CN106198009A - The EMD of a kind of rolling bearing, spectrum kurtosis and smooth iteration envelope Analysis Method - Google Patents
The EMD of a kind of rolling bearing, spectrum kurtosis and smooth iteration envelope Analysis Method Download PDFInfo
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Abstract
The invention discloses the EMD of a kind of rolling bearing, spectrum kurtosis and smooth iteration envelope Analysis Method, primary signal is decomposed by the method first with ensemble empirical mode decomposition method, then utilize the rearrangement of data and substitute the noise component(s) and trend term operated in eliminating decomposition result, use spectrum kurtosis method that filtered signal for the first time is analyzed the most again, obtain mid frequency and the bandwidth of optimal filter, then utilize this wave filter that filtered signal for the first time is carried out second time again to filter, then use smooth iteration envelope Analysis Method that the filtered signal of second time is carried out Envelope Analysis, the fault type of rolling bearing is determined finally according to envelope spectrum.The present invention is suitable for processing complicated rolling bearing fault signal, it is possible to determines the fault type of rolling bearing exactly, has good noise immunity and robustness, it is simple to engineer applied.
Description
Technical field
The present invention relates to condition monitoring for rotating machinery and fault diagnosis field, be specifically related to the EMD of a kind of rolling bearing, spectrum
Kurtosis and smooth iteration envelope Analysis Method.
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: the most existing Envelope Analysis technology or directly primary signal is analyzed, or only to original
Signal is analyzed after simply filtering again, and the most existing method is easily subject to the dry of noise, trend and other composition
Disturb, thus cause the analysis precision of prior art relatively low；The most existing Envelope Analysis technology is to be transformed to basis with Hilbert,
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 to be polluted, but signal the most to be analyzed the most strictly meets the bar of simple component and arrowband
Part, so may result in prior art and easily occurs erroneous judgement problem because precision is the highest；3. the envelope spectrum obtained by traditional method
There is end effect.
Summary of the invention
The problem to be solved in the present invention is for above not enough, proposes the EMD of a kind of rolling bearing, spectrum kurtosis and smooths repeatedly
For envelope Analysis Method, after using the envelope Analysis Method of the present invention, there is analysis result accuracy and degree of accuracy is high, and can be accurate
The advantage really detecting rotating machinery fault type.
For solving above technical problem, the technical scheme that the present invention takes is as follows: the EMD of a kind of rolling bearing, spectrum kurtosis
With smooth iteration envelope Analysis Method, it is characterised in that comprise the following steps:
Step 1: utilize acceleration transducer to measure the vibration signal x(k of rolling bearing with sample frequency fs), (k=1,2,
..., N), N is the length of sampled signal；
Step 2: use empirical mode decomposition (Empirical Mode Decomposition, EMD) algorithm by signal x(k) point
Solution becomes n component and a trend term sum, i.e., wherein, ciK () represents by EMD algorithm
The i-th component obtained, rnK () represents the trend term obtained by EMD algorithm；
Step 3: to ciK () performs reordering operations and substitutes operation, data c that rearranged operation obtainsi shuffleK () represents,
Data c are obtained after substituting operationi FTranK () represents；
Step 4: to ci(k), ci shuffle(k) and ci FTranK () performs multi-fractal respectively and removes trend fluction analysis
(Multifractal Detrended Fluctuation Analysis, MFDFA), obtains generalized Hurst index curve, ci
The generalized Hurst index curve H of (k)iQ () represents；ci shuffleThe generalized Hurst index curve H of (k)i shuffle(q) table
Show；ci FTranThe generalized Hurst index curve H of (k)i FTranQ () represents；
Step 5: if Hi(q) and Hi shuffle(q) or Hi(q) and Hi FTranQ the relative error between () is less than 5%, or Hi
(q), Hi shuffle(q) and Hi FTranQ () three do not change with q, then abandon the c of correspondencei(k) component；
Step 6: to remaining ci(k) component sue for peace, by this and be designated as signal rearranged and substitute filtered result xf1(k)；
Step 7: to xf1K () performs spectrum kurtosis analysis, obtain the mid frequency f corresponding to signal kurtosis maximum0And bandwidth B；
Step 8: according to mid frequency f0With bandwidth B to xf1K () carries out bandpass filtering, obtain xf2(k)；
Step 9: to signal xf2K () performs smooth iteration Envelope Analysis, obtain signal envelope eov(k)；
Step 10: the signal envelope eov(k to obtaining) perform discrete Fourier transform obtain envelope spectrum, according to envelope spectrum feature
Frequency judges the fault type of machine.
A kind of prioritization scheme, in described step 2, Empirical Mode Decomposition Algorithm comprises the following steps:
1) first screening process: find out data x(k respectively) upper and lower Local Extremum, use cubic spline curve respectively
The upper and lower Local Extremum of matching, obtains signal x(k) local maximum envelope and local minimum envelope, then by this two
The value of the respective points of bar envelope is averaged, and obtains averaged curve m1；
Seek signal x(k again) and this averaged curve m1Difference, i.e. h10=x(k)-m1, so far first screening process terminates；
2) second screening process: h10Again new data, repeat the above steps 1 it are taken as), available h11= h10-m11, here
Parameter m11Represent h10Mean curve, repeat this process j time, < when 0.3, screening process stops, here until 0.2 < SD, now, h1j= h1(j-1)-m1j, at this moment it is believed that h1jMould is grasped in being one
State function (Intrinsic Mode Function, IMF), defining the 1st IMF is c1= h1j；
3) from x(k) deduct c1, r can be obtained1=x(k)-c1, then by r1As new data, and repeat above-mentioned two step operations, this
Sample can obtain the 2nd IMF；
4) the available a series of IMF of step 3) operation are repeated, if rnHave changed into a monotonous curve, then screening process is stopped
Only, primary signal is decomposed into following form the most at last:。
Further, in described step 3, data rearrangement operation comprises the following steps:
Upset component c at randomiPutting in order of (k).
Further, in described step 3, the operation of data replacement comprises the following steps:
1) to component ciK () performs discrete Fourier transform, it is thus achieved that component ciThe phase place of (k)；
2) component c is replaced with one group of pseudo-independent same distribution number being positioned in (-π, π) intervaliThe original phase of (k)；
3) frequency domain data after phase place substitutes is performed inverse discrete Fourier transform and obtain data ci IFFTK (), asks for number
According to ci IFFTThe real part of (k).
Further, in described step 4, MFDFA method comprises the following steps:
1) structure x (k) (k=1,2 ..., N) profile Y (i):
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, owing to data length N is generally not capable of dividing exactly s,
Can not utilize so one piece of data can be remained；
In order to make full use of the length of data, then from the opposite direction of data with identical length segmentation, obtain the most altogether 2NSSection
Data；
3) utilize the polynomial trend of the every segment data of least square fitting, then calculate the variance of every segment data:
yvI () is the trend of the v segment data of matching, if the polynomial trend of matching is m rank, then remember that this goes the trend process to be
(MF-) DFAm；In this example, m=1；
4) meansigma methods of q rank wave function is calculated:
；
5) if x (k) exists self-similarity characteristics, then meansigma methods F of q rank wave functionqExist between (s) and time scale s
Power law relation:
As q=0, the formula in step 4) dissipates, and at this moment H (0) is determined by logarithmic mean process defined in following formula:
；
6) are taken the logarithm in the formula both sides in step 5) and can obtain ln [Fq(s)]=H (q) ln (s)+c(c is constant), thus can obtain
Obtain slope H (q) of straight line.
Further, the spectrum kurtosis method in described step 7 comprises the following steps:
1) one cut-off frequency of structure is fcLow 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) structure passband is [0,0.25]0N () and passband are [0.25,0.5]
Quasi-high pass filter h1(n),
;
3) signal ci kN () is through h0(n)、 h1N () resolves into low frequency part c after filtering and being down-sampled2i k+1(n) and HFS
c2i+1 k+1N (), the down-sampled factor is 2, then shaping filter tree after successive ignition filters, and kth layer has 2kIndividual frequency band, wherein
ci kThe output signal of the i-th wave filter on kth layer in (n) expression wave filter tree, i=0 ..., 2k-1,0≤k≤K-1, this example
Middle K=8；c0N () represents x in step 7 described in claim 1f1(k)；
4) the mid frequency f of the i-th wave filter on kth layer in decomposition treekiAnd bandwidth BkIt is respectively
;
5) each filter results c is calculatedi k(n)( i=0,…, 2k-1) kurtosis；
6) all of spectrum kurtosis is collected, obtain the spectrum kurtosis that signal is total.
Further, the smooth iteration envelope Analysis Method in described step 9 comprises the following steps:
1) local mean value function is calculated: determine all of Local Extremum n of signal x (k)i, calculate adjacent two extreme point niWith
ni+1Meansigma methods mi, i.e.
Meansigma methods m by all adjacent two extreme pointsiConnect with broken line, then use rolling average method to carry out smooth place
Reason, obtains local mean value function m11(k)；In this example, the smooth step-length in rolling average method is set to 5；The 1st iteration
In, x (k) represents x in step 9 described in claim 1f2(k)；
2) envelope value of signal is estimated: use Local Extremum niCalculate envelope estimated value ai
Equally, by all adjacent two envelope estimated values aiConnect with broken line, then use rolling average method to carry out smooth place
Reason, obtains envelope estimation function a11(k)；
3) by local mean value function m11K () separates from primary signal x (k), obtain
4) h is used11K () is divided by envelope estimation function a11(k) thus to h11K () is demodulated, obtain
It is desirable that s11K () is a pure FM signal, i.e. its envelope estimation function a12K () meets a12(k)=1；If s11
K () condition is not satisfied, then by s11K () repeats above iterative process m time as new data, until obtaining a pure FM signal
s1m(k), i.e. s1mK () meets-1≤s1m(k)≤1, its envelope estimation function a1(m+1)K () meets a1(m+1)K ()=1, therefore has
In formula
The condition of iteration ends is
In actual applications, an amount of change Δ can be set, when meeting 1-Δ≤a1mDuring (k)≤1+ Δ, iteration ends；This
Amount of change Δ=0.01 in example；
5) all envelope estimation functions produced in iterative process can be obtained envelope signal mutually at convenience
。
The present invention uses above technical scheme, compared with prior art, the invention have the advantages that
1) utilize empirical mode decomposition (EMD) algorithm that primary signal is decomposed, then utilize the rearrangement of data and substitute behaviour
Make to get rid of noise therein and trend component, the only useful component in stick signal component, thus avoid noise and trend
The component impact on Envelope Analysis result, analysis result accuracy and degree of accuracy are high.
2) smooth iteration envelope Analysis Method is utilized to be kept completely separate with frequency modulating section by signal envelope, it is possible to avoid frequency
The impact on signal envelope analysis result of the rate modulating part, thus 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 traditional method, and the envelope spectrum obtained by the present invention it can be avoided that
End effect.
The present invention will be further described with embodiment below in conjunction with the accompanying drawings.
Accompanying drawing explanation
Accompanying drawing 1 is the flow chart of envelope Analysis Method in the embodiment of the present invention；
Accompanying drawing 2 is to use low pass and high pass filter that signal is carried out the schematic diagram of preliminary exposition in the embodiment of the present invention；
Accompanying drawing 3 is the schematic diagram using tree-shaped filter construction quickly to calculate spectrum kurtosis in the embodiment of the present invention；
Accompanying drawing 4 is the bearing vibration signal in the embodiment of the present invention with inner ring fault；
Accompanying drawing 5 is to use the tradition envelope Analysis Method analysis to inner ring faulty bearing vibration signal in the embodiment of the present invention
Result；
Accompanying drawing 6 is to use envelope Analysis Method of the present invention to divide inner ring faulty bearing vibration signal in the embodiment of the present invention
Analysis result；
Accompanying drawing 7 is the bearing vibration signal in the embodiment of the present invention with outer ring fault；
Accompanying drawing 8 is to use the tradition envelope Analysis Method analysis to outer ring faulty bearing vibration signal in the embodiment of the present invention
Result；
Accompanying drawing 9 is to use envelope Analysis Method of the present invention to divide outer ring faulty bearing vibration signal in the embodiment of the present invention
Analysis result.
Detailed description of the invention
Embodiment, as shown in Figure 1, Figure 2, Figure 3 shows, the EMD of a kind of rolling bearing, spectrum kurtosis and smooth iteration Envelope Analysis side
Method, it is characterised in that comprise the following steps:
Step 1: utilize acceleration transducer to measure the vibration signal x(k of rolling bearing with sample frequency fs), (k=1,2,
..., N), N is the length of sampled signal；
Step 2: use empirical mode decomposition (Empirical Mode Decomposition, EMD) algorithm by signal x(k) point
Solution becomes n component and a trend term sum, i.e., wherein, ciK () represents by EMD algorithm
The i-th component obtained, rnK () represents the trend term obtained by EMD algorithm；
Step 3: to ciK () performs reordering operations and substitutes operation, data c that rearranged operation obtainsi shuffleK () represents,
Data c are obtained after substituting operationi FTranK () represents；
Step 4: to ci(k), ci shuffle(k) and ci FTranK () performs multi-fractal respectively and removes trend fluction analysis
(Multifractal Detrended Fluctuation Analysis, MFDFA), obtains generalized Hurst index curve, ci
The generalized Hurst index curve H of (k)iQ () represents；ci shuffleThe generalized Hurst index curve H of (k)i shuffle(q) table
Show；ci FTranThe generalized Hurst index curve H of (k)i FTranQ () represents；
Step 5: if Hi(q) and Hi shuffle(q) or Hi(q) and Hi FTranQ the relative error between () is less than 5%, or Hi
(q), Hi shuffle(q) and Hi FTranQ () three do not change with q, then abandon the c of correspondencei(k) component；
Step 6: to remaining ci(k) component sue for peace, by this and be designated as signal rearranged and substitute filtered result xf1(k)；
Step 7: to xf1K () performs spectrum kurtosis analysis, obtain the mid frequency f corresponding to signal kurtosis maximum0And bandwidth B；
Step 8: according to mid frequency f0With bandwidth B to xf1K () carries out bandpass filtering, obtain xf2(k)；
Step 9: to signal xf2K () performs smooth iteration Envelope Analysis, obtain signal envelope eov(k)；
Step 10: the signal envelope eov(k to obtaining) perform discrete Fourier transform obtain envelope spectrum, according to envelope spectrum feature
Frequency judges the fault type of machine.
In step 2, Empirical Mode Decomposition Algorithm comprises the following steps:
1) first screening process: find out data x(k respectively) upper and lower Local Extremum, use cubic spline curve respectively
The upper and lower Local Extremum of matching, obtains signal x(k) local maximum envelope and local minimum envelope, then by this two
The value of the respective points of bar envelope is averaged, and obtains averaged curve m1；
Seek signal x(k again) and this averaged curve m1Difference, i.e. h10=x(k)-m1, so far first screening process terminates；
2) second screening process: h10Again new data, repeat the above steps 1 it are taken as), available h11= h10-m11, here
Parameter m11Represent h10Mean curve, repeat this process j time, < when 0.3, screening process stops, here until 0.2 < SD, now, h1j= h1(j-1)-m1j, at this moment it is believed that h1jMould is grasped in being one
State function (Intrinsic Mode Function, IMF), defining the 1st IMF is c1= h1j；
3) from x(k) deduct c1, r can be obtained1=x(k)-c1, then by r1As new data, and repeat above-mentioned two step operations, this
Sample can obtain the 2nd IMF；
4) the available a series of IMF of step 3) operation are repeated, if rnHave changed into a monotonous curve, then screening process is stopped
Only, primary signal is decomposed into following form the most at last:。
In step 3, data rearrangement operation comprises the following steps:
Upset component c at randomiPutting in order of (k).
In step 3, the operation of data replacement comprises the following steps:
1) to component ciK () performs discrete Fourier transform, it is thus achieved that component ciThe phase place of (k)；
2) component c is replaced with one group of pseudo-independent same distribution number being positioned in (-π, π) intervaliThe original phase of (k)；
3) frequency domain data after phase place substitutes is performed inverse discrete Fourier transform and obtain data ci IFFTK (), asks for number
According to ci IFFTThe real part of (k).
In step 4, MFDFA method comprises the following steps:
1) structure x (k) (k=1,2 ..., N) profile Y (i):
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, owing to data length N is generally not capable of dividing exactly s,
Can not utilize so one piece of data can be remained；
In order to make full use of the length of data, then from the opposite direction of data with identical length segmentation, obtain the most altogether 2NSSection
Data；
3) utilize the polynomial trend of the every segment data of least square fitting, then calculate the variance of every segment data:
yvI () is the trend of the v segment data of matching, if the polynomial trend of matching is m rank, then remember that this goes the trend process to be
(MF-) DFAm；In this example, m=1；
4) meansigma methods of q rank wave function is calculated:
；
5) if x (k) exists self-similarity characteristics, then meansigma methods F of q rank wave functionqExist between (s) and time scale s
Power law relation:
As q=0, the formula in step 4) dissipates, and at this moment H (0) is determined by logarithmic mean process defined in following formula:
；
6) are taken the logarithm in the formula both sides in step 5) and can obtain ln [Fq(s)]=H (q) ln (s)+c(c is constant), thus can obtain
Obtain slope H (q) of straight line.
Spectrum kurtosis method in step 7 comprises the following steps:
1) one cut-off frequency of structure is fcLow 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) structure passband is [0,0.25]0N () and passband are [0.25,0.5]
Quasi-high pass filter h1(n),
;
3) signal ci kN () is through h0(n)、 h1N () resolves into low frequency part c after filtering and being down-sampled2i k+1(n) and HFS
c2i+1 k+1N (), the down-sampled factor is 2, then shaping filter tree after successive ignition filters, and kth layer has 2kIndividual frequency band, wherein
ci kThe output signal of the i-th wave filter on kth layer in (n) expression wave filter tree, i=0 ..., 2k-1,0≤k≤K-1, this example
Middle K=8；c0N () represents x in step 7 described in claim 1f1(k)；
4) the mid frequency f of the i-th wave filter on kth layer in decomposition treekiAnd bandwidth BkIt is respectively
;
5) each filter results c is calculatedi k(n)( i=0,…, 2k-1) kurtosis；
6) all of spectrum kurtosis is collected, obtain the spectrum kurtosis that signal is total.
Smooth iteration envelope Analysis Method in step 9 comprises the following steps:
1) local mean value function is calculated: determine all of Local Extremum n of signal x (k)i, calculate adjacent two extreme point niWith
ni+1Meansigma methods mi, i.e.
Meansigma methods m by all adjacent two extreme pointsiConnect with broken line, then use rolling average method to carry out smooth place
Reason, obtains local mean value function m11(k)；In this example, the smooth step-length in rolling average method is set to 5；The 1st iteration
In, x (k) represents x in step 9 described in claim 1f2(k)；
2) envelope value of signal is estimated: use Local Extremum niCalculate envelope estimated value ai
Equally, by all adjacent two envelope estimated values aiConnect with broken line, then use rolling average method to carry out smooth place
Reason, obtains envelope estimation function a11(k)；
3) by local mean value function m11K () separates from primary signal x (k), obtain
4) h is used11K () is divided by envelope estimation function a11(k) thus to h11K () is demodulated, obtain
It is desirable that s11K () is a pure FM signal, i.e. its envelope estimation function a12K () meets a12(k)=1；If s11
K () condition is not satisfied, then by s11K () repeats above iterative process m time as new data, until obtaining a pure FM signal
s1m(k), i.e. s1mK () meets-1≤s1m(k)≤1, its envelope estimation function a1(m+1)K () meets a1(m+1)K ()=1, therefore has
In formula
The condition of iteration ends is
In actual applications, an amount of change Δ can be set, when meeting 1-Δ≤a1mDuring (k)≤1+ Δ, iteration ends；This
Amount of change Δ=0.01 in example；
5) all envelope estimation functions produced in iterative process can be obtained envelope signal mutually at convenience
。
Test 1, utilizes the bearing vibration data with inner ring fault to test the performance of algorithm of the present invention
Card.
Experiment bearing used is 6205-2RS JEM SKF, utilizes electric discharge machining method working depth on bearing inner race
For 0.2794mm, width be the groove of 0.3556mm to simulate bearing inner race fault, this experiment load is about 0.7457kW, drives
Motor turns frequency and is about 29.5Hz, and bearing inner race fault characteristic frequency is about 160Hz, and sample frequency is 4.8KHz, during signal sampling
A length of 1s.
The inner ring fault-signal collected is as shown in Figure 4.
Initially with traditional envelope Analysis Method, the signal shown in Fig. 4 is analyzed, the analysis result obtained such as Fig. 5
Shown in.From fig. 5, it can be seen that the fault signature of bearing is blanked completely, the most traditional envelope Analysis Method can not be effectively
Extract the fault signature of bearing；Additionally, the left end point of envelope spectrum shown in Fig. 5 also exists abnormal high level, this explanation is by traditional method
The envelope spectrum obtained also exists end effect.
Use method proposed by the invention that signal shown in Fig. 4 is analyzed, the analysis result obtained such as Fig. 6 institute
Show.From fig. 6, it can be seen that the spectral line corresponding to 160Hz and 320Hz is apparently higher than other spectral line, the two frequency correspondence respectively
1 frequency multiplication of bearing inner race fault characteristic frequency and 2 frequencys multiplication, may determine that bearing has inner ring fault accordingly；Can from Fig. 6
Go out, the present invention envelope spectrum obtained does not has end effect.
Showing through many experiments, in the case of load and fault dimensional depth are constant, the present invention can reliable recognition
Minimum inner ring fault dimension width is about 0.21mm, and traditional method can reliable recognition minimum inner ring fault dimension width about
For 0.53mm, precision improves 60.4%.
Test 2, utilizes the bearing vibration data with outer ring fault to test the performance of algorithm of the present invention
Card.
Experiment bearing used is 6205-2RS JEM SKF, utilizes electric discharge machining method working depth on bearing outer ring
For 0.2794mm, width be the groove of 0.5334mm to simulate bearing outer ring fault, this experiment load is about 2.237 kW, drives
Motor turns frequency and is about 28.7Hz, and bearing outer ring fault characteristic frequency is about 103Hz, and sample frequency is 4.8KHz, during signal sampling
A length of 1s.
The outer ring fault-signal collected is as shown in Figure 7.
Initially with traditional envelope Analysis Method, the signal shown in Fig. 7 is analyzed, the analysis result obtained such as Fig. 8
Shown in.From figure 8, it is seen that the fault signature of bearing is blanked completely, the most traditional envelope Analysis Method can not be effectively
Extract the fault signature of bearing；Additionally, the left end point of envelope spectrum shown in Fig. 8 also exists abnormal high level, this explanation is by traditional method
The envelope spectrum obtained also exists end effect.
Use method proposed by the invention that signal shown in Fig. 7 is analyzed, the analysis result obtained such as Fig. 9 institute
Show.From fig. 9, it can be seen that the spectral line corresponding to 103Hz and 206Hz is apparently higher than other spectral line, the two frequency correspondence respectively
1 frequency multiplication of bearing outer ring fault characteristic frequency and 2 frequencys multiplication, may determine that bearing has outer ring fault accordingly；Can from Fig. 9
Go out, the present invention envelope spectrum obtained does not has end effect.
Showing through many experiments, in the case of load and fault dimensional depth are constant, the present invention can reliable recognition
Minimum outer ring fault dimension width is about 0.33mm, and traditional method can reliable recognition minimum outer ring fault dimension width 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 after merely through simple process
Primary signal carries out Envelope Analysis, different from traditional envelope Analysis Method, and primary signal is carried out by the present invention first with EMD
Decompose, then utilize the rearrangement of data and substitute operation eliminating noise therein and trend component, only in stick signal component
Useful component, thus avoid the impact on Envelope Analysis result of noise and trend component, improve accuracy and precision.
2) traditional envelope Analysis Method is transformed to basis with Hilbert, 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 signal the most to be analyzed condition that the most strictly meets simple component and arrowband, so may result in prior art because of precision not
High and erroneous judgement problem easily occur, different from tradition envelope Analysis Method, the present invention utilizes the smooth iteration envelope Analysis Method will
Signal envelope is kept completely separate with frequency modulating section, it is possible to avoid the frequency modulating section impact on signal envelope analysis result,
Thus 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 traditional method, and the envelope spectrum obtained by the present invention it can be avoided that
End effect.
5) each step effect:
1st) step: gather vibration signal；
2nd) step: primary signal is resolved into the form of different component sum, some of which component correspondence noise and trend term, some
Component correspondence useful signal；
3rd) ~ 5) step: the signal that obtains above-mentioned decomposition performs reordering operations and substitutes operation, reject noise component(s) therein and
Trend term, only retains useful signal；
6th) step: remaining useful signal is sued for peace, should and as signal rearranged and substitute filtered result xf1(k)；
7th) step: to filtered signal xf1K () performs spectrum kurtosis analysis, obtain center frequency corresponding at signal maximum kurtosis
Rate f0And bandwidth B；
8th) step: according to mid frequency f0With bandwidth B to xf1K () carries out bandpass filtering, obtain signal xf2(k)；
9th) step: signal calculated xf2Envelope eov (k) of (k)；
10th) step: eov (k) is performed discrete Fourier transform and obtains envelope spectrum, judge the failure classes of bearing according to envelope spectrum
Type.
One skilled in the art would recognize that above-mentioned detailed description of the invention is exemplary, be 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
According to technical solution of the present invention improvements introduced, each fall within protection scope of the present invention.
Claims (7)
1. the EMD of a rolling bearing, spectrum kurtosis and smooth iteration envelope Analysis Method, it is characterised in that comprise the following steps:
Step 1: utilize acceleration transducer to measure the vibration signal x(k of rolling bearing with sample frequency fs), (k=1,2,
..., N), N is the length of sampled signal；
Step 2: use empirical mode decomposition (Empirical Mode Decomposition, EMD) algorithm by signal x(k) point
Solution becomes n component and a trend term sum, i.e., wherein, ciK () represents by EMD algorithm
The i-th component obtained, rnK () represents the trend term obtained by EMD algorithm；
Step 3: to ciK () performs reordering operations and substitutes operation, data c that rearranged operation obtainsi shuffleK () represents,
Data c are obtained after substituting operationi FTranK () represents；
Step 4: to ci(k), ci shuffle(k) and ci FTranK () performs multi-fractal respectively and removes trend fluction analysis
(Multifractal Detrended Fluctuation Analysis, MFDFA), obtains generalized Hurst index curve, ci
The generalized Hurst index curve H of (k)iQ () represents；ci shuffleThe generalized Hurst index curve H of (k)i shuffle(q) table
Show；ci FTranThe generalized Hurst index curve H of (k)i FTranQ () represents；
Step 5: if Hi(q) and Hi shuffle(q) or Hi(q) and Hi FTranQ the relative error between () is less than 5%, or Hi
(q), Hi shuffle(q) and Hi FTranQ () three do not change with q, then abandon the c of correspondencei(k) component；
Step 6: to remaining ci(k) component sue for peace, by this and be designated as signal rearranged and substitute filtered result xf1(k)；
Step 7: to xf1K () performs spectrum kurtosis analysis, obtain the mid frequency f corresponding to signal kurtosis maximum0And bandwidth B；
Step 8: according to mid frequency f0With bandwidth B to xf1K () carries out bandpass filtering, obtain xf2(k)；
Step 9: to signal xf2K () performs smooth iteration Envelope Analysis, obtain signal envelope eov(k)；
Step 10: the signal envelope eov(k to obtaining) perform discrete Fourier transform obtain envelope spectrum, according to envelope spectrum feature
Frequency judges the fault type of machine.
The EMD of a kind of rolling bearing the most according to claim 1, spectrum kurtosis and smooth iteration envelope Analysis Method, it is special
Levying and be, in described step 2, Empirical Mode Decomposition Algorithm comprises the following steps:
1) first screening process: find out data x(k respectively) upper and lower Local Extremum, use cubic spline curve respectively
The upper and lower Local Extremum of matching, obtains signal x(k) local maximum envelope and local minimum envelope, then by this two
The value of the respective points of bar envelope is averaged, and obtains averaged curve m1；
Seek signal x(k again) and this averaged curve m1Difference, i.e. h10=x(k)-m1, so far first screening process terminates；
2) second screening process: h10Again new data, repeat the above steps 1 it are taken as), available h11= h10-m11, here
Parameter m11Represent h10Mean curve, repeat this process j time, < when 0.3, screening process stops, here until 0.2 < SD, now, h1j= h1(j-1)-m1j, at this moment it is believed that h1jMould is grasped in being one
State function (Intrinsic Mode Function, IMF), defining the 1st IMF is c1= h1j；
3) from x(k) deduct c1, r can be obtained1=x(k)-c1, then by r1As new data, and repeat above-mentioned two step operations, so
The 2nd IMF can be obtained；
4) the available a series of IMF of step 3) operation are repeated, if rnHave changed into a monotonous curve, then screening process stops,
Primary signal is decomposed into following form the most at last:。
The EMD of a kind of rolling bearing the most according to claim 1, spectrum kurtosis and smooth iteration envelope Analysis Method, it is special
Levying and be, in described step 3, data rearrangement operation comprises the following steps:
Upset component c at randomiPutting in order of (k).
The EMD of a kind of rolling bearing the most according to claim 1, spectrum kurtosis and smooth iteration envelope Analysis Method, it is special
Levy and be: in described step 3, the operation of data replacement comprises the following steps:
1) to component ciK () performs discrete Fourier transform, it is thus achieved that component ciThe phase place of (k)；
2) component c is replaced with one group of pseudo-independent same distribution number being positioned in (-π, π) intervaliThe original phase of (k)；
3) frequency domain data after phase place substitutes is performed inverse discrete Fourier transform and obtain data ci IFFTK (), asks for data
ci IFFTThe real part of (k).
The EMD of a kind of rolling bearing the most according to claim 1, spectrum kurtosis and smooth iteration envelope Analysis Method, it is special
Levy and be: in described step 4, MFDFA method comprises the following steps:
1) structure x (k) (k=1,2 ..., N) profile Y (i):
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, divides with identical length from the opposite direction of data
Section, obtains 2NSSegment data；
3) utilize the polynomial trend of the every segment data of least square fitting, then calculate the variance of every segment data:
yvI () is the trend of the v segment data of matching, if the polynomial trend of matching is m rank, then remember that this goes the trend process to be
(MF-) DFAm；
4) meansigma methods of q rank wave function is calculated:
；
5) if x (k) exists self-similarity characteristics, then meansigma methods F of q rank wave functionqPower is there is between (s) and time scale s
Rule relation:
As q=0, the formula in step 4) dissipates, and at this moment H (0) is determined by logarithmic mean process defined in following formula:
；
6) are taken the logarithm in the formula both sides in step 5) and can obtain ln [Fq(s)]=H (q) ln (s)+c(c is constant), thus can obtain
Obtain slope H (q) of straight line.
The EMD of a kind of rolling bearing the most according to claim 1, spectrum kurtosis and smooth iteration envelope Analysis Method, it is special
Levy and be: the spectrum kurtosis method in described step 7 comprises the following steps:
1) one cut-off frequency of structure is fcLow pass filter h (n) of=0.125+ ε；
2) based on the quasi-low pass filter h that h (n) structure passband is [0,0.25]0N () and passband are [0.25,0.5]
Quasi-high pass filter h1(n),
;
3) signal ci kN () is through h0(n)、 h1N () resolves into low frequency part c after filtering and being down-sampled2i k+1(n) and HFS c2i +1 k+1N (), the down-sampled factor is 2, then shaping filter tree after successive ignition filters, and kth layer has 2kIndividual frequency band, wherein ci k
The output signal of the i-th wave filter on kth layer in (n) expression wave filter tree, i=0 ..., 2k-1,0≤k≤K-1；
4) the mid frequency f of the i-th wave filter on kth layer in decomposition treekiAnd bandwidth BkIt is respectively
;
5) each filter results c is calculatedi k(n)( i=0,…, 2k-1) kurtosis；
6) all of spectrum kurtosis is collected, obtain the spectrum kurtosis that signal is total.
The EMD of a kind of rolling bearing the most according to claim 1, spectrum kurtosis and smooth iteration envelope Analysis Method, it is special
Levying and be, the smooth iteration envelope Analysis Method in described step 9 comprises the following steps:
1) local mean value function is calculated: determine all of Local Extremum n of signal x (k)i, calculate adjacent two extreme point niWith
ni+1Meansigma methods mi, i.e.
Meansigma methods m by all adjacent two extreme pointsiConnect with broken line, then use rolling average method to be smoothed,
Obtain local mean value function m11(k)；
2) envelope value of signal is estimated: use Local Extremum niCalculate envelope estimated value ai
Equally, by all adjacent two envelope estimated values aiConnect with broken line, then use rolling average method to carry out smooth place
Reason, obtains envelope estimation function a11(k)；
3) by local mean value function m11K () separates from primary signal x (k), obtain
4) h is used11K () is divided by envelope estimation function a11(k) thus to h11K () is demodulated, obtain
It is desirable that s11K () is a pure FM signal, i.e. its envelope estimation function a12K () meets a12(k)=1；If s11
K () condition is not satisfied, then by s11K () repeats above iterative process m time as new data, until obtaining a pure FM signal
s1m(k), i.e. s1mK () meets-1≤s1m(k)≤1, its envelope estimation function a1(m+1)K () meets a1(m+1)K ()=1, therefore has
In formula
The condition of iteration ends is
In actual applications, an amount of change Δ can be set, when meeting 1-Δ≤a1mDuring (k)≤1+ Δ, iteration ends；This
Amount of change Δ=0.01 in example；
5) all envelope estimation functions produced in iterative process can be obtained envelope signal mutually at convenience
。
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| CN107102247A (en) * | 2017-04-18 | 2017-08-29 | 西南交通大学 | A kind of CRH3 types EMUs traction invertor IGBT open fault diagnostic methods |
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| CN114486263A (en) * | 2022-02-15 | 2022-05-13 | 浙江大学 | Noise reduction and demodulation method for vibration signal of rolling bearing of rotary machine |
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| CN114486263B (en) * | 2022-02-15 | 2023-04-25 | 浙江大学 | Noise reduction demodulation method for vibration signal of rolling bearing of rotary machine |
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