CN106198012B - A kind of envelope Analysis Method for decomposing and composing kurtosis based on local mean value - Google Patents

A kind of envelope Analysis Method for decomposing and composing kurtosis based on local mean value Download PDF

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CN106198012B
CN106198012B CN201610492432.8A CN201610492432A CN106198012B CN 106198012 B CN106198012 B CN 106198012B CN 201610492432 A CN201610492432 A CN 201610492432A CN 106198012 B CN106198012 B CN 106198012B
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signal
envelope
data
mean value
local mean
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CN106198012A (en
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林近山
窦春红
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Weifang University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/04—Bearings
    • G01M13/045—Acoustic or vibration analysis

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Abstract

The invention discloses a kind of envelope Analysis Methods for being decomposed and being composed kurtosis 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 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, convenient for engineer application.

Description

A kind of envelope Analysis Method for decomposing and composing kurtosis based on local mean value
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 With the envelope Analysis Method of 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 directly analyzes original signal or only to original Signal analyzed again after simply filtering, therefore existing method is easily done be subject to noise, trend and other ingredients 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 conversion 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 so may result in the prior art and erroneous judgement problem be susceptible to due to precision is not high；3. the envelope spectrum obtained by conventional method There is end effects.
The content of the invention
The problem to be solved in the present invention is for above deficiency, proposes a kind of bag for being decomposed and being composed kurtosis based on local mean value Network analysis method after envelope Analysis Method using the present invention, has that analysis result accuracy and accuracy are high, and can be exactly The advantages of detecting rotating machinery fault type.
For solution more than technical problem, the technical solution that the present invention takes is as follows：One kind is decomposed and composed based on local mean value The envelope Analysis Method of kurtosis, which is characterized 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 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） 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）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 cubic 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 comprises the following steps in the step 2：
1）Calculate local mean value function：Determine all Local Extremum n of original signal x (k)i, calculate two neighboring pole It is worth point niAnd ni+1Average value mi, i.e.,
By the average value m of all two neighboring extreme pointsiIt is connected, is then carried out using rolling average method smooth with broken line Processing, obtains local mean value function m11(k)；In this example, the smooth step-length in rolling average method is arranged to 5；
2）Estimate the envelope value of signal：Using Local Extremum niCalculate envelope estimate ai
Equally, by all two neighboring envelope estimate aiIt is connected with broken line, is then put down using rolling average method Sliding processing, obtains envelope estimation function a11(k)；
3）By local mean value function m11(k) from original signal x（k）In separate, obtain
4）Use h11(k) divided by envelope estimation function a11(k) so as to h11(k) it is demodulated, obtains
It is desirable that s11(k) be a pure FM signal, i.e. its envelope estimation function a12(k) a is met12(k)=1；
If s11(k) condition is not satisfied, then by s11(k) more than iterative process is repeated m times as new data, until To a pure FM signal s1m(k), i.e. s1m(k) -1≤s is met1m(k)≤1, its envelope estimation function a1(m+1)(k) meet a1(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 signal a1(k) and pure FM signal s1m(k) the 1st component of original signal can be obtained by being multiplied
；
7）By the 1st component c1(k) separated from original signal x (k), obtain a new signal r1(k), by r1 (k) above step is repeated as new data, n times is cycled, until rn(k) until for a monotonic function
So far, original signal x (k) is decomposed into n component and a monotonic function rnThe sum of (k), i.e.,
。
Further, data rearrangement operation comprises the following steps in the step 3：
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）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 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 the data of s, since data length N generally can not be whole Except s, 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 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 are self-similarity characteristics, the average value F of q rank wave functions by x (k)q(s) between time scale s There are power law relations：
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）One cutoff frequency of construction is fcThe low-pass filter h (n) of=0.125+ ε；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+1(n) and radio-frequency head Divide c2i+1 k+1(n), the down-sampled factor is 2, then the shaping filter tree after successive ignition filters, kth layer have 2kA frequency band, Middle ci k(n) the 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 summarized, 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) the local extremum of ∣；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 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), 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 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 and replacement operation of data 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 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) 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 for decomposing and composing kurtosis based on local mean value, 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 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） 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）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 cubic 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 comprises the following steps in step 2：
1）Calculate local mean value function：Determine all Local Extremum n of original signal x (k)i, calculate two neighboring pole It is worth point niAnd ni+1Average value mi, i.e.,
By the average value m of all two neighboring extreme pointsiIt is connected, is then carried out using rolling average method smooth with broken line Processing, obtains local mean value function m11(k)；In this example, the smooth step-length in rolling average method is arranged to 5；
2）Estimate the envelope value of signal：Using Local Extremum niCalculate envelope estimate ai
Equally, by all two neighboring envelope estimate aiIt is connected with broken line, is then put down using rolling average method Sliding processing, obtains envelope estimation function a11(k)；
3）By local mean value function m11(k) from original signal x（k）In separate, obtain
4）Use h11(k) divided by envelope estimation function a11(k) so as to h11(k) it is demodulated, obtains
It is desirable that s11(k) be a pure FM signal, i.e. its envelope estimation function a12(k) a is met12(k)=1；
If s11(k) condition is not satisfied, then by s11(k) more than iterative process is repeated m times as new data, until To a pure FM signal s1m(k), i.e. s1m(k) -1≤s is met1m(k)≤1, its envelope estimation function a1(m+1)(k) meet a1(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 signal a1(k) and pure FM signal s1m(k) the 1st component of original signal can be obtained by being multiplied
；
7）By the 1st component c1(k) separated from original signal x (k), obtain a new signal r1(k), by r1 (k) above step is repeated as new data, n times is cycled, until rn(k) until for a monotonic function
So far, original signal x (k) is decomposed into n component and a monotonic function rnThe sum of (k), i.e.,
。
Data rearrangement operation comprises the following steps in step 3：
Upset component c at randomi（k）Put in order.
Data substitute operation and comprise 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 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 the data of s, since data length N generally can not be whole Except s, 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 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 are self-similarity characteristics, the average value F of q rank wave functions by x (k)q(s) between time scale s There are power law relations：
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）One cutoff frequency of construction is fcThe low-pass filter h (n) of=0.125+ ε；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+1(n) and radio-frequency head Divide c2i+1 k+1(n), the down-sampled factor is 2, then the shaping filter tree after successive ignition filters, kth layer have 2kA frequency band, Middle ci k(n) the 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 summarized, 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) the local extremum of ∣；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 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), 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, 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.
The inner ring fault-signal collected 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 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. 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, 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 0.21mm, and conventional method is capable of the minimum inner ring failure dimension width of reliable recognition about For 0.53mm, precision improves 60.4%.
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.
The outer ring fault-signal collected 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, 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 0.33mm, 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 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 and replacement operation of data, 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 conversion 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, so may result in the prior art because of precision not High and be susceptible to erroneous judgement problem, 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) 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：Gather 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 it is rearranged as signal 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 present invention, should not be understood as limiting the scope of the invention, as long as Technical solution improvements introduced according to the present invention each falls within protection scope of the present invention.

Claims (7)

1. a kind of envelope Analysis Method for decomposing and composing kurtosis based on local mean value, which is characterized 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 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 of the component obtained by local mean value decomposition algorithm, rn（k）Generation The trend term that table is 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 cubic 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.
2. a kind of envelope Analysis Method for being decomposed and being composed kurtosis based on local mean value according to claim 1, feature exist In local mean value decomposition algorithm comprises the following steps in the step 2：
1）Calculate local mean value function：Determine all Local Extremum n of vibration signal x (k)i, calculate two neighboring extreme point ni And ni+1Average value mi, i.e.,
By the average value m of all two neighboring extreme pointsiIt is connected with broken line, is then smoothed using rolling average method, Obtain local mean value function m11(k)；In this example, the smooth step-length in rolling average method is arranged to 5；
2）Estimate the envelope value of signal：Using Local Extremum niCalculate envelope estimate ai
Equally, by all two neighboring envelope estimate aiIt is connected with broken line, is then smoothly located using rolling average method Reason, obtains envelope estimation function a11(k)；
3）By local mean value function m11(k) from vibration signal x（k）In separate, obtain
4）Use h11(k) divided by envelope estimation function a11(k) so as to h11(k) it is demodulated, obtains
It is desirable that s11(k) be a pure FM signal, i.e. its envelope estimation function a12(k) a is met12(k)=1；If s11 (k) condition is not satisfied, then by s11(k) more than iterative process is repeated m times as new data, until obtaining a pure FM signal s1m(k), i.e. s1m(k) -1≤s is met1m(k)≤1, its envelope estimation function a1(m+1)(k) a is met1(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 signal a1(k) and pure FM signal s1m(k) the 1st component of original signal is mutually obtained at convenience
；
7）By the 1st component c1(k) separated from vibration signal x (k), obtain a new signal r1(k), by r1(k) Above step is repeated as new data, n times are cycled, until rn(k) until for a monotonic function
So far, vibration signal x (k) is decomposed into n component and a monotonic function rnThe sum of (k), i.e.,
。
3. a kind of envelope Analysis Method for being decomposed and being composed kurtosis based on local mean value according to claim 1, feature exist In data rearrangement is operated and comprised the following steps in the step 3：
Upset component c at randomi（k）Put in order.
4. a kind of envelope Analysis Method for being decomposed and being composed kurtosis based on local mean value according to claim 1, feature exist In：Data substitute operation and comprise 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.
5. a kind of envelope Analysis Method for being decomposed and being composed kurtosis based on local mean value according to claim 1, feature exist In：MFDFA methods comprise the following steps in the step 4：
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：
4P`F)18O2626ZX3J9SV283R
Y$[`H}@AV[I7X%IJ6A_JQWC；
y v (i) for the of fittingvThe 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：
0R(8CJGG2TXCM$2NT2@((TH；
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) determined by logarithmic mean process defined in following formula：
S42M8HF%L8]B11YUNN21RY7；
6）To step 5）In formula both sides take the logarithm can obtain ln [F q (s)]=H(q)ln(s)+c,cFor constant, straight line is derived from SlopeH(q)。
6. a kind of envelope Analysis Method for being decomposed and being composed kurtosis based on local mean value according to claim 1, feature exist In：Spectrum kurtosis method in the step 7 comprises the following steps：
1）One cutoff frequency of construction is fcThe low-pass filter h (n) of=0.125+ ε；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) and passband is [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+1(n) and high frequency section c2i +1 k+1(n), the down-sampled factor is 2, then the shaping filter tree after successive ignition filters, kth layer have 2kA frequency band, wherein ci k (n) the output signal of i-th of wave filter in expression wave filter tree on kth layer, i=0 ..., 2k- 1,0≤k≤K-1, in this example K=8；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 summarized, obtain the total spectrum kurtosis of signal.
7. a kind of envelope Analysis Method for being decomposed and being composed kurtosis based on local mean value according to claim 1, feature exist In 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) 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 cubic spline interpolation 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), 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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