CN106096313B - A kind of envelope Analysis Method based on unusual spectral factorization and spectrum kurtosis - Google Patents
A kind of envelope Analysis Method based on unusual spectral factorization and spectrum kurtosis Download PDFInfo
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Abstract
The envelope Analysis Method based on unusual spectral factorization and spectrum kurtosis that the invention discloses a kind of, this method decomposes original signal first with singular spectrum decomposition method, then noise component(s) and trend term in decomposition result are excluded using the rearrangement of data and substitution operation, then filtered signal for the first time is analyzed using spectrum kurtosis method again, obtain the centre frequency and bandwidth of optimal filter, then second of filtering is carried out again to filtered signal for the first time using the filter, then Envelope Analysis is carried out to second of filtered signal using cubic spline iteration smoothed envelope analysis method, the fault type of rotating machinery is finally determined according to envelope spectrum.The present invention is suitable for the complicated rotating machinery fault signal of processing, can accurately determine the fault type of rotating machinery, 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 one kind based on unusual spectral factorization and
Compose the envelope Analysis Method of kurtosis.
Background technique
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 lower so as to cause the analysis precision of the prior art；2. existing Envelope Analysis technology is based on being converted by Hilbert,
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 of signal is polluted as a result, still signal to be analyzed at present does not meet the item of simple component and narrowband strictly
Part will lead to the prior art because precision is not high in this way and be easy to appear erroneous judgement problem；3. the envelope spectrum obtained by conventional method
There is end effects.
Summary of the invention
The problem to be solved in the present invention is against the above deficiency, to propose a kind of envelope based on unusual spectral factorization and spectrum kurtosis
Analysis method has analysis result accuracy and accuracy high, and can accurately examine after envelope Analysis Method of the invention
The advantages of measuring rotating machinery fault type.
In order to solve the above technical problems, the technical solution adopted by the present invention is as follows: one kind based on unusual spectral factorization and compose it is high and steep
The envelope Analysis Method of degree, which comprises the following steps:
Step 1: measuring the vibration signal x(k of rotating machinery with sample frequency fs using acceleration transducer), (k=1,
2 ..., N), N is the length of sampled signal；
Step 2: using unusual spectral factorization (Singular Spectrum Decomposition) algorithm by signal x(k)
The sum of n component is resolved into, i.e.,, wherein ci(k) the obtained by singular spectrum decomposition algorithm is represented
I 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) reordering operations and substitution operation are executed, it is rearranged to operate obtained data ci shuffle(k) table
Show, obtains data c after substitution operationi FTran(k) it indicates；
Step 4: to ci(k), ci shuffle(k) and ci FTran(k) multi-fractal is executed respectively remove trend fluction analysis
(Multifractal Detrended Fluctuation Analysis, MFDFA), obtains 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) and Hi shuffle(q) or Hi(q) and Hi FTran(q) relative error between 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, 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) analysis of cubic spline iteration smoothed envelope is executed, signal envelope eov(k is obtained)；
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, data rearrangement operation in the step 3 the following steps are included:
Upset component c at randomi(k) put in order.
Further, in the step 3 data substitution operation the following steps are included:
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), it seeks
Data ci IFFT(k) real part.
Further, in the step 4 MFDFA method the following steps are included:
1) the profile Y (i) of x (k) (k=1,2 ..., N) is constructed:
,
X (k) represents the c in the step 4i(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 opposite direction of data
2NSSegment data；
3) it is fitted the polynomial trend of every segment data using least square method, then calculates the variance of every segment data:
yv(i) trend for the v segment data of fitting remembers that this goes trend process if the polynomial trend of fitting is m rank
For (MF-) DFAm；In this example, m=1；
4) average value of q rank wave function is calculated:
；
5) if there are self-similarity characteristics, the average value F of q rank wave function by x (k)q(s) between time scale s
There are power law relations:
As q=0, the formula in step 4) dissipates, and at this moment H (0) is by logarithmic mean process defined in following formula come really
It is fixed:
；
6) take logarithm that can obtain ln [F on the formula both sides in step 5)q(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 the following steps are included:
1) constructing a cutoff frequency is fcThe low-pass filter h (n) of=0.125+ ε；ε > 0, f in this examplec=0.3;
It 2) is the quasi- low-pass filter h of [0,0.25] based on h (n) construction passband0(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 the step 7 is representedf1(k)；
4) the centre frequency f of i-th of filter in decomposition tree on kth layerkiAnd bandwidth BkRespectively
；
5) each filter results c is calculatedi k(n)( i=0,…, 2k- 1) kurtosis
；
6) all spectrum kurtosis are summarized, obtains the total spectrum kurtosis of signal.
Further, the cubic spline iteration smoothed envelope analysis method in the step 9 the following steps are included:
1) signal is calculatedz(k) Jue Dui Zhi ∣z(k) the local extremum of ∣；In the 1st iteration,z(k) represent the step
X in 9f2(k)；
2) envelope eov is obtained using cubic spline interpolation Local Extremum1(k)；
3) rightz(k) be normalized to obtain；
4) the 2nd iteration:z 1(k) it is re-used as new data, repeat above-mentioned steps 1) ~ 3),
It obtains；
5) i-th iteration:z i-1(k) it is re-used as new data, repeat above-mentioned steps 1) ~ 3),
It obtains；
If 6)nWhat secondary iteration obtainedz n (k) amplitude be less than or equal to 1, then iterative process stop, finally obtaining
Signalz(k) envelope be。
The invention adopts the above technical scheme, compared with prior art, the invention has the following advantages that
1) original signal is decomposed using unusual spectral factorization, then excludes it using the rearrangement of data and substitution operation
In noise and trend component, the only useful component in stick signal component, so as to avoid noise and trend component to packet
Network analyzes the influence of result, and analysis result accuracy and accuracy are high.
2) signal envelope and frequency modulating section are kept completely separate using cubic spline iteration smoothed envelope analysis method, energy
Influence of the frequency modulating section to signal envelope analysis result is enough avoided, 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 can be avoided by the envelope spectrum that the present invention obtains
End effect.
The present invention will be further described with reference to the accompanying drawings and examples.
Detailed description of the invention
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 in the embodiment of the present invention with inner ring failure；
Attached drawing 5 is using traditional envelope Analysis Method in the embodiment of the present invention to inner ring faulty bearing vibration signal
Analyze 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 in the embodiment of the present invention with outer ring failure；
Attached drawing 8 is using traditional envelope Analysis Method in the embodiment of the present invention to outer ring faulty bearing vibration signal
Analyze result；
Attached drawing 9 is the present invention in the embodiment of the present invention to the analysis result of outer ring faulty bearing vibration signal.
Specific embodiment
Embodiment, as shown in Figure 1, Figure 2, Figure 3 shows, a kind of envelope Analysis Method based on unusual spectral factorization and spectrum kurtosis, packet
Include following steps:
Step 1: measuring the vibration signal x(k of rotating machinery with sample frequency fs using acceleration transducer), (k=1,
2 ..., N), N is the length of sampled signal；
Step 2: using unusual spectral factorization (Singular Spectrum Decomposition) algorithm by signal x(k)
Resolve into the sum of n component, that is, wherein, ci(k) i-th of the component obtained by singular spectrum decomposition algorithm, singular spectrum point are represented
Solution 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) reordering operations and substitution operation are executed, it is rearranged to operate obtained data ci shuffle(k) table
Show, obtains data c after substitution operationi FTran(k) it indicates；
Step 4: to ci(k), ci shuffle(k) and ci FTran(k) multi-fractal is executed respectively remove trend fluction analysis
(Multifractal Detrended Fluctuation Analysis, MFDFA), obtains 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) and Hi shuffle(q) or Hi(q) and Hi FTran(q) relative error between 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, 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) analysis of cubic spline iteration smoothed envelope is executed, signal envelope eov(k is obtained)；
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.
In step 3 data rearrangement operation the following steps are included:
Upset component c at randomi(k) put in order.
In step 3 data substitution operation the following steps are included:
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), it seeks
Data ci IFFT(k) real part.
MFDFA method in step 4 the following steps are included:
1) the profile Y (i) of x (k) (k=1,2 ..., N) is constructed:
,
,
X (k) represents the c in the step 4i(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 opposite direction of data
2NSSegment data；
3) it is fitted the polynomial trend of every segment data using least square method, then calculates the variance of every segment data:
yv(i) trend for the v segment data of fitting remembers that this goes trend process if the polynomial trend of fitting is m rank
For (MF-) DFAm；In this example, m=1；
4) average value of q rank wave function is calculated:
；
5) if there are self-similarity characteristics, the average value F of q rank wave function by x (k)q(s) between time scale s
There are power law relations:
As q=0, the formula in step 4) dissipates, and at this moment H (0) is by logarithmic mean process defined in following formula come really
It is fixed:
6) take logarithm that can obtain ln [F on the formula both sides in step 5)q(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 the following steps are included:
1) constructing a cutoff frequency is fcThe low-pass filter h (n) of=0.125+ ε；ε > 0, f in this examplec=0.3;
It 2) is the quasi- low-pass filter h of [0,0.25] based on h (n) construction passband0(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 the step 7 is representedf1(k)；
4) the centre frequency f of i-th of filter in decomposition tree on kth layerkiAnd bandwidth BkRespectively
；
5) each filter results c is calculatedi k(n)( i=0,…, 2k- 1) kurtosis
；
6) all spectrum kurtosis are summarized, obtains the total spectrum kurtosis of signal.
Cubic spline iteration smoothed envelope analysis method in step 9 the following steps are included:
1) signal is calculatedz(k) Jue Dui Zhi ∣z(k) the local extremum of ∣；In the 1st iteration,z(k) represent the step
X in 9f2(k)；
2) envelope eov is obtained using cubic spline interpolation Local Extremum1(k)；
3) rightz(k) be normalized to obtain；
4) the 2nd iteration:z 1(k) it is re-used as new data, repeat above-mentioned steps 1) ~ 3),
It obtains；
5) i-th iteration:z i-1(k) it is re-used as new data, repeat above-mentioned steps 1) ~ 3),
It obtains；
If 6)nWhat secondary iteration obtainedz n (k) amplitude be less than or equal to 1, then iterative process stop, finally obtaining
Signalz(k) envelope be。
Test 1, tests the performance of algorithm of the present invention using the bearing vibration data with inner ring failure
Card.
Testing 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, this explanation is by passing from fig. 5, it can be seen that the left end point of envelope spectrum is there is abnormal high level
There is end effects for the envelope spectrum that system method obtains.
Signal shown in Fig. 4 is analyzed using method proposed by the invention, obtained analysis result such as Fig. 6 institute
Show.From fig. 6, it can be seen that spectral line corresponding to 160Hz and 320Hz is apparently higher than other spectral lines, the two frequencies are respectively corresponded
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
Out, there is no end effect by the envelope spectrum that the present invention obtains.
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 0.23 mm, and conventional method is capable of the minimum inner ring failure dimension width of reliable recognition
About 0.53mm, precision improve 56.6%.
Test 2, tests the performance of algorithm of the present invention using the bearing vibration data with outer ring failure
Card.
Testing 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, this explanation is by passing from figure 8, it is seen that the left end point of envelope spectrum is there is abnormal high level
There is end effects for the envelope spectrum that system method obtains.
Signal shown in Fig. 7 is analyzed using method proposed by the invention, obtained analysis result such as Fig. 9 institute
Show.From fig. 9, it can be seen that spectral line corresponding to 103Hz and 206Hz is apparently higher than other spectral lines, the two frequencies are respectively corresponded
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
Out, there is no end effect by the envelope spectrum that the present invention obtains.
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 0.33mm, and conventional method is capable of the minimum outer ring failure dimension width of reliable recognition about
For 0.68mm, precision improves 51.5%.
According to 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 then excludes noise and trend component therein, Jin Jinbao using the rearrangement of data and substitution operation
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) based on traditional envelope Analysis Method is converted by Hilbert, 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, will lead to the prior art in this way because of precision not
High and be easy to appear erroneous judgement problem, different from traditional envelope Analysis Method, the present invention utilizes cubic spline iteration smoothed envelope to divide
Signal envelope and frequency modulating section are kept completely separate by analysis method, be can be avoided frequency modulating section and are analyzed result to signal envelope
Influence, 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 can be avoided by the envelope spectrum that the present invention obtains
End effect.
5) each step effect:
The 1) step: acquisition vibration signal；
Original signal: being resolved into the form of different component sums by the 2) step, and some of them component corresponds to noise and trend term,
Some components correspond to useful signal；
The 3) ~ 5) step: reordering operations are executed to the signal that above-mentioned decomposition obtains and substitution operates, reject noise therein point
Amount and trend term only retain useful signal；
The 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)；
The 9) step: signal x is calculatedf2(k) envelope eov (k)；
The 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 better understand the content of present invention, should not be construed as limiting the scope of protection of the present invention, as long as
Technical solution improvements introduced according to the present invention each falls within protection scope of the present invention.
Claims (6)
1. a kind of envelope Analysis Method based on unusual spectral factorization and spectrum kurtosis, which comprises the following steps:
), step 1: measuring the vibration signal x(k of rotating machinery with sample frequency fs using acceleration transducer k=1,2 ...,
N, N are the length of sampled signal；
Step 2: being decomposed signal x(k) using unusual spectral factorization (Singular Spectrum Decomposition) algorithm
At the sum of n component, i.e.,, wherein ci(k) i-th point obtained by singular spectrum decomposition algorithm is represented
Amount, unusual spectral factorization are known；
Step 3: to ci(k) reordering operations and substitution operation are executed, it is rearranged to operate obtained data ci shuffle(k) it indicates,
Data c is obtained after substitution operationi FTran(k) it indicates；
Step 4: to ci(k), ci shuffle(k) and ci FTran(k) multi-fractal is executed respectively remove trend fluction analysis
(Multifractal Detrended Fluctuation Analysis, MFDFA), obtains 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) and Hi shuffle(q) or Hi(q) and Hi FTran(q) relative error between is 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, 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) analysis of cubic spline iteration smoothed envelope is executed, signal envelope eov(k is obtained)；
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 envelope Analysis Method based on unusual spectral factorization and spectrum kurtosis according to claim 1, which is characterized in that
In the step 3 data rearrangement operation the following steps are included:
Upset component c at randomi(k) put in order.
3. a kind of envelope Analysis Method based on unusual spectral factorization and spectrum kurtosis according to claim 1, it is characterised in that:
In the step 3 data substitution operation the following steps are included:
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), data are sought
ci IFFT(k) real part.
4. a kind of envelope Analysis Method based on unusual spectral factorization and spectrum kurtosis according to claim 1, it is characterised in that:
MFDFA method in the step 4 the following steps are included:
1) x is constructedy(k) profileY(i), k=1,2 ..., N:
,
,
xy(k) c in the step 4 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 opposite direction of data 2 are obtained with identical length segmentation, such oneN s Section
Data；
3) it is fitted the polynomial trend of every segment data using least square method, then calculates the variance of every 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；m=1；
4) the is calculatedqThe average value of rank wave function:
；
If 5) xy(k) there are self-similarity characteristics, thenqThe average value of rank wave functionF q (s) and time scalesBetween exist
Power law relation:
；
WhenqWhen=0, the formula in step 4) dissipates, at this momentH(0) it is determined by logarithmic mean process defined in following formula:
；
6) to the formula both sides in step 5) 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 envelope Analysis Method based on unusual spectral factorization and spectrum kurtosis according to claim 1, it is characterised in that:
Spectrum kurtosis method in the step 7 the following steps are included:
1) constructing a cutoff frequency is fcThe low-pass filter h (n) of=0.125+ ε；ε > 0, fc=0.3;
It 2) is the quasi- low-pass filter h of [0,0.25] based on h (n) construction passband0(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, K=8；c0
(n) x in the step 7 is representedf1(k)；
4) the centre frequency f of i-th of filter in decomposition tree on kth layerkiAnd bandwidth BkRespectively
；
5) each filter results c is calculatedi k(n) i=0,…, 2k- 1 kurtosis
；
6) all spectrum kurtosis are summarized, obtains the total spectrum kurtosis of signal.
6. a kind of envelope Analysis Method based on unusual spectral factorization and spectrum kurtosis according to claim 1, which is characterized in that
Cubic spline iteration smoothed envelope analysis method in the step 9 the following steps are included:
1) signal is calculatedz(k) Jue Dui Zhi ∣z(k) the local extremum of ∣；In the 1st iteration,z(k) represent in the step 9
xf2(k)；
2) envelope eov is obtained using cubic spline interpolation Local Extremum1(k)；
3) rightz(k) be normalized to obtain；
4) the 2nd iteration:z 1(k) it is re-used as new data, repeat above-mentioned steps 1) ~ 3),
It obtains；
5) i-th iteration:z i-1(k) it is re-used as new data, repeat above-mentioned steps 1) ~ 3), it obtains
；
If 6)nWhat secondary iteration obtainedz n (k) amplitude be less than or equal to 1, then iterative process stop, finally obtaining signalz
(k) envelope be。
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| CN108489719B (en) * | 2018-04-09 | 2019-11-05 | 常州湖南大学机械装备研究院 | A kind of combined failure of rotating machinery diagnostic method based on the unusual spectral factorization of G-P |
| CN108731945B (en) * | 2018-08-02 | 2019-12-13 | 南昌航空大学 | Method for extracting fault signal characteristic information of aircraft engine rotor system |
| CN109141885B (en) * | 2018-09-04 | 2020-04-10 | 厦门理工学院 | Bearing vibration signal envelope demodulation method, device and equipment based on MRSVD |
| CN109187023B (en) * | 2018-09-04 | 2021-01-26 | 温州大学激光与光电智能制造研究院 | Automobile generator bearing fault diagnosis method |
| CN109612726A (en) * | 2018-11-20 | 2019-04-12 | 南京航空航天大学 | A kind of multiple superstage analysis method extracted for vibration signal characteristics |
| CN112305380A (en) * | 2020-09-01 | 2021-02-02 | 华南理工大学 | Partial discharge white noise suppression method based on S transformation and spectral kurtosis |
| CN112595515A (en) * | 2020-12-04 | 2021-04-02 | 中国船舶工业综合技术经济研究院 | Power shafting bearing fault detection method and system |
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