlinear model, this method is decomposed first with nonlinear model 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 cubic 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 a kind of based on nonlinear model point
The envelope Analysis Method of solution and spectrum kurtosis.
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 is 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
There is end effect.
The content of the invention
The problem to be solved in the present invention is the deficiency for more than, and proposition is a kind of to be decomposed and composed kurtosis based on nonlinear model
Envelope Analysis Method, after envelope Analysis Method of the invention, there is analysis result accuracy and accuracy height, and can be accurate
Ground detects the advantages of rotating machinery fault type.
To solve above technical problem, the technical scheme that the present invention takes is as follows：One kind based on nonlinear model decompose and
Compose the envelope Analysis Method of kurtosis, 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：(Nonlinear Mode Decomposition) algorithm is decomposed by signal x using nonlinear model（k）
N component sum is resolved into, i.e.,, wherein, ci（k）Represent what is obtained by nonlinear model decomposition algorithm
I-th of component, nonlinear model are decomposed it is well known that seeing document
Dmytro Iatsenko, Peter V. E. McClintock, Aneta Stefanovska. Nonlinear
mode decomposition: A noise-robust, adaptive decomposition method, PHYSICAL
REVIEW E, 2015, 92: 032916；
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 cubic 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）Construct the profile Y (i) of x (k) (k=1,2 ..., N)：
X (k) represents the c in step 4 described in claim 1i（k）Or ci shuffle（k）Or ci FTran（k）；
2）Signal profile Y (i) is divided into nonoverlapping NSSegment length is s data, because data length N generally can not be whole
Except s, 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
2NSSegment data；
3）Using polynomial trend of the least square fitting per segment data, the variance per segment data is then calculated：
yv(i) it is the trend for the v segment datas being fitted, if the polynomial trend of fitting is m ranks, remembers that this goes trend process
For（MF-）DFAm；In this example, m=1；
4）Calculate the average value of q rank wave functions：
；
5）If there is self-similarity characteristics, the average value F of q rank wave functions in x (k)q(s) between time scale s
Power law relation be present：
As q=0, step 4）In formula diverging, at this moment H (0) come by logarithmic mean process defined in following formula true
It is fixed：
6）To step 5）In formula both sides take the logarithm and can obtain ln [Fq(s)]=H(q)ln(s)+c（C is constant）, thus may be used
To obtain the slope H (q) of straight line.
Further, the spectrum kurtosis method in the step 7 comprises the following steps：
1）It is f to construct a cut-off frequencyc=0.125+ ε low pass filter h (n)；ε>0, f in this examplec=0.3;
2）Based on the quasi- low pass filter h that h (n) construction passbands are [0,0.25]0(n) be with passband [0.25,
0.5] quasi- high-pass filter h1(n),
；
3）Signal ci k(n) through h0(n)、 h1(n) filter and resolve into low frequency part c after down-sampled2i k+1And radio-frequency head (n)
Divide c2i+1 k+1(n), the down-sampled factor is 2, then the shaping filter tree after successive ignition filters, kth layer have 2kIndividual frequency band, its
Middle ci k(n) output signal of i-th of wave filter in expression wave filter tree on kth layer, i=0 ..., 2k- 1,0≤k≤K-1, this
K=8 in example；c0(n) x in step 7 described in claim 1 is representedf1（k）；
4）The centre frequency f of i-th of wave filter in decomposition tree on kth layerkiAnd bandwidth BkRespectively
；
5）Calculate each filter results ci k(n)( i=0,…, 2k- 1) kurtosis；
6）All spectrum kurtosis are collected, obtain the total spectrum kurtosis of signal.
Further, the cubic 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 cubic spline interpolation 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) decomposed using nonlinear model and primary signal is decomposed, then the rearrangement using data and replacement operation row
Except noise therein and trend component, the only useful component in stick signal component, so as to avoid noise and trend component
Influence to Envelope Analysis result, analysis result accuracy and accuracy are high.
2) signal envelope and frequency modulating section are kept completely separate using cubic 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 side for decomposing and composing kurtosis based on nonlinear model
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：(Nonlinear Mode Decomposition) algorithm is decomposed by signal x using nonlinear model（k）
N component sum is resolved into, i.e.,, wherein, ci（k）Represent what is obtained by nonlinear model decomposition algorithm
I-th of component, nonlinear model are decomposed it is well known that seeing document
Dmytro Iatsenko, Peter V. E. McClintock, Aneta Stefanovska. Nonlinear
mode decomposition: A noise-robust, adaptive decomposition method, PHYSICAL
REVIEW E, 2015, 92: 032916；
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 cubic 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）Construct the profile Y (i) of x (k) (k=1,2 ..., N)：
X (k) represents the c in step 4 described in claim 1i（k）Or ci shuffle（k）Or ci FTran（k）；
2）Signal profile Y (i) is divided into nonoverlapping NSSegment length is s data, because data length N generally can not be whole
Except s, 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
2NSSegment data；
3）Using polynomial trend of the least square fitting per segment data, the variance per segment data is then calculated：
yv(i) it is the trend for the v segment datas being fitted, if the polynomial trend of fitting is m ranks, remembers that this goes trend process
For（MF-）DFAm；In this example, m=1；
4）Calculate the average value of q rank wave functions：
；
5）If there is self-similarity characteristics, the average value F of q rank wave functions in x (k)q(s) between time scale s
Power law relation be present：
As q=0, step 4）In formula diverging, at this moment H (0) come by logarithmic mean process defined in following formula true
It is fixed：
6）To step 5）In formula both sides take the logarithm and can obtain ln [Fq(s)]=H(q)ln(s)+c（C is constant）, thus may be used
To obtain the slope H (q) of straight line.
Spectrum kurtosis method in step 7 comprises the following steps：
1）It is f to construct a cut-off frequencyc=0.125+ ε low pass filter h (n)；ε>0, f in this examplec=0.3;
2）Based on the quasi- low pass filter h that h (n) construction passbands are [0,0.25]0(n) be with passband [0.25,
0.5] quasi- high-pass filter h1(n),
；
3）Signal ci k(n) through h0(n)、 h1(n) filter and resolve into low frequency part c after down-sampled2i k+1And radio-frequency head (n)
Divide c2i+1 k+1(n), the down-sampled factor is 2, then the shaping filter tree after successive ignition filters, kth layer have 2kIndividual frequency band, its
Middle ci k(n) output signal of i-th of wave filter in expression wave filter tree on kth layer, i=0 ..., 2k- 1,0≤k≤K-1, this
K=8 in example；c0(n) x in step 7 described in claim 1 is representedf1（k）；
4）The centre frequency f of i-th of wave filter in decomposition tree on kth layerkiAnd bandwidth BkRespectively
；
5）Calculate each filter results ci k(n)( i=0,…, 2k- 1) kurtosis；
6）All spectrum kurtosis are collected, obtain the total spectrum kurtosis of signal.
Cubic 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 cubic spline interpolation 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, the left end point of envelope spectrum shown in Fig. 5, there is abnormal high level, this explanation is by conventional method
There is end effect for obtained envelope spectrum.
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 0.23 mm, and conventional method is capable of the minimum inner ring failure dimension width of reliable recognition
About 0.53mm, precision improve 56.6%.
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, the left end point of envelope spectrum shown in Fig. 8, there is abnormal high level, this explanation is by conventional method
There is end effect for obtained envelope spectrum.
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 0.33mm, and conventional method is capable of the minimum outer ring failure dimension width of reliable recognition about
For 0.68mm, precision improves 51.5%.
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 nonlinear model point
Solution is decomposed to primary signal, then excludes noise and trend component therein using the rearrangement and replacement operation of data, only
Useful component only in stick signal component, so as to avoid the influence of noise and trend component to Envelope Analysis result, improve
Accuracy and precision.
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 cubic 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 for decomposing and composing kurtosis based on nonlinear model, 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：(Nonlinear Mode Decomposition) algorithm is decomposed by signal x using nonlinear model（k）Decompose
Into n component sum, i.e.,, wherein, ci（k）Represent i-th obtained by nonlinear model decomposition algorithm
Individual component, nonlinear model decompose 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 cubic 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 for decomposing and composing kurtosis based on nonlinear model according to claim 1, its feature
It is, data rearrangement is operated and comprised the following steps in the step 3：
Upset component c at randomi（k）Put in order.
3. a kind of envelope Analysis Method for decomposing and composing kurtosis based on nonlinear model according to claim 1, its feature
It is：Data substitute operation and comprised 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.
4. a kind of envelope Analysis Method for decomposing and composing kurtosis based on nonlinear model according to claim 1, its feature
It is, the cubic 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 1 institute
State x in step 9f2（k）；
2）Envelope eov is obtained using cubic spline interpolation 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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| EP2581725A2 (en) * | 2011-10-13 | 2013-04-17 | General Electric Company | Methods and systems for automatic rolling-element bearing fault detection |
| CN103900815A (en) * | 2014-04-02 | 2014-07-02 | 兰州交通大学 | Rolling bearing fault diagnosis method based on EEMD and distribution fitting testing |
| CN104677632A (en) * | 2015-01-21 | 2015-06-03 | 大连理工大学 | Rolling bearing fault diagnosis method using particle filtering and spectral kurtosis |
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| EP2581725A2 (en) * | 2011-10-13 | 2013-04-17 | General Electric Company | Methods and systems for automatic rolling-element bearing fault detection |
| CN103900815A (en) * | 2014-04-02 | 2014-07-02 | 兰州交通大学 | Rolling bearing fault diagnosis method based on EEMD and distribution fitting testing |
| CN104677632A (en) * | 2015-01-21 | 2015-06-03 | 大连理工大学 | Rolling bearing fault diagnosis method using particle filtering and spectral kurtosis |
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| 基于非平稳时间序列双标度指数特征的齿轮箱故障诊断;林近山等;《机械工程学报》;20120731;第48卷(第13期);全文 * |
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