CN108982107A - It is a kind of based on morphology and it is multiple dimensioned arrangement entropy mean value bearing fault quantify trend diagnosis method - Google Patents
It is a kind of based on morphology and it is multiple dimensioned arrangement entropy mean value bearing fault quantify trend diagnosis method Download PDFInfo
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- 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
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Abstract
The invention discloses a kind of based on morphology and the bearing fault of multiple dimensioned arrangement entropy mean value quantifies trend diagnosis method, when bearing inner race or outer ring failure change in size, the degree of modulation of its vibration signal can change, these variations influence the complexity and randomness of its vibration signal.This method applies superiority of the multiple dimensioned arrangement entropy in terms of characterizing vibration signal degree of uncertainty, draws multiple dimensioned arrangement entropy mean value and failure size relation figure, then realizes and quantify trend diagnosis to rolling bearing fault.It tests and contains very heavy noise and a large amount of interference signal in collected vibration signal, in order to remove the interference of noise and enhance the impact characteristics of vibration signal, Multiscale Morphological is referred in the present invention, the accuracy that rolling bearing fault quantifies trend is substantially increased.
Description
Technical field
The invention belongs to fault diagnosis technology fields, are related to a kind of bearing fault quantitative Diagnosis method, in particular to a kind of
Bearing fault based on morphology and multiple dimensioned arrangement entropy mean value quantifies trend diagnosis method
Background technique
Rolling bearing is indispensable part in rotating machinery, but their crash rates under severe working condition are non-
Chang Gao.It is only far from enough from prevention and maintenance of the qualitative angle research rolling bearing fault to entire mechanical transmission mechanism
, rolling bearing fault severity is only known about, preferably mechanical equipment could be instructed to safeguard.
The arrangement plan method that Christoph is proposed is that detection time puts in order the method for randomness and complexity, this
Method has many advantages, such as that calculation amount is small, strong robustness.Vakharia selects multiple dimensioned arrangement entropy most preferably as an index
Small echo then makes fault diagnosis to rolling bearing.Li combines multiple dimensioned arrangement entropy and support vector machines, qualitatively to rolling
Dynamic bearing abort situation judges.It is much ground although multiple dimensioned arrangement entropy has been made in rolling bearing fault diagnosis
Study carefully, but be all mostly qualitative analysis rolling bearing fault, multiple dimensioned arrangement entropy is not also introduced into rolling bearing and quantifies trend
In diagnosis.When rolling bearing inner ring or outer ring fault degree difference, the complexity of collected vibration signal can be different,
Therefore, multiple dimensioned arrangement entropy can be used as an index of reflection rolling bearing fault degree.But the collected vibration of experiment
Contain very heavy noise and a large amount of interference signal in signal, directly affects the complexity of vibration signal, this will certainly be to rolling
Bearing quantitative fault diagnosis increases difficulty.
Summary of the invention
The object of the present invention is to provide a kind of based on morphology and the bearing fault of multiple dimensioned arrangement entropy mean value is quantitative
Trend diagnosis method, to solve the problems, such as that rolling bearing fault quantifies trend diagnosis.
To achieve the above object, the technical solution adopted by the present invention is a kind of based on morphology and multiple dimensioned arrangement entropy mean value
Bearing fault quantify trend diagnosis method, this method includes the bearing vibration signal for acquiring different faults size, to failure axis
Vibration signal is held to carry out Multiscale Morphological analysis, solve the maximum signal work of kurtosis, kurtosis of the vibration signal after morphological analysis
For preprocessed signal, multiple dimensioned arrangement entropy mean value, the multiple dimensioned arrangement entropy mean value of drafting and failure damage are solved to pretreated signal
Hurt the relational graph of degree.
S1 Multiscale Morphological；
Burn into expansion, opening operation and closed operation are the most basic operations of mathematical morphology.
If one-dimensional signal f (n) is the discrete function being defined in F=(0,1 ..., N-1) range, definition structure element g
It (n) is the discrete function in G=(0,1 ..., M-1) range, and N >=M.Wherein, N and M is respectively the sampling of f (n) He g (n)
Points, f (n) are the value of n-th of sampled point of one-dimensional signal f, and g (n) is the value of n-th of sampled point of one-dimensional signal g.
Corrosion and expansion of the f (n) about g (n) is defined as:
F Θ g (n)=min [f (n+m)-g (m)]
In above formula, f (n+m) is the value of one-dimensional signal f (n+m) a sampled point, and f (n-m) is one-dimensional signal f (n-m)
The value of a sampled point；G (n) is the value of n-th of sampled point of one-dimensional signal g, and g (m) is the value of m-th of sampled point of one-dimensional signal g.
F (n) is defined as following formula about the opening operation of g (n) and closed operation:
In above formula, n refers to the value of n-th of sampled point of one-dimensional signal.
It is widely used that there are also difference, Top-Hat, gradient scheduling algorithms.
The difference that one-dimensional signal f (n) expands and corroded by structural element g (n) respectively is known as morphocline filter,
Expression formula are as follows:
In above formula, fAGV(f) refer to that one-dimensional signal f passes through the morphological gradient operation of structural element g；F (n) is one-dimensional signal f
The value of n-th of sampled point, g (n) are the value of n-th of sampled point of one-dimensional signal g.
Top-Hat transform definition are as follows:
HAT (f)=fg (n)-f
Correspondingly, the dual operator of Top-Hat is defined as:
HAT (- f)=f-fg (n)
In above formula, HAT (f) and HAT (- f) respectively refer to Top-Hat operator and Top- that one-dimensional signal f passes through structural element g
Hat dual operator；G (n) is the value of n-th of sampled point of one-dimensional signal g.
Differential filtering operation definition of the f (n) about g (n) are as follows:
In above formula, fDIF(n) refer to that one-dimensional signal f passes through the differential filtering operator of structural element g；G (n) is one-dimensional signal g
The value of n-th of sampled point.
If setting ε as scale, ε=1,2 ... .., λ, then f (n) may be expressed as: about the multiple dimensioned corrosion and expansion of g (n)
In above formula, n refers to the value of n-th of sampled point of one-dimensional signal.G (n) is the value of n-th of sampled point of one-dimensional signal g.
Multiple dimensioned differential filtering operation definition of the f (n) about g (n) are as follows:
In above formula, yε(n) refer to that one-dimensional signal f passes through the multiple dimensioned differential filtering operator of structural element g.
The multiple dimensioned arrangement entropy mean value of S2；
Space Reconstruction is carried out to the vibration signal sequence { x (i), i=1,2 ..., N } that length is N, obtains following sequence:
In formula, m is insertion dimension；λ is time delay；N is the length of vibration signal x (i)；X (i) refers to vibration signal sequence
In i-th of value.
Data in X (i) are arranged according to the order of rising, i.e.,
X (i)={ x (i+ (ji1-1)λ)≤x(i+(ji2-1)λ)......≤x(i+(jm-1)λ)}
X (i+ (j if it existsi1- 1) λ)=x (i+ (ji2- 1) λ), then it is arranged according to j, i.e. x (i+ (ji1-1)λ)≤x(i
+(ji2- 1) λ), wherein i and j is sequential value, so can obtain a group code for any one data X (i):
S (g)={ j1,j2,.....jk}
Wherein, g=1,2,3........k, k≤m！.
If the probability P that every kind of symbol occursg(g=1,2,3........k), thenAt this point, the arrangement of x (i)
Entropy are as follows:
H in above formulaP(m) the arrangement entropy for being x (i).
Standardization arranges entropy HP(m), it may be assumed that
HP=HP(m)/ln(m！)
H in above formulaPFor the arrangement entropy after standardization.
So-called multiple dimensioned arrangement entropy is exactly the arrangement entropy under different scale, and the method for calculating is as follows:
The vibration signal sequence { x (i), i=1,2.....N } for being N for length carries out coarse grain processing, obtains sequenceExpression formula are as follows:
In formula, s is scale factor,For coarse treated sequence.
Mean value is solved to the arrangement entropy under different scale:
In formula, mean (HP) it is multiple dimensioned arrangement entropy mean value.
Obviously, mean (HP) value range be 0≤HP≤1。mean(HP) value size representation signal sequence complexity
Degree.mean(HP) bigger, illustrate that time series is more complicated, anyway, then illustrate that time series is more regular.
To quantify trend diagnosis method and step as follows for bearing fault of the S3 based on morphology and multiple dimensioned arrangement entropy mean value:
The bearing vibration signal acquisition of 3.1 different faults degree.Using acceleration transducer to different faults degree
Rolling bearing experimental bench measure, obtain vibration acceleration signal as signal X (t) to be analyzed；
3.2 pairs of faulty bearings vibration signals carry out Multiscale Morphological analysis.With the form differential filtering operator of different scale ε
Respectively to vibration signal X (t) processing, denoised signal X ε (t) is obtained, wherein ε=1,2 ... .. [fs/fc-2], fs are sampling frequency
Rate, fc are fault characteristic frequency.
3.3 solve the kurtosis of the vibration signal after morphological analysis.To denoised signal X ε (t) solve comentropy K ε, wherein ε=
1,2 ... .. [fs/fc-2], fs are sample frequency, and fc is fault characteristic frequency.
3.4 obtain preprocessed signal X (t) '.Using the maximum vibration signal of kurtosis as preprocessed signal.
3.5 pairs of pretreated signals solve multiple dimensioned arrangement entropy mean value.
3.6 draw multiple dimensioned arrangement entropy mean value and failure size relation figure, then carry out failure and quantify trend diagnosis.
Compared with prior art, the present invention has the advantages that.
Multiscale Morphological and multiple dimensioned arrangement entropy mean value are applied to rolling bearing fault and quantify trend diagnosis by the present invention
In.It tests in collected vibration signal containing very heavy noise and a large amount of interference signal, directly affects answering for vibration signal
Miscellaneous degree then influences the size of multiple dimensioned arrangement entropy.In order to remove the interference of noise and enhance the impact characteristics of vibration signal,
Multiscale Morphological is referred in the present invention.But when analyzing vibration signal with Multiscale Morphological, scale is to vibration signal
Filter effect it is of crucial importance, kurtosis index is selected to suitable vibration signal, to next step solve rolling bearing quantitatively become
Gesture line plays the role of vital.Many researchs have been made in multiple dimensioned arrangement entropy in rolling bearing fault diagnosis, but
Being all is mostly qualitative analysis rolling bearing fault, and multiple dimensioned arrangement entropy is not also introduced into rolling bearing and quantifies trend diagnosis
In.When rolling bearing inner ring or outer ring fault degree difference, the complexity of collected vibration signal can be different, because
This, multiple dimensioned arrangement entropy can be used as an index of reflection rolling bearing fault degree.The present invention seeks multiple dimensioned arrangement entropy
Mean value is taken, multiple dimensioned arrangement entropy mean value and failure size relation figure are drawn, failure is then carried out and quantifies trend diagnosis.
Detailed description of the invention
Fig. 1 is that the bearing fault based on morphology and multiple dimensioned arrangement entropy mean value quantifies trend diagnosis method flow diagram.
Fig. 2 is the vibration experiment signal time-domain diagram for surveying bearing outer ring different faults degree.
Fig. 3 is the vibration experiment signal time-domain diagram for surveying bearing inner race different faults degree.
Fig. 4 is bearing outer ring failure Pretreatment Test signal time-domain diagram.
Fig. 5 is bearing inner race failure Pretreatment Test signal time-domain diagram.
Fig. 6 is the multiple dimensioned arrangement entropy Change in Mean tendency chart of outer ring and inner ring faulty bearings.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and specific embodiments.
Fig. 1 be it is of the invention based on morphology and it is multiple dimensioned arrangement entropy mean value bearing fault quantify trend diagnosis method stream
Cheng Tu.It is former that trend diagnosis method is quantified to the bearing fault based on morphology and multiple dimensioned arrangement entropy mean value below with reference to flow chart
Reason is described in detail.
(1) the bear vibration acceleration signal of different faults degree is obtained as signal to be analyzed using acceleration transducer
X(t)；
(2) Multiscale Morphological analysis is carried out to faulty bearings vibration signal, obtains denoised signal X ε (t), wherein ε=1,
2 ... .. [fs/fc-2], fs are sample frequency, and fc is fault characteristic frequency.Cost in order to save time, the shape of structural element
Shape uses linear type；In morphological operator: opening operation plays smoothing effect to the positive impact of vibration signal, and then for negative impact
Play inhibiting effect；Opposite, closed operation plays inhibiting effect to the positive impact of vibration signal, and then plays suppression for negative impact
Production is used；Differential filtering device is to merge two kinds of operations, can preferably extract the positive negative pulse stuffing signal in signal, so
Morphological analysis is carried out to faulty bearings vibration signal using multiple dimensioned difference morphological operator as final morphological operator.
(3) kurtosis of the vibration signal after morphological analysis is solved.Kurtosis solution formula is as follows:
K is kurtosis value in formula；X ε (t) is the vibration signal after morphological analysis,For the vibration letter after morphological analysis
Number mean value；σtStandard deviation；N is sampling length.
(4) using the maximum vibration signal of kurtosis as preprocessed signal X (t) '.
(5) to pretreated signal X (t) ' solve multiple dimensioned arrangement entropy mean value.
(6) multiple dimensioned arrangement entropy mean value and failure size relation figure are drawn, failure is then carried out and quantifies trend diagnosis.
Fig. 2 is the vibration experiment signal time-domain diagram for surveying bearing outer ring different faults degree.
Fig. 3 is the vibration experiment signal time-domain diagram for surveying bearing outer ring different faults degree.
Bearing model 6307 is chosen in experiment；Turning frequency is 1497r/min, sample frequency 12800Hz, sampling number 8192
A point.Rolling bearing fault is obtained by electrical discharge machining, and fault type is inner ring failure and outer ring failure, and failure size is respectively
0.5mm, 2mm, 3.5mm and 5mm.
Fig. 4 bearing outer ring failure Pretreatment Test signal time-domain diagram.
Fig. 5 bearing outer ring failure Pretreatment Test signal time-domain diagram.
The multiple dimensioned arrangement entropy Change in Mean tendency chart of Fig. 6 bearing outer ring and inner ring.For outer ring failure, with failure ruler
Very little increase, multiple dimensioned arrangement entropy mean value are increasing.For inner ring failure, with the increase of failure size, more rulers
Degree arrangement entropy mean value is reducing.
Claims (2)
1. it is a kind of based on morphology and it is multiple dimensioned arrangement entropy mean value bearing fault quantify trend diagnosis method, it is characterised in that:
This method includes the bearing vibration signal for acquiring different faults size, carries out Multiscale Morphological point to faulty bearings vibration signal
Analysis, solve morphological analysis after vibration signal the maximum signal of kurtosis, kurtosis as preprocessed signal, to pretreated signal
The relational graph for solving multiple dimensioned arrangement entropy mean value, drawing multiple dimensioned arrangement entropy mean value and failure degree of injury；
S1 Multiscale Morphological；
Burn into expansion, opening operation and closed operation are the most basic operations of mathematical morphology；
If one-dimensional signal f (n) is the discrete function being defined in F=(0,1 ..., N-1) range, definition structure element g (n) is
Discrete function in G=(0,1 ..., M-1) range, and N >=M；Wherein, N and M is respectively the sampling number of f (n) He g (n), f
It (n) is the value of n-th of sampled point of one-dimensional signal f, g (n) is the value of n-th of sampled point of one-dimensional signal g；
Corrosion and expansion of the f (n) about g (n) is defined as:
F Θ g (n)=min [f (n+m)-g (m)]
In above formula, f (n+m) is the value of one-dimensional signal f (n+m) a sampled point, and f (n-m) is that (n-m) is a adopts by one-dimensional signal f the
The value of sampling point；G (n) is the value of n-th of sampled point of one-dimensional signal g, and g (m) is the value of m-th of sampled point of one-dimensional signal g；
F (n) is defined as following formula about the opening operation of g (n) and closed operation:
In above formula, n refers to the value of n-th of sampled point of one-dimensional signal；
The difference that one-dimensional signal f (n) expands and corroded by structural element g (n) respectively is known as morphocline filter, expresses
Formula are as follows:
In above formula, fAGV(f) refer to that one-dimensional signal f passes through the morphological gradient operation of structural element g；F (n) is one-dimensional signal f n-th
The value of a sampled point, g (n) are the value of n-th of sampled point of one-dimensional signal g；
Top-Hat transform definition are as follows:
HAT (f)=fg (n)-f
Correspondingly, the dual operator of Top-Hat is defined as:
HAT (- f)=f-fg (n)
In above formula, HAT (f) and HAT (- f) respectively refer to Top-Hat operator and Top-Hat that one-dimensional signal f passes through structural element g
Dual operator；G (n) is the value of n-th of sampled point of one-dimensional signal g；
Differential filtering operation definition of the f (n) about g (n) are as follows:
In above formula, fDIF(n) refer to that one-dimensional signal f passes through the differential filtering operator of structural element g；G (n) is one-dimensional signal g n-th
The value of a sampled point；
If setting ε as scale, ε=1,2 ... .., λ, then f (n) may be expressed as: about the multiple dimensioned corrosion and expansion of g (n)
In above formula, n refers to the value of n-th of sampled point of one-dimensional signal；G (n) is the value of n-th of sampled point of one-dimensional signal g；
Multiple dimensioned differential filtering operation definition of the f (n) about g (n) are as follows:
In above formula, yε(n) refer to that one-dimensional signal f passes through the multiple dimensioned differential filtering operator of structural element g；
The multiple dimensioned arrangement entropy mean value of S2；
Space Reconstruction is carried out to the vibration signal sequence { x (i), i=1,2 ..., N } that length is N, obtains following sequence:
In formula, m is insertion dimension；λ is time delay；N is the length of vibration signal x (i)；X (i) refers in vibration signal sequence
I value；
Data in X (i) are arranged according to the order of rising, i.e.,
X (i)={ x (i+ (ji1-1)λ)≤x(i+(ji2-1)λ)......≤x(i+(jm-1)λ)}
X (i+ (j if it existsi1- 1) λ)=x (i+ (ji2- 1) λ), then it is arranged according to j, i.e. x (i+ (ji1-1)λ)≤x(i+
(ji2- 1) λ), wherein i and j is sequential value, so can obtain a group code for any one data X (i):
S (g)={ j1,j2,.....jk}
Wherein, g=1,2,3........k, k≤m！；
If the probability P that every kind of symbol occursg(g=1,2,3........k), thenAt this point, the arrangement entropy of x (i)
Are as follows:
H in above formulaP(m) the arrangement entropy for being x (i)；
Standardization arranges entropy HP(m), it may be assumed that
HP=HP(m)/ln(m！)
H in above formulaPFor the arrangement entropy after standardization；
So-called multiple dimensioned arrangement entropy is exactly the arrangement entropy under different scale, and the method for calculating is as follows:
The vibration signal sequence { x (i), i=1,2.....N } for being N for length carries out coarse grain processing, obtains sequence Expression formula are as follows:
In formula, s is scale factor,For coarse treated sequence；
Mean value is solved to the arrangement entropy under different scale:
In formula, mean (HP) it is multiple dimensioned arrangement entropy mean value；
Obviously, mean (HP) value range be 0≤HP≤1；mean(HP) value size representation signal sequence complexity；
mean(HP) bigger, illustrate that time series is more complicated, anyway, then illustrate that time series is more regular；
To quantify trend diagnosis method and step as follows for bearing fault of the S3 based on morphology and multiple dimensioned arrangement entropy mean value:
The bearing vibration signal acquisition of S3.1 different faults degree；Rolling using acceleration transducer to different faults degree
Dynamic bearing experimental bench measures, and obtains vibration acceleration signal as signal X (t) to be analyzed；
S3.2 carries out Multiscale Morphological analysis to faulty bearings vibration signal；With the form differential filtering operator point of different scale ε
It is other that denoised signal X ε (t) is obtained, wherein ε=1 to vibration signal X (t) processing, 2 ... .. [fs/fc-2], fs are sampling frequency
Rate, fc are fault characteristic frequency；
S3.3 solves the kurtosis of the vibration signal after morphological analysis；Comentropy K ε is solved to denoised signal X ε (t), wherein ε=1,
2 ... .. [fs/fc-2], fs are sample frequency, and fc is fault characteristic frequency；
S3.4 obtains preprocessed signal X (t) '；Using the maximum vibration signal of kurtosis as preprocessed signal；
S3.5 solves multiple dimensioned arrangement entropy mean value to pretreated signal；
S3.6 draws multiple dimensioned arrangement entropy mean value and failure size relation figure, then carries out failure and quantifies trend diagnosis.
2. a kind of bearing fault based on morphology with multiple dimensioned arrangement entropy mean value according to claim 1 quantifies trend and examines
Disconnected method, it is characterised in that: (1) using the bear vibration acceleration signal of acceleration transducer acquisition different faults degree as
Signal X (t) to be analyzed；
(2) Multiscale Morphological analysis is carried out to faulty bearings vibration signal, obtains denoised signal X ε (t), wherein ε=1,
2 ... .. [fs/fc-2], fs are sample frequency, and fc is fault characteristic frequency；Cost in order to save time, the shape of structural element
Shape uses linear type；In morphological operator: opening operation plays smoothing effect to the positive impact of vibration signal, and then for negative impact
Play inhibiting effect；Opposite, closed operation plays inhibiting effect to the positive impact of vibration signal, and then plays suppression for negative impact
Production is used；Differential filtering device is to merge two kinds of operations, can preferably extract the positive negative pulse stuffing signal in signal, so
Morphological analysis is carried out to faulty bearings vibration signal using multiple dimensioned difference morphological operator as final morphological operator；
(3) kurtosis of the vibration signal after morphological analysis is solved；Kurtosis solution formula is as follows:
K is kurtosis value in formula；X ε (t) is the vibration signal after morphological analysis,It is equal for the vibration signal after morphological analysis
Value；σtStandard deviation；N is sampling length；
(4) using the maximum vibration signal of kurtosis as preprocessed signal X (t) '；
(5) to pretreated signal X (t) ' solve multiple dimensioned arrangement entropy mean value；
(6) multiple dimensioned arrangement entropy mean value and failure size relation figure are drawn, failure is then carried out and quantifies trend diagnosis.
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| CN109977996A (en) * | 2019-02-12 | 2019-07-05 | 华北水利水电大学 | Hydro-structure operating state monitoring system based on Time Series Clustering fusion |
| CN110044620A (en) * | 2019-03-15 | 2019-07-23 | 昆明理工大学 | A kind of Fault Diagnosis of Roller Bearings based on analysis of vibration signal |
| CN110333078A (en) * | 2019-08-21 | 2019-10-15 | 佛山科学技术学院 | A kind of rolling bearing degenerate state stage determines method |
| CN110333078B (en) * | 2019-08-21 | 2021-04-20 | 佛山科学技术学院 | Rolling bearing degradation state stage determination method |
| CN110823575B (en) * | 2019-11-09 | 2021-03-16 | 北京工业大学 | Bearing life prediction method based on performance degradation dictionary structure and similarity |
| CN110823575A (en) * | 2019-11-09 | 2020-02-21 | 北京工业大学 | Bearing life prediction method based on performance degradation dictionary structure and similarity |
| CN111504645A (en) * | 2020-04-30 | 2020-08-07 | 西安交通大学 | Rolling bearing fault diagnosis method based on frequency domain multipoint kurtosis |
| CN112345250A (en) * | 2020-10-29 | 2021-02-09 | 上海电气风电集团股份有限公司 | Bearing vibration monitoring method and system and computer readable storage medium |
| CN112345238A (en) * | 2020-10-29 | 2021-02-09 | 上海电气风电集团股份有限公司 | Method and system for monitoring vibration of gearbox and computer readable storage medium |
| CN112816213A (en) * | 2021-01-06 | 2021-05-18 | 沈阳工业大学 | Fault diagnosis method for wind turbine transmission system |
| CN112816213B (en) * | 2021-01-06 | 2022-08-12 | 沈阳工业大学 | Fault diagnosis method for wind turbine transmission system |
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