CN106487359B - The building method of Morphologic filters based on self-adapting multi-dimension AVG-Hat transformation - Google Patents
The building method of Morphologic filters based on self-adapting multi-dimension AVG-Hat transformation Download PDFInfo
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
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- H03H17/0211—Frequency selective networks using specific transformation algorithms, e.g. WALSH functions, Fermat transforms, Mersenne transforms, polynomial transforms, Hilbert transforms
Abstract
The invention discloses a kind of building methods of Morphologic filters based on self-adapting multi-dimension AVG-Hat transformation, realize that steps are as follows: 1, the parameter index according to set by bearing fault signal, determines the number and initial structural element value of the initial Multi-scale model element of signal；2, by morphological dilations operation, the set of initial Multi-scale model element composition is constructed；3, calculate bearing fault vibration signal under initial Multi-scale model element corresponding morphology AVG-Hat transformation as a result, constructing the set of the result；4, by particle group optimizing method, the ratio of the arrangement entropy and envelope spectrum degree of rarefication of selecting filtered bearing fault vibration signal is adaptive to determine after filtering the initially corresponding optimal weights coefficient of Multi-scale model element as evaluation index；5, according to the weight coefficient, optimal Multiscale Morphological AVG-Hat filter is constructed.It is an advantage of the invention that signal de-noising can be taken into account, fault signature extracts and keep filter result accuracy.
Description
Technical field
The present invention relates to it is a kind of based on self-adapting multi-dimension AVG-Hat transformation Morphologic filters building method,
Belong to mechanical fault diagnosis and signal processing technology field.
Background technique
In Practical Project, rolling bearing fault vibration signal is typical non-linear, non-stationary signal, and failure is special in signal
Sign is easy to be covered by various ambient noises, therefore the difficult of bearing fault is diagnosed under strong background noise.Mathematical Morphology
Be a kind of typical Nonlinear harmonic oscillator method, it is by the structural element of particular dimensions and shape to time domain plethysmographic signal
Local detail be fitted finishing, in extracting signal while main wave character, the dry of ambient noise can be effectively eliminated
It disturbs.Using morphological method handling failure signal, it is important to construct the Morphologic filters of specific structure, traditional morphology
Filter is mainly composed of burn into expansion, opening operation and closed operation, is mainly used for eliminating ambient noise in fault-signal,
The ability for extracting fault signature is weaker.Some new Morphologic filters are such as: differential filtering device, gradient filter, although laying particular stress on
The extraction of fault signature in signal, but the negative value information in signal is become positive value information by these filters, changes letter
Number constituent, the robustness of processing result is poor.
In signal waveform the structural object of particular dimensions can only by the structural elements usually alignment processing of particular dimensions, therefore,
During morphologic filtering, fault signature extracts the selection that structural element scale is depended primarily on the effect of noise reduction filtering.Mesh
It is preceding that mainly fault-signal is handled using the Morphologic filters of single mesostructure element building, still, fault vibration
Signal is extremely complex, the structural object comprising multiple and different scales, and single scale topographical filtering tends not to fully analyze
Signal.Compared to single scale is used, multi-scale morphology filtering can handle different scale size with the structural element of different scale
Structural object.Therefore, carrying out morphologic filtering to signal using multiple and different mesostructure elements has more outstanding suppression
Noise and ability in feature extraction processed.
The diagnosis that rolling bearing fault vibration signal is realized by multi-scale morphology filtering device, needs to solve two and asks
Topic: first is that building one can take into account signal de-noising, fault signature extracts and keep the morphologic filtering of filter result accuracy
Device；Second is that adaptively determining weight coefficient shared by each mesostructure element in multi-scale morphology filtering device composition.And
In the prior art, the relevant technologies that can not solve the two critical issues very well are recorded.This also becomes those skilled in the art
The problem of member's urgent need to resolve.
Summary of the invention
Technical problem to be solved by the invention is to provide one kind can take into account signal de-noising, fault signature is extracted and protected
Hold the building method of the Morphologic filters based on self-adapting multi-dimension AVG-Hat transformation of filter result accuracy.
The present invention adopts the following technical scheme:
A kind of building method of the Morphologic filters based on self-adapting multi-dimension AVG-Hat transformation comprising following step
It is rapid:
Step 1, the parameters index according to set by sensor acquisition bearing fault signal, determine that analysis signal is wanted
The number and initial structural element value of the initial Multi-scale model element used；
Step 2 passes through morphological dilations operation, constructs the set of initial Multi-scale model element composition；
Step 3 calculates the corresponding morphology AVG-Hat change under initial Multi-scale model element of bearing fault vibration signal
It is changing as a result, building under initial Multi-scale model element signal aspect AVG-Hat transformation result set；
Step 4, the bearing fault vibration by particle group optimizing method, after selecting morphology AVG-Hat filter filtering
The arrangement entropy of signal and the ratio of envelope spectrum degree of rarefication are as evaluation index, as the adaptive optimal control of particle group optimizing method
Functional value is spent, population optimizing iterative process is completed, after adaptively determining optimal Multiscale Morphological AVG-Hat filter filtering
The initially corresponding optimal weights coefficient of Multi-scale model element；
Step 5, according to the corresponding weight coefficient of different scale structural element in the step 4, construct optimal multiple dimensioned
Morphology AVG-Hat filter.
Further, building signal aspect AVG-Hat transformation under initial Multi-scale model element in the step 3
As a result set, specifically with the following method:
3-1, the smallest dimension structural element g=[0 0] for obtaining bearing fault vibration signal x (n) and initial setting up, output
The corresponding morphological dilations operation result of signalErosion operation resultOpening operation result (xog)
(n) and closed operation result (xg) (n)；
3-2, bearing fault vibration signal x (n) and the bearing fault vibration signal x (n) are obtained by initial configuration member
It is after plain morphology opening operation, closed operation that bearing fault vibration is subtracted after original bearing fault vibration signal x (n) multiplies 2 as a result, exporting
Dynamic signal x (n) is by morphology opening operation, the difference value of closed operation result sum, mathematic(al) representation are as follows: AVGH (f (n))=2
× x (n)-((xog) (n)+(xg) (n)) is calculated bearing fault signal x (n) and passes through initial single structure element shape
The result of state AVG-Hat filtering
AVGH(f(n))；
F (n) indicates the signal after morphology AVG-Hat filter filtering；
3-3, the initial structural element scale number of initial smallest dimension structural element and setting, export structure member are obtained
After plain λ Multi-scale model element dilation operation as a result, its mathematic(al) representation are as follows:
That is dilation operation λ times, the result after establishing multiple mesostructure element dilation operations
Set: i.e. { g1,g2,L gλ}；
The multiple dimensioned erosion operation result of corresponding bearing fault vibration signal x (n) is calculated simultaneouslyExpansion
Operation resultOpening operation result (xogλ) (n) and closed operation result (xgλ)(n)；
At the time of n spindle holds fault vibration signal x (n) correspondence；
3-4, bearing fault vibration signal x (n) and λ Multi-scale model element lower bearing fault vibration signal x (n) are obtained
Opening operation, closed operation as a result, exporting that morphology AVG-Hat under corresponding λ Multi-scale model element is converted as a result, its number
Learn expression formula are as follows:
AVGH(fλ(n))=2 × x (n)-((xogλ)(n)+(x·gλ) (n)), establish λ Multi-scale model element morphology
The set of signal after AVG-Hat filter filtering: i.e. { f1(n),f2(n),L,fλ(n)}。
Further, optimal Multiscale Morphological AVG- is adaptively determined by particle group optimizing method in the step 4
The specific method is as follows for the corresponding optimal weights coefficient of initial Multi-scale model element after Hat filter filtering: 4-1, obtaining axis
Hold the set { g of fault vibration signal x (n) and λ Multi-scale model element1,g2,L gλ, export λ Multi-scale model element
The set of signal after morphology AVG-Hat filter filtering: i.e. { f1(n),f2(n),L,fλ(n)}；Wherein, f (n) indicates form
Signal after learning AVG-Hat filter filtering；4-2, λ Multi-scale model element morphology AVG-Hat filter filtering is obtained
Set { the f of signal afterwards1(n),f2(n),L,fλAnd the originally determined weight coefficient of filtered signal described in each scale (n) }
ω=(ω1,ω2,L,ωλ),ωi∈ [0,1] (0≤i≤λ), output initial weight coefficient are first with corresponding λ Multi-scale model
The sum of products of signal after plain morphology AVG-Hat filter filtering: i.e.Y indicates Multiscale Morphological
The filtered signal of AVG-Hat；
The arrangement entropy H of the sum of products signal is calculatedPEWith the sparse angle value S of envelope spectrum, by the arrangement entropy HPE
It is divided by obtain fitness function value P of the filtered signal in particle group optimizing method with the sparse angle value S of envelope spectrum, counts
Learn expression formula are as follows:
4-3, after population I time interative computation signal fitness function value PIIt is secondary less than or equal to (I-1) to change
For the fitness function value P of signal after operationI-1When, i.e. PI≤PI-1, remember PIFor optimal fitness function value；And so on, it obtains
The whole process of particle group optimizing method iteration is taken, the minimum fitness letter of all sum of products signals after G interative computation is exported
Numerical value PbestAs fitness function value optimal during entire particle group optimizing, i.e. Pbest=min (P1,P2,L,PG)；Its
In, G is maximum number of iterations；
4-4, the minimum fitness function value P is extractedbestCorresponding Multi-scale model element weights coefficient ωbest=
(ω1,ω2,L,ωλ) it is used as the corresponding optimal weights coefficient of Multi-scale model element.
Further, the method that optimal Multiscale Morphological AVG-Hat filter is constructed in the step 5 is as follows: meter
Calculate optimal weights coefficient ωbest=(ω1,ω2,L,ωλ) and λ Multi-scale model element morphology AVG-Hat filter filtering
Signal f afterwardsi(n) sum of products, optimal more rulers that the sum of products signal is adaptively determined as particle group optimizing method
Structural element morphology AVG-Hat filter composition form is spent, wherein ωi∈ωbest,fi(n)={ f1(n),f2(n),L,fλ
(n)}。
Beneficial effects of the present invention are as follows:
(1) present invention is overcome traditional form filter and is existed by one new morphology AVG-Hat filter of building
The existing defect that cannot be taken into account signal de-noising and fault signature and extract when handling failure signal, can be in handling failure signal
Effectively extract the failure shock characteristic contained in signal.
(2) present invention calculates the arrangement entropy of filtered signal and the ratio of envelope spectrum degree of rarefication as evaluation criterion, utilizes
Particle group optimizing method has adaptively determined each mesostructure member in optimal multi-scale morphology filtering device by interative computation
The corresponding weight coefficient of element, to construct Multiscale Morphological AVG-Hat filter.
The morphology AVG-Hat filter that the present invention constructs can have on the basis of eliminating fault-signal ambient noise
Effect extracts the shock characteristic in fault-signal, and will not change the composition increasing point of signal, does not generate extra interference ingredient, filters
Wave result is accurate and reliable.
(3) present invention building multi-scale morphology filtering device, can choose the structural element pair of multiple and different scale sizes
Fault-signal carries out morphologic filtering, filters compared to single scale topographical, and the fault-signal of analysis composition complicated component is more
It is scientific and reasonable, it effectively overcomes single scaling filter and causes that the defect of signal de-noising and details retentivity cannot be taken into account, mention
The ability of failure shock characteristic is stronger in the number of winning the confidence；
(4) present invention obtains the index of Optimal Signals after evaluation multi-scale filtering, is the row by calculating filtered signal
What the ratio of column entropy and envelope spectrum degree of rarefication obtained.The arrangement entropy of signal represents the regular degree of signal sequence, is to measure letter
Number contain the index of ambient noise size；Signal envelope spectrum degree of rarefication then reflects the size of failure impact ingredient in signal, because
The ratio of both this has comprehensively considered the size of ambient noise and fault signature in signal, has specific physical significance, with
This can effectively choose the Optimal Signals after multi-scale morphology filtering for evaluation criterion.
(5) present invention passes through particle using the adaptive particle group optimizing method for determining multi-scale morphology filtering composition
Group's optimizing iterative process, the minimum corresponding Multi-scale model element weights coefficient of evaluation criterion is as optimal after finding interative computation
The corresponding weight coefficient of multi-scale filtering device, has adaptively determined the building form of multi-scale morphology filtering device, avoid with
Toward defect existing when determining that multi-scale filtering device is formed by artificial experience, filter result is used directly for extracting failure
Feature, and adaptive adjustment can be carried out to the signal analyzed, analysis efficiency is higher.
Detailed description of the invention
Fig. 1 is Multiscale Morphological AVG-Hat filtering structural schematic diagram in the present invention.
Fig. 2 is fitness function value solution procedure schematic diagram in particle group optimizing method in the present invention.
Fig. 3 is the time domain waveform of rolling bearing fault vibration signal in the embodiment of the present invention.
Fig. 4 is the envelope spectrogram of rolling bearing fault vibration signal in the embodiment of the present invention.
Fig. 5 is the time domain waveform of Multiscale Morphological AVG-Hat filtered signal in the embodiment of the present invention.
Fig. 6 is the envelope spectrogram of Multiscale Morphological AVG-Hat filtered signal in the embodiment of the present invention.
Specific embodiment
Self-adapting multi-dimension AVG-Hat is based on to one kind proposed by the invention with specific embodiment with reference to the accompanying drawing
The building method of the Morphologic filters of transformation is described in detail.
According to the spy of failure shock characteristic in the four of Morphological scale-space one-dimensional signal kinds of basic operations and bearing fault signal
Point proposes the definition of morphology AVG-Hat transformation and the building method of morphology AVG-Hat filter.Such as FIG. 1 to FIG. 6 institute
Show, the method that this example describes the Morphologic filters of building self-adapting multi-dimension morphology AVG-Hat transformation, and passes through
This method diagnoses actual housing washer fault vibration signal.
Detailed process is as follows:
Step 101: the sample frequency of acceleration transducer being set, rolling bearing fault vibration signal is acquired；
Step 102: the structural parameters and shaft revolving speed of rolling bearing are obtained, according to each element fault feature of rolling bearing
Frequency calculation formula obtains the fault characteristic frequency of each element of surveyed bearing, in conjunction with the sample frequency of sensor, calculates vibration
Sampling number in signal fault impulse period, in this, as the out to out of structural element used, meanwhile, be arranged it is initial most
Small-scale structure element, the setting of completion morphology filter parameter.
Step 103: by dilation operation, initial configuration element being successively subjected to scale expansion, largest extension to setting
Structural element out to out, to establish the structural element set of multiple and different scales；
Step 104: morphology AVG-Hat filter being constructed respectively to the structural element of different scale, to establish not
With the set of the AVG-Hat filter of scale；
Step 105: the parameters of particle swarm algorithm are set, comprising: maximum number of iterations, population scale, acceleration because
Son, the variation range of random factor and each mesostructure element respective weights coefficient, the range being arranged here is [0,1].
Step 106: rule is determined about the random of weight coefficient according in particle swarm algorithm, when obtaining interative computation for the first time
The corresponding weight coefficient of each mesostructure element；
Step 107: obtain different scale structural element establish AVG-Hat filter filtering signal results set and
The corresponding weight coefficient of different scale structural element constructs the Multiscale Morphological AVG- established for the first time in particle swarm optimization algorithm
Hat filter exports the filtered signal of multi-scale filtering device for the first time；
Step 108: the evaluation criterion of filtering signal for the first time is calculated, in this, as the fitness function value of the signal；Step
109: judging whether the stopping criterion for meeting particle swarm optimization algorithm, if conditions are not met, then carrying out second of interative computation, repeat
Step 106-108 obtains the fitness function value of second signal, records its corresponding each ruler of the smallest fitness function
Degree structural element weight coefficient is optimal result, carries out the stopping criterion for judging whether to meet algorithm again, and so on.If
Meet the stopping criterion of particle swarm algorithm, then terminating particle group optimizing process, exports optimal result.
Step 110: according to the corresponding weight coefficient of mesostructure element each in output optimal result, in conjunction with different scale
Structural element establish AVG-Hat filter filtering signal results set, establish optimization algorithm adaptively determine it is optimal more
Scale topographical filter exports filtered signal.
As shown in Figure 1, details are as follows for Multiscale Morphological AVG-Hat filtering of the present invention:
Step 201: obtaining the smallest dimension structural element g=[0 0] and max architecture element dimensions number of initial setting up
λmax, morphological dilations operation successively is carried out to smallest dimension structural element, until dilation operation to max architecture element dimensions
Number, mathematic(al) representation are as follows:
Wherein, λ is the scale parameter of Multi-scale model element.It thus establishes and is made of multiple and different mesostructure elements
Set { g1, g2,L,gλ}。
Step 202: the morphological dilations operation of signal is carried out to each mesostructure elementErosion operation
(x Θ g) (n), opening operation (xog) (n) and closed operation (xg) (n), establish morphology AVG-Hat filter, mathematic(al) representation
Are as follows:
AVGH (f (n))=2 × x (n)-((xog) (n)+(xg) (n)) (2)
Wherein, x (n) is rolling bearing fault signal.Under each mesostructure element to fault vibration signal respectively into
Capable morphology AVG-Hat filtering processing obtains signal after multiple mesostructure element morphology AVG-Hat filter filterings
Set: { f1(n),f2(n),L,fλ(n)}；
Step 203: obtaining each mesostructure element respective weights coefficient determined during particle group optimizing
ω=(ω1,ω2,L,ωλ),ωi∈ [0,1] (0≤i≤λ), in conjunction with multiple mesostructure element morphology AVG-
The set of Hat filtered signal obtains the filtered final signal of Multiscale Morphological AVG-Hat, indicates are as follows:
Wherein, y is the filtered signal of Multiscale Morphological AVG-Hat.
As shown in Fig. 2, details are as follows for fitness function value solution procedure in particle swarm optimization algorithm of the present invention:
Step 301: during obtaining particle group optimizing, the multiple dimensioned filtered signal y (n) of AVG-Hat；
Step 302: constructing the phase space reconfiguration matrix of filtered signal, obtain matrix are as follows:
Wherein, m and τ is respectively dimension and the delay time of embeded matrix, k=n- (m-1) τ.
A line every in space matrix is regarded as a reconstruct component, is rearranged according to ascending order, j1,j2,K,jmIndicate component
In each element sequence, then group code sequence available for this space matrix:
X (j)=(j1,j2,K,jm), wherein 1≤j≤k.
M-dimensional space matrix shares m！=1 × 2 × K × possible symbol sebolic addressing of m kind, each symbol sebolic addressing occur general
Rate is P1,P2,K,Pk.According to the definition of Shannon entropy, the arrangement entropy of signal after normalization is defined as:
Wherein, HPEFor the arrangement entropy of filtered signal.
Step 303: envelope spectrum analysis being carried out to filtered signal, obtains the envelope spectrum sequence X (n) of the signal.Calculate packet
The degree of rarefication of network spectral sequence indicates are as follows:
Wherein, S is the envelope spectrum degree of rarefication of signal, and N is the length of signal.
Step 304: the sparse angle value of arrangement entropy and envelope spectrum of filtered signal being divided by, particle swarm optimization algorithm is obtained
Evaluation criterion is indicated in this, as the fitness function value of algorithm are as follows:
Wherein, F is the fitness function value of filtered signal.
This example, which describes to convert by self-adapting multi-dimension morphology AVG-Hat, diagnoses actual housing washer
Fault vibration signal.
The housing washer fault-signal of sensor acquisition is expressed as x (n), and wherein the length of signal is 8192 points.
The time domain waveform and envelope spectrum frequency spectrum of fault-signal are as shown in Fig. 4, and apparent failure is not found from time domain plethysmographic signal
Impulse period does not extract apparent outer ring fault characteristic frequency and frequency multiplication ingredient in envelope spectrum yet, therefore can not diagnose this
Bearing outer ring failure；
The structural parameters of rolling bearing are as follows: pitch diameter 176.29mm, and rolling element diameter is 24.74mm, rolling element
Number is 20, and contact angle is 8.83 °.Shaft revolving speed is 465r/min, and the sample frequency of signal is 25600HZ.Calculate axis
Bearing outer-ring fault characteristic frequency is 66.75Hz, and calculating sampled point of the vibration signal in inaction interval is 25600 ÷, 66.75 ≈
385.3, therefore it is g that initial smallest dimension structural element, which is arranged,1=[00], structural element out to out number are 385；
By structural element dilation operation, the set { g of multiple mesostructure elements is established1,g2,L,g384, share 384
The structural element of different scale, and the scale of structural element is sequentially increased；
Morphology AVG-Hat filter under different scale structural element is constructed, fault-signal different scale structural elements are obtained
Set { the x of plain filtered signal1(n),x2(n),L,x384(n)}；
The parameters of particle swarm algorithm: maximum number of iterations G=10, population scale M=20, acceleration factor c are set1
=1.5, c2=1.5, random factor r1=0.9, r2=0.4, the corresponding weight coefficient range of each mesostructure element be [0,
1].According to particle swarm optimization algorithm, the weight coefficient of each mesostructure element is determined at random, constructs Multiscale Morphological AVG-
Hat filter calculates the evaluation criterion of filtered signal, remembers that the smallest evaluation criterion is optimal fitness function value.It carries out
Population interative computation exports the smallest fitness function value and each mesostructure until meeting the stopping criterion of optimization algorithm
The corresponding weight coefficient ω=(ω of element1,ω2,L,ω384),ωi∈[0,1](0≤i≤384)。
The optimal result adaptively exported according to population establishes Multiscale Morphological AVG-Hat filter, to bearing event
Barrier signal is filtered, and the time domain waveform of filtered signal is as shown in Fig. 5, from the time domain waveform of filtered signal
It can clearly find that bearing outer ring failure impacts ingredient.Filtered signal carries out envelope spectrum analysis, envelope spectrum result such as Fig. 6
It is shown, clearly extracted from envelope spectrum housing washer fault characteristic frequency 66.7Hz, two frequencys multiplication and frequency tripling at
Divide 133Hz and 198Hz.
By envelope spectrum analysis, the outer ring feature of bearing fault vibration signal is effectively extracted, has been realized outside the bearing
Enclose the Accurate Diagnosis of failure.
This example establishes multiple scale topographicals by one section of actual housing washer fault vibration signal of analysis
The set of AVG-Hat filtered signal has adaptively determined different scale in multi-scale filtering device by particle swarm optimization algorithm
The corresponding weight coefficient of structural element constructs optimal multi-scale morphological AVG-Hat filter, passes through filtered signal
The envelope spectrum analysis Accurate Diagnosis fault vibration signal.The present invention passes through one new morphology AVG-Hat filter of building,
The fault signature in fault-signal can be effectively extracted on the basis of taking into account signal de-noising performance.Form proposed by the present invention
It learns multi-scale filtering device self-adaptive construction method and provides one effectively for how solution later constructs multi-scale morphology filtering device
Solution, can be according to analyzed signal fault feature, the optimal Morphologic filters of adaptively selected building, this is more
Scale topographical method is applied to mechanical fault diagnosis and provides accurate establishing criteria.
Used herein a specific example illustrates the principle and implementation of the invention, and above embodiments are said
It is bright to be merely used to help understand method and its core concept of the invention；At the same time, for those skilled in the art, foundation
Thought of the invention, there will be changes in the specific implementation manner and application range.To sum up, the content of the present specification should not manage
Solution is limitation of the present invention.
Claims (4)
1. a kind of building method of the Morphologic filters based on self-adapting multi-dimension AVG-Hat transformation, it is characterised in that:
It uses following steps:
Step 1, the parameters index according to set by sensor acquisition bearing fault signal, determine that analysis signal to be used
Initial Multi-scale model element number and initial structural element value；
Step 2 passes through morphological dilations operation, constructs the set of initial Multi-scale model element composition；
Step 3 calculates the corresponding morphology AVG-Hat transformation under initial Multi-scale model element of bearing fault vibration signal
As a result, the set of the building result that signal aspect AVG-Hat is converted under initial Multi-scale model element；
Step 4, the bearing fault vibration signal by particle group optimizing method, after selecting morphology AVG-Hat filter filtering
Arrangement entropy and envelope spectrum degree of rarefication ratio as evaluation index, as the adaptive optimal control degree letter of particle group optimizing method
Numerical value completes population optimizing iterative process, adaptively determines initial after optimal Multiscale Morphological AVG-Hat filter filtering
The corresponding optimal weights coefficient of Multi-scale model element；
Step 5, according to the corresponding weight coefficient of different scale structural element in the step 4, construct optimal Multiscale Morphological
Learn AVG-Hat filter.
2. the building method of the Morphologic filters according to claim 1 based on self-adapting multi-dimension AVG-Hat transformation,
It is characterized by: the building result that signal aspect AVG-Hat is converted under initial Multi-scale model element in the step 3
Set, specifically with the following method:
3-1, the smallest dimension structural element g=[0 0] for obtaining bearing fault vibration signal x (n) and initial setting up, output signal
Corresponding morphological dilations operation resultErosion operation result (x Θ g) (n), opening operation result (zero g of x) (n) and
Closed operation result (xg) (n)；
3-2, bearing fault vibration signal x (n) and the bearing fault vibration signal x (n) are obtained by initial configuration element shape
It is after state opening operation, closed operation that bearing fault vibration letter is subtracted after original bearing fault vibration signal x (n) multiplies 2 as a result, exporting
Number x (n) is by morphology opening operation, the difference value of closed operation result sum, mathematic(al) representation are as follows: AVGH (f (n))=2 × x
(n)-((zero g of x) (n)+(xg) (n)) is calculated bearing fault signal x (n) and passes through initial single structure element morphology
Learn the result AVGH (f (n)) of AVG-Hat filtering；
Wherein, fault vibration signal x (n) is at the time of wherein symbol n refers to the signal；
F (n) indicates the signal after morphology AVG-Hat filter filtering；
3-3, the initial structural element scale number of initial smallest dimension structural element and setting, export structure element λ are obtained
It is after a Multi-scale model element dilation operation as a result, its mathematic(al) representation are as follows:
That is dilation operation λ times, the collection of the result after establishing multiple mesostructure element dilation operations
It closes: i.e. { g1, g2... gλ}；
Multiple dimensioned erosion operation result (the x Θ g of corresponding bearing fault vibration signal x (n) is calculated simultaneouslyλ) (n), dilation operation
As a resultOpening operation result (zero g of xλ) (n) and closed operation result (xgλ)(n)；
3-4, opening for bearing fault vibration signal x (n) and λ Multi-scale model element lower bearing fault vibration signal x (n) is obtained
Operation, closed operation as a result, export morphology AVG-Hat transformation under corresponding λ Multi-scale model element as a result, its mathematical table
Up to formula are as follows:
AVGH(fλ(n))=2 × x (n)-((zero g of x) (n)+(xg) (n)), establishes λ Multi-scale model element morphology
The set of signal after AVG-Hat filter filtering: i.e. { f1(n),f2(n),…,fλ(n)}。
3. the building method of the Morphologic filters according to claim 1 based on self-adapting multi-dimension AVG-Hat transformation,
It is characterized by: adaptively determining optimal Multiscale Morphological AVG-Hat filter by particle group optimizing method in the step 4
Initially the specific method is as follows for the corresponding optimal weights coefficient of Multi-scale model element after the filtering of wave device:
4-1, the set { g for obtaining bearing fault vibration signal x (n) and λ Multi-scale model element1,g2,…gλ, output λ
The set of signal after Multi-scale model element morphology AVG-Hat filter filtering: i.e. { f1(n),f2(n),…,fλ(n)}；
Wherein, f (n) indicates the signal after morphology AVG-Hat filter filtering；
4-2, the set { f for obtaining signal after λ Multi-scale model element morphology AVG-Hat filter filtering1(n),f2
(n),…,fλAnd the originally determined weight coefficient ω=(ω of filtered signal described in each scale (n) }1,ω2,…,ωλ),
ωi∈ [0,1] (0≤i≤λ), output initial weight coefficient are filtered with corresponding λ Multi-scale model element morphology AVG-Hat
The sum of products of device filtered signal:
I.e.Wherein, y indicates the filtered signal of Multiscale Morphological AVG-Hat；
The arrangement entropy H of the sum of products signal is calculatedPEWith the sparse angle value S of envelope spectrum, by the arrangement entropy HPEWith packet
Network composes sparse angle value S and is divided by obtain fitness function value P of the filtered signal in particle group optimizing method, mathematical table
Up to formula are as follows:
4-3, after the 1st interative computation of population signal fitness function value PILess than or equal to (Ι -1) secondary interative computation
The fitness function value P of signal afterwardsI-1When, i.e. PI≤PI-1, remember PIFor optimal fitness function value；And so on, obtain particle
The whole process of group optimizing method iteration exports the minimum fitness function value of all sum of products signals after G interative computation
PbestAs fitness function value optimal during entire particle group optimizing, i.e. Pbest=min (P1, P2..., PG)；Wherein, G
For maximum number of iterations；
4-4, the minimum fitness function value P is extractedbestCorresponding Multi-scale model element weights coefficient ωbest=(ω1,
ω2,…,ωλ) it is used as the corresponding optimal weights coefficient of Multi-scale model element.
4. the building method of the Morphologic filters according to claim 1 based on self-adapting multi-dimension AVG-Hat transformation,
It is characterized by: the method for constructing optimal Multiscale Morphological AVG-Hat filter in the step 5 is as follows:
Calculate optimal weights coefficient ωbest=(ω1,ω2,…,ωλ) filtered with λ Multi-scale model element morphology AVG-Hat
Device filtered signal fi(n) sum of products adaptively determines optimal using the sum of products signal as particle group optimizing method
Multi-scale model element morphology AVG-Hat filter composition form, wherein ωi∈ωbest,fi(n)={ f1(n),f2
(n),…,fλ(n)}。
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