CN105758644A - Rolling bearing fault diagnosis method based on variation mode decomposition and permutation entropy - Google Patents

Abstract

The invention relates to a rolling bearing fault diagnosis method based on variation mode decomposition and permutation entropy. Vibration signals are decomposed with a variation mode decomposition method, so that reactive components and mode aliasing are effectively reduced, all the mode components include characteristic information of different time scales of original signals, and effective multi-scale components are provided for subsequent signal characteristic extraction. With the combination of the features that permutation entropy is simple in calculation, high in noise resisting ability and the like, bearing fault characteristics of all the mode components are extracted from multi-scale angles. Compared with single permutation entropy analysis of rolling bearing vibration, the characteristic information of the signals can be more comprehensively represented through the permutation entropy characteristic extracting method based on multiple scales, the recognition accuracy of a support vector machine is improved, and fault diagnosis of rolling bearings is better achieved.

Description

Fault Diagnosis of Roller Bearings based on variation mode decomposition and arrangement entropy

Technical field

The present invention relates to a kind of Fault Diagnosis of Roller Bearings, particularly to a kind of Fault Diagnosis of Roller Bearings based on variation mode decomposition and arrangement entropy.

Background technology

Rolling bearing is wide variety of parts in plant equipment, and its running status quality will directly affect production efficiency and the safety of equipment.In plant equipment actual motion, if rolling bearing initial failure can not be found in time, the impact that its fault produces can accelerate the damage of rolling bearing, ultimately results in rolling bearing and lost efficacy, and properly functioning the bringing of machinery is had a strong impact on.Rolling bearing is one of element the most fragile in mechanical system, the mechanical equipment fault of about 30% be by rolling bearing local damage fault cause (old enter. mechanical equipment vibration monitoring and fault diagnosis [M]. Shanghai: publishing house of Shanghai Communications University, 1999).Therefore, the fault diagnosis technology of rolling bearing is important component part in mechanical fault diagnosis.

It is mostly multicomponent AM/FM amplitude modulation/frequency modulation signal due to bearing vibration signal, only is difficult to extract fault characteristic information by original vibration signal, it is necessary to after vibration signal is decomposed, then carry out processing characteristic information extraction to each component after decomposing.The vibration signal of bearing has non-stationary characteristic, what current non-stationary signal decomposition method was conventional has wavelet decomposition (Ren Guoquan, Wei Youmin, Zheng Haiqi. the bearing failure diagnosis based on wavelet analysis studies [J]. Hebei Academy of Sciences journal, 2002,19 (2): 112-116) method and empirical mode decomposition (EmpiricalModeDecomposition, it being called for short EMD) method is (high-strength, Du little Shan, Fan Hong, Deng. EMD diagnostic method research [J] of rolling bearing fault. vibration engineering journal, 2007,20 (1): 15-18).Although the Research on Fault Diagnosis Technology such as wavelet transformation and EMD has been achieved for very big progress, these theories and method also need to perfect further.The On The Choice of wavelet basis and filtering threshold in wavelet analysis；The screening of EMD method recurrence lacks error calibration, and noise ratio is more sensitive etc..

Variation mode decomposition (VariationalModeDecomposition, it is called for short VMD) it is a kind of Adaptive Signal Processing side (DragomiretskiyK, ZossoD.Variationalmodedecomposition [J] .IEEETranonSignalProcessing, 2014,62 (3): 531-544), by the optimal solution of iterated search variation mode, constantly update each mode function and mid frequency, obtain some mode functions with certain bandwidth.Signal decomposition can be some intrinsic modal components by the method, can effectively reduce reactive component and modal overlap.

Arrangement entropy (PermutationEntropy, it is called for short PE) algorithm (ChristophB, BerndP.Permutationentropy:anaturalcomplexitymeasureforti meseries. [J] .PhysicalReviewLetters, 2002,88 (17): 174102) being a kind of method detecting time series randomness and kinetics sudden change, it has the features such as calculating is simple, noise resisting ability is strong.And vibration signal often has feature non-linear, non-stationary, arrangement entropy is used for mechanical oscillation signal abrupt climatic change and obtains better effects by existing scholar.

Summary of the invention

The present invention be directed to the problem that in the fault diagnosis of rolling bearing, fault characteristic information extracts difficulty, propose a kind of Fault Diagnosis of Roller Bearings based on variation mode decomposition and arrangement entropy, time series randomness and kinetics sudden change feature can be detected in conjunction with the VMD advantage to signal decomposition and arrangement entropy, better realize feature extraction and the fault diagnosis of rolling bearing.

The technical scheme is that a kind of Fault Diagnosis of Roller Bearings based on variation mode decomposition and arrangement entropy, specifically include following steps:

1) utilize acceleration transducer to measure bearing vibration signal, gather vibration signal under rolling bearing normal condition, inner ring fault, outer ring fault, rolling element malfunction, obtain the vibration data under each state；

2) adopt variation mode decomposition method that the vibration signal data under four kinds of states of bearing are decomposed, namely bearing vibration signal is sought K mode function, the estimation bandwidth sum making each mode is minimum, and each mode function sum is equal to the bearing vibration signal of input；

3) to step 2) K mode function of gained bearing vibration signal, calculate the arrangement entropy measure of each modal components complexity characteristics, and build high dimensional feature vector, using this vector fault diagnosis input vector as SVM；

4) the high dimensional feature vector obtained is inputted support vector machines grader to be trained, obtain the SVM diagnostic cast of each type fault；

5) bearing vibration signal to be measured is gathered, according to step 1), 2), 3) build test sample high dimensional feature vector, input the SVM diagnostic cast trained respectively, fault type and the duty of bearing is obtained, it is achieved the fault diagnosis of rolling bearing by the output result of SVM classifier.

Described step 2) adopt variation mode decomposition method that the vibration signal data under four kinds of states of bearing are decomposed, specifically include following steps:

To each mode function u_kT () carries out Hilbert conversion, obtain its analytic signal:

$\left(\mathrm{\δ}\right(t)+\frac{j}{\mathrm{\π}t})*u_k\left(t\right)$

In formula, δ (t) is impulse function, each mode analytic signal is mixed one and estimates mid frequencyBy each mode spectrum modulation to corresponding Base Band:

$\[\left(\mathrm{\δ}\right(t)+\frac{j}{\mathrm{\π}t})*u_k\left(t\right)\]e^{-{\mathrm{j\ω}}_{k}t}$

Corresponding constraint variation model is as follows:

$\underset{\left\{u_k\right\},\left\{{\mathrm{\ω}}_k\right\}}{\min }\left\{\underset{k}{\Σ}{||{\∂}_t\[\left(\mathrm{\δ}\right(t)+\frac{j}{\mathrm{\π}t})*u_k\left(t\right)\]e^{-{\mathrm{j\ω}}_{k}t}||}_2^2\right\}$

$s.t.\underset{k=1}{\overset{K}{\Σ}}{u}_k=f$

In formula: { u_k}={ u₁, u₂..., u_KFor decomposing K the modal components obtained；{ω_k}={ ω₁, ω₂..., ω_KFor center frequency corresponding to each modal components；

For asking for the optimal solution of above-mentioned constraint variation problem, introduce the argument Lagrange function of following form, it may be assumed that

$\begin{array}{c}L\left(\right\{u_k\},\{{\mathrm{\&omega;}}_k\},\mathrm{\&lambda;})=\mathrm{\&alpha;}\underset{k=1}{\overset{K}{\&Sigma;}}{||{\&part;}_t\&lsqb;\left(\mathrm{\&delta;}\right(t)+\frac{j}{\mathrm{\&pi;}t})*u_k\left(t\right)\&rsqb;e^{-{\mathrm{j\&omega;}}_{k}t}||}_2^2+{||f\left(t\right)-\underset{k=1}{\overset{K}{\&Sigma;}}{u}_k\left(t\right)||}_2^2\\ +<\mathrm{\&lambda;}\left(t\right),f\left(t\right)-\underset{k=1}{\overset{K}{\&Sigma;}}{u}_k\left(t\right)>\end{array}$

In formula: α is punishment parameter；λ is equal to λ (t) for Lagrange multiplier；

Alternating direction multiplier method is utilized alternately to updateAnd λⁿ⁺¹Seek the optimal solution of variational problem, wherein subscriptⁿ⁺¹Represent (n+1)th iteration result of variable, thus bearing vibration signal f (t) being decomposed into K modal components.

Described alternating direction multiplier method is utilized alternately to updateAnd λⁿ⁺¹The optimal solution seeking variational problem specifically comprises the following steps that

A: initialize And n, in formula, ^ is the frequency domain representation utilizing Parseval/Plancherel Fourier's equilong transformation；

B: according to formula

${\hat{u}}_k^{n+1}\left(\mathrm{\&omega;}\right)=\left(\hat{f}\right(\mathrm{\&omega;})-\underset{i\&NotEqual;k}{\&Sigma;}{\hat{u}}_i(\mathrm{\&omega;})+\frac{\widehat{\mathrm{\&lambda;}}\left(\mathrm{\&omega;}\right)}{2})\frac{1}{1+2\mathrm{\&alpha;}{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_k)}^2}$

${\mathrm{\&omega;}}_k^{n+1}=\frac{{\&Integral;}_0^{\mathrm{\&infin;}}\mathrm{\&omega;}{\left|{\hat{u}}_k\left(\mathrm{\&omega;}\right)\right|}^{2}d\mathrm{\&omega;}}{{\&Integral;}_0^{\mathrm{\&infin;}}{\left|{\hat{u}}_k\left(\mathrm{\&omega;}\right)\right|}^{2}d\mathrm{\&omega;}}$

UpdateWithIn formula, ω is frequency variable；

C: update

${\widehat{\mathrm{\&lambda;}}}^{n+1}\left(\mathrm{\&omega;}\right)\&LeftArrow;{\widehat{\mathrm{\&lambda;}}}^n\left(\mathrm{\&omega;}\right)+\mathrm{\&tau;}\left(\hat{f}\right(\mathrm{\&omega;})-\underset{k}{\&Sigma;}{\hat{u}}_k^{n+1}(\mathrm{\&omega;}\left)\right)$

D: repeat step B and C, until meeting iteration stopping conditionIn formula, ε > 0 is given discrimination precision, and end loop finally willBy inverse Fourier transform to time domain u_kT (), obtains K modal components u₁(t), u₂(t)…u_K(t)。

Described step 3) the arrangement entropy measure that calculates each modal components complexity characteristics specifically includes:

By bearing vibration signal being carried out variation mode decomposition decomposition, the mode function u obtained_kT () is a time series { u_k(i), i=1,2 ..., N}, N is length of time series, it is carried out phase space reconfiguration, obtains matrix:

$\left[\begin{array}{cccc}{u}_k\left(1\right)& u_k(1+\mathrm{\&tau;})& \mathrm{...}& u_k(1+(m-1\left)\mathrm{\&tau;}\right)\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ u_k\left(j\right)& u_k(j+\mathrm{\&tau;})& \mathrm{...}& u_k(j+(m-1\left)\mathrm{\&tau;}\right)\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ u_k\left(G\right)& u_k(G+\mathrm{\&tau;})& \mathrm{...}& u_k(G+(m-1\left)\mathrm{\&tau;}\right)\end{array}\right]$

Wherein: m is Embedded dimensions；τ is time delay；G is reconstruct vector number, G=N-(m-1) τ in phase space reconstruction；

Jth in restructuring matrix is reconstructed component { u_k(j), u_k(j+ τ) ..., u_k(j+ (m-1) τ) } rearrange according to ascending order, it may be assumed that { u_k(i+(j₁-1)τ)≤u_k(i+(j₂-1)τ)≤…≤u_k(i+(j_m-1)τ)}.Wherein j₁, j₂..., j_mRepresent the index of each element column in reconstruct component；

Symbol sebolic addressing S (l)=[j of its element size order of a reflection can be obtained for any one the reconstruct vector in phase space reconstruction₁, j₂..., j_m], wherein l=1,2 ..., h, and h≤m！, m！Represent the factorial of m；Tectonic sequence P₁, P₂..., P_h, P_hIt it is the probability size of h kind symbol sebolic addressing appearance；

The arrangement entropy (PE) of each modal components, tries to achieve according to the form of Shannon entropy:

${\mathrm{PE}}_k\left(m\right)=-\underset{l=1}{\overset{h}{\&Sigma;}}{P}_{l}ln{P}_l$

By PE_kM () standardization, the arrangement entropy namely obtaining each mode function is PE_k=PE_k(m)/ln(m！)；

Each modal components is tried to achieve arrangement entropy, builds high dimensional feature vector PE=[PE₁, PE₂…PE_K], in formula, K is the modal components number that vibration signal decomposes.

The beneficial effects of the present invention is: the present invention is based on the Fault Diagnosis of Roller Bearings of variation mode decomposition and arrangement entropy, vibration signal is decomposed by the variation mode decomposition method adopted, effectively reduce reactive component and modal overlap, make each modal components contain the characteristic information of different time scales of primary signal, provide effective multiple dimensioned component for follow-up signal characteristic abstraction.And combine the features such as arrangement entropy calculates simply, noise resisting ability is strong, from each modal components middle (center) bearing fault signature of multiple dimensioned angle extraction.Compared to only bearing vibration substance being arranged entropy analysis, can more comprehensively characterize the characteristic information of signal based on multiple dimensioned arrangement entropy feature extracting method, improve the identification accuracy of support vector machine, better realize the fault diagnosis of rolling bearing.

Accompanying drawing explanation

Fig. 1 is the present invention Fault Diagnosis of Roller Bearings figure based on variation mode decomposition and arrangement entropy；

Fig. 2 is the normal bearing signal graph of the present invention；

Fig. 3 is inner ring fault-signal figure of the present invention；

Fig. 4 is outer ring fault-signal figure of the present invention；

Fig. 5 is rolling element fault-signal figure of the present invention；

Fig. 6 is rolling element fault-signal variation mode decomposition result figure of the present invention；

Fig. 7 is each modal components arrangement entropy vector meansigma methods figure of the present invention.

Detailed description of the invention

Time series randomness and kinetics sudden change feature can be detected, it is proposed to based on the Fault Diagnosis of Roller Bearings of variation mode decomposition and arrangement entropy in conjunction with the VMD advantage to signal decomposition and arrangement entropy.First original vibration signal is carried out VMD decomposition, obtain several intrinsic modal components, calculate the arrangement entropy of each modal components again, finally arrangement entropy is inputted support vector machine (SupportVectorMachine is called for short SVM) grader as characteristic vector and carry out failure modes identification.Based on variation mode decomposition and arrangement entropy rolling bearing fault diagnosis flow chart as it is shown in figure 1, specifically comprise the following steps that

(1) utilize acceleration transducer to measure bearing vibration signal, gather vibration signal under rolling bearing normal condition, inner ring fault, outer ring fault, rolling element malfunction, obtain the vibration data under each state.

(2) adopt variation mode decomposition VMD method that the vibration signal data under four kinds of states of bearing are decomposed, select suitable decomposition number to decompose to obtain and some have certain modal components with frequency, the data source enriched without modal overlap phenomenon and characteristic information is provided for follow-up feature extraction and failure modes identification.Wherein vibration signal is carried out variation mode decomposition to specifically include:

Bearing vibration signal f (t) is sought K mode function u_k(t) so that the estimation bandwidth sum of each mode is minimum, and each mode function sum is equal to the bearing vibration signal f (t) of input.To each mode function u_kT () carries out Hilbert conversion, obtain its analytic signal:

$\left(\mathrm{\&delta;}\right(t)+\frac{j}{\mathrm{\&pi;}t})*u_k\left(t\right)$

In formula, δ (t) is impulse function.Each mode analytic signal is mixed one and estimates mid frequencyBy each mode spectrum modulation to corresponding Base Band:

$\&lsqb;\left(\mathrm{\&delta;}\right(t)+\frac{j}{\mathrm{\&pi;}t})*u_k\left(t\right)\&rsqb;e^{-{\mathrm{j\&omega;}}_{k}t}$

Corresponding constraint variation model is as follows:

$\underset{\left\{u_k\right\},\left\{{\mathrm{\&omega;}}_k\right\}}{\min }\left\{\underset{k}{\&Sigma;}{||{\&part;}_t\&lsqb;\left(\mathrm{\&delta;}\right(t)+\frac{j}{\mathrm{\&pi;}t})*u_k\left(t\right)\&rsqb;e^{-{\mathrm{j\&omega;}}_{k}t}||}_2^2\right\}$

$s.t.\underset{k=1}{\overset{K}{\&Sigma;}}{u}_k=f$

In formula: { u_k}={ u₁, u₂..., u_KFor decomposing K the modal components obtained；{ω_k}={ ω₁, ω₂..., ω_KFor center frequency corresponding to each modal components.

For asking for the optimal solution of above-mentioned constraint variation problem, introduce the argument Lagrange function of following form, it may be assumed that

$\begin{array}{c}L\left(\right\{u_k\},\{{\mathrm{\&omega;}}_k\},\mathrm{\&lambda;})=\mathrm{\&alpha;}\underset{k=1}{\overset{K}{\&Sigma;}}{||{\&part;}_t\&lsqb;\left(\mathrm{\&delta;}\right(t)+\frac{j}{\mathrm{\&pi;}t})*u_k\left(t\right)\&rsqb;e^{-{\mathrm{j\&omega;}}_{k}t}||}_2^2+{||f\left(t\right)-\underset{k=1}{\overset{K}{\&Sigma;}}{u}_k\left(t\right)||}_2^2\\ +<\mathrm{\&lambda;}\left(t\right),f\left(t\right)-\underset{k=1}{\overset{K}{\&Sigma;}}{u}_k\left(t\right)>\end{array}$

In formula: α is punishment parameter；λ is equal to λ (t) for Lagrange multiplier.

Alternating direction multiplier method is utilized alternately to updateAnd λⁿ⁺¹Seek the optimal solution of variational problem, wherein subscriptⁿ⁺¹Represent (n+1)th iteration result of variable, thus bearing vibration signal being decomposed into K modal components.Detailed process is as follows:

1) initialize And n, in formula, ^ is the frequency domain representation utilizing Parseval/Plancherel Fourier's equilong transformation；

2) according to formula

${\hat{u}}_k^{n+1}\left(\mathrm{\&omega;}\right)=\left(\hat{f}\right(\mathrm{\&omega;})-\underset{i\&NotEqual;k}{\&Sigma;}{\hat{u}}_i(\mathrm{\&omega;})+\frac{\widehat{\mathrm{\&lambda;}}\left(\mathrm{\&omega;}\right)}{2})\frac{1}{1+2\mathrm{\&alpha;}{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_k)}^2}$

${\mathrm{\&omega;}}_k^{n+1}=\frac{{\&Integral;}_0^{\mathrm{\&infin;}}\mathrm{\&omega;}{\left|{\hat{u}}_k\left(\mathrm{\&omega;}\right)\right|}^{2}d\mathrm{\&omega;}}{{\&Integral;}_0^{\mathrm{\&infin;}}{\left|{\hat{u}}_k\left(\mathrm{\&omega;}\right)\right|}^{2}d\mathrm{\&omega;}}$

UpdateWithIn formula, ω is frequency variable；

3) update

${\widehat{\mathrm{\&lambda;}}}^{n+1}\left(\mathrm{\&omega;}\right)\&LeftArrow;{\widehat{\mathrm{\&lambda;}}}^n\left(\mathrm{\&omega;}\right)+\mathrm{\&tau;}\left(\hat{f}\right(\mathrm{\&omega;})-\underset{k}{\&Sigma;}{\hat{u}}_k^{n+1}(\mathrm{\&omega;}\left)\right)$

4) step (2) and (3) is repeated, until meeting iteration stopping conditionIn formula, ε > 0 is given discrimination precision, and end loop finally willBy inverse Fourier transform to time domain u_kT (), obtains K modal components u₁(t), u₂(t)…u_K(t)。

(3) calculate the arrangement entropy measure of each modal components complexity characteristics, and build high dimensional feature vector, using this vector fault diagnosis input vector as SVM.Arrangement entropy can detect signal randomness and kinetics catastrophic behavior, and is combined with VMD, and signal of rolling bearing analysis showing, normal condition, inner ring fault, outer ring fault and rolling element fault can effectively be identified by the method.

Calculate each modal components arrangement entropy to specifically include:

By bearing vibration signal is carried out VMD decomposition, the mode function u obtained_kT () is a time series { u_k(i), i=1,2 ..., N}, N is length of time series, it is carried out phase space reconfiguration, obtains matrix:

$\left[\begin{array}{cccc}{u}_k\left(1\right)& u_k(1+\mathrm{\&tau;})& \mathrm{...}& u_k(1+(m-1\left)\mathrm{\&tau;}\right)\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ u_k\left(j\right)& u_k(j+\mathrm{\&tau;})& \mathrm{...}& u_k(j+(m-1\left)\mathrm{\&tau;}\right)\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ u_k\left(G\right)& u_k(G+\mathrm{\&tau;})& \mathrm{...}& u_k(G+(m-1\left)\mathrm{\&tau;}\right)\end{array}\right]$

Wherein: m is Embedded dimensions；τ is time delay；G is reconstruct vector number, G=N-(m-1) τ in phase space reconstruction.

Jth in restructuring matrix is reconstructed component { u_k(j), u_k(j+ τ) ..., u_k(j+ (m-1) τ) } rearrange according to ascending order, it may be assumed that { u_k(i+(j₁-1)τ)≤u_k(i+(j₂-1)τ)≤…≤u_k(i+(j_m-1)τ)}.Wherein j₁, j₂..., j_mRepresent the index of each element column in reconstruct component.

Symbol sebolic addressing S (l)=[j of its element size order of a reflection can be obtained for any one the reconstruct vector in phase space reconstruction₁, j₂..., j_m], wherein l=1,2 ..., h, and h≤m！, m！Represent the factorial of m.Tectonic sequence P₁, P₂..., P_h, P_hIt it is the probability size of h kind symbol sebolic addressing appearance.

The arrangement entropy (PE) of each modal components, it is possible to try to achieve according to the form of Shannon entropy:

${\mathrm{PE}}_k\left(m\right)=-\underset{l=1}{\overset{h}{\&Sigma;}}{P}_{l}ln{P}_l$

By PE_kM () standardization, the arrangement entropy namely obtaining each mode function is PE_k=PE_k(m)/ln(m！).

Each modal components is tried to achieve arrangement entropy, builds high dimensional feature vector PE=[PE₁, PE₂…PE_K], in formula, K is the modal components number that vibration signal decomposes.

(4) the high dimensional feature vector obtained is inputted SVM to be trained, obtain the SVM diagnostic cast of each type fault.SVM classifier is trained by the method adopting " one-to-many ", and the rolling bearing under four kinds of states can obtain four two classification SVM models.

(5) bearing vibration signal to be measured is gathered, test sample high dimensional feature vector is built according to step (1), (2), (3), input the SVM diagnostic cast trained respectively, fault type and the duty of bearing is obtained, it is achieved the fault diagnosis of rolling bearing by the output result of SVM classifier.

Illustrate below by instance data, here the bearing vibration data acquisition rolling bearing data experiment Analysis of CWRU of U.S. electrical engineering laboratory.The rolling bearing selected is 6205-2RSJEMSKF type deep groove ball bearing, and vibration data sample frequency is 12kHz, motor load is 1HP.Test spark erosion technique arranges Single Point of Faliure on bearing, and the diameter of trouble point is 0.1778mm, and the fault degree of depth is 0.2794mm.Handy vibrating sensor gathers the vibration signal of normal condition, inner ring single-point galvanic corrosion, outer ring single-point galvanic corrosion and rolling element 4 kinds of states of single-point galvanic corrosion, four kinds of state bearing vibration signal time domain beamformer as shown in Fig. 2 to 5.

Every kind of bearing state signal is taken 40 groups of data, and data sample length is 2048, totally 160 groups of data.Randomly drawing the data of 25% from every kind of state sample data, namely 10 groups of data are as training sample, using remaining normal, each 30 groups of data of inner ring fault, outer ring fault, four kinds of state bearing vibration signal of rolling element fault as test sample.

Whole characteristic information principles according to avoiding modal overlap and stick signal determine decomposition number, 40 groups of training samples are carried out VMD decomposition, obtains the modal components of each bearing state.Wherein rolling element fault-signal being decomposed number is 4, and decomposition result is as shown in Figure 6.

Arrangement entropy parameter choose Embedded dimensions be 6 and time delay be 1, calculate each bearing state vibration signal arrangement entropy of each modal components after variation mode decomposition.The arrangement entropy of each modal components forms high dimensional feature vector, and the arrangement entropy feature vector meansigma methods of each modal components obtained is as shown in Figure 7.Training sample can form 40 high dimensional feature vectors altogether.

Using 40 characteristic vectors input quantity as support vector machine, input support vector machine is trained.SVM classifier is trained by the method adopting " one-to-many ".Constructing 4 two classification SVM, take the arrangement entropy feature vector under every kind of state successively as positive class, the arrangement entropy feature vector of three kinds of states of residue is as negative class, and input SVM classifier is trained, and obtains 4 SMV diagnostic casts trained.

The 120 groups of bearing vibration signal test data that will collect, carry out variation mode decomposition, calculated permutations entropy according to the method described above, build each modal components characteristic vector.Testing feature vector is inputted respectively 4 SVM diagnostic casts trained and carries out bearing failure diagnosis, table 1 rolling bearing test sample fault diagnosis result.Having an inner ring fault to be diagnosed as rolling element fault as can be seen from the table, two outer ring faults are diagnosed as inner ring fault.Its bearing is normal, the diagnosis discrimination of inner ring fault, outer ring fault, rolling element fault respectively 100%, 96.7%, 93.3% and 100%, and its average accuracy reaches 97.5%, it is seen that this diagnostic method can diagnose identification rolling bearing fault effectively.

Table 1

Diagnostic method feature:

1, VMD method is applied in bearing vibration signal analysis, it is possible to be the modal components with certain bandwidth frequency by signal decomposition, provides the data source abundant without modal overlap phenomenon and characteristic information for follow-up feature extraction and failure modes identification.

2, arrangement entropy can detect signal randomness and kinetics catastrophic behavior, and a kind of new method for diagnosing faults of proposition is combined with VMD, signal of rolling bearing analysis is shown, and normal condition, inner ring fault, outer ring fault and rolling element fault can effectively be identified by the method.

Claims (4)

1. the Fault Diagnosis of Roller Bearings based on variation mode decomposition and arrangement entropy, it is characterised in that specifically include following steps:

1) utilize acceleration transducer to measure bearing vibration signal, gather vibration signal under rolling bearing normal condition, inner ring fault, outer ring fault, rolling element malfunction, obtain the vibration data under each state；

2) adopt variation mode decomposition method that the vibration signal data under four kinds of states of bearing are decomposed, namely bearing vibration signal f (t) is sought K mode function u_k(t) so that the estimation bandwidth sum of each mode is minimum, and each mode function sum is equal to the bearing vibration signal of input；

3) to step 2) K mode function of gained bearing vibration signal, calculate the arrangement entropy measure of each modal components complexity characteristics, and build high dimensional feature vector, using this vector fault diagnosis input vector as SVM；

4) the high dimensional feature vector obtained is inputted support vector machines grader to be trained, obtain the SVM diagnostic cast of each type fault；

5) bearing vibration signal to be measured is gathered, according to step 1), 2), 3) build test sample high dimensional feature vector, input the SVM diagnostic cast trained respectively, fault type and the duty of bearing is obtained, it is achieved the fault diagnosis of rolling bearing by the output result of SVM classifier.

2. according to claim 1 based on the Fault Diagnosis of Roller Bearings of variation mode decomposition and arrangement entropy, it is characterized in that, described step 2) adopt variation mode decomposition method that the vibration signal data under four kinds of states of bearing are decomposed, specifically include following steps:

To each mode function u_kT () carries out Hilbert conversion, obtain its analytic signal:

$\left(\mathrm{\&delta;}\right(t)+\frac{j}{\mathrm{\&pi;}t})*u_k\left(t\right)$

In formula, δ (t) is impulse function, each mode analytic signal is mixed one and estimates mid frequencyBy each mode spectrum modulation to corresponding Base Band:

$\&lsqb;\left(\mathrm{\&delta;}\right(t)+\frac{j}{\mathrm{\&pi;}t})*u_k\left(t\right)\&rsqb;e^{-{\mathrm{j\&omega;}}_{k}t}$

Corresponding constraint variation model is as follows:

$\underset{\left\{u_k\right\},\left\{{\mathrm{\&omega;}}_k\right\}}{min}\left\{\underset{k}{\&Sigma;}\right||{\&part;}_t\&lsqb;\left(\mathrm{\&delta;}\right(t)+\frac{j}{\mathrm{\&pi;}t})*u_k\left(t\right)\&rsqb;e^{-{\mathrm{j\&omega;}}_{k}t}|{|}_2^2\}$

$s.t.\underset{k=1}{\overset{K}{\&Sigma;}}{u}_k=f$

In formula: { u_k}={ u₁, u₂..., u_KFor decomposing K the modal components obtained；{ω_k}={ ω₁, ω₂..., ω_KFor center frequency corresponding to each modal components；

For asking for the optimal solution of above-mentioned constraint variation problem, introduce the argument Lagrange function of following form, it may be assumed that

$\begin{array}{c}L\left(\right\{u_k\},\{{\mathrm{\&omega;}}_k\},\mathrm{\&lambda;})=\mathrm{\&alpha;}\underset{k=1}{\overset{K}{\&Sigma;}}\left|\right|{\&part;}_t\&lsqb;\left(\mathrm{\&delta;}\right(t)+\frac{j}{\mathrm{\&pi;}t})*u_k\left(t\right)\&rsqb;e^{-{\mathrm{j\&omega;}}_{k}t}|{|}_2^2+||f\left(t\right)-\underset{k=1}{\overset{K}{\&Sigma;}}{u}_k\left(t\right)|{|}_2^2\\ +<\mathrm{\&lambda;}\left(t\right),f\left(t\right)-\underset{k=1}{\overset{K}{\&Sigma;}}{u}_k\left(t\right)>\end{array}$

In formula: α is punishment parameter；λ is equal to λ (t) for Lagrange multiplier；

Alternating direction multiplier method is utilized alternately to updateAnd λⁿ⁺¹Seek the optimal solution of variational problem, wherein subscriptⁿ⁺¹Represent (n+1)th iteration result of variable, thus bearing vibration signal f (t) being decomposed into K modal components.

3. according to claim 2 based on the Fault Diagnosis of Roller Bearings of variation mode decomposition and arrangement entropy, it is characterised in that described utilize alternating direction multiplier method alternately to updateAnd λⁿ⁺¹The optimal solution seeking variational problem specifically comprises the following steps that

A: initialize And n, in formula, ^ is the frequency domain representation utilizing Parseval/Plancherel Fourier's equilong transformation；

B: according to formula

${\hat{u}}_k^{n+1}\left(\mathrm{\&omega;}\right)=\left(\hat{f}\right(\mathrm{\&omega;})-\underset{i\&NotEqual;k}{\&Sigma;}{\hat{u}}_i(\mathrm{\&omega;})+\frac{\widehat{\mathrm{\&lambda;}}\left(\mathrm{\&omega;}\right)}{2})\frac{1}{1+2\mathrm{\&alpha;}{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_k)}^2}$

${\mathrm{\&omega;}}_k^{n+1}=\frac{{\&Integral;}_0^{\mathrm{\&infin;}}\mathrm{\&omega;}{\left|{\hat{u}}_k\left(\mathrm{\&omega;}\right)\right|}^{2}d\mathrm{\&omega;}}{{\&Integral;}_0^{\mathrm{\&infin;}}{\left|{\hat{u}}_k\left(\mathrm{\&omega;}\right)\right|}^{2}d\mathrm{\&omega;}}$

UpdateWithIn formula, ω is frequency variable；

C: update

${\widehat{\mathrm{\&lambda;}}}^{n+1}\left(\mathrm{\&omega;}\right)\&LeftArrow;{\widehat{\mathrm{\&lambda;}}}^n\left(\mathrm{\&omega;}\right)+\mathrm{\&tau;}\left(\hat{f}\right(\mathrm{\&omega;})-\underset{k}{\&Sigma;}{\hat{u}}_k^{n+1}(\mathrm{\&omega;}\left)\right)$

D: repeat step B and C, until meeting iteration stopping conditionIn formula, ε > 0 is given discrimination precision, and end loop finally willBy inverse Fourier transform to time domain u_kT (), obtains K modal components u₁(t), u₂(t)…u_K(t)。

4. according to claim 1 based on the Fault Diagnosis of Roller Bearings of variation mode decomposition and arrangement entropy, it is characterized in that, described step 3) the arrangement entropy measure that calculates each modal components complexity characteristics specifically includes: by bearing vibration signal being carried out variation mode decomposition decomposition, the mode function u obtained_kT () is a time series { u_k(i), i=1,2 ..., N}, N is length of time series, it is carried out phase space reconfiguration, obtains matrix:

$\left[\begin{array}{cccc}{u}_k\left(1\right)& u_k(1+\mathrm{\&tau;})& \mathrm{...}& u_k(1+(m-1\left)\mathrm{\&tau;}\right)\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ u_k\left(j\right)& u_k(j+\mathrm{\&tau;})& \mathrm{...}& u_k(j+(m-1\left)\mathrm{\&tau;}\right)\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ u_k\left(G\right)& u_k(G+\mathrm{\&tau;})& \mathrm{...}& u_k(G+(m-1\left)\mathrm{\&tau;}\right)\end{array}\right]$

Wherein: m is Embedded dimensions；τ is time delay；G is reconstruct vector number, G=N-(m-1) τ in phase space reconstruction；

Jth in restructuring matrix is reconstructed component { u_k(j), u_k(j+ τ) ..., u_k(j+ (m-1) τ) } rearrange according to ascending order, it may be assumed that { u_k(i+(j₁-1)τ)≤u_k(i+(j₂-1)τ)≤…≤u_k(i+(j_m-1)τ)}.Wherein j₁, j₂..., j_mRepresent the index of each element column in reconstruct component；

Symbol sebolic addressing S (l)=[j of its element size order of a reflection can be obtained for any one the reconstruct vector in phase space reconstruction₁, j₂..., j_m], wherein l=1,2 ..., h, and h≤m！, m！Represent the factorial of m；Tectonic sequence P₁, P₂..., P_h, P_hIt it is the probability size of h kind symbol sebolic addressing appearance；

The arrangement entropy (PE) of each modal components, tries to achieve according to the form of Shannon entropy:

${\mathrm{PE}}_k\left(m\right)=-\underset{l=1}{\overset{h}{\&Sigma;}}{P}_{l}ln{P}_l$

By PE_kM () standardization, the arrangement entropy namely obtaining each mode function is PE_k=PE_k(m)/ln(m！)；

Each modal components is tried to achieve arrangement entropy, builds high dimensional feature vector PE=[PE₁, PE₂…PE_K], in formula, K is the modal components number that vibration signal decomposes.