CN107368809B - A kind of bearing fault sorting technique based on rarefaction representation and dictionary learning - Google Patents
A kind of bearing fault sorting technique based on rarefaction representation and dictionary learning Download PDFInfo
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Abstract
The invention discloses a kind of bearing fault sorting technique based on rarefaction representation and dictionary learning, it is characterized in that carrying out as follows：The history bearing vibration signal of acquisition is pre-processed, obtains the vibration signal under different working condition, and builds corresponding sub- dictionary respectively, then each sub- dictionary is merged into a redundant dictionary；Using sensor online acquisition bearing vibration signal, sparse coefficient of the signal under redundant dictionary is acquired using generalized orthogonal matching pursuit algorithm, then realizes that vibration signal is classified by reconstructed error, so as to identify bearing working state.The present invention can obtain preferable classifying quality, accelerate the process of dictionary training, improve adaptability of the dictionary to echo signal, so as to the sparse decomposition for more efficiently realizing complex vibration signal and for fault identification.
Description
Technical field
The present invention relates to bearing vibration signal processing method fields, are specifically that one kind is based on rarefaction representation and dictionary
The bearing fault sorting technique of habit
Background technology
Bearing is one of machine components mostly important in rotating machinery, is widely used in electric power, chemical industry, metallurgy, aviation
Etc. each key areas, while bearing is also one of element for being easiest to damage.The quality of bearing performance and operating mode directly affects
To the performance of entire machine equipment, defect can cause equipment to generate abnormal vibrations and noise or even cause equipment damage.Cause
This, diagnoses rolling bearing fault, particularly important especially for the analysis of initial failure.In equipment vibrating signal
In gatherer process, the various symbiosis factors such as noise, signal modulation cause the redundancy of information, and the characteristic component of mechanical breakdown is often
It is showed in overall signal openness.Therefore, the feature extraction of vibration signal is substantially also an information redundance compression
Process.On this basis it is possible to the signal for extraction of seeking peace signal inside heterogeneity structure and details of morphology altimeter is sparse
Decomposition algorithm becomes research hotspot emerging in vibration signal characteristics extracting method.The rarefaction representation of signal is in mistake by signal
It is decomposed on complete dictionary, if the atom in dictionary is similar to the main component of signal, a small number of atoms is only needed, with regard to that can obtain
More accurate expression signal, decomposition result also will be sparse.Cannot be obtained if inappropriate dictionary is selected one it is good
Expression, this phenomenon is known as information and waters down, very unfavorable to subsequent analysis work.Therefore, seeking appropriate dictionary becomes
One of research focus of sparse representation theory.A kind of thinking is to consider the dictionary of the pre- structure of selection, such as DCT dictionaries, small echo dictionary
Deng during using this type dictionary, quickly, but their rarefaction power limitations are in designed signal for calculating speed, it is impossible to
For arbitrary interested new signal class.
In order to break this limitation, the method that researchers propose dictionary learning, from the relevant instruction of signal to be analyzed
Practice in sample and train dictionary, the potential internal structure of signal acquisition that this method can be adaptive, so as to preferably represent
Signal.
Aharon etc. proposes K-SVD algorithms, and the iteration that two processes are solved by dictionary updating and coefficient realizes dictionary
Study, but when the algorithm solves sparse coefficient using match tracing, each iteration chooses the atom of most related one in dictionary,
So that this method solve when than relatively time-consuming.
The content of the invention
In place of the present invention is overcomes the shortcomings of the prior art, a kind of axis based on rarefaction representation and dictionary learning is provided
Fault Classification is held, to which the process of dictionary training can be accelerated, adaptability of the dictionary to echo signal is improved, so as to higher
It realizes the sparse decomposition of complex vibration signal and for fault identification in effect ground.
In order to achieve the above object, the technical solution adopted in the present invention is：
A kind of the characteristics of bearing fault sorting technique based on rarefaction representation and dictionary learning of the present invention, comprises the following steps：
Step 1 is obtained comprising the training sample set Y={ Y corresponding to K class bearing fault-signals1,Y2,...,Yi,...,
YK, YiIt represents comprising the training sample set corresponding to the i-th class bearing fault-signal, and has： Represent j-th of training sample in the training sample set corresponding to the i-th class bearing fault-signal
This；1≤i≤K, 1≤j≤M；Each sample is the dimensional vector of H × 1；
Step 2, the method being combined using generalized orthogonal match tracing with K-SVD dictionary learnings are to comprising the i-th class bearing
Training sample set Y corresponding to fault-signaliIt is trained, obtains the dictionary D corresponding to the i-th class bearing fault-signali, institute
State i-th of dictionary DiDimension be H × N；And N ＞ H；Each column in dictionary is known as atom；
Step 2.1, using formula (1) establish i-th of dictionary DiTraining pattern：
In formula (1),ε tolerates parameter for error；
I-th step 2.2, random initializtion of dictionary Di；
Step 2.3, based on i-th of dictionary DiEstablish the rarefaction representation of j-th of training sample as shown in formula (2)
Object function；
In formula (2), λ represents Lagrange gene；
Step 2.4 solves formula (2) using generalized orthogonal matching pursuit algorithm, wherein each iteration chooses s atom, obtains
To the rarefaction representation of j-th of training sample corresponding to the i-th class bearing fault-signal
Step 2.5 repeats step 2.3- steps 2.4, obtains M experienced sample corresponding to the i-th class bearing fault-signal
Rarefaction representation Xi；
Step 2.6 updates i-th of dictionary D using formula (3)i：
In formula (3), | | | |FThe Frobenius norms of representing matrix；
Step 2.7 judgesIt is whether true, if so, it then represents to obtain the i-th class bearing fault-signal
Corresponding dictionary Di, and step 3 is performed, otherwise, by updated i-th of dictionary DiIt substitutes into step 2.3, and repeats
Step 2.3- steps 2.7；
Step 3 repeats step 2, so as to obtain the dictionary { D corresponding to K class bearing fault-signals1,D2,…,Di,…,
DK, and it is spliced into redundant dictionary D=[D1,D2,…,Di,…,DK]；
Step 4 obtains any one bearing signal as test signal y, and formula is solved using orthogonal matching pursuit algorithm
(4), sparse coefficient xs of the test signal y under redundant dictionary D is obtained, and is had
X=[x1,1,x1,2,...,x1,N,...,xi,1,xi,2,...,xi,N,...,xK,1,xK,2,...,xK,N]：
In formula (4), | | x | |0Represent the number of nonzero term in sparse coefficient x；
Step 5 calculates reconstructed error, and the identification that the corresponding fault category of Select Error value minimum is test signal y
As a result：
Step 5.1 obtains the test signal y in i-th of dictionary D using formula (5)iOn reconstruction signal
In formula (5), δi(x) it is a function, for i-th × N to i-th × N+N-1 element in sparse coefficient x to be taken
Go out, remaining element is set to zero, i.e.,：δi(x)=[0 ..., 0, xi,1,xi,2,...,xi,N,0,...,0]；
Step 5.2 obtains classification i belonging to the test signal y by the use of formula (6) as recognition result：
In formula (6), | | y-D δi(x)||2Represent reconstructed error.
Compared with the prior art, beneficial effects of the present invention are embodied in：
1st, the method that the present invention uses dictionary learning directly using the original vibration signal of rolling bearing as training set, saves
Complicated characteristic extraction procedure is removed；And dictionary is trained from the relevant training sample of signal to be analyzed, it can be adaptive
The potential internal structure of signal acquisition answered improves the expression ability of dictionary.
2nd, during generalized orthogonal matching pursuit algorithm is introduced into dictionary learning by the present invention, in each of match tracing
Suitable atomicity is selected in iteration, the time loss of dictionary training while dictionary quality is kept, can be reduced.
3rd, the present invention is using rarefaction representation sorting algorithm, by the sparse coefficient of echo signal on each sub- dictionary to original
The error that signal is reconstructed, classifies to signal, improves the performance of classification.
Description of the drawings
Fig. 1 is the method for the present invention flow diagram；
Fig. 2 a are inner ring fault vibration signal time-domain diagram used in present invention experiment；
Fig. 2 b are rolling element fault vibration signal time-domain diagram used in present invention experiment；
Fig. 2 c are 6 o'clock of outer ring position failure vibration signal time-domain diagram used in present invention experiment；
Fig. 2 d are 3 o'clock of outer ring position failure vibration signal time-domain diagram used in present invention experiment；
Fig. 2 e are 12 o'clock of outer ring position failure vibration signal time-domain diagram used in present invention experiment；
Fig. 2 f are vibration signal time-domain diagram under normal condition used in present invention experiment；
Fig. 3 a are sparse coefficient distribution map of the inner ring fault-signal in redundant dictionary；
Fig. 3 b are sparse coefficient distribution map of the rolling element fault-signal in redundant dictionary；
Fig. 3 c are sparse coefficient distribution map of the outer ring 6 o'clock position failure signal in redundant dictionary；
Fig. 3 d are sparse coefficient distribution map of the outer ring 3 o'clock position failure signal in redundant dictionary；
Fig. 3 e are sparse coefficient distribution map of the outer ring 12 o'clock position failure signal in redundant dictionary；
Fig. 3 f are sparse coefficient distribution map of the vibration signal in redundant dictionary under normal condition.
Specific embodiment
As shown in Figure 1, a kind of bearing fault sorting technique based on rarefaction representation and dictionary learning is the history to acquisition
Bearing vibration signal is pre-processed, and obtains the vibration signal under different working condition, and builds corresponding sub- dictionary respectively, then
Each sub- dictionary is merged into a redundant dictionary；Using sensor online acquisition bearing vibration signal, generalized orthogonal is used
Sparse coefficient of the signal under redundant dictionary is acquired with tracing algorithm, then realizes that vibration signal is classified by reconstructed error, from
And identify bearing working state；Specifically, it is to carry out as follows：
Step 1 is obtained from the historical failure vibration signal of bearing comprising the training sample corresponding to K class bearing fault-signals
This set Y={ Y1,Y2,...,Yi,...,YK, YiIt represents comprising the training sample set corresponding to the i-th class bearing fault-signal,
And have： It represents in the training sample set corresponding to the i-th class bearing fault-signal j-th
Training sample；1≤i≤K, 1≤j≤M；Each sample is the dimensional vector of H × 1；In Fig. 2 a- Fig. 2 f for rolling bearing in different operating modes
(rolling element failure, inner ring failure, normal, outer ring three position failure, outer ring six-o ' clock position failure, nine o'clock of outer ring position
Put failure) under vibration signal time-domain diagram, signal difference is more apparent, therefore vibration signal when can be rotated based on bearing
Its failure is identified in data.One of signal of the length for H=128 as inner ring failure can be intercepted in experiment
Sample；
Step 2, the method being combined using generalized orthogonal match tracing with K-SVD dictionary learnings are to comprising the i-th class bearing
Training sample set Y corresponding to fault-signaliIt is trained, i.e., uses generalized orthogonal in the rarefaction representation stage of dictionary learning
Matching pursuit algorithm solves sparse coefficient, updates dictionary atom using singular value decomposition in the dictionary updating stage；Obtain the i-th class axis
Hold the dictionary D corresponding to fault-signali, i-th of dictionary DiDimension be H × N；And N ＞ H；Each column in dictionary is known as original
Son；
Step 2.1, using formula (1) establish i-th of dictionary DiTraining pattern：
In formula (1),ε tolerates parameter for error；
I-th step 2.2, random initializtion of dictionary Di；
Step 2.3, based on i-th of dictionary DiEstablish the rarefaction representation of j-th of training sample as shown in formula (2)Mesh
Scalar functions；
In formula (2), λ represents Lagrange gene；
Step 2.4 solves formula (2) using generalized orthogonal matching pursuit algorithm, wherein each iteration chooses s atom, i.e.,
The related coefficient of the sample signal and each atom in dictionary, s atom of selection wherein coefficient maximum are asked, s can take 3 or 5；
Obtain the rarefaction representation of j-th of training sample corresponding to the i-th class bearing fault-signal
Step 2.5 repeats step 2.3- steps 2.4, obtains M experienced sample corresponding to the i-th class bearing fault-signal
Rarefaction representation Xi；
Step 2.6, the X acquired with previous stepiI-th of dictionary D is updated column by column using formula (3) for initial valuei：In update word
During the i-th row of allusion quotation, other each row are all fixed；
In formula (3), | | | |FThe Frobenius norms of representing matrix；
Step 2.7 judgesIt is whether true, if so, it then represents to obtain the i-th class bearing fault-signal
Corresponding dictionary Di, and step 3 is performed, otherwise, by updated i-th of dictionary DiIt substitutes into step 2.3, and repeats
Step 2.3- steps 2.7；
Step 3 repeats step 2, so as to obtain the dictionary { D corresponding to K class bearing fault-signals1,D2,…,Di,…,
DK, and it is spliced into redundant dictionary D=[D1,D2,…,Di,…,DK], this experiment is respectively for rolling bearing in different operating modes
(rolling element failure, inner ring failure, normal, outer ring three position failure, outer ring six-o ' clock position failure, nine o'clock of outer ring position
Put failure) under vibration signal, have trained six sub- dictionaries, dictionary is trained for off-line procedure, after the completion of training, exists afterwards
Line sorting phase is always maintained at constant；
Step 4, using vibrating sensor, obtain a bearing vibration signal as signal y to be analyzed, the length of signal and
Sample frequency will be consistent with the dictionary training stage, solved formula (4) using orthogonal matching pursuit algorithm, obtained signal y and exist
Sparse coefficient x under redundant dictionary D, and have
X=[x1,1,x1,2,...,x1,N,...,xi,1,xi,2,...,xi,N,...,xK,1,xK,2,...,xK,N]：
In formula (4), | | x | |0It represents the number of nonzero term in sparse coefficient x, is one section of rolling element failure as shown in Figure 3a
Sparse coefficient distribution map of the signal under dictionary D, the longitudinal axis are the size of coefficient value, and transverse axis is corresponding with dictionary columns；In experiment
Every sub- dictionary has 200 row, therefore dictionary D is 1200 row, wherein 1-200 dependents of dead military hero are in D1, i.e. rolling element fault-signal is corresponding
Dictionary；As can be seen from the figure 200 row before this sparse coefficient of inner ring fault-signal under dictionary D is mainly distributed on.Fig. 3 b, figure
3c, Fig. 3 d, Fig. 3 e, Fig. 3 f are respectively one section of inner ring failure, normal, outer ring three position failure, outer ring six-o ' clock position event
Barrier, sparse coefficient distribution map of the outer ring nine o'clock position failure signal under dictionary D, it can be seen that coefficient is also concentrated mainly on respectively
On self-corresponding dictionary position.
Step 5, the classification that signal can be substantially judged from the index profile of signal, in order to more accurately be divided
Class using only coefficient approximate representation original signal of the various types of signal on its generic dictionary, that is, calculates reconstructed error, and selects
The corresponding fault category of error amount minimum is the recognition result of test signal y：
Step 5.1 obtains test signal y in i-th of dictionary D using formula (5)iOn reconstruction signal
In formula (5), δi(x) it is a function, for i-th × N to i-th × N+N-1 element in sparse coefficient x to be taken
Go out, remaining element is set to zero, i.e.,：δi(x)=[0 ..., 0, xi,1,xi,2,...,xi,N, 0 ..., 0], i=1,2 ..., K；
Step 5.2 obtains classification i belonging to test signal y by the use of formula (6) as recognition result：
In formula (6), | | y-D δi(x)||2Represent reconstructed error.
The implementation result of bearing fault sorting technique based on rarefaction representation and dictionary learning：
Using the discrimination of test sample test various types of signal, the results are shown in Table 1, and average recognition rate reaches 95%.
Table 1
Claims (1)
1. a kind of bearing fault sorting technique based on rarefaction representation and dictionary learning, feature comprise the following steps：
Step 1 is obtained comprising the training sample set Y={ Y corresponding to K class bearing fault-signals1,Y2,...,Yi,...,YK,
YiIt represents comprising the training sample set corresponding to the i-th class bearing fault-signal, and has：
Represent j-th of training sample in the training sample set corresponding to the i-th class bearing fault-signal；1≤i≤K, 1≤j≤M；Each
Sample is the dimensional vector of H × 1；
Step 2, the method being combined using generalized orthogonal match tracing with K-SVD dictionary learnings are to comprising the i-th class bearing failure
Training sample set Y corresponding to signaliIt is trained, obtains the dictionary D corresponding to the i-th class bearing fault-signali, i-th of word
Allusion quotation DiDimension be H × N；And N ＞ H；Each column in dictionary is known as atom；
Step 2.1 establishes i-th of dictionary D using formula (1)iTraining pattern：
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In formula (6), | | y-D δi(x)||2Represent reconstructed error.
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