CN106053069B - A kind of SSD of rolling bearing, spectrum kurtosis and smooth iteration envelope Analysis Method - Google Patents
A kind of SSD of rolling bearing, spectrum kurtosis and smooth iteration envelope Analysis Method Download PDFInfo
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- CN106053069B CN106053069B CN201610492448.9A CN201610492448A CN106053069B CN 106053069 B CN106053069 B CN 106053069B CN 201610492448 A CN201610492448 A CN 201610492448A CN 106053069 B CN106053069 B CN 106053069B
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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 SSD of rolling bearing, compose kurtosis and smooth iteration envelope Analysis Method, this method decomposes original signal first with singular spectrum decomposition method, then it utilizes the rearrangement of data and substitutes the noise component(s) and trend term in operation exclusion decomposition result, 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 filter, then Envelope Analysis is carried out to second of filtered signal using smooth iteration envelope Analysis Method, the fault type of rolling bearing is finally determined according to envelope spectrum.The present invention is suitable for the complicated rolling bearing fault signal of processing, can accurately determine the fault type of rolling bearing, has good noise immunity and robustness, is convenient for engineer application.
Description
Technical field
The present invention relates to condition monitoring for rotating machinery and fault diagnosis field, and in particular to a kind of SSD 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:1. existing Envelope Analysis technology either directly analyzes original signal, or only to original
Signal analyzed again after simply filtering, therefore existing method is easy to be done by 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 it must be the narrow band signal of simple component that Hilbert transformation, which requires analyzed signal, otherwise the frequency modulating section of signal will
The amplitude envelope analysis result of signal is polluted, but signal to be analyzed at present does not meet the item of simple component and narrowband strictly
Part may result in the prior art and is susceptible to erroneous judgement problem because precision is not high in this way;3. the envelope spectrum obtained by conventional method
There is end effects.
Invention content
The problem to be solved in the present invention be for above insufficient, propose a kind of SSD of rolling bearing, spectrum kurtosis and it is smooth repeatedly
For envelope Analysis Method, after envelope Analysis Method using the present invention, have analysis result accuracy and accuracy high, and can be accurate
The advantages of really detecting rotating machinery fault type.
In order to solve the above technical problems, the technical solution adopted by the present invention is as follows:A kind of SSD of rolling bearing, spectrum kurtosis
With smooth iteration envelope Analysis Method, which is characterized in that include the following steps:
Step 1:The vibration signal x of rolling bearing is measured with sample frequency fs using acceleration transducer(k), (k=1,
2, …,N), N is the length of sampled signal;
Step 2:Using unusual spectral factorization (Singular Spectrum Decomposition, SSD) algorithm by signal x
(k)The sum of n component is resolved into, i.e.,, wherein ci(k)Representative is obtained by singular spectrum decomposition algorithm
I-th of component, unusual spectral factorization is it is well known that be shown in 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 ci(k)It executes 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 indicates;
Step 4:To ci(k)、ci shuffle(k)And ci FTran(k)Multi-fractal is executed respectively removes trend fluction analysis
(Multifractal Detrended Fluctuation Analysis, MFDFA), obtain generalized Hurst index curve, ci
(k)Generalized Hurst index curve Hi(q)It indicates;ci shuffle(k)Generalized Hurst index curve Hi shuffle(q)Table
Show;ci FTran(k)Generalized Hurst index curve Hi FTran(q)It indicates;
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 executed, the centre frequency f corresponding to signal kurtosis maximum is found out0And band
Wide B;
Step 8:According to centre frequency f0With bandwidth B to xf1(k)Bandpass filtering is carried out, x is obtainedf2(k);
Step 9:To signal xf2(k)Smooth iteration Envelope Analysis is executed, signal envelope eov is obtained(k);
Step 10:To obtained signal envelope eov(k)It executes discrete Fourier transform and obtains envelope spectrum, according to envelope spectrum
Characteristic frequency judges the fault type of machine.
A kind of prioritization scheme, in the step 3 data rearrangement operation include the following steps:
Upset component c at randomi(k)Put in order.
Further, the operation of data replacement includes the following steps in the step 3:
1)To component ci(k)Discrete Fourier transform is executed, component c is obtainedi(k)Phase;
2)It is located at the pseudo- independent same distribution number in the section (- π, π) with one group to replace component ci(k)Original phase;
3)Inverse discrete Fourier transform is executed to the frequency domain data after phase substitutes and obtains data ci IFFT(k), seek
Data ci IFFT(k)Real part.
Further, MFDFA methods include the following steps in the step 4:
1)Construct the profile Y (i) of (k) (k=1,2 ..., N) x:
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)Then polynomial trend using least square fitting per segment data calculates the variance per segment data:
yv(i) trend for the v segment datas of fitting remembers that this goes trend process if the polynomial trend of fitting is m ranks
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 logarithm that 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 includes 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) it filters and resolves 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) output signal of i-th of filter in expression 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 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, the total spectrum kurtosis of signal is obtained.
Further, the smooth iteration envelope Analysis Method in the step 9 includes the following steps:
1)Calculate local mean value function:Determine all Local Extremum n of 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, then uses rolling average method to carry out smooth
Processing, obtains local mean value function m11(k);In this example, the smooth step-length in rolling average method is set as 5;In the 1st iteration
In, x (k) represents x in step 9 described in claim 1f2(k);
2)Estimate the envelope value of signal:Using Local Extremum niCalculate envelope estimated value ai
Equally, by all two neighboring envelope estimated value 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) it separates, obtains from original signal x (k)
4)Use h11(k) divided by envelope estimation function a11(k) to h11(k) it is demodulated, is obtained
It is desirable that s11(k) be a pure FM signal, i.e. its envelope estimation function a12(k) meet a12(k)=1;If
s11(k) condition is not satisfied, then by s11(k) it is used as new data to repeat the above iterative process m times, until obtaining a pure frequency modulation
Signal s1m(k), i.e. s1m(k) meet -1≤s1m(k)≤1, its envelope estimation function a1(m+1)(k) meet a1(m+1)(k)=1, because
This has
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
。
The present invention uses above technical scheme, and compared with prior art, the present invention has the following advantages:
1) original signal is decomposed using unusual spectral factorization (SSD), then utilize the rearrangement of data and substitutes operation
Noise and trend component therein are excluded, only the useful component in stick signal component, so as to avoid noise and trend point
The influence to Envelope Analysis result is measured, analysis result accuracy and accuracy are high.
2) signal envelope and frequency modulating section are kept completely separate using smooth iteration envelope Analysis Method, frequency can be avoided
Influence of the rate modulating part to signal envelope analysis result, to improve the precision of Envelope Analysis.
3) fault type of rotating machinery can be accurately detected.
4) there are end effects for the envelope spectrum obtained by conventional method, and the envelope spectrum obtained by the present invention can avoid
End effect.
The present invention will be further described with reference to the accompanying drawings and examples.
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 with inner ring failure in the embodiment of the present invention;
Attached drawing 5 is using traditional envelope Analysis Method in the embodiment of the present invention to inner ring faulty bearing vibration signal
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 with outer ring failure in the embodiment of the present invention;
Attached drawing 8 is using traditional envelope Analysis Method in the embodiment of the present invention to outer ring faulty bearing vibration signal
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 implementation mode
Embodiment, as shown in Figure 1, Figure 2, Figure 3 shows, a kind of SSD of rolling bearing, spectrum kurtosis and smooth iteration Envelope Analysis side
Method includes the following steps:
Step 1:The vibration signal x of rolling bearing is measured with sample frequency fs using acceleration transducer(k), (k=1,
2, …,N), N is the length of sampled signal;
Step 2:Using unusual spectral factorization (Singular Spectrum Decomposition, SSD) algorithm by signal x
(k)The sum of n component is resolved into, i.e.,, wherein ci(k)Representative is obtained by singular spectrum decomposition algorithm
I-th of component, unusual spectral factorization is it is well known that be shown in 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 ci(k)It executes 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 indicates;
Step 4:To ci(k)、ci shuffle(k)And ci FTran(k)Multi-fractal is executed respectively removes trend fluction analysis
(Multifractal Detrended Fluctuation Analysis, MFDFA), obtain generalized Hurst index curve, ci
(k)Generalized Hurst index curve Hi(q)It indicates;ci shuffle(k)Generalized Hurst index curve Hi shuffle(q)Table
Show;ci FTran(k)Generalized Hurst index curve Hi FTran(q)It indicates;
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 executed, the centre frequency f corresponding to signal kurtosis maximum is found out0And band
Wide B;
Step 8:According to centre frequency f0With bandwidth B to xf1(k)Bandpass filtering is carried out, x is obtainedf2(k);
Step 9:To signal xf2(k)Smooth iteration Envelope Analysis is executed, signal envelope eov is obtained(k);
Step 10:To obtained signal envelope eov(k)It executes discrete Fourier transform and obtains envelope spectrum, according to envelope spectrum
Characteristic frequency judges the fault type of machine.
Data rearrangement operation includes the following steps in step 3:
Upset component c at randomi(k)Put in order.
Data substitute operation and include the following steps in step 3:
1)To component ci(k)Discrete Fourier transform is executed, component c is obtainedi(k)Phase;
2)It is located at the pseudo- independent same distribution number in the section (- π, π) with one group to replace component ci(k)Original phase;
3)Inverse discrete Fourier transform is executed to the frequency domain data after phase substitutes and obtains data ci IFFT(k), seek
Data ci IFFT(k)Real part.
MFDFA methods include the following steps in step 4:
1)Construct the profile Y (i) of (k) (k=1,2 ..., N) x:
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)Then polynomial trend using least square fitting per segment data calculates the variance per segment data:
yv(i) trend for the v segment datas of fitting remembers that this goes trend process if the polynomial trend of fitting is m ranks
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 logarithm that 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 includes 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) it filters and resolves 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) output signal of i-th of filter in expression 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 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, the total spectrum kurtosis of signal is obtained.
Smooth iteration envelope Analysis Method in step 9 includes the following steps:
1)Calculate local mean value function:Determine all Local Extremum n of 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, then uses rolling average method to carry out smooth
Processing, obtains local mean value function m11(k);In this example, the smooth step-length in rolling average method is set as 5;In the 1st iteration
In, x (k) represents x in step 9 described in claim 1f2(k);
2)Estimate the envelope value of signal:Using Local Extremum niCalculate envelope estimated value ai
Equally, by all two neighboring envelope estimated value 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) it separates, obtains from original signal x (k)
4)Use h11(k) divided by envelope estimation function a11(k) to h11(k) it is demodulated, is obtained
It is desirable that s11(k) be a pure FM signal, i.e. its envelope estimation function a12(k) meet a12(k)=1;If
s11(k) condition is not satisfied, then by s11(k) it is used as new data to repeat the above iterative process m times, until obtaining a pure frequency modulation
Signal s1m(k), i.e. s1m(k) meet -1≤s1m(k)≤1, its envelope estimation function a1(m+1)(k) meet a1(m+1)(k)=1, because
This has
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
。
Experiment 1, tests the performance of algorithm of the present invention using the bearing vibration data with inner ring failure
Card.
Experiment bearing used is 6205-2RS JEM SKF, using electric discharge machining method on bearing inner race working depth
The groove for being 0.3556mm for 0.2794mm, width simulates bearing inner race failure, 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, when signal sampling
A length of 1s.
Collected inner ring fault-signal is as shown in Figure 4.
Signal shown in Fig. 4 is analyzed using traditional envelope Analysis Method first, obtained analysis result such as Fig. 5
It is shown.From fig. 5, it can be seen that the fault signature of bearing is blanked completely, therefore traditional envelope Analysis Method cannot be effectively
Extract the fault signature of bearing;In addition, there is abnormal high level for the left end point of envelope spectrum shown in Fig. 5, this explanation is by conventional method
There is end effects for obtained envelope spectrum.
Signal shown in Fig. 4 is analyzed using method proposed by the invention, obtained analysis result such as Fig. 6 institutes
Show.From fig. 6, it can be seen that the spectral line corresponding to 160Hz and 320Hz is apparently higher than other spectral lines, the two frequencies correspond to respectively
1 frequency multiplication and 2 frequencys multiplication of bearing inner race fault characteristic frequency may determine that bearing has inner ring failure accordingly;It can from Fig. 6
Go out, the envelope spectrum obtained by the present invention does not have end effect.
Show that the present invention is capable of reliable recognition in the case where load and failure dimensional depth are constant through many experiments
Minimum inner ring failure dimension width is about 0.24 mm, and conventional method is capable of the minimum inner ring failure dimension width of reliable recognition
About 0.53mm, precision improve 54.7%.
Experiment 2, tests the performance of algorithm of the present invention using the bearing vibration data with outer ring failure
Card.
Experiment bearing used is 6205-2RS JEM SKF, using electric discharge machining method on bearing outer ring working depth
The groove for being 0.5334mm for 0.2794mm, width simulates bearing outer ring failure, 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, when signal sampling
A length of 1s.
Collected outer ring fault-signal is as shown in Figure 7.
Signal shown in Fig. 7 is analyzed using traditional envelope Analysis Method first, obtained analysis result such as Fig. 8
It is shown.From figure 8, it is seen that the fault signature of bearing is blanked completely, therefore traditional envelope Analysis Method cannot be effectively
Extract the fault signature of bearing;In addition, there is abnormal high level for the left end point of envelope spectrum shown in Fig. 8, this explanation is by conventional method
There is end effects for obtained envelope spectrum.
Signal shown in Fig. 7 is analyzed using method proposed by the invention, obtained analysis result such as Fig. 9 institutes
Show.From fig. 9, it can be seen that the spectral line corresponding to 103Hz and 206Hz is apparently higher than other spectral lines, the two frequencies correspond to respectively
1 frequency multiplication and 2 frequencys multiplication of bearing outer ring fault characteristic frequency may determine that bearing has outer ring failure accordingly;It can from Fig. 9
Go out, the envelope spectrum obtained by the present invention does not have end effect.
Show that the present invention is capable of reliable recognition in the case where load and failure dimensional depth are constant through many experiments
Minimum outer ring failure dimension width is about 0.32mm, and conventional method is capable of the minimum outer ring failure dimension width of reliable recognition about
For 0.68mm, precision improves 52.9%.
According to test result, think after analysis:
1) traditional envelope Analysis Method directly carries out Envelope Analysis to original signal, or to merely through simple process
Original signal afterwards carries out Envelope Analysis, and different from traditional envelope Analysis Method, the invention firstly uses unusual spectral factorizations pair
Original signal is decomposed, and is then utilized the rearrangement of data and is substituted operation exclusion noise therein and trend component, Jin Jinbao
The useful component in signal component is stayed, the influence so as to avoid noise and trend component to Envelope Analysis result improves standard
Exactness and accuracy.
2) traditional envelope Analysis Method is based on Hilbert is converted, and Hilbert transformation requires analyzed letter
Number must be the narrow band signal of simple component, otherwise the frequency modulating section of signal will pollute signal Envelope Analysis as a result, but
It is the condition that signal to be analyzed does not meet simple component and narrowband strictly at present, may result in the prior art in this way because of precision not
High and be susceptible to erroneous judgement problem, different from traditional envelope Analysis Method, the present invention utilizes smooth iteration envelope Analysis Method general
Signal envelope is kept completely separate with frequency modulating section, can avoid influence of the frequency modulating section to signal envelope analysis result,
To improve the precision of Envelope Analysis.
3) fault type of rotating machinery can be accurately detected.
4) there are end effects for the envelope spectrum obtained by conventional method, and the envelope spectrum obtained by the present invention can avoid
End effect.
5)Each step effect:
1) step:Acquire vibration signal;
2) step:Original signal is resolved into the form of different component sums, some of which component corresponds to noise and trend term,
Some components correspond to useful signal;
3) ~ 5) step:Is executed by reordering operations and is substituted for the signal that above-mentioned decomposition obtains and is operated, noise therein point is rejected
Amount and trend term only retain useful signal;
6) step:Remaining useful signal is summed, by this and as signal it is rearranged and substitute filtered result xf1
(k);
7) step:To filtered signal xf1(k) spectrum kurtosis analysis is executed, corresponding center at signal maximum kurtosis is found out
Frequency f0And bandwidth B;
8) step:According to centre frequency f0With bandwidth B to xf1(k) bandpass filtering is carried out, signal x is obtainedf2(k);
9) step:Calculate signal xf2(k) envelope eov (k);
10) step:Discrete Fourier transform is executed 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 the above specific embodiments are only exemplary, it is to make ability
Field technique personnel can be better understood from the content of present invention, should not be understood as limiting the scope of the invention, as long as
According to technical solution of the present invention improvements introduced, protection scope of the present invention is each fallen within.
Claims (6)
1. a kind of SSD of rolling bearing, spectrum kurtosis and smooth iteration envelope Analysis Method, which is characterized in that include the following steps:
Step 1:The vibration signal x of rolling bearing is measured with sample frequency fs using acceleration transducer(k), k=1, 2, …,
N, N are the length of sampled signal;
Step 2:Using unusual spectral factorization (Singular Spectrum Decomposition, SSD) algorithm by signal x(k)
The sum of n component is resolved into, i.e.,, wherein ci(k)Represent the obtained by singular spectrum decomposition algorithm
I component;
Step 3:To ci(k)It executes reordering operations and substitutes and operate, it is rearranged to operate obtained data ci shuffle(k)It indicates,
Data c is obtained after substituting operationi FTran(k)It indicates;
Step 4:To ci(k)、ci shuffle(k)And ci FTran(k)Multi-fractal is executed respectively removes trend fluction analysis
(Multifractal Detrended Fluctuation Analysis, MFDFA), obtain generalized Hurst index curve, ci
(k)Generalized Hurst index curve Hi(q)It indicates;ci shuffle(k)Generalized Hurst index curve Hi shuffle(q)Table
Show;ci FTran(k)Generalized Hurst index curve Hi FTran(q)It indicates;
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 executed, the centre frequency f corresponding to signal kurtosis maximum is found out0And bandwidth B;
Step 8:According to centre frequency f0With bandwidth B to xf1(k)Bandpass filtering is carried out, x is obtainedf2(k);
Step 9:To signal xf2(k)Smooth iteration Envelope Analysis is executed, signal envelope eov is obtained(k);
Step 10:To obtained signal envelope eov(k)It executes discrete Fourier transform and obtains envelope spectrum, according to envelope spectrum signature
Frequency judges the fault type of machine.
2. a kind of SSD of rolling bearing according to claim 1, spectrum kurtosis and smooth iteration envelope Analysis Method, special
Sign is that data rearrangement operates and includes the following steps in the step 3:
Upset component c at randomi(k)Put in order.
3. a kind of SSD of rolling bearing according to claim 1, spectrum kurtosis and smooth iteration envelope Analysis Method, special
Sign is:Data substitute operation and include the following steps in the step 3:
1)To component ci(k)Discrete Fourier transform is executed, component c is obtainedi(k)Phase;
2)It is located at the pseudo- independent same distribution number in the section (- π, π) with one group to replace component ci(k)Original phase;
3)Inverse discrete Fourier transform is executed to the frequency domain data after phase substitutes and obtains data ci IFFT(k), seek data
ci IFFT(k)Real part.
4. a kind of SSD of rolling bearing according to claim 1, spectrum kurtosis and smooth iteration envelope Analysis Method, special
Sign is:MFDFA methods include 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)Then polynomial trend using least square fitting per segment data calculates the variance per segment data:
;
y v (i) it is 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:
;
5)If xy(k) there are self-similarity characteristics, thenqThe average value of rank wave functionF q (s) and time scalesBetween exist
Power law relation:
F q (s)~s H(q);
WhenqWhen=0, step 4)In formula diverging, at this momentH(0) it is determined by logarithmic mean process defined in following formula:
;
6)To step 5)In formula both sides take logarithm can obtain ln [F q (s)]=H(q)ln(s)+c,cFor constant, it is possible thereby to obtain
The slope of straight lineH(q)。
5. a kind of SSD of rolling bearing according to claim 1, spectrum kurtosis and smooth iteration envelope Analysis Method, special
Sign is:Spectrum kurtosis method in the step 7 includes 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) it filters and resolves 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) output signal of i-th of filter in expression 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 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, the total spectrum kurtosis of signal is obtained.
6. a kind of SSD of rolling bearing according to claim 1, spectrum kurtosis and smooth iteration envelope Analysis Method, special
Sign is that the smooth iteration envelope Analysis Method in the step 9 includes the following steps:
1)Calculate local mean value function:Determine all Local Extremum n of signal x (k)i, calculate two neighboring extreme point niWith
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 set as 5;In the 1st iteration, x
(k) x in step 9 described in claim 1 is representedf2(k);
2)Estimate the envelope value of signal:Using Local Extremum niCalculate envelope estimated value ai
Equally, by all two neighboring envelope estimated value 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) it separates, obtains from original signal x (k)
4)Use h11(k) divided by envelope estimation function a11(k) to h11(k) it is demodulated, is obtained
It is desirable that s11(k) be a pure FM signal, i.e. its envelope estimation function a12(k) meet a12(k)=1;If s11
(k) condition is not satisfied, then by s11(k) it is used as new data to repeat the above iterative process m times, until obtaining a pure FM signal
s1m(k), i.e. s1m(k) meet -1≤s1m(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 ends;This
Variation Δ=0.01 in example;
5)All envelope estimation functions multiplication generated in iterative process can be obtained envelope signal
。
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