CN110514444A - Rolling bearing Weak fault feature extracting method based on variation mode decomposition and phase space parallel factor analysis - Google Patents
Rolling bearing Weak fault feature extracting method based on variation mode decomposition and phase space parallel factor analysis 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
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Abstract
The present invention relates to a kind of rolling bearing Weak fault feature extracting method based on variation mode decomposition and phase space parallel factor analysis, comprising the following steps: acquire bearing vibration signal using vibrating sensor, obtain Weak fault signal x (t)；Penalty factor α, Decomposition order K are set, variation mode decomposition is carried out to vibration signal, obtains corresponding intrinsic mode function component；According to kurtosis criterion, the maximum intrinsic mode function component of kurtosis is chosen as optimal component；Phase space parallel factor analysis is carried out to optimal component, at least one isolated component is obtained in higher-dimension phase space；The maximum isolated component of kurtosis is chosen from least one isolated component obtained in the 4th step and carries out envelope spectrum analysis, and obtains fault characteristic frequency；The present invention effectively extracts fault characteristic frequency, realizes accurately identifying for rolling bearing fault type.
Description
Technical field
The present invention relates to a kind of rolling bearing Weak fault based on variation mode decomposition and phase space parallel factor analysis
Feature extracting method belongs to mechanical fault diagnosis technical field.
Background technique
Rolling bearing is one of most common and vital part in rotating machinery, and operating status directly affects
The working performance of whole equipment.According to incompletely statistics, about 30% mechanical breakdown is as caused by bearing failure.This is just meaned
The local defect of rolling bearing to detect for Practical Project field be very necessary；Therefore, how rolling is identified as early as possible
Dynamic bearing failure and to prevent accident be an important topic of current research.
In the rolling bearing initial failure stage, recurrent pulse fault-signal is vulnerable to the microsize of local defect and strong
The influence of ambient noise is difficult to be accurately detected its fault characteristic information using traditional signal processing algorithm.Some experts
Scholar proposes many effective Weak fault diagnostic methods.But there is also some limitations, such as accidental resonance
(Stochastic resonance, SR) algorithm needs to be arranged more parameter；The robustness of minimum entropy deconvolution is poor；Experience
Mode decomposition the problems such as there are modal overlaps.
Summary of the invention
The present invention provides a kind of rolling bearing Weak fault based on variation mode decomposition and phase space parallel factor analysis
Feature extracting method, effectively extraction fault characteristic frequency, realize accurately identifying for rolling bearing fault type.
The technical solution adopted by the present invention to solve the technical problems is:
A kind of rolling bearing Weak fault feature extraction side based on variation mode decomposition and phase space parallel factor analysis
Method, comprising the following steps:
Step 1: acquiring bearing vibration signal using vibrating sensor, Weak fault signal x (t) is obtained；
Step 2: setting penalty factor α, Decomposition order K, carry out variation mode decomposition to vibration signal, obtain corresponding sheet
Levy mode function component；
Step 3: choosing the maximum intrinsic mode function component of kurtosis as optimal component according to kurtosis criterion；
Step 4: carrying out phase space parallel factor analysis to optimal component, at least one is obtained in higher-dimension phase space solely
Vertical component；
It is wrapped step 5: choosing the maximum isolated component of kurtosis from least one isolated component obtained in the 4th step
Network spectrum analysis, and obtain fault characteristic frequency；
As present invention further optimization, variation mode decomposition described in second step can regard a kind of constraint change as
Divide optimization problem:
The constraint variation model expression of the above-mentioned original Weak fault signal x for being, wherein | | | |2For 2 models
Number, δ (t) are impulse function,For functional gradient, j is imaginary unit, if ukIt (t) is k-th of intrinsic mode function, if wk
For ukCentre frequency；Budget secondary penalty factor α and Lagrange multiplier operator λ, by restrictive variational problem become it is non-about
Beam variational problem:
Above-mentioned formula is solved using alternating direction multiplication operator, for k=1,2 ..., K, wherein K is all eigen modes
Maximum value in state function, k and all frequencies omega >=0 update each intrinsic mode function component uk(t) and its centre frequency
ωk:
Wherein, uiFor except ukIntrinsic mode function component in addition, α are secondary penalty factor, and x (t) is to obtain faint event
Hinder signal, ωkFor center frequency；For all frequencies omega >=0, λ is updated:
Wherein, λ is Lagrange multiplier operator, and θ is the undated parameter of λ, ukFor k-th of intrinsic mode function；It repeats more
The new above process, until meeting the following condition of convergence:
Wherein ε is traditionally arranged to be 10-6, thus, obtain corresponding intrinsic mode function component uk(t), k=1,2 ..., K；
As present invention further optimization, kurtosis criterion described in third step is
WhereinT is signal time length,For uk(t) mean value,
S.t.:subject to expression meets condition, ukFor k-th of intrinsic mode function,For optimal component；
As present invention further optimization, phase space parallel factor analysis described in the 4th step is mainly comprised the following steps
Enabling y is the optimal component chosen in third step, and higher-dimension phase space can be written as
Wherein,For the phase space signal of reconstruct, L=N- (M-1) τ, L=N- (M-1) τ is
The points of phase space, N are signal length, and M is Embedded dimensions, and τ is delay time, and wherein M, τ numerical value can be preset, and other parameters are all
Be it is known, higher-dimension phase space signal Y is represented by Y=AS
Wherein,For hybrid matrix, S is isolated component；Higher-dimension phase space signal Y is divided into D
A nonoverlapping data block, each data block contain P=L/D data point, and L is the points of phase space；Therefore, higher-dimension phase space
Signal Y is also denoted as
Y=[Y1 Y2 … YD]=A [S1 S2 … SD]
WhereinFor M higher-dimension phase space of d data block
Signal；For M isolated component of d data block；YdCovariance
Matrix is represented by
Wherein, For SdAssociation
Variance matrix；
In order to simplify the mathematic sign of subsequent derivation, annotation symbol is as follows:
Wherein,For m in d data block1A higher-dimension phase space signal, m1=1,2 ..., M；For d number
According to m in block2A higher-dimension phase space signal, m1=1,2 ..., M；m2=1,2 ..., M；R is covariance matrix；
Wherein,For m in d data block1A isolated component, m1=1,2 ..., M；For in d data block
M2A isolated component, m1=1,2 ..., M；m2=1,2 ..., M；According tom1≠m2, can obtain
In this wayIt is represented by
Wherein, ammFor the element in matrix A, m=1,2 ..., M；Define a matrix
Its expression formula is
By each covariance matrixD=1,2 ..., D is superposed to three rank tensor forms
Its element is represented by
Wherein,For the element in tensor R, ammFor the element in matrix A,For matrix RsIn member
Element, above formula are PARAFAC model；Three rank tensor R are subjected to section operation along z-axis, obtain two-dimensional matrix R of equal valueMD×M:
It is defined as follows objective function
In formula, off () is the quadratic sum of matrix off diagonal element, and W is separation matrix；It is rotated using Givens to this
Objective function carries out minimum optimization, estimates separation matrix W, to obtain isolated component S=WY, Y is the phase space of reconstruct
Signal；
Selection for delay time and Embedded dimensions, wherein M indicates that Embedded dimensions, τ indicate delay time, in order to avoid
The blindness artificially selected proposes the global kurtosis maximal criterion of isolated component；The criterion basic step are as follows: 1) setting delay
The variation range of time and Embedded dimensions；2) it under different parameters, is obtained accordingly using phase space parallel factor analysis algorithm
Isolated component, and calculate corresponding kurtosis value；3) relationship between two parameters and the maximum kurtosis value of isolated component is obtained；4)
The corresponding parameter of overall situation maximum kurtosis value is optimal delay time and Embedded dimensions.Its cost function is represented by
Wherein, kurt (sm), m=1,2 ..., M are m-th of isolated component smKurtosis value,For the maximum of Embedded dimensions
Value；For the maximum value of delay time, N is signal length, and M is Embedded dimensions, MoFor optimal embedding dimension, τoFor optimal delay
Time.
By above technical scheme, compared with the existing technology, the invention has the following advantages:
1, fault-signal is decomposed into several intrinsic modal components using variation mode decomposition by the present invention, and utilizes kurtosis
Criterion is chosen the maximum component of kurtosis and is further analysed, and its object is to eliminate the noise jamming of extraneous features frequency band；
2, phase space parallel factor analysis is carried out to optimal component, chooses the maximum isolated component of global kurtosis, purpose
It is to inhibit the noise jamming in feature band；
3, envelope spectrum analysis is carried out to the maximum isolated component of global kurtosis, effectively extraction fault characteristic frequency, thus real
Existing rolling bearing fault type accurately identifies；
4, it is the blindness for avoiding artificial parameter selection, proposes isolated component overall situation kurtosis maximal criterion, selects optimal
Embedded dimensions and delay time parameter.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples.
Fig. 1 is the Weak fault feature extraction flow chart of the preferred embodiment of the present invention；
Fig. 2 is the collected various data of rolling bearing Weak fault signal of the preferred embodiment of the present invention, wherein 2a is
Time domain waveform, 2b are FFT spectrum, and 2c is envelope spectrum；
Fig. 3 is that the vibration signal of the preferred embodiment of the present invention obtains four intrinsic mode functions point through intrinsic mode decomposition
The data of amount, wherein 3a is time domain waveform, and 3b is FFT spectrum；
Fig. 4 is the kurtosis value of the preferred embodiment of the present invention intrinsic mode function component.
Fig. 5 is the maximum kurtosis value and two parameters (delay time, insertion dimensions of the preferred embodiment of the present invention isolated component
Number) between relationship；
Fig. 6 is isolated component in the preferred embodiment of the present invention higher-dimension phase space；
Fig. 7 is the corresponding kurtosis value of the preferred embodiment of the present invention isolated component；
Fig. 8 is the envelope that the preferred embodiment of the present invention carries out that Envelope Demodulation Analysis is obtained to the isolated component of maximum kurtosis
Spectrum, wherein 8a is envelope spectrum analysis, the fault characteristic frequency that 8b is.
Specific embodiment
In conjunction with the accompanying drawings, the present invention is further explained in detail.These attached drawings are simplified schematic diagram, only with
Illustration illustrates basic structure of the invention, therefore it only shows the composition relevant to the invention.
As shown in Figure 1, the rolling bearing of the invention based on variation mode decomposition and phase space parallel factor analysis is faint
Fault signature extracting method, comprising the following steps:
Step 1: acquiring bearing vibration signal using vibrating sensor, Weak fault signal x (t) is obtained；
Step 2: setting penalty factor α, Decomposition order K, carry out variation mode decomposition to vibration signal, obtain corresponding sheet
Levy mode function component；
Step 3: choosing the maximum intrinsic mode function component of kurtosis as optimal component according to kurtosis criterion；
Step 4: carrying out phase space parallel factor analysis to optimal component, at least one is obtained in higher-dimension phase space solely
Vertical component；
It is wrapped step 5: choosing the maximum isolated component of kurtosis from least one isolated component obtained in the 4th step
Network spectrum analysis, and obtain fault characteristic frequency；
Specifically include the following steps, acquire bearing vibration signal using vibrating sensor, obtains Weak fault letter
Number x (t), the various data of this Weak fault signal are as shown in Figure 2 at this time, wherein 2a is time domain waveform, and 2b is FFT spectrum, 2c
For envelope spectrum；
Embodiment 1:
Penalty factor α=4000, Decomposition order K=4 are set, variation mode decomposition is carried out to vibration signal, obtains a system
Column intrinsic mode function component；
Variation mode decomposition can regard a kind of constraint variation optimization problem as:
The constraint variation model expression of the above-mentioned original Weak fault signal x for being, wherein | | | |2For 2 models
Number, δ (t) are impulse function,For functional gradient, j is imaginary unit, if ukIt (t) is k-th of intrinsic mode function, if wk
For ukCentre frequency；Budget secondary penalty factor α and Lagrange multiplier operator λ, by restrictive variational problem become it is non-about
Beam variational problem:
Above-mentioned formula is solved using alternating direction multiplication operator, for k=1,2 ..., K, wherein K is all eigen modes
Maximum value in state function, k and all frequencies omega >=0 update each intrinsic mode function component uk(t) and its centre frequency
ωk:
Wherein, uiFor except ukIntrinsic mode function component in addition, α are secondary penalty factor, and x (t) is to obtain faint event
Hinder signal, ωkFor center frequency；For all frequencies omega >=0, λ is updated:
Wherein, λ is Lagrange multiplier operator, and θ is the undated parameter of λ, ukFor k-th of intrinsic mode function；It repeats more
The new above process, until meeting the following condition of convergence:
Wherein ε is traditionally arranged to be 10-6, vibration signal obtains four intrinsic modal components, time domain through variation mode decomposition
As shown in 3a in Fig. 3, FFT is composed as shown in 3b in Fig. 3 waveform.
Embodiment 2:
Shown in Fig. 4, the kurtosis value of intrinsic mode is calculated, is according to kurtosis criterion
WhereinT is signal time length,For uk(t) mean value,
S.t.:subject to expression meets condition, ukFor k-th of intrinsic mode function: choosing the maximum eigen mode of kurtosis
State component 2 is used as optimal component, is further analyzed；
Embodiment 3:
Phase space parallel factor analysis is carried out to optimal component, several isolated components are obtained in high phase space,
It mainly comprises the following steps
Enabling y is the optimal component chosen in third step, and higher-dimension phase space can be written as
Wherein,For the phase space signal of reconstruct, L=N- (M-1) τ, L=N- (M-1) τ are phase
The points in space, N are signal length, and M is Embedded dimensions, and τ is delay time, and wherein M, τ numerical value can be preset, and other parameters are all
Known, higher-dimension phase space signal Y is represented by Y=AS
Wherein,For hybrid matrix, S is isolated component；Higher-dimension phase space signal Y is divided into D
A nonoverlapping data block, each data block contain P=L/D data point, and L is the points of phase space；Therefore, higher-dimension phase space
Signal Y is also denoted as
Y=[Y1 Y2 … YD]=A [S1 S2 … SD]
WhereinFor M higher-dimension phase space of d data block
Signal；For M isolated component of d data block；YdAssociation side
Poor matrix is represented by
Wherein, For
SdCovariance matrix；
In order to simplify the mathematic sign of subsequent derivation, annotation symbol is as follows:
Wherein,For m in d data block1A higher-dimension phase space signal, m1=1,2 ..., M；For d number
According to m in block2A higher-dimension phase space signal, m1=1,2 ..., M；m2=1,2 ..., M；R is covariance matrix；
Wherein,For m in d data block1A isolated component, m1=1,2 ..., M；For in d data block
M2A isolated component, m1=1,2 ..., M；m2=1,2 ..., M；According tom1≠m2, can obtain
In this wayIt is represented by
Wherein, amm is the element in matrix A, m=1,2 ..., M；Define a matrixIts
Expression formula is
By each covariance matrixD=1,2 ..., D is superposed to three rank tensor formsIts
Element is represented by
Wherein,For the element in tensor R, amm is the element in matrix A,For matrix RsIn member
Element, above formula are PARAFAC model；Three rank tensor R are subjected to section operation along z-axis, obtain two-dimensional matrix R of equal valueMD×M:
It is defined as follows objective function
In formula, off () is the quadratic sum of matrix off diagonal element, and W is separation matrix；It is rotated using Givens to this
Objective function carries out minimum optimization, estimates separation matrix W, to obtain isolated component S=WY, Y is the phase space of reconstruct
Signal；
Embodiment 4:
Selection for delay time and Embedded dimensions, M indicate Embedded dimensions, and the variation range that Embedded dimensions are arranged is
[1,200], τ indicate delay time, and the variation range that delay time is arranged is that [1,11] utilizes phase space under different parameters
Parallel factor analysis algorithm obtains corresponding isolated component, and calculates corresponding kurtosis value；To obtain two parameters and independence
Relationship between the maximum kurtosis value of component, as shown in Figure 5；As seen from Figure 5, global maximum kurtosis value is corresponding optimal prolongs
Slow time and Embedded dimensions are respectively 10 and 163, and Fig. 6 is the independent separate under optimized parameter in higher-dimension phase space, and calculates phase
The kurtosis value answered, as shown in Figure 7；
Embodiment 5:
Shown in 8a in Fig. 8, therefrom chooses the maximum isolated component of kurtosis and carry out envelope spectrum analysis, and obtain fault signature
Frequency, it can be seen that fault characteristic frequency and its 2 frequencys multiplication from the 8b of Fig. 8.
Those skilled in the art of the present technique are appreciated that unless otherwise defined, all terms used herein (including technology art
Language and scientific term) there is meaning identical with the general understanding of those of ordinary skill in the application fields.Should also
Understand, those terms such as defined in the general dictionary, which should be understood that, to be had and the meaning in the context of the prior art
The consistent meaning of justice, and unless defined as here, it will not be explained in an idealized or overly formal meaning.
The meaning of "and/or" described herein refers to that the case where respective individualism or both exists simultaneously wraps
Including including.
The meaning of " connection " described herein can be between component be directly connected to be also possible to pass through between component
Other components are indirectly connected with.
Taking the above-mentioned ideal embodiment according to the present invention as inspiration, through the above description, relevant staff is complete
Various changes and amendments can be carried out without departing from the scope of the technological thought of the present invention' entirely.The technology of this invention
Property range is not limited to the contents of the specification, it is necessary to which the technical scope thereof is determined according to the scope of the claim.
Claims (4)
1. a kind of rolling bearing Weak fault feature extracting method based on variation mode decomposition and phase space parallel factor analysis,
It is characterized by comprising following steps:
Step 1: acquiring bearing vibration signal using vibrating sensor, Weak fault signal x (t) is obtained；
Step 2: setting penalty factor α, Decomposition order K, carry out variation mode decomposition to vibration signal, obtain corresponding eigen mode
State function component；
Step 3: choosing the maximum intrinsic mode function component of kurtosis as optimal component according to kurtosis criterion；
Step 4: carrying out phase space parallel factor analysis to optimal component, at least one is obtained in higher-dimension phase space and is independently divided
Amount；
Step 5: choosing the maximum isolated component of kurtosis from least one isolated component obtained in the 4th step carries out envelope spectrum
Analysis, and obtain fault characteristic frequency.
2. the faint event of the rolling bearing according to claim 1 based on variation mode decomposition and phase space parallel factor analysis
Hinder feature extracting method, it is characterised in that: variation mode decomposition described in second step can regard a kind of constraint variation optimization as
Problem:
The constraint variation model expression of the above-mentioned original Weak fault signal x for being, wherein | | | |2For 2 norms, δ (t)
For impulse function,For functional gradient, j is imaginary unit, if ukIt (t) is k-th of intrinsic mode function, if wkFor ukIn
Frequency of heart；Budget secondary penalty factor α and Lagrange multiplier operator λ, become non-binding variation for restrictive variational problem
Problem:
Above-mentioned formula is solved using alternating direction multiplication operator, for k=1,2 ..., K, wherein K is all intrinsic mode letters
Maximum value in number, k and all frequencies omega >=0 update each intrinsic mode function component uk(t) and its centre frequency ωk:
Wherein, uiFor except ukIntrinsic mode function component in addition, α are secondary penalty factor, and x (t) is to obtain faint failure letter
Number, ωkFor center frequency；For all frequencies omega >=0, λ is updated:
Wherein, λ is Lagrange multiplier operator, and θ is the undated parameter of λ, ukFor k-th of intrinsic mode function；Repetition updates above-mentioned
Process, until meeting the following condition of convergence:
Wherein ε is traditionally arranged to be 10-6, thus, obtain corresponding intrinsic mode function component uk(t), k=1,2 ..., K.
3. rolling bearing Weak fault feature extracting method shown according to claim 1, it is characterised in that: described in third step
Kurtosis criterion be
WhereinT is signal time length,For uk(t) mean value, s.t.:subject to
Expression meets condition, ukFor k-th of intrinsic mode function,For optimal component.
4. rolling bearing Weak fault feature extracting method shown according to claim 1, it is characterised in that: described in the 4th step
Phase space parallel factor analysis, mainly comprise the following steps
Enabling y is the optimal component chosen in third step, and higher-dimension phase space can be written as
Wherein,For the phase space signal of reconstruct, L=N- (M-1) τ, L=N- (M-1) τ are the point of phase space
Number, N is signal length, and M is Embedded dimensions, and τ is delay time, and wherein M, τ numerical value can be preset, other parameters be all it is known,
Higher-dimension phase space signal Y is represented by
Y=AS
Wherein,For hybrid matrix, S is isolated component；Higher-dimension phase space signal Y is divided into D not to be overlapped
Data block, each data block contains P=L/D data point, and L is the points of phase space；Therefore, higher-dimension phase space signal Y is also
It is represented by
Y=[Y1 Y2 … YD]=A [S1 S2 … SD]
WhereinFor M higher-dimension phase space signal of d data block；For M isolated component of d data block；YdCovariance matrix
It is represented by
Wherein, For SdCovariance matrix；
In order to simplify the mathematic sign of subsequent derivation, annotation symbol is as follows:
Wherein,For m in d data block1A higher-dimension phase space signal, m1=1,2 ..., M；For d data block
In m2A higher-dimension phase space signal, m1=1,2 ..., M；m2=1,2 ..., M；R is covariance matrix；
Wherein,For m in d data block1A isolated component, m1=1,2 ..., M；For m in d data block2It is a
Isolated component, m1=1,2 ..., M；m2=1,2 ..., M；According tom1≠m2, can obtain
In this wayIt is represented by
Wherein, ammFor the element in matrix A, m=1,2 ..., M；Define a matrixIts expression formula
For
By each covariance matrixD=1,2 ..., D is superposed to three rank tensor formsIts element
It is represented by
Wherein,For the element in tensor R, ammFor the element in matrix A,For matrix RsIn element, above formula
As PARAFAC model；Three rank tensor R are subjected to section operation along z-axis, obtain two-dimensional matrix R of equal valueMD×M:
It is defined as follows objective function
In formula, off () is the quadratic sum of matrix off diagonal element, and W is separation matrix；It is rotated using Givens to this target
Function carries out minimum optimization, estimates separation matrix W, to obtain isolated component S=WY, Y is the phase space signal of reconstruct；
Selection for delay time and Embedded dimensions, wherein M indicates Embedded dimensions, and τ indicates delay time, in order to avoid artificial
The blindness of selection proposes the global kurtosis maximal criterion of isolated component；The criterion basic step are as follows: 1) delay time is set
With the variation range of Embedded dimensions；2) under different parameters, corresponding independence is obtained using phase space parallel factor analysis algorithm
Component, and calculate corresponding kurtosis value；3) relationship between two parameters and the maximum kurtosis value of isolated component is obtained；4) global
The corresponding parameter of maximum kurtosis value is optimal delay time and Embedded dimensions.Its cost function is represented by
Wherein, kurt (sm), m=1,2 ..., M are m-th of isolated component smKurtosis value,For the maximum value of Embedded dimensions；For the maximum value of delay time, N is signal length, and M is Embedded dimensions, MoFor optimal embedding dimension, τoWhen for optimal delay
Between.
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| CN112113766A (en) * | 2020-09-01 | 2020-12-22 | 兰州理工大学 | Characteristic extraction method for early damage state of rolling bearing |
| CN112431753A (en) * | 2021-01-25 | 2021-03-02 | 赛腾机电科技（常州）有限公司 | Multiple quantitative diagnosis method for shoe loosening fault of axial plunger pump |
| CN113204051A (en) * | 2021-06-10 | 2021-08-03 | 成都理工大学 | Low-rank tensor seismic data denoising method based on variational modal decomposition |
| CN113204051B (en) * | 2021-06-10 | 2022-04-15 | 成都理工大学 | Low-rank tensor seismic data denoising method based on variational modal decomposition |
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