CN110146279A - A kind of marine shafting imbalance fault diagnostic method based on vector evidential reasoning - Google Patents

A kind of marine shafting imbalance fault diagnostic method based on vector evidential reasoning Download PDF

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CN110146279A
CN110146279A CN201910423412.9A CN201910423412A CN110146279A CN 110146279 A CN110146279 A CN 110146279A CN 201910423412 A CN201910423412 A CN 201910423412A CN 110146279 A CN110146279 A CN 110146279A
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CN110146279B (en
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徐晓滨
叶梓发
方丹枫
高海波
高迪驹
侯平智
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Hangzhou Dianzi University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/02—Gearings; Transmission mechanisms
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/02—Gearings; Transmission mechanisms
    • G01M13/028—Acoustic or vibration analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/08—Feature extraction
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/12—Classification; Matching

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Abstract

The present invention relates to a kind of marine shafting imbalance fault diagnostic method based on vector evidential reasoning.The present invention is combined main variables according to contribution rate size, and the input feature vector variable after combination forms input vector；Comprehensive similarity of the fault sample about input vector and output irregularity fault reference grade is obtained using qualitative information conversion method, and constructs reflection input reference vector and exports the cultellation statistical form of fault relationship；The corresponding diagnostic evidence of each reference vector is obtained according to the table, constructs vector evidence matrix table；The reliability and evidence weight of input vector can be obtained according to the contribution rate of input main variables；The evidence for obtaining each group of input sample vector of sample set, obtains fusion results using evidential reasoning rule, therefrom reasoning obtains marine shafting unbalanced system fault level.The present invention can form on-line monitoring system with hardware such as combination sensor, data collectors, realize the real-time state monitoring and fault diagnosis of marine shafting bearing mechanical equipment.

Description

A kind of marine shafting imbalance fault diagnostic method based on vector evidential reasoning
Technical field
The invention belongs to marine mechanical equipment state-detections and fault diagnosis technology field, are related to a kind of based on vector evidence The marine shafting imbalance fault diagnostic method of reasoning.
Background technique
Marine propulsion shafting mainly realizes the energy transmission between host and propeller, while again rotating propeller and generating Axial thrust hull is passed to by shafting, push ship to advance, it is the important component of Ship Power Equipment.With Requirement to ocean carrying capacity is gradually increased, and the length and span of large ship shafting constantly increase.Since shafting cannot be considered as The rigid body of one rotation has certain elasticity and inertia, therefore shafting inevitably twists vibration and transverse-vibration It is dynamic, in addition stress is sufficiently complex when its operating, it is easy to because fatigue leads to the generation of accident.Therefore the status monitoring of shaft It is highly important for the transport by sea for guaranteeing steady safety with fault diagnosis.
For rotating machinery as such as large ship shafting, it can arrange that vibration passes in its each key position Sensor acquires the vibration signal of equipment, and the fault characteristic information extracted from these vibration signals can reflect the various of equipment Failure.Two problems are faced at this time, first is that needing to find a kind of simple and easy mode in engineering, to the failure of a large amount of multidimensional Feature monitoring data are analyzed and processed, so that its diagnostic evidence provided is objective credible；Second is that how to realize that fault signature is believed The synthesis of breath.Usually using single sensor provide characteristic information cannot completely consersion unit failure, need multiple sensings The information that device provides is merged to promote the precision of diagnosis.
Summary of the invention
The purpose of the present invention is to propose to a kind of marine shafting imbalance fault diagnostic method based on vector evidential reasoning leads to It crosses and vibration displacement sensor is installed on the pedestal and bracket of marine shafting propulsion system to acquire fault characteristic information, and utilize Principal component analysis (PCA) method carries out feature extraction to these information, then constructs input feature value, then based on input reference Vector counts the likelihood reliability that each failure occurs from fault signature data and obtains input vector evidence matrix, then conclusion evidence Reliability factor and weight, finally using the evidence of evidential reasoning rule fusion input sample vector activation, and according to fusion As a result fault mode is determined.The shortcomings that the method overcome single source fault characteristic information diagnostic techniques, and greatly reduce input Amount, at low cost, precision is high, and realizes the real-time detection and Precise Diagnosis of failure.
The present invention mention the following steps are included:
(1) marine shafting bearing imbalance fault set Θ={ Y is set1,…,Yn,…,YN, YnRepresenting fault set Θ In n-th of imbalance fault grade, n=1,2 ..., N, N be fault level number；If being mounted on marine shafting bearing equipotential The time domain vibration acceleration signal sequence that the 4 vibration displacement sensors set obtain position is respectively S1(t),S2(t), S3(t),S4(t), n times are acquired respectively under every kind of imbalance fault grade, are acquired T=N*n times, sampling instant t=1 altogether, 2 ..., T, between double sampling between be divided into 0.8ms.
(2) the time-domain signal sequence S of acquisition will be sampled every time in step (1)1(t),S2(t),S3(t),S4(t) it carries out fast Fast Fourier transformation obtains corresponding frequency domain sequence signal, by 1 frequency multiplication (1X), 2 frequencys multiplication (2X) and 3 times in each spectrum sequence Frequently the vibration amplitude of (3X) can extract 3 fault signature variables, amount in t moment as fault signature variable, each sensor P=3*4=12 characteristic variable can be obtained, x is denoted as1(t),…xp(t),…xP(t), p=1 ..., P；By { x1(t),…xp (t),…x12(t) } it is expressed as sample set X={ x (t) | t=1,2 ..., T }, wherein x (t)=[x1(t),…xp(t),…x12 It (t)] is a feature samples vector.
(3) the 12 dimension primitive character sample set X for obtaining sampling in step (2) are carried out by principal component analysis (PCA) method Feature extraction, detailed process is as follows:
Operation, the matrix form for being first expressed as X is normalized to sample set X in (3-1)
Using formula (1) to each element x in matrixp(t) it is normalized
WhereinAnd σpRespectively xp(t) mean value and standard deviation, calculation method are
The matrix obtained after step (3-1) normalization is denoted as by (3-2)
Then it asks againCovariance matrix
(3-3) carries out Eigenvalues Decomposition to covariance matrix V, seeks eigenvalue λpWith corresponding feature vector ωp, to spy Value indicative λpDescending arrangement is carried out, calculates the corresponding characteristic value of p-th of principal component in the sum of All Eigenvalues of covariance matrix V Shared specific gravity, i.e. contribution rate, contribution rate is bigger, illustrates that the ability of the comprehensive former indication information of the principal component is stronger, contribution rate meter Calculating formula is
(3-4) calculates accumulative variance contribution ratio size, the sum of the characteristic value of d < 12 principal component before contribution rate of accumulative total indicates The shared specific gravity in All Eigenvalues summation, this ratio is bigger, and d principal component can more represent initial data comprehensively before illustrating The information having, calculation formula are
As accumulative variance contribution ratio Md>=0.95, determine the value of d, corresponding preceding d characteristic value Λ=diag [λ1, λ2,...,λd] and corresponding characteristic vector Wd=[ω1,ω2,...,ωd] base as subspace, then the d principal component extracted For
Note main variables collection is combined into F={ fi| i=1 ..., d }, wherein main variables fi=[fi(1),fi(2),…, fi(T)]T, superscript notation " T " expression vector transposition.
(4) vector matrix is constructed, establishing input is main variables vector fiWith output irregularity fault level YnBetween Mapping relations, the specific steps are as follows:
(4-1) definition input main variables fiReference value setWhereinAnd WithRespectively fiMinimum value and maximum value, J fiReference value number；Take imbalance fault mode It is denoted as y (t), y (t) ∈ Θ, result reference set Y=Θ is set, by fi(t) and y (t) is expressed as sample set S={ [fi(t), Y (t)] }, wherein [fi(t), y (t)] be a tape jam label fault sample vector.
(4-2) can be obtained according to step (3), input main variables fiCorresponding contribution rate isContribution rate is according to descending Arrangement, whereinAnd f1Contribution rate it is maximum, thus can be according to contribution rate to input main variables fiIt is combined, Input feature vector signal after combination constitutes the form of vector, as follows
Wherein K indicates the total number of input vector, and K ∈ [3,4], h are the number of the input f of each vector of composition, for Input vector { Rk| k=1,2 ..., K }, corresponding reference vector collection is combined intoWherein
It is { R that input vector, which can be obtained, by step (4-2) in (4-3)1(t),…,Rk(t),…,RK(t) }, it is expressed as sample This vector set U={ [R1(t),…,Rk(t),…,RK(t)] | t=1,2 ..., T }, by T sample vector [Rk(t),y(t)] In sample to (Rk(t), y (t)) it is respectively the form about reference vector similarity, tool with the variation of qualitative information conversion method Steps are as follows for body:
(4-3-1) sample is to (Rk(t), y (t)) input vector Rk(t) reference vector is matchedSimilarity distribution are as follows:
Wherein βk,jIndicate input vector Rk(t) j-th of reference vector is matchedSimilarity, calculation method is as follows:
WhereinThen indicate input vector Rk(t) and reference vectorMatching degree.
(4-3-2) according to step (4-3-1), sample is to (Rk(t), y (t)) it is converted into the form of similarity distribution (βk,1,...,βk,J), wherein βk,jIndicate sample to (Rk(t), y (t)) in input vector match reference vectorResult simultaneously Value is YnSimilarity.
(4-3-3) is similar to being converted by all samples in sample set U according to step (4-3-1) and step (4-3-2) The form of degree can construct all samples to the statistical form for carrying out cultellation in the form of similarity with them, and table 1 gives sample pair (R1(t), y (t)) cultellation statistical form, wherein an,jIndicate all input vector R1(t) reference vectors are matchedAnd failure Type is YnSample to (R1(t), y (t)) comprehensive similarity sum, other samples are to (Rk(t), y (t)) cultellation statistical form It is similar with the table, it can be obtained by same procedure；
1 sample of table is to (R1(t), y (t)) cultellation statistical form
(4-4) constructs vector matrix, according to the cultellation statistical form in step (4-3), can get and works as input vector Rk(t) it takes Reference vectorWhen, end value y (t) is reference value YnReliability are as follows:
Wherein,Indicate all end value y (t) matching reference value YnSample to the sum of comprehensive similarity, AndAnd haveIt then can define and correspond to reference vectorEvidence be
Therefore, evidence matrix table can be constructed to describe input vector RkRelationship between result y, provides input vector R1Evidence matrix it is as shown in table 2
2 input vector R of table1Evidence matrix table
Other input vectors RkEvidence matrix table it is similar with the table, can be obtained by the above method.
(5) the reliability r of evidence is definedkThe input vector R of description input information source compositionkJudge imbalance fault type Ability；Define the weight w of evidencekEvidence e is describedkCompared to the relative importance of other evidences, the specific steps are as follows:
(5-1) is by the contribution rate of each principal component obtained in step (3)It is normalized
IfFor each input feature vector variable fiReliability, then input vector RkReliability are as follows:
(5-2) sets evidence ekWeight wkEqual to corresponding reliability rk, this is because the higher evidence of reliability ought to It is corresponding with higher evidence weight.
(6) after obtaining one group of sample data x (t) online, the evidence in vector evidence matrix is activated, and these are activated Evidence utilizes the fusion of evidential reasoning (ER) rule, the specific steps are as follows:
(6-1) utilizes step (3) sample x (t)=[x1(t),…xp(t),…x12(t)] pivot variable obtains pivot change Duration set F={ fi| i=1 ..., d }, input feature value R is obtained further according to step (4-2)k。
(6-2) is for input vector Rk(t), all reference vectors will be activatedCorresponding evidenceThen input Rk(t) Evidence can be by reference vector evidenceIt is obtained in the form of weighted sum
ek={ (Yn,pn,k), n=1 ..., N } (12a)
(6-3) obtains input vector R using formula (12a) and formula (12b)k(t) evidence { ek| k=1 ..., K }, and set Initial evidence weight wk=rk, they are merged using evidential reasoning rule, obtaining fusion results is
O(Rk)={ (Yn,pn,e(K)), n=1 ..., N } (13a)
Wherein formula (13b)It is to be recursively obtaining by following evidential reasoning fusion rule
M in formula (14a)n,e(k-1)With MP(Θ),e(k-1)It is obtained respectively by formula (14b) and formula (14c)
Mk={ (Yn,Mn,k), k=1 ..., K (14d)
M in formula (14d)kIndicate input RkThe reliability of acquisition, wherein Mn,k=wkpn,k, pn,kIt can be acquired by formula (12b).
(7) K evidence fusion result can be acquired with iteration as O (R by the evidence fusion rule of step (6)k(t))= {(Yn,pn,e(K)), n=1 ..., N }, the maximum p of valuen,e(K)Corresponding YnAs required imbalance fault grade.
It is proposed by the present invention to be examined based on principal component analysis and the marine shafting imbalance fault failure of vector evidential reasoning Disconnected method carries out feature extraction by PCA method according to the input feature vector variable of acquisition, obtains input main variables；According to Contribution rate size is combined main variables, and the input feature vector variable after combination constitutes input vector；Utilize qualitative letter It ceases conversion method and obtains sample to the comprehensive similarity about input vector and output reference grade, and construct reflection input reference The cultellation statistical form of vector and output relation；The corresponding evidence of each reference vector is obtained according to the table, constructs vector evidence matrix Table；The reliability and evidence weight of input vector can be obtained according to the contribution rate of input main variables；It is every to obtain sample set The evidence of one group of input sample vector obtains fusion results using evidential reasoning rule, and therefrom reasoning obtains marine shafting injustice Balance system fault level.The program (translation and compiling environment matlab, C++ etc.) worked out according to the method for the present invention can be in monitoring computer Upper operation, and the hardware such as combination sensor, data collector form on-line monitoring system, configure on ship, to realize ship The real-time state monitoring and fault diagnosis of oceangoing ship propulsion system shafting bearing mechanical equipment.
Detailed description of the invention
Fig. 1 is the flow chart of the method for the present invention；
Fig. 2 is marine shafting propulsion system simulated experiment platform data collection system knot in the embodiment using the method for the present invention Composition.
Specific embodiment
Flow diagram of the present invention is as shown in Figure 1, comprising the following steps:
(1) marine shafting bearing imbalance fault set Θ={ Y is set1,…,Yn,…,YN, YnRepresenting fault set Θ In n-th of imbalance fault grade, n=1,2 ..., N, N be fault level number；If being mounted on marine shafting bearing equipotential The time domain vibration acceleration signal sequence that the 4 vibration displacement sensors set obtain position is respectively S1(t),S2(t), S3(t),S4(t), n times are acquired respectively under every kind of imbalance fault grade, are acquired T=N*n times, sampling instant t=1 altogether, 2 ..., T, between double sampling between be divided into 0.8ms.
(2) the time-domain signal sequence S of acquisition will be sampled every time in step (1)1(t),S2(t),S3(t),S4(t) it carries out fast Fast Fourier transformation obtains corresponding frequency domain sequence signal, by 1 frequency multiplication (1X), 2 frequencys multiplication (2X) and 3 times in each spectrum sequence Frequently the vibration amplitude of (3X) can extract 3 fault signature variables, amount in t moment as fault signature variable, each sensor P=3*4=12 characteristic variable can be obtained, x is denoted as1(t),…xp(t),…xP(t), p=1 ..., P；By { x1(t),…xp (t),…x12(t) } it is expressed as sample set X={ x (t) | t=1,2 ..., T }, wherein x (t)=[x1(t),…xp(t),…x12 It (t)] is a feature samples vector.
(3) the 12 dimension primitive character sample set X for obtaining sampling in step (2) are carried out by principal component analysis (PCA) method Feature extraction, detailed process is as follows:
Operation, the matrix form for being first expressed as X is normalized to sample set X in (3-1)
Using formula (1) to each element x in matrixp(t) it is normalized
WhereinAnd σpRespectively xp(t) mean value and standard deviation, calculation method are
The matrix obtained after step (3-1) normalization is denoted as by (3-2)
Then it asks againCovariance matrix
(3-3) carries out Eigenvalues Decomposition to covariance matrix V, seeks eigenvalue λpWith corresponding feature vector ωp, to spy Value indicative λpDescending arrangement is carried out, calculates the corresponding characteristic value of p-th of principal component in the sum of All Eigenvalues of covariance matrix V Shared specific gravity, i.e. contribution rate, contribution rate is bigger, illustrates that the ability of the comprehensive former indication information of the principal component is stronger, contribution rate meter Calculating formula is
(3-4) calculates accumulative variance contribution ratio size, the sum of the characteristic value of d < 12 principal component before contribution rate of accumulative total indicates The shared specific gravity in All Eigenvalues summation, this ratio is bigger, and d principal component can more represent initial data comprehensively before illustrating The information having, calculation formula are
As accumulative variance contribution ratio Md>=0.95, determine the value of d, corresponding preceding d characteristic value Λ=diag [λ1, λ2,...,λd] and corresponding characteristic vector Wd=[ω1,ω2,...,ωd] base as subspace, then the d principal component extracted For
Note main variables collection is combined into F={ fi| i=1 ..., d }, wherein main variables fi=[fi(1),fi(2),…, fi(T)]T, superscript notation " T " expression vector transposition.
(4) vector matrix is constructed, establishing input is main variables vector fiWith output irregularity fault level YnBetween Mapping relations, the specific steps are as follows:
(4-1) definition input main variables fiReference value setWherein And WithRespectively fiMinimum value and maximum value, J fiReference value number；Take imbalance fault mould Formula is denoted as y (t), y (t) ∈ Θ, result reference set Y=Θ is set, by fi(t) and y (t) is expressed as sample set S={ [fi (t), y (t)] }, wherein [fi(t), y (t)] be a tape jam label fault sample vector.
For the ease of the understanding to main variables input reference, illustrate here.It is assumed that under 5 kinds of fault levels 300 sample vectors are measured respectively and constitute T=1500 group sample set, share 12 input feature vector variable { x1(t),…xp (t),…x12(t) } 10 input main variables, are extracted from 12 dimensional feature variables by step (3) PCA algorithm {f1f2,…,f10, input main variables f1(here with f1For illustrate) minimum value and maximum value be respectively 0.0005 He 0.0177, then input main variables f1Input reference set a1=0.0005,0.0040,0.0074,0.0109, 0.0143,0.0177}。
(4-2) can be obtained according to step (3), input main variables fiCorresponding contribution rate isContribution rate is according to descending Arrangement, whereinAnd f1Contribution rate it is maximum, thus can be according to contribution rate to input main variables fiIt is combined, Input feature vector variable after combination constitutes the form of vector, as follows
Wherein K indicates the total number of input vector, and K ∈ [3,4], h are the number of the input f of each vector of composition, for Input vector { Rk| k=1,2 ..., K }, corresponding reference vector collection is combined intoWherein
For the ease of the understanding to input vector, illustrate here.10 input principal components are extracted according to step (3) Variable { f1f2,…,f10, corresponding input vector is R1=[f1,f2,f3],R2=[f4,f5,f6],R3=[f7,f8,f9,f10], Input vector R1(here with R1For illustrate) reference vector is
It is { R that input vector, which can be obtained, by step (4-2) in (4-3)1(t),…,Rk(t),…,RK(t) }, it is expressed as sample This vector set U={ [R1(t),…,Rk(t),…,RK(t)] | t=1,2 ..., T }, by T sample vector [Rk(t),y(t)] In sample to (Rk(t), y (t)) it is respectively the form about reference vector similarity, tool with the variation of qualitative information conversion method Steps are as follows for body:
(4-3-1) sample is to (Rk(t), y (t)) input vector Rk(t) reference vector is matchedSimilarity distribution are as follows:
Wherein βk,jIndicate input vector Rk(t) j-th of reference vector is matchedSimilarity, calculation method is as follows:
WhereinThen indicate input vector Rk(t) and reference vectorMatching degree.
(4-3-2) according to step (4-3-1), sample is to (Rk(t), y (t)) it is converted into the form of similarity distribution (βk,1,...,βk,J), wherein βk,jIndicate sample to (Rk(t), y (t)) in input vector match reference vectorResult simultaneously Value is YnSimilarity.
(4-3-3) is similar to being converted by all samples in sample set U according to step (4-3-1) and step (4-3-2) The form of degree can construct all samples to the statistical form for carrying out cultellation in the form of similarity with them, and table 1 gives sample pair (R1(t), y (t)) cultellation statistical form, wherein an,jIndicate all input vector R1(t) reference vectors are matchedAnd failure Type is YnSample to (R1(t), y (t)) comprehensive similarity sum, other samples are to (Rk(t), y (t)) cultellation statistical form It is similar with the table, it can be obtained by same procedure；
1 sample of table is to (R1(t), y (t)) cultellation statistical form
In order to deepen to sample to (Rk(t), y (t)) similarity understanding, it is assumed here that a sample vector { (R1 (t), y (t)) }={ [0.0123,0.0060,0.0063], Y1, continue to use the input reference vector collection of step (4-2) example hypothesis It closes, input value R can be obtained by formula (8a)-(8b)1(t) similarity of reference vector is matched, and then can get sample to (R1(t),Y1) Similarity be distributed (β1,1,β1,2,...,β1,6)=(0.0802,0.1209,0.2240,0.3166,0.1611,0.0973).
Sample is to (R in order to facilitate understandingk(t), y (t)) cultellation statistical form, continue to use the sample set in step (4-2) With reference vector set, all T=1500 samples of sample set are obtained to (R according to step (4-3)1(t), y (t)) it is similar Degree distribution, can construct cultellation statistical form, as shown in table 3 below
3 sample of table is to (R1(t), y (t)) cultellation statistical form
(4-4) constructs vector matrix, according to the cultellation statistical form in step (4-3), can get and works as input vector Rk(t) it takes Reference vectorWhen, end value y (t) is reference value YnReliability are as follows:
Wherein,Indicate all end value y (t) matching reference value YnSample to the sum of comprehensive similarity, AndAnd haveThen definition corresponds to reference vectorEvidence be
Therefore, evidence matrix table can be constructed to describe input vector RkRelationship between result y, provides input vector R1Evidence matrix it is as shown in table 2
2 input vector R of table1Evidence matrix table
Other input vectors RkEvidence matrix table it is similar with the table, can be obtained by the above method.
Continue to use input vector R in step (4-3)1Cultellation statistical form deepen understanding to evidence matrix table shown in upper table. According to table 4, input vector R can be obtained by formula (9) and formula (10)1(t) reference vector is taken When it is corresponding Evidence be
Similarly, the corresponding evidence of other reference vectors can be sought, then input vector R can be constructed1Evidence matrix Table, as shown in table 4
4 input vector R of table1Evidence matrix table
(5) the reliability r of evidence is definedkThe input vector R of description input information source compositionkJudge imbalance fault type Ability；Define the weight w of evidencekEvidence e is describedkCompared to the relative importance of other evidences, the specific steps are as follows:
(5-1) can be by the contribution rate of each principal component obtained in step (3)It is normalized
IfFor each input feature vector variable fiReliability, then input vector RkReliability are as follows:
(5-2) sets evidence ekWeight wkEqual to corresponding reliability rk, this is because the higher evidence of reliability ought to It is corresponding with higher evidence weight.
(6) after obtaining one group of sample data x (t) online, the evidence in vector evidence matrix is activated, and these are activated Evidence utilizes the fusion of evidential reasoning (ER) rule, the specific steps are as follows:
(6-1) utilizes step (3) sample x (t)=[x1(t),…xp(t),…x12(t)] pivot variable obtains pivot change Duration set F={ fi| i=1 ..., d }, input feature value R is obtained further according to step (4-2)k。
(6-2) is for input vector Rk(t), all reference vectors will be activatedCorresponding evidenceThen input Rk(t) Evidence by reference vector evidenceIt is obtained in the form of weighted sum
ek={ (Yn,pn,k), n=1 ..., N } (12a)
(6-3) obtains input vector R using formula (12a) and formula (12b)k(t) evidence { ek| k=1 ..., K }, and set Initial evidence weight wk=rk, they are merged using evidential reasoning rule, obtaining fusion results is
O(Rk)={ (Yn,pn,e(K)), n=1 ..., N } (13a)
Wherein formula (13b)It is to be recursively obtaining by following evidential reasoning fusion rule
M in formula (14a)n,e(k-1)With MP(Θ),e(k-1)It is obtained respectively by formula (14b) and formula (14c)
Mk={ (Yn,Mn,k), k=1 ..., K (14d)
M in formula (14d)kIndicate input RkThe reliability of acquisition, wherein Mn,k=wkpn,k, pn,kIt can be acquired by formula (12b).
(7) K evidence fusion result can be acquired with iteration as O (R by the evidence fusion rule of step (6)k(t))= {(Yn,pn,e(K)), n=1 ..., N }, the maximum p of valuen,e(K)Corresponding YnAs required imbalance fault grade.
Below in conjunction with attached drawing, the embodiment of the method for the present invention is discussed in detail:
The flow chart of the method for the present invention is as shown in Figure 1, core is: acquisition different faults grade bottom base and bracket etc. The temporal signatures signal of position；The data of acquisition are passed through into Fast Fourier Transform (FFT), acquisition samples corresponding frequency domain character every time； Feature is extracted from input feature vector variable by PCA method, obtains main variables；Input feature vector is become according to contribution rate size Amount is combined into input vector；It calculates the similarity of sample pair and constructs the cultellation statistical form of all samples pair；It is counted according to cultellation The evidence matrix table of table construction input vector；The reliability and weight of input information source are determined according to principal component contributor rate size； Finally using the evidence of evidential reasoning rule fusion input sample vector activation and from fusion results reasoning fault level.
Below in conjunction with the data instance that marine shafting propulsion system simulated experiment platform in Fig. 2 acquires, the present invention is discussed in detail Each step of method.
1, the acquisition and pretreatment of experimental data
Vibration displacement sensor is placed in acquisition on the pedestal and backing positions of shafting propulsion system simulated experiment platform to turn Sub- vibration signal, being respectively provided with failure " rotor unbalance ", (there are four types of non-equilibrium state Y altogether1,Y2,Y3,Y4), " normal " (Y5), then failure collection is Θ={ Y1,Y2,Y3,Y4,Y5}；It is acquired respectively under every kind of fault mode 300 times, then acquires T=altogether 1500 times, between double sampling between be divided into 0.8ms；The time domain vibration acceleration signal sampled every time carries out fast Fourier change It changes, is transformed to corresponding frequency-region signal, when a fault has occurred, the increase feelings of frequency and its amplitude that different failures is shown Condition is also different, and the vibrational energy of failure mostly concentrates on 1X~3X, so choosing 1 times of fundamental frequency, 2 times of fundamental frequencies and 3 times of fundamental frequencies Amplitude is as fault characteristic signals；4 sensors of installation are total 12 fault signature variable x1(t),…xp(t),…x12 (t), by { x1(t),…xp(t),…x12(t) } it is expressed as sample set X={ x (t) | t=1,2 ..., T }, wherein x (t)=[x1 (t),…xp(t),…,x12It (t)] is a feature samples vector.
2, feature extraction is carried out to primitive character sample set X using PCA method
Primitive character sample is operated using the PCA method in step (3) of the invention, acquires 12 principal components Contribution rate is respectively as follows: It can proper accumulative variance contribution ratio MdWhen >=0.95, d=10 takes preceding 10 principal components at this time Variable remembers that main variables collection is combined into F={ f as input feature vector1,f2,…,f10}。
3, the selection of main variables reference value is inputted
It chooses: input main variables f1Input reference set a1=0.0005,0.0040,0.0074,0.0109, 0.0143,0.0177}；Input main variables f2Input reference set a2=0.0003,0.0024,0.0045, 0.0066,0.0087,0.0108}；Input main variables f3Input reference set a3=0.0004,0.0035, 0.0065,0.0095,0.0126,0.0156}；Input main variables f4Input reference set a4=0.0020, 0.0119,0.0218,0.0317,0.0415,0.0514}；Input main variables f5Input reference set a5= {0.0583,0.0700,0.0818,0.0935,0.1052,0.1169}；Input main variables f6Input reference set a6 ={ 0.0012,0.0158,0.0305,0.0452,0.0598,0.0745 }；Input main variables f7Input reference collection Close a7={ 0.0003,0.0059,0.0114,0.0170,0.0225,0.0281 }；Input main variables f8Input reference Set a8={ 0.0808,0.0963,0.1119,0.1275,0.1431,0.1587 }；Input main variables f9Input reference Value set a9={ 0.0334,0.0399,0.0463,0.0528,0.0593,0.0657 }；Input main variables f10Input With reference to value set a10={ 0.0035,0.0210,0.0386,0.0561,0.0737,0.0913 }.
4, input main variables are combined into input vector
The 10 input main variables { f extracted1f2,…,f10, forming corresponding input vector is R1=[f1, f2,f3],R2=[f4,f5,f6],R3=[f7,f8,f9,f10], then input vector R1Reference vector is Input vector R2Reference vector is Input vector R3Reference vector is
5, sample is obtained to (Rk(t), y (t)) similarity form about reference vector, sample is constructed to (Rk(t),y (t)) cultellation statistical form
Using all samples in the method for the present invention step (4-3) acquisition T=1500 group sample set to (Rk(t),y(t)) Similarity distribution, construct the cultellation statistical form as shown in table 1 in the method for the present invention step (4-3), input sample is to (R1(t), y(t))、(R2(t), y (t)) and (R3(t), y (t)) cultellation statistical form respectively as shown in the following table 5, table 6 and table 7
5 sample of table is to (R1(t), y (t)) cultellation statistical form
6 sample of table is to (R2(t), y (t)) cultellation statistical form
7 sample of table is to (R3(t), y (t)) cultellation statistical form
6, vector evidence matrix table is constructed
Step (4-3) obtains each input R according to the method for the present inventionkCultellation statistical form after, according to the method for the present invention Step (4-4) obtains input vector RkThe corresponding evidence of each reference vector, and then construct input vector R1, R2And R3Evidence Matrix table, as shown in the following table 8, table 9 and table 10
8 input vector R of table1Evidence matrix table
9 input vector R of table2Evidence matrix table
10 input vector R of table3Evidence matrix table
7, the reliability of evidence is defined
Step (5) obtains the objective reliability r of input vector according to the method for the present inventionk, each master is obtained by step (3) first The reliability of ingredient, Then input to Measure R1Corresponding reliabilityInput vector R2Corresponding reliabilityInput vector R3Corresponding reliability
8, according to the method for the present invention in step (6) reasoning sample set every group of sample imbalance fault grade
Such as sample input vector { R1(t),R2(t),R3(t) }=[0.0026,0.0039,0.0059], [0.0147,0.0793,0.0218], [0.0049,0.1089,0.0452,0.0132] }, step (4-4) according to the method for the present invention Sample input vector R can be obtained1(t) with similarity (β1,1,β1,2,...,β1,6)=(0.0214,0.8272,0.1498, 0.0016,0,0) entire evidence is activatedInput vector R2(t) with similarity (β2,1,β2,2,...,β2,6)=(0, 0.5401,0.4599,0,0,0 entire evidence) is activatedInput vector R3(t) with similarity (β3,1, β3,2,...,β3,6)=(0,0.9900,0.0100,0,0,0) activation entire evidenceIt walks according to the method for the present invention Suddenly the formula (12) of (6-2) can obtain e1=[0.2104,0.0531,0.0436,0.5531,0.1397], e2=[0.0900, 0.0487,0.0443,0.4193,0.3977],e3=[0.1091,0.0928,0.1778,0.5826,0.0377], it is then sharp With the formula (13) and (14) evidential reasoning fusion rule of step (6-3), fusion results can be obtained are as follows: O (R (k))={ (Y1, 0.0335),(Y2,0.0073),(Y3,0.0095),(Y4,0.9058),(Y5, 0.0439) }, imbalance fault grade can be obtained For Y4。

Claims (1)

1. a kind of marine shafting imbalance fault diagnostic method based on vector evidential reasoning, it is characterised in that this method include with Lower step:
(1) marine shafting bearing imbalance fault set Θ={ Y is set1,…,Yn,…,YN, YnIn representing fault set Θ N-th of imbalance fault grade, n=1,2 ..., N, N are fault level number；If being mounted on 4 on marine shafting position of bearings The time domain vibration acceleration signal sequence that a vibration displacement sensor obtains position is respectively S1(t),S2(t),S3(t),S4 (t), n times are acquired respectively under every kind of imbalance fault grade, altogether acquisition T=N*n times, sampling instant t=1,2 ..., T, twice 0.8ms is divided between sampling；
(2) the time-domain signal sequence S of acquisition will be sampled every time in step (1)1(t),S2(t),S3(t),S4(t) it carries out in quick Fu Leaf transformation obtains corresponding frequency domain sequence signal, and the vibration amplitude of 1 frequency multiplication, 2 frequencys multiplication and 3 frequencys multiplication in each spectrum sequence is made For fault signature variable, each sensor can extract 3 fault signature variables, and P=3*4=12 can be obtained in t moment by amounting to Characteristic variable is denoted as x1(t),…xp(t),…xP(t), p=1 ..., P；By { x1(t),…xp(t),…x12(t) } it is expressed as sample This set X={ x (t) | t=1,2 ..., T }, wherein x (t)=[x1(t),…xp(t),…x12(t)] for feature samples to Amount；
(3) the 12 dimension primitive character sample set X for obtaining sampling in step (2) carry out feature by principal component analysis (PCA) method It extracts, detailed process is as follows:
Operation, the matrix form for being first expressed as X is normalized to sample set X in (3-1)
Using formula (1) to each element x in matrixp(t) it is normalized
WhereinAnd σpRespectively xp(t) mean value and standard deviation calculate as follows
The matrix obtained after step (3-1) normalization is denoted as by (3-2)
Then it asks againCovariance matrix
(3-3) carries out Eigenvalues Decomposition to covariance matrix V, seeks eigenvalue λpWith corresponding feature vector ωp, to characteristic value λpDescending arrangement is carried out, it is shared in the sum of All Eigenvalues of covariance matrix V to calculate the corresponding characteristic value of p-th of principal component Specific gravity, i.e. contribution rate, contribution rate calculation formula be
(3-4) calculates accumulative variance contribution ratio size, and calculation formula is
As accumulative variance contribution ratio Md>=0.95, determine the value of d, corresponding preceding d characteristic value Λ=diag [λ1,λ2,..., λd] and corresponding characteristic vector Wd=[ω1,ω2,…,ωd] base as subspace, then the d principal component extracted be
Note main variables collection is combined into F={ fi| i=1 ..., d }, wherein main variables fi=[fi(1),fi(2),…,fi (T)]T, superscript notation " T " expression vector transposition；
(4) vector matrix is constructed, establishing input is main variables vector fiWith output irregularity fault level YnBetween mapping Relationship, the specific steps are as follows:
(4-1) definition input main variables fiReference value setWhereinAnd WithRespectively fiMinimum value and maximum value, J fiReference value number；Take imbalance fault grade It is denoted as y (t), y (t) ∈ Θ, result reference set Y=Θ is set, by fi(t) and y (t) is expressed as sample set S={ [fi(t), Y (t)] }, wherein [fi(t), y (t)] be a tape jam label fault sample vector；
(4-2) can be obtained according to step (3), input main variables fiCorresponding contribution rate isContribution rate is arranged according to descending, WhereinAnd f1Contribution rate it is maximum, thus can be according to contribution rate to input main variables fiIt is combined, after combination Input feature vector signal constitute the form of vector, as follows
Wherein K indicates the total number of input vector, and K ∈ [3,4], h are the number of the input f of each vector of composition, for input Vector { Rk| k=1,2 ..., K }, corresponding reference vector collection is combined intoWherein
It is { R that input vector, which can be obtained, by step (4-2) in (4-3)1(t),…,Rk(t),…,RK(t) }, be expressed as sample to Duration set U={ [R1(t),…,Rk(t),…,RK(t)] | t=1,2 ..., T }, by T sample vector [Rk(t), y (t)] in Sample is to (Rk(t), y (t)) it is respectively the form about reference vector similarity with the variation of qualitative information conversion method, it is specific to walk It is rapid as follows:
(4-3-1) sample is to (Rk(t), y (t)) input vector Rk(t) reference vector is matchedSimilarity distribution are as follows:
Wherein βk,jIndicate input vector Rk(t) j-th of reference vector is matchedSimilarity, calculate it is as follows:
WhereinThen indicate input vector Rk(t) and reference vectorMatching degree；
(4-3-2) according to step (4-3-1), by sample to (Rk(t), y (t)) it is converted into the form (β of similarity distributionk,1,..., βk,J), wherein βk,jIndicate sample to (Rk(t), y (t)) in input vector match reference vectorEnd value is Y simultaneouslynPhase Like degree；
(4-3-3) according to step (4-3-1) and step (4-3-2), by all samples in sample set U to being converted into similarity Form can construct all samples to the statistical form for carrying out cultellation in the form of similarity with them, and table 1 gives sample to (R1 (t), y (t)) cultellation statistical form, wherein an,jIndicate all input vector R1(t) reference vectors are matchedAnd failure classes Type is YnSample to (R1(t), y (t)) comprehensive similarity sum, other samples are to (Rk(t), y (t)) cultellation statistical form with The table is similar, can thus obtain；
1 sample of table is to (R1(t), y (t)) cultellation statistical form
(4-4) constructs vector matrix, according to the cultellation statistical form in step (4-3), can get and works as input vector Rk(t) reference is taken VectorWhen, end value y (t) is reference value YnReliability are as follows:
Wherein,Indicate all end value y (t) matching reference value YnSample to the sum of comprehensive similarity, andAnd haveThen definition corresponds to reference vectorEvidence be
Therefore, evidence matrix table can be constructed to describe input vector RkRelationship between result y provides input vector R1's Evidence matrix is as shown in table 2
2 input vector R of table1Evidence matrix table
Other input vectors RkEvidence matrix table it is similar with the table, can thus obtain；
(5) the reliability r of evidence is definedkThe input vector R of description input information source compositionkJudge the energy of imbalance fault type Power；Define the weight w of evidencekEvidence e is describedkCompared to the relative importance of other evidences, the specific steps are as follows:
(5-1) is by the contribution rate of each principal component obtained in step (3)It is normalized
IfFor each input feature vector variable fiReliability, then input vector RkReliability are as follows:
(5-2) sets evidence ekWeight wkEqual to corresponding reliability rk；
(6) after obtaining one group of sample data x (t) online, the evidence in vector evidence matrix is activated, and these are activated into evidence It is merged using evidential reasoning rule, the specific steps are as follows:
(6-1) utilizes step (3) sample x (t)=[x1(t),…xp(t),…x12(t)] pivot variable, winner's metavariable set F={ fi| i=1 ..., d }, input feature value R is obtained further according to step (4-2)k；
(6-2) is for input feature value Rk(t), all reference vectors will be activatedCorresponding evidenceThen input Rk(t) Evidence by reference vector evidenceIt is obtained in the form of weighted sum
ek={ (Yn,pn,k), n=1 ..., N } (12a)
(6-3) obtains input vector R using formula (12a) and formula (12b)k(t) evidence { ek| k=1 ..., K }, and set initial Evidence weight wk=rk, they are merged using evidential reasoning rule, obtaining fusion results is
O(Rk)={ (Yn,pn,e(K)), n=1 ..., N } (13a)
Wherein formula (13b)It is to be recursively obtaining by following evidential reasoning fusion rule
M in formula (14a)n,e(k-1)With MP(Θ),e(k-1)It is obtained respectively by formula (14b) and formula (14c)
Mk={ (Yn,Mn,k), k=1 ..., K (14d)
M in formula (14d)kIndicate input RkThe reliability of acquisition, wherein Mn,k=wkpn,k, pn,kIt can be acquired by formula (12b)；
(7) acquiring K evidence fusion result by the evidence fusion rule iteration of step (6) is O (Rk(t))={ (Yn, pn,e(K)), n=1 ..., N }, the maximum p of valuen,e(K)Corresponding YnAs required imbalance fault grade.
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