CN108332970A - A kind of Method for Bearing Fault Diagnosis based on LS-SVM and D-S evidence theory - Google Patents
A kind of Method for Bearing Fault Diagnosis based on LS-SVM and D-S evidence theory Download PDFInfo
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Abstract
The invention discloses a kind of Method for Bearing Fault Diagnosis based on LS SVM and D S evidence theories.By multi-layer information fusion method, least square method supporting vector machine LS SVM are used in characteristic layer, D S evidence theories are used in decision-making level, to solve the problems, such as that single-sensor fault diagnosis precision is low, sensitive features are not easy to extract.The signal-to-noise ratio of bearing vibration signal is improved first with wavelet de-noising technology, and introduces time domain and frequency domain characteristic parameter of totally eight parameters as bear vibration.Secondly, fault identification is carried out to bearing using LS SVM.Finally, the output of LS SVM features is inputted as D S evidence theories, failure decision is carried out using D S evidence theories.This method can effectively improve rolling bearing fault diagnosis precision.The present invention has certain meaning to the reliability for improving rolling bearing fault diagnosis precision and diagnostic system.
Description
Technical field
The present invention relates to fault identification technical fields, and in particular to a kind of bearing based on LS-SVM and D-S evidence theory
Method for diagnosing faults.
Background technology
Important spare part of the rolling bearing as rotating machinery has in industries such as industry, agricultural, transports and widely answers
With operating status is directly related to the safety and efficiency of mechanical equipment.Rolling bearing under severe operating conditions, due to by
To the influence of the factors such as load, installation, lubrication, various types of failures will be will produce after operating a period of time.Therefore, the axis of rolling
Hold is that more the link of weakness, the method for diagnosing faults for studying rolling bearing are of great significance in rotating machinery.
In recent years, many methods are used for the fault detect of bearing, such as vibration signal detection, oil analysis detection, temperature
Detection, acoustic emission detection etc..It is most widely used, is summarized in rolling bearing fault diagnosis based on the method for analysis of vibration signal
Getting up can be divided into three classes：Time-domain analysis, frequency-domain analysis and time frequency analysis.These three methods are not independent from each other, but
It complementary can use in many instances.
Vibration signal for bearing failure diagnosis needs to be obtained by sensor.Since single-sensor is in signal acquisition
Limited on data bulk and type, once and sensor failure will be unable to obtain bearing state signal.Therefore, it utilizes
The operating status that multiple sensors detect bearing simultaneously can obtain more diagnostic messages, and improve the reliability of diagnosis.But
It is that random error is influenced in by the precision difference of different sensors and measurement, actual measuring signal may be far and expected
It is different.So the collected bearing information of multiple sensors, which is carried out fusion, can get higher diagnostic accuracy and reliability.
Multi-sensor information fusion is to combine data and relevant information from multiple sensors, is passed solely than single with obtaining
The more accurate reasoning in more detail of vertical sensor.The it is proposed of concept combined of multi-sensor information and application are the normal quilts in military field
In the case that expected analysis result can not directly give.With theoretical maturation and development, multi-sensor information fusion
It is widely used in the fields such as medical image, non-destructive testing, remote sensing and fault diagnosis.According to the source of data, information is melted
Conjunction can be divided into homologous information fusion (data are obtained by same class sensor) and non-homogeneous information merge (data are passed by different type
Sensor obtains).It can be divided into pixel-based fusion, feature-based fusion and decision level fusion, the fusion of different stage by function or structure
Method and syncretizing effect also differ.Data Layer, which merges common method, Kalman filter；Many sides of Feature-level fusion
Sources of law are from pattern classification and pattern-recognition, such as intelligent Neural Network；Decision-level fusion is based primarily upon Uncertainty Analysis Method, such as
Bayesian theory, D-S evidence theory, fuzzy decision.
Invention content
Based on background above technology, the present invention utilizes information fusion technology, provides a kind of feature based layer and decision-making level
Multi-layer Fault Diagnosis of Roller Bearings.First, the bearing vibration signal of acquisition is dropped by the method for wavelet de-noising
It makes an uproar processing, the characteristic parameter for introducing time domain and frequency domain is used to extract the feature of vibration signal；Secondly, using LS-SVM to not simultaneous interpretation
The characteristic parameter collection of sensor signal merges, and obtains fault identification result；Finally, defeated to LS-SVM features using D-S evidence theory
Go out to carry out Decision-level fusion, obtains final fault diagnosis result.
To achieve the goals above, the present invention uses following technical scheme：
A kind of Method for Bearing Fault Diagnosis based on LS-SVM and D-S evidence theory, which is characterized in that can be divided into following several
Part：
1) Signal Pretreatment：Acceleration transducer acquires the vibration signal of bearing, passes through the method pair of wavelet de-noising first
The vibration signal carries out noise reduction process, and then introduced feature parameter is used to extract the feature of vibration signal；The feature is joined
Number is normalized；
2) feature fusion：The characteristic parameter collection of different sensors signal is merged using LS-SVM, is obtained
Failure modes result；
3) decision-making level's information merges：Using D-S evidence theory, LS-SVM features are exported and carry out Decision-level fusion, are obtained
Final fault diagnosis result；
Wherein, the characteristic parameter includes：Time domain parameter and frequency domain parameter.
Specifically, the time domain parameter includes：Peak index KCF, pulse index KIF, nargin coefficient L and kurtosis index Ku；
The frequency domain parameter includes：Mean frequency value umf, center frequency ufc, frequency root-mean-square value urmsfWith frequency standard deviation ustdf；
Wherein：
Specifically, 2) described is specially partly：
S1, by after normalization time domain parameter and frequency domain parameter be respectively divided into training set and test set；
S2, it is trained using training set and respectively obtains LS-SVM graders；
S3, test set is predicted using LS-SVM graders；
S4, formula is utilizedThe time domain and frequency domain of LS-SVM is calculated
Posterior probability, obtain LS-SVM time domain posterior probability output and LS-SVM frequency domain posterior probability output；
Wherein pij(i|j；X) indicate that the binary classifier that the i-th class and jth class are constituted calculates the posteriority that gained x belongs to the i-th class
Probability.
Specifically, 3) is specially partly：The output of LS-SVM frequency domain posterior probability is defeated as the feature of D-S evidence theory
Enter, the fusion diagnosis result finally obtained.
Preferably, the vibration signal is acquired by being distributed in the PCB acceleration transducers of three different directions of bearing.
It is highly preferred that three different directions are respectively horizontal direction, vertical direction and axial direction.
Beneficial effects of the present invention
The present invention is directed to rolling bearing fault diagnosis present situation, it is proposed that is merged based on LS-SVM and D-S evidence theory information
Fault Diagnosis of Roller Bearings, and the multi-source vibration signal of rolling bearing is carried out based on high-speed EMUs transmission experiment platform
Convergence analysis.It is obtained from experimental result, the LS-SVM fault identification precision based on frequency domain character parameter, which is higher than, is based on temporal signatures
The LS-SVM fault identification precision of parameter.It is used as feature, input D-S cards by the fault signature recognition result for obtaining characteristic layer
According to theory, final decision-making level's fault diagnosis result is obtained.The results show that comprehensive by characteristic layer and decision-making level's information fusion
The fault diagnosis result arrived, the more single LS-SVM classification of accuracy have large increase.The present invention is to improving rolling bearing event
Barrier diagnostic accuracy and the reliability of diagnostic system have certain meaning.
Description of the drawings
Fig. 1 is the confidence interval of evidence theory；
Fig. 2 is high speed EMU transmission experiment platform of the present invention；
Fig. 3 is Troubleshooting Flowchart in the present invention.
Specific implementation mode
The present invention is specifically described below by embodiment, it is necessary to which indicated herein is that the present embodiment is served only for pair
The present invention is further described, and should not be understood as limiting the scope of the invention, and the person skilled in the art in the field can
To make some nonessential modifications and adaptations according to the content invented above.In the absence of conflict, the reality in the present invention
The feature applied in example and embodiment can be combined with each other.
1. least square method supporting vector machine (LS-SVM)：
Support vector machines (SVMs) is to be based on Statistical Learning Theory and structure by one kind of Vapnik and his colleague's exploitation
The machine learning method of risk minimization principle.With good generalization ability, and global optimum can be found when its training
Solution, thus be widely used in empirical modeling field.But the quadratic programming that the training of SVM is a belt restraining is asked
Topic, and constrain number and be equal to number of samples, this point causes the training time longer, may compare in certain situation numbers of samples
Greatly, at this moment the training time may be difficult to receive.Least square method supporting vector machine is to be improved to obtain in SVM, significantly
Solving speed is improved, has and is widely applied very much, its advantage is also embodied in complex industrial process.
LS-SVM is the improvement to standard SVM based on Regularization Theory, and quadratic loss function generation is used in object function
For the insensitive loss function in SVM, it converts the quadratic programming problem in SVM to Solving Linear, is ensureing precision
While greatly reduce computational complexity, accelerate solving speed.
If training sample set is (xi, yi)(xi∈Rn, yi∈R；I=1,2 ..., n), n is sample size, then regression function is
Y (X)=ωTX+b (1)
Wherein, X=(x1, x2..., xn) it is non-linear transform function, the sample in luv space is mapped to as height
Vector in dimension space；ω=(ω1, ω2..., ωn) it is weight coefficient；B is departure.
Principle (Structural Risk Minimization, SRM) is minimized based on structure, regression optimization problem can be with
It is described as solving following point：
And at the same time meeting
yi=＜ ω X ＞+b+ ξi (3)
Wherein c is penalty factor；ξiFor error variance；<·>For nuclear space mapping function.
Lagrange equations are introduced into above formula, obtaining least square method supporting vector machine decision function is
2.D-S evidence theories：
2.1 evidence theories are sketched
D-S evidence theory is uncertain, incomplete, Imprecise information the main means of processing, is obtained in information fusion field
Extensive approval and application are arrived.As the expansion of bayesian theory, D-S evidence theory is come using belief function and likelihood function
Quantify the uncertainty of evidence, it simulate the given uncertainty assumed or discussed be how the mistake accumulated in reasoning with evidence
It is reduced in journey.The D-S evidence theory most important be reasoning and decision can in or conflict inadequate in evidence into
Row[16]。
2.2D-S evidence theories basis
2.2.1 identification framework
If non-empty domain Θ indicates that all possible outcomes to problem θ to be solved are the finite aggregate that element is constituted, and
All elements in Θ are mutual exclusions two-by-two, then Θ is referred to as the identification framework of θ, i.e. Θ={ θ1, θ2..., θn}.Including Θ institutes
There is the collection of subset to be collectively referred to as the power set of Θ, the element for being denoted as Θ power sets is 2nIt is a.
2.2.2 basic reliability distribution function
2Θ={ φ, { θ1..., { θn..., { θ1, θ2, { θ1, θ3..., Θ (5)
If Θ is an identification framework, if function m：2Θ→ [0,1] meets following condition：
Then m is known as basic reliability distribution function (Basic Probability Assignment, BPA).
M (A) is degree of belief of the evidence as obtained from analysis to A.Basic reliability distribution function is as to obtained by
Data analysis or expert rule of thumb obtain.In D-S evidence theory, all trust values can be arbitrarily assigned to 2ΘIn
Any subset known then distributed as remaining trust value for ignorant subset without distributing its trust value by force
Each entire space Θ is as uncertain factor, as long as ensureing that all trust values obtain and are 1.This is in D-S evidence theory and probability
By most significant difference.
2.2.3 belief function and likelihood function
Belief function (Belief Function, Bel) is defined as follows：If 2Θ→ [0,1] meets following condition：
Then Bel is referred to as belief function, it indicates that the corresponding propositions of A are trusted as genuine degree.Since Bel (A) can only table
Show that proposition A be genuine trusting degree, so being only incomplete come the degree of belief for describing proposition with belief function.Therefore draw
Enter likelihood function and carrys out additional notes.
If the function Pl (Plausibility Function) on identification framework Θ：2Θ→ [0,1] meets following condition：
Then Pl is referred to as likelihood function, and reflection A corresponds to proposition degree not under a cloud.By formula (8) can release Bel (A)≤
Pl (A), this shows that, compared to likelihood function, belief function is more conservative.
2.2.4 confidence interval
D-S evidence theory generally builds the trust section to a certain proposition by belief function and likelihood function, to
The trusting degree of the proposition is described.The estimation range up and down that section [Bel (A), Pl (A)] gives proposition generation comes
Indicate the uncertainty measure to A.The confidence interval of evidence theory is as shown in Figure 1.
2.2.5 the rule of combination of evidence theory
If m1And m2It is two basic confidence levels under same identification framework Θ
Partition function, m1And m2Constructed by the information from two different information sources.According to Dempster Orthogonal Methods
Then, have：
Wherein
The size of K values reflects the conflict spectrum of evidence, and coefficient 1-K is known as normalization factor, its effect is to keep away
Exempt from that the probability of non-zero is assigned to empty set in synthesis.K values are bigger, and the conflict spectrum of evidence is higher, the information obtained after combination
It is fewer.
For multiple evidences can two evidence of analogy rule of combination.If there is n basic confidence levels under same identification framework Θ
Partition function m1, m2..., mn, conflict factor K can be given by：
Basic reliability distribution function m (A) after combination can be given by：
3 rolling bearing fault diagnosis based on information fusion
3.1 experimental provision
Present invention experiment is based on high-speed EMUs transmission experiment platform, as shown in Figure 2.It is dynamic that the experimental bench can be used for simulating certain type
The kind of drive of vehicle group EEF bogie and the fault diagnosis for carrying out the parts such as bearing, gear, motor, experimental bench is mainly by operating
Case, motor, gear-box, driving wheel, rail wheel, bearing and generating set at.
Control box have open/stop, emergency stop, speed governing and real-time parameter (including given speed, actual frequency, output speed, reality
Border pressure and actual current) display function.The parameter and working method of motor and gear-box simulate EMU completely；Rail wheel
Contact when simulating EMU operation between wheel track；Generator simulates resistance when EMU operation.
Experiment rolling bearing model 351306 used, shares three state, respectively：Normal bearing (N), outer ring failure
Bearing (O) and roller faulty bearings (R), bearing state definition are as shown in table 1.
Table 1. tests bearing state definition
3.2 fusion fault diagnosis frames
As shown in figure 3, the present invention is based on the diagnosing information fusion fault method of LS-SVM and D-S evidence theory can be divided into
Under several parts：
1. Signal Pretreatment：Noise reduction process is carried out to the vibration signal of acquisition by the method for wavelet de-noising first, then
Introduced feature parameter is used to extract the feature of vibration signal.
2. feature fusion：The characteristic parameter collection of different sensors signal is merged using LS-SVM, is obtained
Failure modes result.
3. decision-making level's information fusion：Using D-S evidence theory, LS-SVM features are exported and carry out Decision-level fusion, are obtained
Final fault diagnosis result.
It is longitudinal, axial and vertical to be directed to 3 kinds of different conditions bearings (normal, outer ring failure and inner ring failure) respectively first
3 sensors (sensor 1, sensor 2 and sensor 3), acquire 3 kinds of this 3 directions of bearing vibration signal (vibration signal 1,
Vibration signal 2 and vibration signal 3), to extracting 4 temporal signatures and 4 frequency domain characters after signal wavelet de-noising；Each direction
The characteristic value of different conditions bearing is respectively combined as time domain and frequency domain training set and test set, totally 6 pairs, is trained and surveys respectively
Examination obtains 6 groups of LS-SVM posterior probability outputs；Nicety of grading higher 3 is chosen from temporal signatures and frequency domain character by comparing
Input of the group as D-S evidence theory, by obtaining final fault diagnosis result after Decision-level fusion.
3.3 rolling bearing fault diagnosis
Experimental bench has chosen three kinds of states altogether close to the rolling bearing of motor side in the present embodiment, respectively normally, interior
Circle failure and roller failure are held as follow-up off-axis.Another side bearing is normal.Motor speed is 3000rpm, simulates certain type
Rotating speed when EMU 250km/h.The sample frequency of vibration signal is 8kHz, sampling number 40960.Three are held in follow-up off-axis
A different directions are respectively arranged a PCB acceleration transducer (356A16).Under 3 kinds of different bearing states, the biography in 3 directions
Sensor respectively acquires 6 groups of data, amounts to 54 groups of data.
Choosing has the characteristic parameter of higher faulty section indexing, establishes rolling bearing fault diagnosis model.The time domain of selection
Parameter is respectively peak index KCF, pulse index KIF, nargin coefficient L and kurtosis index Ku；Frequency domain parameter is respectively mean frequency value
umf, center frequency ufc, frequency root-mean-square value urmsfWith frequency standard deviation ustdf.As shown in table 2.
Because the definition of these parameters is different, these characteristic parameter collection are normalized.Time domain and frequency domain are each
54 groups of data.36 groups (12 groups of each state) are taken to be used as training set in 54 groups of data, remaining 18 groups are used as test set.Using not
Data with sensor are trained respectively, obtain 3 LS-SVM graders.
2. time domain of table, frequency domain parameter
The sigmoid functions that Platt is proposed, are mapped to [0,1] by the output f (x) of SVM, it is general to give two classification posteriority
Rate output form：
Posterior probability modeling for more classification problems, since the relatively effective methods of the LS-SVM exported firmly are " a pair of
One " algorithm obtains approximate posterior probability so being combined the result that multiple two classify using " ballot method ".
Ballot method determines that test sample x belongs to the posterior probability of the i-th class and is defined as
Wherein pij(i|j；X) indicate that the binary classifier that the i-th class and jth class are constituted calculates the posteriority that gained x belongs to the i-th class
Probability.
If one group of training sample can be separated by an optimal classification surface or Generalized optimal classifying face, for test specimens
The desired upper bound of this classification error rate is that the ratio that supporting vector average in training sample accounts for total number of training is：
Wherein N indicates training sample sum, E (nsv) indicate supporting vector number average value.
Two classification LS-SVM BPA be：
That employed in the present invention is the LS-SVM that classifies more, and the algorithm that can refer to two classification LS-SVM acquires BPA outputs.It is first
First the mean value of all kinds of supporting vectors is found out, the identification error upper bound is then obtained by formula (14), then added with the precision lower limit of SVM
The probability output of Platt is weighed, i.e.,
mi(x)=pi(1-E(Perror)) i=1,2 ... M (18)
mΘ=E (Perror) (19)
The posterior probability that the time domain and frequency domain of each LS-SVM are acquired by above formula, as shown in table 3, table 4.
From table 3 and table 4 as can be seen that in time domain and frequency domain character Parameter analysis, the failure for mistake all occur is known
Not, but the frequency of occurrences is less than time domain in frequency domain, this illustrates fault distinguish ability of the frequency domain character parameter than time domain charactreristic parameter
By force.Higher fault identification precision in order to obtain selects the fault identification result that frequency domain character parameter obtains to be managed as D-S evidences
The feature of opinion inputs.The results are shown in Table 5 for the fusion diagnosis finally obtained.
Table 3.LS-SVM time domain parameter classification results
Table 4.LS-SVM frequency domain parameter classification results
5. Decision-level fusion diagnostic result of table
It is obtained from experimental result, the LS-SVM fault identification precision based on frequency domain character parameter is higher than is joined based on temporal signatures
Several LS-SVM fault identification precision.It is used as feature by the fault signature recognition result for obtaining characteristic layer, inputs D-S evidences
Theory obtains final decision-making level's fault diagnosis result.The results show that being obtained by characteristic layer and decision-making level's information fusion synthesis
Fault diagnosis result, accuracy it is more single LS-SVM classification have large increase.
Obviously, described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.Based on this
Embodiment in invention, every other reality obtained by those of ordinary skill in the art without making creative efforts
Example is applied, the scope of the present invention is belonged to.
Claims (6)
1. a kind of Method for Bearing Fault Diagnosis based on LS-SVM and D-S evidence theory, which is characterized in that following a few portions can be divided into
Point：
1) Signal Pretreatment：Acceleration transducer acquires vibration signal, is believed first the vibration by the method for wavelet de-noising
Number noise reduction process is carried out, then introduced feature parameter is used to extract the feature of vibration signal；The characteristic parameter is subjected to normalizing
Change is handled；
2) feature fusion：The characteristic parameter collection of different sensors signal is merged using LS-SVM, must be out of order
Classification results；
3) decision-making level's information merges：Using D-S evidence theory, LS-SVM features are exported and carry out Decision-level fusion, obtained final
Fault diagnosis result；
Wherein, the characteristic parameter includes：Time domain parameter and frequency domain parameter.
2. the bearing failure diagnosis according to claim 1 based on LS-SVM and D-S evidence theory, which is characterized in that institute
Stating time domain parameter includes：Peak index KCF, pulse index KIF, nargin coefficient L and kurtosis index Ku；The frequency domain parameter includes：
Mean frequency value umf, center frequency ufc, frequency root-mean-square value urmsfWith frequency standard deviation ustdf；
Wherein：
3. the Method for Bearing Fault Diagnosis according to claim 1 based on LS-SVM and D-S evidence theory, feature exist
In 2) described is specially partly：
S1, by after normalization time domain parameter and frequency domain parameter be respectively divided into training set and test set；
S2, it is trained using training set and respectively obtains LS-SVM graders；
S3, test set is predicted using LS-SVM graders；
S4, formula is utilizedAfter time domain and the frequency domain of LS-SVM is calculated
Probability is tested, the output of LS-SVM time domain posterior probability and the output of LS-SVM frequency domain posterior probability are obtained；
Wherein pij(i|j；X) indicate binary classifier that the i-th class and jth class are constituted calculate gained x belong to the i-th class posteriority it is general
Rate.
4. the Method for Bearing Fault Diagnosis according to claim 3 based on LS-SVM and D-S evidence theory, feature exist
In 3) is specially partly：Feature by the output of LS-SVM frequency domain posterior probability as D-S evidence theory inputs, and finally obtains
Fusion diagnosis result.
5. the Method for Bearing Fault Diagnosis according to claim 1 based on LS-SVM and D-S evidence theory, feature exist
In the vibration signal is acquired by being distributed in the PCB acceleration transducers of three different directions of bearing.
6. the Method for Bearing Fault Diagnosis according to claim 5 based on LS-SVM and D-S evidence theory, feature exist
In three different directions are respectively horizontal direction, vertical direction and axial direction.
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