CN106198010B - A kind of envelope Analysis Method that filtering is decomposed based on local mean value - Google Patents
A kind of envelope Analysis Method that filtering is decomposed based on local mean value Download PDFInfo
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Abstract
The invention discloses a kind of envelope Analysis Methods that filtering is decomposed based on local mean value, this method decomposes original signal first with part mean decomposition method, then the noise component(s) and trend term in decomposition result are excluded using the rearrangement of data and replacement operation, 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 accurately determine the fault type of rotating machinery, have good noise immunity and robustness, convenient for engineer application.
Description
Technical field
The present invention relates to condition monitoring for rotating machinery and fault diagnosis field, and in particular to one kind is decomposed based on local mean value
The envelope Analysis Method of filtering.
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 directly analyzes original signal or only to original
Signal analyzed again, therefore existing method is easily done by noise, trend and other ingredients after simply filtering
It disturbs, it is relatively low so as to cause the analysis precision of the prior art；2. existing Envelope Analysis technology is based on Hilbert is converted,
And the signal that Hilbert transformation requirements are analyzed 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 item of simple component and narrowband strictly
Part may result in the prior art and erroneous judgement problem be susceptible to due to precision is not high in this way；3. the envelope spectrum obtained by conventional method
There are end effects.
Invention content
The problem to be solved in the present invention is for a kind of above insufficient, envelope point that filtering is decomposed based on local mean value of proposition
Analysis method after envelope Analysis Method using the present invention, has that analysis result accuracy and accuracy are high, and can accurately detect
The advantages of going out rotating machinery fault type.
For solution more than technical problem, the technical solution that the present invention takes is as follows：One kind decomposes filtering based on local mean value
Envelope Analysis Method, which is characterized in that include 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 local mean value decomposition algorithm by signal x（k）The sum of n component and trend term are resolved into, i.e.,, wherein, ci（k）Represent i-th of the component obtained by local mean value decomposition algorithm, rn（k）It represents
The trend term obtained by local mean value decomposition algorithm；
Step 3：To ci（k）It performs reordering operations and substitutes and operate, it is rearranged to operate obtained data ci shuffle（k）Table
Show, data c is obtained after substituting operationi FTran（k）It represents；
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）It represents；ci shuffle（k）Generalized Hurst index curve Hi shuffle（q）Table
Show；ci FTran（k）Generalized Hurst index curve Hi FTran（q）It represents；
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 denoted as signal rearranged and substitute filtered result xf1
（k）；
Step 7：To xf1（k）Spectrum kurtosis analysis is performed, the centre frequency f corresponding to signal kurtosis maximum is obtained0And 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）It performs discrete Fourier transform and obtains envelope spectrum, according to envelope spectrum
Characteristic frequency judges the fault type of machine.
A kind of prioritization scheme, local mean value decomposition algorithm includes the following steps in the step 2：
1）Calculate local mean value function：Determine original signalx(k) all Local Extremumn i , calculate two neighboring pole
Value pointn i Withn i+1Average valuem i , i.e.,
By the average value of all two neighboring extreme pointsm i It is connected, is then carried out using rolling average method smooth with broken line
Processing, obtains local mean value functionm 11(k) ；In this example, the smooth step-length in rolling average method is set as 5；
2）Estimate the envelope value of signal：Using Local Extremumn i Calculate envelope estimated valuea i
Equally, by all two neighboring envelope estimated valuesa i It is connected with broken line, is then put down using rolling average method
Sliding processing, obtains envelope estimation functiona 11(k)；
3）By local mean value functionm 11(k) from original signalx(k) in separate, obtain
h 11(k)= x(k)- m 11(k)；
4）Withh 11(k) divided by envelope estimation functiona 11(k) so as to righth 11(k) be demodulated, it obtains
It is desirable thats 11(k) be a pure FM signal, i.e. its envelope estimation functiona 12(k) meeta 12(k)=1；Ifs 11(k) condition is not satisfied, then wills 11(k) as initial data repeatedly more than iterative process m times, until obtaining a pure tune
Frequency signals 1m(k), i.e.,s 1m(k) satisfaction -1≤s 1m(k)≤1, its envelope estimation functiona 1(m+1)(k) meeta 1(m+1)(k)=1；
Therefore have
In formula
The condition of iteration ends is
In practical applications, a variation Δ can be set, when meeting 1- Δs≤a1m(k)≤1+ Δs when, iteration is whole
Only；Variation Δ=0.01 in this example；
5）All envelope estimation functions multiplication generated in iterative process can be obtained envelope signal
6）By envelope signala 1 (k) and pure FM signals 1m (k) can be obtained by being multiplied by 1st point of original signal
Amount
c 1 (k)=a 1(k)s 1m(k)；
7）By the 1st componentc 1 (k) from original signalx(k) in separate, obtain a new signalr 1 (k), it willr 1 (k) as new data repetition above step, cyclenIt is secondary, untilr n (k) for until monotonic function
So far, by original signalx(k) be decomposed intonA component and a monotonic functionr n (kThe sum of), i.e.,
。
Further, data rearrangement operation includes the following steps in the step 3：
Upset component c at randomi（k）Put in order.
Further, the operation of data replacement includes the following steps in the step 3：
1）To component ci（k）Discrete Fourier transform is performed, obtains component ci（k）Phase；
2）It is located at the pseudo- independent same distribution number in (- π, π) section with one group to replace component ci（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 include 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 lengthNIt generally can not be whole
It removess, so the remaining one piece of data of meeting cannot utilize；
In order to make full use of the length of data, then it is obtained with identical length segmentation, such one from the negative 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 fitting thevThe trend of segment data, if the polynomial trend of fitting ismRank then remembers 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) there are self-similarity characteristics, thenqThe average value of rank wave functionF q (s) and time scalesBetween
There are power law relations：
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 includes the following steps：
1）Constructing a cutoff frequency isf c =0.125+εLow-pass filterh(n)；ε>0, in this examplef c =0.3；
2）It is based onh(n) construction passband be [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 section, the down-sampled factor is 2, then the shaping filter tree after successive ignition filters, kth layer have 2 k A frequency band, whereinIt represents the in wave filter treekOn layeriThe output signal of a wave filter,i=0,…,2k- 1,0≤k≤K-1, this example
Middle K=8；c 0(n) represent x in step 7 described in claim 1f1（k）；
4）In decomposition treekOn layeriThe centre frequency of a 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 summarized, obtain the total spectrum kurtosis of signal.
Further, the rational spline iteration smoothed envelope analysis method in the step 9 includes the following steps：
1）Calculate signalz(k) Jue Dui Zhi ∣z(k) the local extremum of ∣；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 re-used as, repeat above-mentioned steps 1）~3）, obtain；
5）Ith iteration：z i-1(k) new data is re-used as, repeat above-mentioned steps 1）~ 3) it, obtains；
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 is using above technical scheme, and compared with prior art, the present invention has the following advantages：
1) original signal is decomposed using local mean value decomposition, is then excluded using the rearrangement of data and replacement operation
Noise and trend component therein, the only useful component in stick signal component, so as to avoid noise and trend component pair
The influence of Envelope 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 accurately detected.
4) envelope spectrum obtained by conventional method is there are end effect, and can be avoided by the envelope spectrum that the present invention obtains
End effect.
The present invention will be further described with reference to the accompanying drawings and examples.
Description of the drawings
Attached drawing 1 is the flow chart of the method for the present invention in the embodiment of the present invention.
Attached 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.
Attached drawing 3 is the schematic diagram for quickly calculating spectrum kurtosis in the embodiment of the present invention using tree-shaped filter construction.
Attached drawing 4 is the bearing vibration signal for having in the embodiment of the present invention inner ring failure.
Attached drawing 5 is to inner ring faulty bearing vibration signal in the embodiment of the present invention using traditional envelope Analysis Method
Analysis result.
Attached drawing 6 is the present invention in the embodiment of the present invention to the analysis result of inner ring faulty bearing vibration signal.
Attached drawing 7 is the bearing vibration signal for having in the embodiment of the present invention outer ring failure.
Attached drawing 8 is to outer ring faulty bearing vibration signal in the embodiment of the present invention using traditional envelope Analysis Method
Analysis result.
Attached drawing 9 is the present invention in the embodiment of the present invention to the analysis result of outer ring faulty bearing vibration signal.
Specific embodiment
Embodiment, as shown in Figure 1, Figure 2, Figure 3 shows, a kind of envelope Analysis Method that filtering is decomposed based on local mean value, including
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 local mean value decomposition algorithm by signal x（k）The sum of n component and trend term are resolved into, i.e.,, wherein, ci（k）Represent i-th of the component obtained by local mean value decomposition algorithm, rn（k）It represents
The trend term obtained by local mean value decomposition algorithm；
Step 3：To ci（k）It performs reordering operations and substitutes and operate, it is rearranged to operate obtained data ci shuffle（k）Table
Show, data c is obtained after substituting operationi FTran（k）It represents；
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）It represents；ci shuffle（k）Generalized Hurst index curve Hi shuffle（q）Table
Show；ci FTran（k）Generalized Hurst index curve Hi FTran（q）It represents；
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 denoted as signal rearranged and substitute filtered result xf1
（k）；
Step 7：To xf1（k）Spectrum kurtosis analysis is performed, the centre frequency f corresponding to signal kurtosis maximum is obtained0And 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）It performs discrete Fourier transform and obtains envelope spectrum, according to envelope spectrum
Characteristic frequency judges the fault type of machine.
Local mean value decomposition algorithm includes the following steps in step 2：
1）Calculate local mean value function：Determine original signalx(k) all Local Extremumn i , calculate two neighboring pole
Value pointn i Withn i+1Average valuem i , i.e.,
By the average value of all two neighboring extreme pointsm i It is connected, is then carried out using rolling average method smooth with broken line
Processing, obtains local mean value functionm 11(k) ；In this example, the smooth step-length in rolling average method is set as 5；
2）Estimate the envelope value of signal：Using Local Extremumn i Calculate envelope estimated valuea i
Equally, by all two neighboring envelope estimated valuesa i It is connected with broken line, is then put down using rolling average method
Sliding processing, obtains envelope estimation functiona 11(k)；
3）By local mean value functionm 11(k) from original signalx(k) in separate, obtain
h 11(k)= x(k)- m 11(k)；
4）Withh 11(k) divided by envelope estimation functiona 11(k) so as to righth 11(k) be demodulated, it obtains
It is desirable thats 11(k) be a pure FM signal, i.e. its envelope estimation functiona 12(k) meeta 12(k)=1；Ifs 11(k) condition is not satisfied, then wills 11(k) as initial data repeatedly more than iterative process m times, until obtaining a pure tune
Frequency signals 1m(k), i.e.,s 1m(k) satisfaction -1≤s 1m(k)≤1, its envelope estimation functiona 1(m+1)(k) meeta 1(m+1)(k)=1；
Therefore have
In formula
The condition of iteration ends is
In practical applications, a variation Δ can be set, when meeting 1- Δs≤a1m(k)≤1+ Δs when, iteration is whole
Only；Variation Δ=0.01 in this example；
5）All envelope estimation functions multiplication generated in iterative process can be obtained envelope signal
6）By envelope signala 1 (k) and pure FM signals 1m (k) can be obtained by being multiplied by 1st point of original signal
Amount
c 1(k)=a 1(k)s 1m(k)；
7）By the 1st componentc 1 (k) from original signalx(k) in separate, obtain a new signalr 1 (k), it willr 1 (k) as new data repetition above step, cyclenIt is secondary, untilr n (k) for until monotonic function
So far, by original signalx(k) be decomposed intonA component and a monotonic functionr n (kThe sum of), i.e.,
。
Data rearrangement operation includes the following steps in step 3：
Upset component c at randomi（k）Put in order.
Data substitute operation and include the following steps in step 3：
1）To component ci（k）Discrete Fourier transform is performed, obtains component ci（k）Phase；
2）It is located at the pseudo- independent same distribution number in (- π, π) section with one group to replace component ci（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 include 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 lengthNIt generally can not be whole
It removess, so the remaining one piece of data of meeting cannot utilize；
In order to make full use of the length of data, then it is obtained with identical length segmentation, such one from the negative 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 fitting thevThe trend of segment data, if the polynomial trend of fitting ismRank then remembers 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) there are self-similarity characteristics, thenqThe average value of rank wave functionF q (s) and time scalesBetween
There are power law relations：
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 includes the following steps：
1）Constructing a cutoff frequency isf c =0.125+εLow-pass filterh(n)；ε>0, in this examplef c =0.3；
2）It is based onh(n) construction passband be [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 section, the down-sampled factor is 2, then the shaping filter tree after successive ignition filters, kth layer have 2 k A frequency band, whereinIt represents the in wave filter treekOn layeriThe output signal of a wave filter,i=0,…,2k- 1,0≤k≤K-1, this example
Middle K=8；c 0(n) represent x in step 7 described in claim 1f1（k）；
4）In decomposition treekOn layeriThe centre frequency of a 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 summarized, obtain the total spectrum kurtosis of signal.
Rational spline iteration smoothed envelope analysis method in step 9 includes the following steps：
1）Calculate signalz(k) Jue Dui Zhi ∣z(k) the local extremum of ∣；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 re-used as, repeat above-mentioned steps 1）~3）, obtain；
5）Ith iteration：z i-1(k) new data is re-used as, repeat above-mentioned steps 1）~ 3) it, obtains；
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, tests the performance of algorithm of the present invention using the bearing vibration data with inner ring failure
Card.
Bearing used in experiment be 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, 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.
Collected inner ring fault-signal is as shown in Figure 4.
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 cannot 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 has abnormal high level, this explanation is by tradition
There is end effects for the envelope spectrum that 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 is apparently higher than other spectral lines, the two frequencies correspond to respectively
1 frequency multiplication and 2 frequencys multiplication of bearing inner race fault characteristic frequency may determine that bearing has inner ring failure accordingly；It can from Fig. 6
Go out, the envelope spectrum obtained by the present invention does not have end effect.
Show that the present invention is capable of reliable recognition in the case where loading and failure dimensional depth being constant through many experiments
Minimum inner ring failure dimension width is about 0.19mm, and conventional method is capable of the minimum inner ring failure dimension width of reliable recognition about
For 0.53mm, precision improves 64.2%.
Experiment 2, tests the performance of algorithm of the present invention using the bearing vibration data with outer ring failure
Card.
Bearing used in experiment be 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, 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.
Collected outer ring fault-signal is as shown in Figure 7.
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 cannot 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 effects 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 is apparently higher than other spectral lines, the two frequencies correspond to respectively
1 frequency multiplication and 2 frequencys multiplication of bearing outer ring fault characteristic frequency may determine that bearing has outer ring failure accordingly；It can from Fig. 9
Go out, the envelope spectrum obtained by the present invention does not have end effect.
Show that the present invention is capable of reliable recognition in the case where loading and failure dimensional depth being constant through many experiments
Minimum outer ring failure dimension width is about 0.29mm, and conventional method is capable of the minimum outer ring failure dimension width of reliable recognition about
For 0.68mm, precision improves 57.4%.
According to result of the test, think after analysis：
1) traditional envelope Analysis Method directly carries out original signal Envelope Analysis or to merely through simple process
Original signal afterwards carries out Envelope Analysis, different from traditional envelope Analysis Method, and the present invention is decomposed first with local mean value
Original signal is decomposed, then excludes noise and trend component therein using the rearrangement of data and replacement operation, only
Useful component in stick signal component so as to avoid the influence of noise and trend component to Envelope Analysis result, improves
Accuracy and precision.
2) traditional envelope Analysis Method is based on Hilbert is converted, and the letter that Hilbert transformation requirements are analyzed
Number must be the narrow band signal of simple component, otherwise the frequency modulating section of signal will pollute signal Envelope Analysis as a result, but
It is the condition that signal to be analyzed does not meet simple component and narrowband strictly at present, may result in the prior art in this way because of precision not
High and be susceptible to erroneous judgement problem, 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 accurately detected.
4) envelope spectrum obtained by conventional method is there are end effect, and can be avoided by the envelope spectrum that the present invention obtains
End effect.
5）Each step effect：
1) step：Acquire vibration signal；
2) step：Original 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：Is performed by reordering operations and is substituted for the signal that above-mentioned decomposition obtains and is operated, rejects noise therein point
Amount and trend term only retain useful signal；
6) step：Remaining useful signal is summed, using this and as signal it is rearranged and substitute filtered result xf1
(k)；
7) step：To filtered signal xf1(k) spectrum kurtosis analysis is performed, corresponding center at signal maximum kurtosis is obtained
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 specific embodiment is only exemplary, it is to make ability
Field technique personnel can be better understood from the content of 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 (7)
1. a kind of envelope Analysis Method that filtering is decomposed based on local mean value, which is characterized in that include 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 local mean value decomposition algorithm by vibration signal x（k）The sum of n component and trend term are resolved into, i.e.,, wherein, ci（k）Represent i-th point obtained by local mean value decomposition algorithm
Amount, rn（k）Represent the trend term obtained by local mean value decomposition algorithm；
Step 3：To ci（k）It performs reordering operations and substitutes and operate, it is rearranged to operate obtained data ci shuffle（k）It represents,
Data c is obtained after substituting operationi FTran（k）It represents；
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）It represents；ci shuffle（k）Generalized Hurst index curve Hi shuffle（q）Table
Show；ci FTran（k）Generalized Hurst index curve Hi FTran（q）It represents；
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 denoted as signal rearranged and substitute filtered result xf1（k）；
Step 7：To xf1（k）Spectrum kurtosis analysis is performed, the centre frequency f corresponding to signal kurtosis maximum is obtained0And 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）It performs discrete Fourier transform and obtains envelope spectrum, according to envelope spectrum signature
Frequency judges the fault type of machine.
A kind of 2. envelope Analysis Method that filtering is decomposed based on local mean value according to claim 1, which is characterized in that institute
Local mean value decomposition algorithm in step 2 is stated to include the following steps：
1）Calculate local mean value function：Determine vibration signalx(k) all Local Extremumn i , calculate two neighboring extreme pointn i
Withn i+1Average valuem i , i.e.,
By the average value of all two neighboring extreme pointsm i It is connected with broken line, is then smoothed using rolling average method,
Obtain local mean value functionm 11(k) ；In this example, the smooth step-length in rolling average method is set as 5；
2）Estimate the envelope value of signal：Using Local Extremumn i Calculate envelope estimated valuea i
Equally, by all two neighboring envelope estimated valuesa i It is connected with broken line, is then smoothly located using rolling average method
Reason, obtains envelope estimation functiona 11(k)；
3）By local mean value functionm 11(k) from vibration signalx(k) in separate, obtain
h 11(k)= x(k)- m 11(k)；
4）Withh 11(k) divided by envelope estimation functiona 11(k) so as to righth 11(k) be demodulated, it obtains
It is desirable thats 11(k) be a pure FM signal, i.e. its envelope estimation functiona 12(k) meeta 12(k)=1；Ifs 11
(k) condition is not satisfied, then wills 11(k) as initial data repeatedly more than iterative process m times, until obtaining a pure frequency modulation letter
Numbers 1m(k), i.e.,s 1m(k) satisfaction -1≤s 1m(k)≤1, its envelope estimation functiona 1(m+1)(k) meeta 1(m+1)(k)=1；Therefore
Have
In formula
The condition of iteration ends is
In practical applications, a variation Δ is set, when meeting 1- Δs≤a1m(k)≤1+ Δs when, iteration ends；In this example
Variation Δ=0.01；
5）All envelope estimation functions generated in iterative process are mutually obtained envelope signal at convenience
6）By envelope signala 1 (k) and pure FM signals 1m (k) the 1st component of original signal is mutually obtained at convenience
c 1 (k)= a 1 (k)s 1m(k)；
7）By the 1st componentc 1 (k) from vibration signalx(k) in separate, obtain a new signalr 1 (k), it willr 1
(k) as new data repetition above step, cyclenIt is secondary, untilr n (k) for until monotonic function
So far, by vibration signalx(k) be decomposed intonA component and a monotonic functionr n (kThe sum of), i.e.,
。
A kind of 3. envelope Analysis Method that filtering is decomposed based on local mean value according to claim 1, which is characterized in that institute
Data rearrangement operation in step 3 is stated to include the following steps：
Upset component c at randomi（k）Put in order.
4. a kind of envelope Analysis Method that filtering is decomposed based on local mean value according to claim 1, it is characterised in that：Institute
It states data in step 3 and substitutes to operate and include the following steps：
1）To component ci（k）Discrete Fourier transform is performed, obtains component ci（k）Phase；
2）It is located at the pseudo- independent same distribution number in (- π, π) section with one group to replace component ci（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.
5. a kind of envelope Analysis Method that filtering is decomposed based on local mean value according to claim 1, it is characterised in that：Institute
MFDFA methods in step 4 are stated to include the following steps：
1）Construct xy(k) profileY(i), k=1,2 ..., N：
,
,
xy(k) c in step 4 described in claim 1 is representedi（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 lengthNIt generally can not divide exactlys,
So the remaining one piece of data of meeting cannot utilize；
In order to make full use of the length of data, then from the negative direction of data 2 are obtained with identical length segmentation, such oneN s Section
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 fitting thevThe trend of segment data, if the polynomial trend of fitting ismRank then remembers that this goes the trend process to be
（MF-）DFAm；In this example, m=1；
4）Calculate theqThe average value of rank wave function：
；
5）If xy(k) there are self-similarity characteristics, thenqThe average value of rank wave functionF q (s) and time scalesBetween exist
Power law relation：
F q (s)~s H(q)；
WhenqWhen=0, step 4）In formula diverging, at this momentH(0) it is determined by logarithmic mean process defined in following formula：
；
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 to obtain straight line
SlopeH(q)。
6. a kind of envelope Analysis Method that filtering is decomposed based on local mean value according to claim 1, it is characterised in that：Institute
The spectrum kurtosis method stated in step 7 includes the following steps：
1）Constructing a cutoff frequency isf c =0.125+εLow-pass filterh(n)；ε>0, in this examplef c =0.3；
2）It is based onh(n) construction passband be [0;0.25] quasi- low-pass filterh 0(n) and passband be [0.25;0.5] standard
High-pass filterh 1 (n),
；
3）SignalThroughh 0(n)、h 1 (n) filter and resolve into low frequency part after down-sampledAnd high frequency section, the down-sampled factor is 2, then the shaping filter tree after successive ignition filters, kth layer have 2 k A frequency band, whereinIt represents the in wave filter treekOn layeriThe output signal of a 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 a 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 summarized, obtain the total spectrum kurtosis of signal.
A kind of 7. envelope Analysis Method that filtering is decomposed based on local mean value according to claim 1, which is characterized in that institute
The rational spline iteration smoothed envelope analysis method stated in step 9 includes the following steps：
1）Calculate signalz(k) Jue Dui Zhi ∣z(k) the local extremum of ∣；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 re-used as, repeat above-mentioned steps 1）~3）, obtain；
5）Ith iteration：z i-1(k) new data is re-used as, repeat above-mentioned steps 1）~ 3) it, obtains；
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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| CN105004523A (en) * | 2015-08-04 | 2015-10-28 | 潍坊学院 | Rolling bearing state monitoring method based on weighted similarity measure |
| CN105067262A (en) * | 2015-08-04 | 2015-11-18 | 潍坊学院 | Rolling bearing state monitoring method |
| CN105092239A (en) * | 2014-05-09 | 2015-11-25 | 潍坊学院 | Method for detecting early stage fault of gear |
| CN105588717A (en) * | 2015-12-10 | 2016-05-18 | 潍坊学院 | Gearbox fault diagnosis method |
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| CN105092239A (en) * | 2014-05-09 | 2015-11-25 | 潍坊学院 | Method for detecting early stage fault of gear |
| CN105004523A (en) * | 2015-08-04 | 2015-10-28 | 潍坊学院 | Rolling bearing state monitoring method based on weighted similarity measure |
| CN105067262A (en) * | 2015-08-04 | 2015-11-18 | 潍坊学院 | Rolling bearing state monitoring method |
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