CN107631866A - A kind of initial failure recognition methods of low speed operation rotating machinery - Google Patents

A kind of initial failure recognition methods of low speed operation rotating machinery Download PDF

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CN107631866A
CN107631866A CN201710775197.XA CN201710775197A CN107631866A CN 107631866 A CN107631866 A CN 107631866A CN 201710775197 A CN201710775197 A CN 201710775197A CN 107631866 A CN107631866 A CN 107631866A
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CN107631866B (en
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陈景龙
刘子俊
訾艳阳
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Xian Jiaotong University
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Abstract

A kind of initial failure recognition methods of low speed operation rotating machinery of the present invention, solves the problems, such as that PAA dimensionality reductions window length is chosen, substantially reduces the calculating mistake of round domain statistical indicator, effectively increase the reliability of mechanical equipment state identification.Methods described includes, step (1), obtain the vibration signal under Low-speed rotating machinery normal operating condition, carry out wavelet decomposition and reconstruct low frequency signal, carry out FFT and draw its spectrum envelope, frequency peak is identified, obtains critical frequency, and then chooses multiple various dimensions PAA dimensionality reductions window length；Step (2), using various dimensions PAA to vibration signal to be identified successively dimension-reduction treatment, bearing state feature is extracted, circle domain statistical characteristics is calculated after being represented in circle domain；Step (3), by the index averaged of the same race in multigroup round domain statistical characteristics of acquisition, 4 averagely round domain statistical characteristics are obtained, Low-speed rotating machinery running state recognition are realized, so as to judge whether initial failure occurs.

Description

A kind of initial failure recognition methods of low speed operation rotating machinery
Technical field
The present invention relates to mechanical equipment state monitoring method, specially a kind of initial failure of low speed operation rotating machinery is known Other method.
Background technology
During plant equipment is widely used in living and produced, status monitoring is carried out to it can find the failure of machine in time With the generation of prevention apparatus serious accident, so as to avoid the injures and deaths of personnel and economic loss.Operate under low-speed heave-load operating mode Plant equipment easily breaks down, therefore identifies Low-speed rotating machinery state, to improving Low-speed rotating machinery functional reliability tool There is important meaning.Meanwhile and effectively assessment equipment overall efficiency there is an urgent need to for extension device service life, protect Demonstrate,proving its safety in utilization has important engineering use value.
Low-speed rotating machinery fault signature has the spies such as failure-frequency is low, failure impact interval is long, shock response frequency is low Point so that the fault signature extraction of Low-speed rotating machinery has larger difficulty, it is impossible to using the state of conventional rotating speed rotating machinery Recognition methods.Currently used Low-speed rotating machinery state identification method mainly has the multiclass interconnection vector machine based on sound emission Method and method based on empirical mode decomposition etc..But these methods are all using complicated signal processing technology, processing speed Slowly, it is impossible to meet the rapidity demand monitored in real time in engineering, remain in research aspect.Part Methods employ sound emission etc. Unconventional sensor, its maturity and popularization degree are not so good as vibrating sensor, and in occasions such as strong electromagnetics and do not apply to.It is based on Circle domain statistical nature method is handled the vibration signal of Low-speed rotating machinery, identifies low speed rotation equipment state, is a kind of Quick technological approaches, but (PiecewiseAggregateApproximation, aggregation is flat paragraph by paragraph by wherein committed step PAA ) missing of the long choosing method of dimensionality reduction window and the limitation of single PAA dimension reduction methods cause subsequently to justify domain statistical indicator and can not counted Calculate or larger error occur, it is impossible to effectively identify mechanical equipment state.Therefore, previous methods are difficult to meet Low-speed rotating machinery event Hinder the needs of identification.
The content of the invention
For problems of the prior art, the present invention provides a kind of initial failure identification of low speed operation rotating machinery Method, the problem of PAA dimensionality reductions window length is chosen is this method solve, the calculating mistake of round domain statistical indicator is substantially reduced, effectively carries The high reliability of mechanical equipment state identification so that this method can be efficiently applied to engineering reality.
The present invention is to be achieved through the following technical solutions：
A kind of initial failure recognition methods of low speed operation rotating machinery, comprises the following steps,
Step (1), the vibration signal under Low-speed rotating machinery normal operating condition is obtained, carry out wavelet decomposition and reconstruct low Frequency signal, carry out FFT and draw its spectrum envelope, identify frequency peak, obtain critical frequency, and then choose multiple multidimensional Spend PAA dimensionality reductions window length；
Step (2), using various dimensions PAA to vibration signal to be identified successively dimension-reduction treatment, bearing state feature is extracted, Circle domain statistical characteristics is calculated after being represented in circle domain；
Step (3), by the index averaged of the same race in multigroup round domain statistical characteristics of acquisition, obtain 4 averagely Circle domain statistical characteristics, realizes Low-speed rotating machinery running state recognition, so as to judge whether initial failure occurs.
Preferably, step (1) chooses comprising the following steps that for various dimensions PAA dimensionality reductions window length,
1) vibration signal under Low-speed rotating machinery normal operating condition is measured；
2) wavelet decomposition is carried out to vibration signal, and reconstructs low frequency signal；
3) FFT is carried out to the vibration signal after reconstruct, draws amplitude frequency diagram；
4) envelope spectrum of amplitude frequency diagram is drawn based on Hilbert envelope approach；
5) magnitude peak in envelope spectrum is identified, records its corresponding frequency fi, and ascending order is pressed, form peak It is worth frequency array, is designated as f=(f1,f2,...,fj,...,fn)；
6) in crest frequency array f, adjacent two crest frequency forms frequency separation, and then component frequency section array F= ((f1,f2),(f2,f3),...,(fj,fj+1),...(fn-1,fn))；
7) follow critical frequency and ask for rule, travel through all elements in frequency separation array F, ask for critical frequency successively λFace j, critical frequency array is formed, is designated as λFace=(λFace 1,λFace 2,...,λFace j,...,λFace p)：
8) according to obtained λFaceThe window length of various dimensions PAA dimensionality reductions is calculated, the long array of PAA windows is formed, is designated as w=(w1, w2,...,wj,...,wp), wherein wjFor λFace jCorresponding PAA windows length.
Further, in step (1), it is as follows that the critical frequency asking for following during critical frequency asks for rule：
a)1≤p≤n；Wherein, p is the quantity of PAA dimensionality reductions window length；
b)λFace j∈(fi,fi+1), wherein j ∈ j | 1≤j≤p, j ∈ N*},i∈{i|1≤i≤n-1,i∈N*}；
c)(fs/(4·λFace j))∈N*, wherein fs is signal sampling frequencies；
If d) same frequency section has multiple critical frequencies, maximum is taken to be designated as λFace j；
If e) certain frequency separation exists without critical frequency, next section is jumped to.
Further, in step 8), the method for calculating the long array of PAA dimensionality reduction windows is, by λFaceAll elements substitute into down successively Formula：
Preferably, what step (2) PAA dimensionality reductions and circle domain statistical characteristics calculated comprises the following steps that,
First, the Low-speed rotating machinery vibration signal x=(x of state to be identified are measured1,x2,...,xi,...,xN), wherein xiFor the vibration amplitude at i moment；
Secondly, by vibration signal x=(x1,x2,...,xN) PAA dimensionality reductions are carried out, obtain by n average value ykThe drop of composition Dimensional signal Y=(y1,y2,...,yk,...,yn)；
Then, dimensionality reduction signal Y is equally divided into m subsignal, draws neighborhood correlation point diagram respectively to each subsignal, and Identification state feature；
Finally, by state feature in circle domain representation, and round domain statistical characteristics is calculated：Circle domain averageCircle domain variance V, circle domain degree of skewness s and circle domain kurtosis k, is designated as
Preferably, the acquisition of the multigroup round domain statistical nature of step (3) and its mean value calculation comprise the following steps that,
First, the p long w of PAA dimensionality reduction windows step (1) obtained1,w2,...,wpSubstitute into respectively in step (2), obtain p Group circle domain statistical characteristics G1,G2,...,Gp；
Then, averagely round domain statistical characteristics is calculatedWhereinFor average round domain average,It is flat Round domain variance,For average round domain degree of skewness andFor average round domain kurtosis.
Further, in step (3), averagely round domain statistical characteristics is calculatedMethod such as following formula：
Preferably, in step (3), by Low-speed rotating machinery running state recognition, whether initial failure occurs specific Judgement is as follows,
It is a steady state value, degree of skewness and kurtosis all convergences when average and variance is calculated after circle domain representation in state feature When zero, Low-speed rotating machinery does not break down；
After state feature is in circle domain representation, its average and variance are changed, and degree of skewness is close to ± 1, and kurtosis is leaned on to 1 Closely, then there is exceptional value in state feature, and initial failure occurs for Low-speed rotating machinery.
Compared with prior art, the present invention has technique effect beneficial below：
A kind of initial failure recognition methods of low speed operation rotating machinery of the present invention, according to low speed rotation machine under normal condition Tool vibration signal determines the window length of various dimensions PAA dimensionality reductions, afterwards by measuring Low-speed rotating machinery vibration signal to be identified, base Equipment state feature is obtained in the method for various dimensions PAA dimensionality reductions, multigroup round domain statistical characteristics is obtained based on circle domain statistical method, It is based ultimately upon weighted average method and calculates averagely round domain statistical indicator identification Low-speed rotating machinery state.This method can effectively be chosen PAA dimensionality reductions window is grown, and improves circle domain statistical indicator computational accuracy, the reliability of increase mechanical equipment state identification, and have speed The characteristics of fast and simple and easy, it is easy to apply in engineering in practice.Realize the long choosing method of window, more of various dimensions PAA dimensionality reductions The mixing of the round domain statistical nature computational methods of dimension PAA dimension reduction methods, poly domain statistical nature value-acquiring method peace；Solve The problem of PAA dimensionality reductions window length is chosen, significantly improve the computational accuracy of round domain statistical indicator, increase mechanical equipment state identification Reliability, have the characteristics that it is quick, easy, real-time, suitable for live Real time identification Low-speed rotating machinery state, favorably In improving Low-speed rotating machinery functional reliability and security, the identification that rotating machinery initial failure state is run for low speed provides New approaches and new method, have an important engineering practical value.
Brief description of the drawings
Fig. 1 is the initial failure recognition methods flow chart that low speed of the present invention runs rotating machinery.
Fig. 2 is Low-speed rotating machinery normal operating condition step vibration signal wavelet decomposition frequency spectrum.
Fig. 3 is that signal wavelet decomposition spectrum envelope is composed under equipment normal operating condition.
Fig. 4 is the average statistical characteristics figure in the averagely round domain of low-speed rolling bearing described in present example.
Fig. 5 is the variance statistic characteristic value figure in the averagely round domain of low-speed rolling bearing described in present example.
Fig. 6 is the degree of skewness statistical characteristics figure in the averagely round domain of low-speed rolling bearing described in present example.
Fig. 7 is the kurtosis statistical characteristics figure in the averagely round domain of low-speed rolling bearing described in present example.
Embodiment
With reference to specific embodiment, the present invention is described in further detail, it is described be explanation of the invention and It is not to limit.
Shown in reference picture 1, the initial failure recognition methods of rotating machinery is run for low speed of the present invention, it includes following step Suddenly, the vibration signal under Low-speed rotating machinery normal operating condition is obtained, wavelet decomposition is carried out to it and reconstructs low frequency signal, is entered Row FFT simultaneously draws its spectrum envelope line chart, identifies frequency peak, obtains critical frequency, and then calculates multiple PAA dimensionality reductions window length； Using multiple PAA windows length to vibration signal to be identified successively dimension-reduction treatment, bearing state feature is extracted, table is carried out by circle domain Show, calculate circle domain statistical characteristics, obtain multigroup round domain statistical characteristics；By the similar index in multigroup round domain statistical characteristics Averaged, 4 averagely round domain statistical characteristics are obtained, Low-speed rotating machinery running state recognition are realized, so as to judge morning Whether phase failure occurs.
The present invention is implemented using vibration signal identification Low-speed rotating machinery running status by step in detail below：
(1) the window length of various dimensions PAA dimensionality reductions is chosen；
1) vibration signal under Low-speed rotating machinery normal operating condition is measured；
2) wavelet decomposition is carried out to vibration signal, low frequency signal is reconstructed；
3) FFT (FastFourierTransformation, Fast Fourier Transform (FFT)) is carried out to the vibration signal after reconstruct Conversion, draw amplitude frequency diagram；
4) envelope spectrum of amplitude frequency diagram is drawn based on Hilbert envelope approach；
5) magnitude peak in envelope spectrum is identified, records its corresponding frequency fi, and ascending order is pressed, form peak It is worth frequency array, is designated as f=(f1,f2,...,fj,...,fn)；
6) in crest frequency array f, adjacent two crest frequency forms frequency separation, and then component frequency section array F= ((f1,f2),(f2,f3),...,(fj,fj+1),...(fn-1,fn))；
7) follow following critical frequency and ask for rule, travel through all elements in frequency separation array F, ask for critical frequency successively Rate λFace j, critical frequency array is formed, is designated as λFace=(λFace 1,λFace 2,...,λFace j,...,λFace p)：
a)1≤p≤n；
b)λFace j∈(fi,fi+1), wherein j ∈ j | 1≤j≤p, j ∈ N*},i∈{i|1≤i≤n-1,i∈N*}；
c)(fs/(4·λFace j))∈N*, wherein fs is signal sampling frequencies；
If d) same frequency section has multiple critical frequencies, maximum is taken to be designated as λFace j；
If e) certain frequency separation exists without critical frequency, next section is jumped to.
8) by λFaceSubstitute into following formula to calculate, obtain the window length of various dimensions PAA dimensionality reductions, form the long array of PAA windows, be designated as w= (w1,w2,...,wj,...,wp), wherein wjFor λFace jCorresponding PAA windows length：
(2) PAA dimensionality reductions and circle domain statistical characteristics calculate；
First, the Low-speed rotating machinery vibration signal x=(x of state to be identified are measured1,x2,...,xi,...,xN), wherein xiFor the vibration amplitude at i moment；
Secondly, by vibration signal x=(x1,x2,...,xN) PAA dimensionality reductions are carried out, obtain by n average value ykThe drop of composition Dimensional signal Y=(y1,y2,...,yk,...,yn)；
Then, dimensionality reduction signal Y is equally divided into m subsignal, draws neighborhood correlation point diagram respectively to each subsignal, and Identification state feature；
Finally, by state feature in circle domain representation, and round domain statistical characteristics is calculated：Circle domain averageCircle domain variance V, circle domain degree of skewness s and circle domain kurtosis k, is designated as
(3) acquisition of poly domain statistical nature and its mean value calculation
First, the p long w of PAA dimensionality reduction windows step (1) obtained1,w2,...,wpStep (2) is substituted into respectively, obtains p groups Circle domain statistical characteristics G1,G2,...,Gp；
Then, averagely round domain statistical characteristics is calculatedWhereinFor average round domain average,It is flat Round domain variance,For average round domain degree of skewness andFor average round domain kurtosis, such as following formula：
When Low-speed rotating machinery does not break down, step (2) identifies that machine performance is normal by neighborhood correlation point diagram, this When, average is calculated after circle domain representation in state feature and variance is a steady state value, and degree of skewness and kurtosis all level off to zero.When Initial failure occurs, and exceptional value occurs in state feature, and after circle domain representation, its average and variance change, and degree of skewness is to ± 1 Close, kurtosis is close to 1.Therefore, Low-speed rotating machinery state can be identified by the average value of circle 4 indexs in domain.
A concrete application example procedure given below, while demonstrate validity of the present invention in engineer applied.
This experiment is carried out in SQ experimental benches, Selection of Bearings experimental bench self-contained bearing, model ER16K, shares normal, outer ring Pitting fault, inner ring pitting fault, rolling element pitting fault, the class bearing of compound pitting fault 5.Away from motor end bearing block edge Radially installed Kistler acceleration transducer, and it is acquired record using CoCo80 hand-held data recorders.Measure respectively For bearing block when installing 5 class bearing, rotating shaft rotating speed is the vibration signal under 1Hz operating modes.
Using the method for the invention, first, the low-speed rolling bearing vibration signal of normal operation is gathered, carries out small wavelength-division Solution and reconstruct low frequency signal, and FFT is carried out, as shown in Fig. 2 Low-speed rotating machinery normal operating condition step vibration signal In wavelet decomposition frequency spectrum, frequency spectrum is more chaotic, frequency peak not easy to identify.
The envelope spectrum of frequency spectrum is obtained again, as shown in figure 3, showing three frequency peak λ in figure1=0Hz, λ2= 82.68Hz,λ3=184Hz, form two frequency peak sections (0Hz, 82.68Hz), (82.68Hz, 184Hz).According to step 4 rules in one, obtain 2 critical frequency λFace 1=80Hz, λFace 2=160Hz, and then the long w of PAA dimensionality reduction windows can be calculated1= 80, w2=40；Secondly, the bearing vibration signal of running status to be identified is obtained, be i.e. 5 groups of vibration signals corresponding to 5 class bearings, is made Data reduction is carried out with PAA dimension reduction methods, wherein PAA dimensionality reductions window length takes w1=80；Then, every group of data are bisected into 10 parts points The state representation based on neighborhood relevance is not carried out, and respectively in circle domain representation, and calculate round domain statistical characteristics；Afterwards, take The long w of PAA dimensionality reduction windows2=40, repeat the above steps, calculate circle domain statistical characteristics；Finally by two groups of circle domain statistical characteristics Index averaged of the same race, obtain 4 averagely round domain statistical characteristics.
Experiment 10 times is repeated, is handled according to the above method measuring vibration signal every time, calculates 4 averagely round domain systems Characteristic value is counted, such as table 1 to table 5.The index graph-based that will be calculated, averagely justify domain statistical characteristics figure for each, By 10 value broken line connections of same type bearing, normal bearing is represented into the left side in figure, remaining 4 kinds of faulty bearings represents scheming Middle right side, as shown in figs. 4-7.Fig. 4-Fig. 7 averagely justifies domain statistical characteristics for totally 4, and each averagely round domain statistical characteristics figure is horizontal Coordinate is index sequence number, and normal bearing abscissa is 1-10, and faulty bearings abscissa is 11-20；Ordinate is corresponding index value Size；Wherein：Represent normal bearing；Represent outer ring faulty bearingsRepresent inner ring failure axle Hold；Represent ball faulty bearings；Represent combined failure bearing.It can be found that the average value of normal bearing It is stable -2.34, variance is stable 1, and degree of skewness and kurtosis value stabilization are near 0；And the averagely round domain of 4 of 4 kinds of faulty bearings Statistical characteristics fluctuates.Therefore, averagely round domain statistical characteristics may recognize that the normal and failure of low-speed rolling bearing State, demonstrate validity of the present invention in identification low-speed rolling bearing state aspect.
The normal condition bearing of table 1 justifies domain statistical characteristics and averagely round domain statistical characteristics
The outer ring malfunction bearing circle domain statistical characteristics of table 2 and averagely round domain statistical characteristics
The inner ring malfunction bearing of table 3 justifies domain statistical characteristics and averagely round domain statistical characteristics
The rolling element malfunction bearing of table 4 justifies domain statistical characteristics and averagely round domain statistical characteristics
The combined failure state bearing of table 5 justifies domain statistical characteristics and averagely round domain statistical characteristics

Claims (8)

  1. A kind of 1. initial failure recognition methods of low speed operation rotating machinery, it is characterised in that comprise the following steps,
    Step (1), the vibration signal under Low-speed rotating machinery normal operating condition is obtained, carry out wavelet decomposition and reconstruct low frequency letter Number, carry out FFT and draw its spectrum envelope, identify frequency peak, obtain critical frequency, and then choose multiple various dimensions PAA dimensionality reductions window is grown；
    Step (2), using various dimensions PAA to vibration signal to be identified successively dimension-reduction treatment, bearing state feature is extracted, in circle domain Circle domain statistical characteristics is calculated after middle expression；
    Step (3), by the index averaged of the same race in multigroup round domain statistical characteristics of acquisition, obtain 4 averagely round domains Statistical characteristics, Low-speed rotating machinery running state recognition is realized, so as to judge whether initial failure occurs.
  2. A kind of 2. initial failure recognition methods of low speed operation rotating machinery according to claim 1, it is characterised in that step Suddenly (1) chooses comprising the following steps that for various dimensions PAA dimensionality reductions window length,
    1) vibration signal under Low-speed rotating machinery normal operating condition is measured；
    2) wavelet decomposition is carried out to vibration signal, and reconstructs low frequency signal；
    3) FFT is carried out to the vibration signal after reconstruct, draws amplitude frequency diagram；
    4) envelope spectrum of amplitude frequency diagram is drawn based on Hilbert envelope approach；
    5) magnitude peak in envelope spectrum is identified, records its corresponding frequency fi, and ascending order is pressed, composition peak value frequency Rate array, it is designated as f=(f1,f2,...,fj,...,fn)；
    6) in crest frequency array f, adjacent two crest frequency forms frequency separation, and then component frequency section array F=((f1, f2),(f2,f3),...,(fj,fj+1),...(fn-1,fn))；
    7) follow critical frequency and ask for rule, travel through all elements in frequency separation array F, ask for critical frequency λ successivelyFace j, group Into critical frequency array, λ is designated asFace=(λFace 1,λFace 2,...,λFace j,...,λFace p)：
    8) according to obtained λFaceThe window length of various dimensions PAA dimensionality reductions is calculated, the long array of PAA windows is formed, is designated as w=(w1,w2,..., wj,...,wp), wherein wjFor λFace jCorresponding PAA windows length.
  3. A kind of 3. initial failure recognition methods of low speed operation rotating machinery according to claim 2, it is characterised in that step Suddenly in (1), it is as follows that the critical frequency asking for following during critical frequency asks for rule：
    a)1≤p≤n；Wherein, p is the quantity of PAA dimensionality reductions window length；
    b)λFace j∈(fi,fi+1), wherein j ∈ j | 1≤j≤p, j ∈ N*},i∈{i|1≤i≤n-1,i∈N*}；
    c)(fs/(4·λj))∈N*, wherein fs is signal sampling frequencies；
    If d) same frequency section has multiple critical frequencies, maximum is taken to be designated as λFace j；
    If e) certain frequency separation exists without critical frequency, next section is jumped to.
  4. A kind of 4. initial failure recognition methods of low speed operation rotating machinery according to claim 2, it is characterised in that step It is rapid 8) in, calculate the long array of PAA dimensionality reduction windows method be, by λFaceAll elements substitute into following formula successively：
  5. A kind of 5. initial failure recognition methods of low speed operation rotating machinery according to claim 1, it is characterised in that step What (2) PAA dimensionality reductions and circle domain statistical characteristics calculated suddenly comprises the following steps that,
    First, the Low-speed rotating machinery vibration signal x=(x of state to be identified are measured1,x2,...,xi,...,xN), wherein xiFor i The vibration amplitude at moment；
    Secondly, by vibration signal x=(x1,x2,...,xN) PAA dimensionality reductions are carried out, obtain by n average value ykThe dimensionality reduction signal of composition Y=(y1,y2,...,yk,...,yn)；
    Then, dimensionality reduction signal Y is equally divided into m subsignal, draws neighborhood correlation point diagram respectively to each subsignal, and identify State feature；
    Finally, by state feature in circle domain representation, and round domain statistical characteristics is calculated：Circle domain averageCircle domain variance V, circle domain Degree of skewness s and circle domain kurtosis k, is designated as
  6. A kind of 6. initial failure recognition methods of low speed operation rotating machinery according to claim 1, it is characterised in that step Suddenly the acquisition of (3) multigroup round domain statistical nature and its mean value calculation comprise the following steps that,
    First, the p long w of PAA dimensionality reduction windows step (1) obtained1,w2,...,wpSubstitute into respectively in step (2), obtain p groups circle Domain statistical characteristics G1,G2,...,Gp；
    Then, averagely round domain statistical characteristics is calculatedWhereinFor average round domain average,For average round domain Variance,For average round domain degree of skewness andFor average round domain kurtosis.
  7. A kind of 7. initial failure recognition methods of low speed operation rotating machinery according to claim 6, it is characterised in that step Suddenly in (3), averagely round domain statistical characteristics is calculatedMethod such as following formula：
    <mrow> <mover> <mi>G</mi> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>p</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>p</mi> </munderover> <msub> <mi>G</mi> <mi>i</mi> </msub> <mo>.</mo> </mrow>
  8. A kind of 8. initial failure recognition methods of low speed operation rotating machinery according to claim 1, it is characterised in that step Suddenly in (3), by Low-speed rotating machinery running state recognition, the specific judgement whether initial failure occurs is as follows,
    When average is calculated after circle domain representation and variance is a steady state value in state feature, degree of skewness and kurtosis all level off to zero When, Low-speed rotating machinery does not break down；
    After state feature is in circle domain representation, its average and variance change, and degree of skewness is close to ± 1, and kurtosis is close to 1, Then there is exceptional value in state feature, and initial failure occurs for Low-speed rotating machinery.
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CN110160765B (en) * 2019-06-04 2021-01-15 安徽智寰科技有限公司 Impact characteristic identification method and system based on sound or vibration signal
CN111076933A (en) * 2019-12-14 2020-04-28 西安交通大学 Method for establishing sensitive characteristic index set and identifying health state of machine tool spindle bearing

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