CN108446458B - A kind of Weighted Fusion rotor method for diagnosing faults based on DS evidence theory - Google Patents
A kind of Weighted Fusion rotor method for diagnosing faults based on DS evidence theory Download PDFInfo
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Abstract
The present invention is based on evidence theories, provide a kind of method of fault diagnosis, are related to fault diagnosis field.The present invention establishes triangle fuzzy model to each failure, triangle fuzzy model is established to testing data, Basic probability assignment function is generated according to overlapping degree between model to be measured and fault model, feature weight is generated according to similitude between fault model, the Basic probability assignment function Weighted Fusion generated under each feature is realized into fault diagnosis with evidence theory rule of combination and feature weight.Basic probability assignment function generation method proposed by the present invention, realizes the processing to fuzzy message well；Feature weight Weighted Fusion method proposed by the present invention, achieves preferable syncretizing effect；The fault diagnosis of rotor may be implemented in method for diagnosing faults proposed by the present invention.
Description
Technical field
The present invention relates to fault diagnosis fields, are a kind of methods for realizing fault diagnosis based on DS evidence theory.
Background technique
Fault diagnosis technology is one and combines closely and produce actual engineering science, is the product of modern production development.
With application of the modern science and technology in equipment, the structure of equipment becomes increasingly complex, and function is also more and more perfect, automates journey
It spends higher and higher, since many unavoidable factors influence, will lead to equipment and various failures occur, to reduce or lose pre-
Fixed function, or even will cause serious or even catastrophic accident.
Fault diagnosis technology is exactly to grasp the operation shape of equipment in equipment operation or in the case where not detaching equipment substantially
Condition is analyzed and processed according to the useful information acquired to diagnosed object test, judge diagnosed object state whether
In abnormality or malfunction.
Information fusion technology is collaboration using multi-source information, to obtain more objective to things or target, more essential understanding
Informix processing technique is one of the key technology of intelligence science research.In many Fusion Models and method, D-S card
It is maximally efficient one of algorithm according to theoretical algorithm.Evidence theory widens the space of elementary events in probability theory for elementary event
Power set, also known as framework of identification establishes Basic probability assignment function (Basic Probability on framework of identification
Assignment, BPA).In addition, evidence theory additionally provides a Dempster rule of combination, which can be in no elder generation
The fusion of evidence is realized in the case where testing information.Particularly, when BPA is only allocated in the list collection proposition of framework of identification
When, BPA is converted to the probability in probability theory, and the fusion results of rule of combination are identical as the Bayes formula in probability theory.From
From the point of view of this angle, DS evidence theory more effectively can indicate and handle uncertain information than probability theory, these features make it
It is widely used in information fusion field.Have in terms of uncertain knowledge expression just because of DS evidence theory excellent
Performance, so its theoretical and application development was very fast in recent years, the theory is in multi-sensor information fusion, medical diagnosis, military affairs
Important function has been played in terms of commander, target identification.
Evidence theory has many advantages, such as, is applied preferably handle in fault diagnosis and appears in device sensor
Uncertain information in signal.
Summary of the invention
In order to realize fault diagnosis, the present invention is based on DS evidence theories, provide a kind of method of rotor fault diagnosis.
The uncertain information in rotor sensor signal can be preferably handled using the fault diagnosis that this method is realized, accurately
Diagnosis is made to rotor failure.
The technical solution adopted by the present invention to solve the technical problems includes the following steps:
Step 1: the fault sample data D of input n kind failure, k kind featureij, i=1,2 ..., n, j=1,2 ..., k, institute
Stating fault signature can be used to do the feature of failure modes, and the fault sample data are the measured values of fault signature, to every
Kind every kind of feature of failure establishes Triangular Fuzzy Number model, and framework of identification is Θ={ F1,F2,...,Fn, the Triangular Fuzzy Number is
A fuzzy set on given domain U, refers to any x ∈ U have several μ (x) ∈ [0,1] to be corresponding to it, and μ (x) is known as
Subordinating degree function of the x to U, the method for the Triangular Fuzzy Number model foundation are as follows:
By failure Fi(i=1,2 ..., n) feature j sample data DijMinimum value minDij, mean value aveDijAnd maximum value
maxDijRespectively as failure FiThe minimum value of feature j Triangular Fuzzy Number model, mean value, maximum value, then failure FiThe three of feature j
Angle Fuzzy Math Model is
Step 2: rotor k kind feature sample to be tested data T to be measured is inputtedj, Triangular Fuzzy Number model is generated, it is described
The method of Triangular Fuzzy Number model foundation are as follows:
By feature j sample to be tested data TjMinimum value minTj, mean value aveTjAnd maximum value maxTjRespectively as to be measured
The minimum value of feature j Triangular Fuzzy Number model, mean value, maximum value, then the Triangular Fuzzy Number model of feature j to be measured be
Step 3: the Triangular Fuzzy Number model to be measured under feature j is generated substantially with failure Triangular Fuzzy Number Model Matching
Probability distribution function mj, the Basic probability assignment function is defined as belonging to any one the subset of Θ in evidence theory
A, m (A) ∈ [0,1], and meetThen m is 2ΘOn Basic probability assignment function, wherein 2ΘFor identification
The power set of frame,It is described substantially general
Rate partition function mjGeneration method are as follows:
It willWithIntersecting area withThe ratio of area under the curve is as corresponding single subset elements { FiReliability, willThe intersecting area of fuzzy number corresponding with the more a failures of feature j withThe ratio of area under the curve is as corresponding more subset elements
Reliability, single subset elements { FiRefer in step 1 and if only if the i-th (i ∈ that subset A includes in framework of identification Θ
[1, N]) a element, more subset elements refer to that subset A includes more than two elements, note in framework of identification Θ in step 1
The sum of reliability of above-mentioned generation is Sum, if Sum >=1, the reliability of above-mentioned generation is normalized, the method for normalizing are as follows:If Sum < 1, by mj{F1,F2,,FnIt is updated to mj{F1,F2,,Fn}+1-Sum；
Step 4: feature weight W is generated1,W2,…Wj, Weight generation method are as follows:
(1) each failure Triangular Fuzzy Number overlapping interval length between any two is found out under feature j, their sum is denoted as
CoverLengthj, the overlapping interval length calculation method are as follows: for two Triangular Fuzzy NumbersMinA, minB, maxA, maxB are arranged from big to small
Sequence, second largest and the third-largest difference is fuzzy number in ranking resultsOverlapping interval length；
(2) the sum of each failure Triangular Fuzzy Number siding-to-siding block length under feature j is found out, LengthSum is denoted asj；
(3) remember φj=CoverLengthj/LengthSumj, by 1- φ1,1-φ2,…,1-φkNormalization obtains spy
Levy weight, the method for normalizing are as follows:
Step 5: by the k BPA feature weight W of generation1,W2,…WjWeighted average obtains mA, i.e.,WhereinThen use evidence theory rule of combination by mAK-1 times, which is merged, with itself obtains mF,
The rule of combination of the evidence theory isWhereinm1,m2For
Two groups of BPA to be fused, m m1With m2Fused BPA, K m1,m2The conflict factor,
Step 6: step 5 is merged using Pignistic probability transformation method
mFBe converted to probability distribution P, the conversion method are as follows:Wherein
Step 7: diagnosis is made to rotor failure according to obtained probability distribution P, if P ({ Fi) in maximum probability
Greater than 0.5, then P ({ F is takeni) in the corresponding classification of maximum probability as rotor fault diagnosis result (otherwise it is assumed that nothing
Method makes diagnosis).
The beneficial effects of the present invention are the present invention to combine realization fault diagnosis with Triangular Fuzzy Number using evidence theory,
Have the advantages that calculate simple；Present invention Triangular Fuzzy Number models fault signature, solves the problems, such as the expression of fuzzy message；
Basic probability assignment function generation method proposed by the present invention, realizes the processing to fuzzy message well；The present invention proposes
Feature weight Weighted Fusion method, achieve preferable syncretizing effect；Method for diagnosing faults proposed by the present invention, may be implemented
The fault diagnosis of rotor.
Detailed description of the invention
The general flow chart that Fig. 1 present invention realizes.
Fig. 2 is failure F12 sample data D of feature12。
Fig. 3 is 2 testing data T of feature2。
Fig. 4 is the triangle fuzzy model to be measured of feature 2 and failure triangle fuzzy model.
Fig. 5 is the intersecting area of two fuzzy numbers.
Fig. 6 is the intersecting area of three fuzzy numbers.
Fig. 7 is the overlapping interval of two fuzzy numbers.
Specific embodiment
The present invention is further described with example with reference to the accompanying drawing.The example for providing rotor fault diagnosis herein,
Experimental data comes from [1].[1] three kinds of failures are provided in altogether, use F herein1,F2,F3It indicates, there are four types of characteristics for every kind of failure
According to respectively comprising five groups of data, every group of 40 observations.To the characteristic of each feature of every kind of failure, four groups are chosen as instruction
Practice sample and generates failure Triangular Fuzzy Number model.Choose failure F3The remaining one group of data of four features are said as test sample
The implementation steps of bright proposed method for diagnosing faults.
Step 1: the fault sample data D of three kinds of failures of input, four kinds of featuresij, i=1,2 ..., 3, j=1,2 ..., 4,
The fault signature can be used to do the feature of failure modes, and the fault sample data are the measured values of fault signature, right
Every kind of feature of every kind of failure establishes Triangular Fuzzy Number model, and framework of identification is Θ={ F1,F2,F3, the Triangular Fuzzy Number be to
The fuzzy set come to a conclusion on the U of domain, refers to any x ∈ U have several μ (x) ∈ [0,1] to be corresponding to it, μ (x) is known as x
To the subordinating degree function of U, the method for the Triangular Fuzzy Number model foundation are as follows:
We are with failure F12 Triangular Fuzzy Number of feature illustrates the method for failure Triangular Fuzzy Number model foundation for establishing,
Failure F12 characteristic of feature such as Fig. 2.By failure F12 sample data D of feature12Minimum value 0.1343, mean value 0.1481 and most
Big value 0.3468 is respectively as failure FiThe minimum value of feature j Triangular Fuzzy Number model, mean value, maximum value, then failure F1Feature 1
Triangular Fuzzy Number be
Step 2: 4 kinds of feature sample to be tested data T of rotor to be measured are inputtedj, Triangular Fuzzy Number model is generated, it is described
The method of Triangular Fuzzy Number model foundation are as follows:
We illustrate the method for Triangular Fuzzy Number model foundation to be measured by taking the foundation of the Triangular Fuzzy Number to be measured of feature 2 as an example, to
Survey 2 data of feature such as Fig. 3.By 2 sample to be tested data T of feature2Minimum value 0.3328, mean value 0.3511 and maximum value 0.3647
Respectively as the minimum value of 2 Triangular Fuzzy Number model of feature to be measured, mean value, maximum value, then the Triangular Fuzzy Number of feature 2 to be measured be
Step 3: the Triangular Fuzzy Number model to be measured under feature j is generated substantially with failure Triangular Fuzzy Number Model Matching
Probability distribution function mj, the Basic probability assignment function is defined as belonging to any one the subset of Θ in evidence theory
A, m (A) ∈ [0,1], and meetThen m is 2ΘOn Basic probability assignment function, wherein 2ΘFor identification
The power set of frame,It is described substantially general
Rate partition function mjGeneration method are as follows:
It willWithIntersecting area withThe ratio of area under the curve is as corresponding single subset elements { FiReliability, willWith the intersecting areas of the more a failure fuzzy numbers of feature j withLetter of the ratio of area under the curve as corresponding more subset elements
Degree, single subset elements { FiRefer in step 1 and if only if the i-th (i ∈ that subset A includes in framework of identification Θ
[1, N]) a element, more subset elements refer to that subset A includes more than two elements, note in framework of identification Θ in step 1
The sum of reliability of above-mentioned generation is Sum, if Sum >=1, the reliability of above-mentioned generation is normalized, the method for normalizing are as follows:If Sum < 1, by mj{F1,F2,,FnIt is updated to mj{F1,F2,,Fn}+1-Sum；
We are with m2Illustrate BPA generation method for generation:
(1) it calculatesArea under the curve S=(0.3647-0.3328) * 1/2=0.0319；
(2)m2({F1), m2({F2), m2({F3) generation:
It calculatesWithIntersecting areaThen
It calculatesWithIntersecting areaThen
It calculatesWithIntersecting areaThen
(3)m2({F1,F2), m2({F1,F3), m2({F2,F3), m2({F1,F2,F3) generation:
It calculatesWithIntersecting areaThen
It calculatesWithIntersecting areaThen
It calculatesWithIntersecting areaThen
It calculatesWithIntersecting areaThen
(4) the sum of reliability of above-mentioned generation Sum=0.9382, therefore update m2({F1,F2,F3)=0+1-Sum=
0.0824。
M is produced with same method1,m3,m4, it is as a result as follows:
m1({F1)=0, m1({F2)=0, m1({F3)=0.9998, m1({F1,F2)=0, m1({F1,F3)=0, m1
({F2,F3)=0, m1({F1,F2,F3)=0.0002；
m3({F1)=0.0135, m3({F2)=0, m3({F3)=0.9649, m3({F1,F2)=0, m3({F1,F3})
=0.0135, m3({F2,F3)=0, m3({F1,F2,F3)=0.0081；
m4({F1)=0, m4({F2)=0, m4({F3)=0.5487, m4({F1,F2)=0, m4({F1,F3)=0, m4
({F2,F3)=0, m4({F1,F2,F3)=0.4513；
Step 4: feature weight W is generated1,W2,…Wj, Weight generation method are as follows:
(1) each failure Triangular Fuzzy Number overlapping interval length between any two is found out under feature j, their sum is denoted as
CoverLengthj, the overlapping interval length calculation method are as follows: for two Triangular Fuzzy NumbersMinA, minB, maxA, maxB are arranged from big to small
Sequence, second largest and the third-largest difference is fuzzy number in ranking resultsOverlapping interval length；
(2) the sum of each failure Triangular Fuzzy Number siding-to-siding block length under feature j is found out, LengthSum is denoted asj；
(3) remember φj=CoverLengthj/LengthSumj, by 1- φ1,1-φ2,…,1-φkNormalization obtains spy
Levy weight, the method for normalizing are as follows:
We are with W2Generation for illustrate feature weight generation method:
(1) each failure Triangular Fuzzy Number overlapping interval length between any two is found out under feature 2, their sum is denoted as
Length2,WithOverlapping interval length is 0.0397,WithOverlapping interval length is 0.0436,WithOverlay region
Between length be 0.0667, they and be 0.15, therefore Length2=0.15；
(2) the sum of each failure Triangular Fuzzy Number siding-to-siding block length under feature 2 is found out,Siding-to-siding block length is 0.3468-0.1343
=0.2125,Siding-to-siding block length is 0.3507-0.3071=0.0436,Siding-to-siding block length is 0.3616-0.2801=
0.0815, they and be 0.3376, therefore LengthSum2It is 0.3376；
(3) remember φj=CoverLengthj/LengthSumj, by 1- φ1,1-φ2,1-φ3,1-φ4Normalization obtains
Feature weight, the method for normalizing are as follows:
Finally obtained feature weight is W1=0.2440, W2=0.1703, W3=0.2984, W4=0.2873；
Step 5: by 4 BPA feature weight W of generation1,W2,W3,W4Weighted average obtains mA, i.e.,WhereinThen use evidence theory rule of combination by mAK-1 times, which is merged, with itself obtains mF,
The rule of combination of the evidence theory isWhereinm1,m2For
Two groups of BPA to be fused, m m1With m2Fused BPA, K m1,m2The conflict factor,
By 4 BPA feature weight W of generationjWeighted average obtains mA, as a result are as follows: mA({F1)=0.0075, mA
({F2)=0.0303, mA({F3)=0.7747, mA({F1,F2)=0.0035, mA({F1,F3)=0.0075, mA({F2,
F3)=0.0303, mA({F1,F2,F3)=0.1462；
With evidence theory rule of combination by mA3 times are merged with itself obtains mF, fusion results are as follows: mF({F1)=0.0002,
mF({F2)=0.0011, mF({F3)=0.9974, mF({F1,F2)=0, mF({F1,F3)=0.0001, mF({F2,F3})
=0.0006, mF({F1,F2,F3)=0.0006；
Step 6: step 5 is merged using Pignistic probability transformation method
mFBe converted to probability distribution P, the conversion method are as follows:Wherein
Step 7: diagnosis is made to rotor failure according to obtained probability distribution P, if P ({ Fi) in maximum probability
Greater than 0.5, then P ({ F is takeni) in the corresponding classification of maximum probability as rotor fault diagnosis result, otherwise it is assumed that nothing
Method makes diagnosis；
Maximum probability is P ({ F in probability distribution P3) and P ({ F3) > 0.5, therefore rotor failure is diagnosed as F3, with
True fault type is consistent.
Bibliography
[1] Wen Chenglin, Xu Xiaobin multi-source uncertain information blending theory and application [M] Science Press, 2012.
Claims (1)
1. a kind of Weighted Fusion rotor method for diagnosing faults based on DS evidence theory, it is characterised in that first according to input
Fault sample data establish failure Triangular Fuzzy Number model, establish Triangular Fuzzy Number to be measured according to input sample to be tested data later
Then sample to be tested Triangular Fuzzy Number model and failure Triangular Fuzzy Number model are carried out Model Matching and generate BPA, root by model
Feature weight is generated according to similitude between fault model, finally with the BPA generated under each feature of feature weight Weighted Fusion, and according to
Fusion results diagnose fault type；Wherein, include the following steps:
Step 1: the fault sample data D of input n kind failure, k kind featureij, i=1,2 ..., n, j=1,2 ..., k, the event
Barrier feature can be used to do the feature of failure modes, and the fault sample data are the measured values of fault signature, to every kind of event
Hinder every kind of feature and establish Triangular Fuzzy Number model, framework of identification is Θ={ F1,F2,...,Fn, the Triangular Fuzzy Number is given
A fuzzy set on domain U, refers to any x ∈ U, has several μ (x) ∈ [0,1] to be corresponding to it, μ (x) is known as x to U
Subordinating degree function, the method for the Triangular Fuzzy Number model foundation are as follows:
By failure FiFeature j sample data DijMinimum value minDij, mean value aveDijAnd maximum value maxDijRespectively as failure Fi
The minimum value of feature j Triangular Fuzzy Number model, mean value, maximum value, then failure FiThe Triangular Fuzzy Number model of feature j is
Step 2: rotor k kind feature sample to be tested data T to be measured is inputtedj, generate Triangular Fuzzy Number model, the Triangle Module
Paste the method that exponential model is established are as follows:
By feature j sample to be tested data TjMinimum value minTj, mean value aveTjAnd maximum value maxTjRespectively as feature j to be measured
The minimum value of Triangular Fuzzy Number model, mean value, maximum value, then the Triangular Fuzzy Number model of feature j to be measured be
Step 3: by the Triangular Fuzzy Number model to be measured and failure Triangular Fuzzy Number Model Matching generation elementary probability under feature j
Partition function mj, the Basic probability assignment function is defined as belonging to any one the subset A, m of Θ in evidence theory
(A) [0,1] ∈, and meetThen m is 2ΘOn Basic probability assignment function, wherein 2ΘTo recognize frame
The power set of frame,The elementary probability
Partition function mjGeneration method are as follows:
It willWithIntersecting area withThe ratio of area under the curve is as corresponding single subset elements { FiReliability, willWith
The more a failures of feature j correspond to the intersecting area of fuzzy number withLetter of the ratio of area under the curve as corresponding more subset elements
Degree, single subset elements { FiRefer in step 1 and if only if the i-th (i ∈ that subset A includes in framework of identification Θ
[1, N]) a element, more subset elements refer to that subset A includes more than two elements, note in framework of identification Θ in step 1
The sum of reliability of above-mentioned generation is Sum, if Sum >=1, the reliability of above-mentioned generation is normalized, the method for normalizing are as follows:If Sum < 1, by mj{F1,F2,…,FnIt is updated to mj{F1,F2,…,Fn}+1-Sum；
Step 4: feature weight W is generated1,W2,…Wj, Weight generation method are as follows:
(1) each failure Triangular Fuzzy Number overlapping interval length between any two is found out under feature j, their sum is denoted as
CoverLengthj, the overlapping interval length calculation method are as follows: for two Triangular Fuzzy NumbersMinA, minB, maxA, maxB are arranged from big to small
Sequence, second largest and the third-largest difference is fuzzy number in ranking resultsOverlapping interval length；
(2) the sum of each failure Triangular Fuzzy Number siding-to-siding block length under feature j is found out, LengthSum is denoted asj；
(3) remember φj=CoverLengthj/LengthSumj, by 1- φ1,1-φ2,…,1-φkNormalization obtains feature power
Weight, the method for normalizing are as follows:
Step 5: by the k BPA feature weight W of generation1,W2,…WjWeighted average obtains mA, i.e.,WhereinThen use evidence theory rule of combination by mAK-1 times, which is merged, with itself obtains mF,
The rule of combination of the evidence theory isWhereinm1,m2For
Two groups of BPA to be fused, m m1With m2Fused BPA, K m1,m2The conflict factor,
Step 6: the m for being merged step 5 using Pignistic probability transformation methodFTurn
It is changed to probability distribution P, the conversion method are as follows:Wherein
Step 7: diagnosis is made to rotor failure according to obtained probability distribution P, if P ({ Fi) in maximum probability be greater than
0.5, then take P ({ Fi) in the corresponding classification of maximum probability as rotor fault diagnosis result, otherwise it is assumed that can not do
It diagnoses out.
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