CN106053069A - SSD, spectral kurtosis and smooth iteration envelope analysis method of antifriction bearing - Google Patents

SSD, spectral kurtosis and smooth iteration envelope analysis method of antifriction bearing Download PDF

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CN106053069A
CN106053069A CN201610492448.9A CN201610492448A CN106053069A CN 106053069 A CN106053069 A CN 106053069A CN 201610492448 A CN201610492448 A CN 201610492448A CN 106053069 A CN106053069 A CN 106053069A
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signal
envelope
data
spectrum
ssd
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CN106053069B (en
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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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02—Preprocessing
    • G06F2218/04—Denoising

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  • Acoustics & Sound (AREA)
  • General Physics & Mathematics (AREA)
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Abstract

The invention discloses an SSD, spectral kurtosis and smoothing iteration envelope analysis method of an antifriction bearing. Firstly, an original signal is decomposed by a singular spectrum decomposition method, and then, the noise component and the trend term in the decomposition result are eliminated by the data rearrangement and substitution operation, the signal after the primary filtering is analyzed by the spectral kurtosis method to obtain the center frequency and bandwidth of an optimal filter, the filter filters the signal after the primary filtering secondarily, the signal after the secondary filtering is subjected to envelope analysis by means of the smooth iteration envelope analysis method, and at the end, the fault type of the antifriction bearing can be determined based on the spectrum envelope. The method is suitable for dealing with complex antifriction bearing fault signals, can accurately determine the fault type of the antifriction bearing, is good in noise resistance and robustness, and is convenient for engineering application.

Description

The SSD of a kind of rolling bearing, spectrum kurtosis and smooth iteration envelope Analysis Method
Technical field
The present invention relates to condition monitoring for rotating machinery and fault diagnosis field, be specifically related to the SSD 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 SSD 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 SSD 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 singular spectrum to decompose (Singular Spectrum Decomposition, SSD) algorithm by signal x(k) Resolve into n component sum, i.e., wherein, ciK () represents the obtained by singular spectrum decomposition algorithm I component, singular spectrum decomposes it is well known that see document
P. Bonizzi, J.M. KAREL, O. Meste, R.L. Peeters, Singular spectrum decomposition: A new method for time series decomposition, Advances in Adaptive Data Analysis, 2014,6 (4): 1-29；
Step 3: to 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 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 singular spectrum to decompose (SSD) primary signal is decomposed, then utilize the rearrangement of data and substitute operation eliminating Noise therein and trend component, the only useful component in stick signal component, thus avoid noise and trend component pair The impact of 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
Fig. 1 is the flow chart of the inventive method in the embodiment of the present invention；
Fig. 2 is to use low pass filter and high pass filter that signal is carried out the schematic diagram of preliminary exposition in the embodiment of the present invention；
Fig. 3 is the schematic diagram using tree-shaped filter construction quickly to calculate spectrum kurtosis in the embodiment of the present invention；
Fig. 4 is the bearing vibration signal in the embodiment of the present invention with inner ring fault；
Fig. 5 is to use tradition envelope Analysis Method to tie the analysis of inner ring faulty bearing vibration signal in the embodiment of the present invention Really；
Fig. 6 is the present invention analysis result to inner ring faulty bearing vibration signal in the embodiment of the present invention；
Fig. 7 is the bearing vibration signal in the embodiment of the present invention with outer ring fault；
Fig. 8 is to use tradition envelope Analysis Method to tie the analysis of outer ring faulty bearing vibration signal in the embodiment of the present invention Really；
Fig. 9 is the present invention analysis result to outer ring faulty bearing vibration signal in the embodiment of the present invention.
Detailed description of the invention
Embodiment, as shown in Figure 1, Figure 2, Figure 3 shows, the SSD of a kind of rolling bearing, spectrum kurtosis and smooth iteration Envelope Analysis side Method, comprises 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 singular spectrum to decompose (Singular Spectrum Decomposition, SSD) algorithm by signal x(k) Resolve into n component sum, i.e., wherein, ciK () representative is obtained by singular spectrum decomposition algorithm I-th component, singular spectrum decomposes it is well known that see document
P. Bonizzi, J.M. KAREL, O. Meste, R.L. Peeters, Singular spectrum decomposition: A new method for time series decomposition, Advances in Adaptive Data Analysis, 2014,6 (4): 1-29；
Step 3: to 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 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 0.24 mm, and traditional method can the minimum inner ring fault dimension width of reliable recognition Being about 0.53mm, precision improves 54.7%.
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 0.32mm, and traditional method can reliable recognition minimum outer ring fault dimension width about For 0.68mm, precision improves 52.9%.
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 the present invention decomposes original first with singular spectrum Signal decomposes, and then utilizes the rearrangement of data and substitutes operation eliminating noise therein and trend component, only retaining letter Useful component in number component, thus avoid the impact on Envelope Analysis result of noise and trend component, improve accuracy And degree of accuracy.
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 (6)

1. the SSD 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 singular spectrum to decompose (Singular Spectrum Decomposition, SSD) algorithm by signal x(k) Resolve into n component sum, i.e.；
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 SSD 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 SSD 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 SSD 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 SSD 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 SSD 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)；In this example, the smooth step-length in rolling average method is set to 5；In the 1st iteration, 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；
5) all envelope estimation functions produced in iterative process can be obtained envelope signal mutually at convenience
。
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CN106291293A (en) * 2016-10-27 2017-01-04 西南石油大学 A kind of Partial discharge signal self-adaptive solution method based on spectrum kurtosis with S-transformation
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