CN113269057A - Motor rotor fault prediction method based on confidence rule base reasoning - Google Patents

Motor rotor fault prediction method based on confidence rule base reasoning Download PDF

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CN113269057A
CN113269057A CN202110494498.1A CN202110494498A CN113269057A CN 113269057 A CN113269057 A CN 113269057A CN 202110494498 A CN202110494498 A CN 202110494498A CN 113269057 A CN113269057 A CN 113269057A
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徐晓滨
董峻
侯平智
马枫
孙杰
俞卓辰
章振杰
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Nanjing Smart Water Transportation Technology Co ltd
Hangzhou Dianzi University
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Hangzhou Dianzi University
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Abstract

The invention discloses a motor rotor fault prediction method based on confidence rule base reasoning. The method comprises the steps of firstly collecting vibration acceleration signals at different positions of a motor rotor, converting the vibration acceleration signals into frequency domain signals through a fast Fourier transform method, taking amplitude values of 1 frequency multiplication as fault characteristic variables, sequencing the collected different fault characteristic variable values respectively in a time sequence to obtain a reference evidence matrix corresponding to a reference value set and a fault type mapping relation, then establishing a corresponding BRB model for each fault characteristic variable, and obtaining prediction evidence according to a predicted value and a corresponding REM. And finally, constructing a fault information fusion decision model, fusing the obtained prediction evidence, wherein the input of the information fusion decision model is the prediction value of all fault characteristic variables, and the output is the fault type of the motor rotor at the future moment. The method has better model precision, can accurately predict the fault type in time and is convenient for engineering realization.

Description

Motor rotor fault prediction method based on confidence rule base reasoning
Technical Field
The invention relates to a motor rotor fault prediction method based on Belief Rule Base (BRB) reasoning, and belongs to the technical field of industrial equipment state detection and fault diagnosis.
Background
The motor rotor is used as a main component of motor equipment, and any unbalance fault of the motor rotor can bring great influence on the operation of the motor and the normal operation of the equipment. The method for predicting the unbalance fault of the motor rotor is a main means for guaranteeing the production safety and stability of the industrial field with the motor, and can predict the fault in advance so as to effectively avoid major accidents. Under normal conditions, the centrifugal force of a motor rotor reaches balance, the motor is in a static state, a dynamic state and an even balance state, power required in industrial production can be provided, speed regulation of the motor can be realized, and the like, and the motor has great influence on safe operation of motor equipment.
However, the motor belongs to high-power electrical equipment, a large amount of heat energy and mechanical wear can be generated during working, if the motor rotor has an unbalanced fault, the motor can be greatly influenced, the safety of the equipment operated by the motor can be directly influenced, and once the safety of the equipment has a problem, certain property and other losses can be brought. Therefore, in order to ensure the normal operation of the devices, the motor rotor needs to be ensured to be in a balanced state, so that the motor rotor unbalance fault can be predicted in advance by researching the motor rotor unbalance fault prediction method, further, the great loss caused by the problems of the motor is avoided, and the guarantee is provided for the safe operation of the motor device.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a motor rotor fault prediction method based on confidence rule base reasoning.
The invention firstly collects vibration acceleration signals at different positions of a motor rotor, then converts the vibration acceleration signals into frequency domain signals by a fast Fourier transform method, takes amplitude of 1 frequency multiplication as fault characteristic variables, sorts the collected different fault characteristic variable values respectively by time series to obtain a Reference Evidence Matrix (REM) corresponding to a reference value set and a fault type mapping relation, then establishes a corresponding BRB model for each fault characteristic variable, the input of the model is sampling values corresponding to fault characteristic variables at different moments, the output is a predicted value of the fault characteristic variables at a future moment, prediction evidence can be obtained through the predicted value and corresponding REM, finally, a fault information fusion decision model is constructed, the obtained prediction evidence is fused, the input of the fault information fusion decision model is the predicted value of all the fault characteristic variables, and the output is the fault type of the motor rotor at the future moment. According to the method, the motor rotor fault characteristic variable value acquired by the vibration acceleration sensor which is cheap and can be simply installed is utilized, and the motor rotor fault type can be predicted at the future moment.
The invention comprises the following steps:
(1) setting a motor rotor unbalance fault set theta ═ F1,F2,...,Fh,...,FH|h＝1,2,...,H}，FhRepresents the H-th fault, H, in the set of faults Θ>3 is the number of fault categories;
(2) j at rotor of electric machine under different classes of unbalance of rotor of electric machine>Collecting vibration acceleration signals at 3 different positions, converting the vibration acceleration signals into frequency domain signals by using a fast Fourier transform method, taking 1 frequency multiplication amplitude as a fault characteristic variable and recording the frequency multiplication amplitude as { f }jJ |, 1,2,., J }, then J fault characteristic variables are obtained;
(3) for J fault characteristic variables, respectively designing corresponding BRB models to predict the characteristic variables, and setting a fault characteristic variable fjIs sampled by fj,tDenotes that t ∈ N+Is the sampling instant, N+Is a positive integer of infinity, for the jth fault signature variable fjCorresponding BRBjThe input of the model is { fj,t-l+1,...,fj,t-1,fj,t}，l>1 is the number of model inputs, the output variable yj,t+oRepresenting the value f of the fault characteristic variable at the future t + o momentj,t+oPredicted value of (a), here o>0 is the o-th instant after the current instant t;
(3-1) in BRBjIn the model, f isj,t-l+1,...,fj,t-1,fj,tAre respectively recorded as variable x1,x2,...,xn...,xlThe model inputs a set of reference values of
Figure BDA0003053727290000021
Wherein R is>1 is the number of reference values per input, xnIs the value of the fault characteristic variable at the nth input of the model,
Figure BDA0003053727290000022
wherein
Figure BDA0003053727290000023
Is the reference value of the r-th reference level of the n-th input, and outputs yj,t+oThe set of reference values of (a) is:
Dj＝{Di j|j＝1,2,...,J；i＝1,2,…,N} (2)
wherein D1 j<D2 j<…<Di j<…<DN j，Di jIs the reference value of the ith reference level of the output, N>1 is the number of output reference values, and a rule base BRBj is constructed based on the number of output reference values;
(3-2) the rule base BRBj constructed by K rules, wherein the value of K is BRBjProduct of reference value numbers of all inputs in the model, wherein the k-th rule RkIs described as
Figure BDA0003053727290000024
Wherein the content of the first and second substances,
Figure BDA0003053727290000025
the nth input fault characteristic variable value x of the model is expressed in the kth rulenCorresponding reference value, mi,kCorresponding to D under the k rulei jAnd satisfies the k rule
Figure BDA0003053727290000031
(3-3) obtaining a sampling sequence f at the time tj,t-l+1，...，fj,t-1，fj,tThen, the input x of the BRBj model can be obtained1＝fj,t-l+1，x2＝fj,t-l+2，...，xl＝fj,tAnd calculating the matching degree of each input corresponding reference value, which comprises the following specific steps:
(a) when in use
Figure BDA0003053727290000032
Or
Figure BDA0003053727290000033
When xnTo pair
Figure BDA0003053727290000034
And
Figure BDA0003053727290000035
degree of matching of (a)n,1And alphan,RValues are all 1, and the matching degrees of other reference values are all 0;
(b) when in use
Figure BDA0003053727290000036
When p is 2,3, …, R-1, xnFor the
Figure BDA0003053727290000037
And
Figure BDA0003053727290000038
respectively has a matching degree of
Figure BDA0003053727290000039
Figure BDA00030537272900000310
At this time, the model inputs xnThe matching degrees for other reference values are all 0;
(3-4) calculating each input x of the BRBj model according to the matching degree of the input corresponding to the reference value obtained in the step (3-3)1,x2,...,xlActivated activation weight corresponding to kth rule
Figure BDA00030537272900000311
Is composed of
Figure BDA00030537272900000312
Wherein
Figure BDA00030537272900000318
Inputting x for the modelnCorresponding reference value under the kth rule
Figure BDA00030537272900000313
The degree of matching of (a) to (b),
Figure BDA00030537272900000314
is the weight of the kth rule, λ is more than or equal to 0nThe reliability of the nth input of the model is less than or equal to 1;
(3-5) obtaining the activation weight of the kth rule according to the step (3-4)
Figure BDA00030537272900000315
Then, the obtained product is subjected to correspondence D under the k rulei jConfidence m ofi,kFusing all the rules to obtain support Di jHas a confidence of
Figure BDA00030537272900000316
(3-6) calculating the future t + o time fj,t+oPredicted value y ofj,t+oIs composed of
Figure BDA00030537272900000317
(4) For each fault signature variable fjObtaining corresponding BRB according to the step (3)jModel, and obtaining predicted values y of J fault characteristic variables on linej,t+o；
(5) Constructing a fault information fusion decision model, which comprises the following specific steps:
(5-1) setting a fault characteristic variable fjStill follow the reference value set D in equation (2)i jIs marked as Aj＝{Aj,iJ | (1, 2.. J); 1,2, …, N }, wherein aj,1＝Di j,A1,2＝D2 j,...,Aj,i＝Di j,Aj,N＝DN j，Aj,iFor the jth fault signature variable fjAnd (3) obtaining a set of 'sample pairs' from the fault characteristic variable samples collected in the steps (1) to (3) and the corresponding fault types, and recording the set as U { (f) for the corresponding ith reference levelj,t,Fh)}；
(5-2) establishing a fault characteristic variable f according to the sample pair set UjCorresponding reference value set AjAnd fault type FhReference Evidence Matrix (REM) of mapping relationshipsj) See Table 1
TABLE 1 fjReference evidence matrix of
Figure BDA0003053727290000041
Wherein the content of the first and second substances,
Figure BDA0003053727290000042
is the jth fault signature variable fjSupported fault type F corresponding to ith reference levelhAnd it supports the sum of the reliabilities of all fault types
Figure BDA0003053727290000043
Each column confidence in REMj is recorded as the sum of the reference value Aj,iCorresponding reference evidence
Figure BDA0003053727290000044
For each fault signature variable fjAll the corresponding REMj are established, and J are established in total;
(5-3) comparing the fault characteristic variable f in the step (4)jPredicted value y ofj,t+oActivating evidence e as input to a fault information fusion decision modeljThe specific process is as follows:
(a) when y isj,t+o≤Aj,1Or yj,t+o≥Aj,NWhen y isj,t+oTo Aj,1And Aj,NDegree of similarity ηj,1And ηj,NValues are all 1, and the similarity of other reference values is all 0;
(b) when A isj,q≤yj,t+o≤Aj,q+1When q is 2,3, …, N-1, xnFor Aj,qAnd Aj,q+1Respectively has a matching degree of
ηj,q＝(Aj,q+1-yj,t+o)/(Aj,q+1-Aj,q) (8a)
ηj,q+1＝(yj,t+o-Aj,q)/(Aj,q+1-Aj,q) (8b)
At this time, yj,t+oThe matching degrees for other reference values are all 0;
(c) for the input predicted value yj,t+oIt will fall within an interval [ A ] formed by some two reference valuesj,i,Aj,i+1]When the two reference values correspond to evidence
Figure BDA0003053727290000051
And
Figure BDA0003053727290000052
is activated, then yj,t+oCan be verified by the reference value
Figure BDA0003053727290000053
And
Figure BDA0003053727290000054
obtained as a weighted sum
ej＝{(Fh,ph,j),h＝1,...,H} (9a)
Figure BDA0003053727290000055
(5-4) obtaining J pieces of evidence together according to the step (5-3), taking the fault set theta in the step (1) as an identification frame, taking the power set of the fault set theta as P (theta), and taking the fault set as the set of all subsets of the set theta, wherein the power set of the fault set is P (theta), and the power set is the set of all subsets of the set theta
Figure BDA0003053727290000056
Setting an evidence importance factor omegajAnd reliability factor r of evidencejBoth are equal, r is more than or equal to 0j≤1，0≤ωj≤1，
Figure BDA0003053727290000057
One piece of evidence in the Evidence Reasoning (ER) rule is expressed as
Figure BDA0003053727290000058
Wherein the degree of confidence
Figure BDA0003053727290000059
Representing while taking into account rjAnd ωjIn case of (e)jTo proposition
Figure BDA00030537272900000510
Is defined as
Figure BDA00030537272900000511
Wherein m isθ,j＝ωjpθ,j，crω,j＝1/(1+ωj-rj) Is a normalization factor;
(5-5) fusing the J evidences by utilizing an ER rule to obtain a fusion result
Z(f(t+o))＝{(Fh,ph,e(J))|h＝1,2,...,H} (12)
Figure BDA00030537272900000512
Wherein J is 1,2h,e(J)After all J evidences are fused, supporting a fault type FhThe union of (a) supports the confidence level, f (t + o) ═ f1,t+o,f2,t+o...,fj,t+o...,fJ,t+o) And performing final decision on the predicted value vectors of J BRB models corresponding to J fault characteristic variables at the time of t + o by Z (f (t + o)), and determining the fault type supported by the maximum reliability as the fault type to which the sample vector f (t + o) belongs.
The invention has the beneficial effects that: the method can acquire different fault characteristic variables according to different fault characteristic variable values acquired by vibration acceleration sensors arranged at different positions of a motor rotor, establish corresponding BRB models, respectively predict different fault characteristic variable values at a future moment, further predict fault types at the future moment according to the predicted fault characteristic variable values at the future moment and the established fault prediction information fusion decision model, and achieve better prediction effect.
Drawings
FIG. 1 is a block flow diagram of the method of the present invention;
fig. 2 is a sampling value sequence of 5 fault characteristic variables collected under 5 fault types at different times in the embodiment of the method of the present invention;
fig. 3 is a comparison graph of predicted values and actual values of 5 fault characteristic variables at different times in the embodiment of the method of the present invention.
Detailed description of the invention
The invention provides a motor rotor fault prediction method based on confidence rule base reasoning, a flow diagram of which is shown in figure 1, and the method comprises the following steps:
(1) setting a motor rotor unbalance fault set theta ═ F1,F2,...,Fh,...,FH|h＝1,2,...,H}，FhRepresents the H-th fault, H, in the set of faults Θ>3 is the number of fault categories;
(2) j at rotor of electric machine under different classes of unbalance of rotor of electric machine>Collecting vibration acceleration signals at 3 different positions, converting the vibration acceleration signals into frequency domain signals by using a fast Fourier transform method, taking 1 frequency multiplication amplitude as a fault characteristic variable and recording the frequency multiplication amplitude as { f }jJ |, 1,2,., J }, then J fault characteristic variables are obtained;
(3) for J fault characteristic variables, respectively designing corresponding BRB models to predict the characteristic variables, and setting a fault characteristic variable fjIs sampled by fj,tDenotes that t ∈ N+Is the sampling instant, N+Is a positive integer of infinity, for the jth fault signature variable fjCorresponding BRBjThe input of the model is { fj,t-l+1,...,fj,t-1,fj,t}，l>1 is the number of model inputs, the output variable yj,t+oRepresenting the value f of the fault characteristic variable at the future t + o momentj,t+oPredicted value of (a), here o>0 is the o-th instant after the current instant t;
(3-1) in BRBjIn the model, f isj,t-l+1,...,fj,t-1,fj,tAre respectively recorded as variable x1,x2,...,xn...,xlThe model input reference value set is:
Figure BDA0003053727290000071
wherein R is>1 is the number of reference values per input, xnIs the value of the fault characteristic variable at the nth input of the model,
Figure BDA0003053727290000072
wherein
Figure BDA0003053727290000073
Is the reference value of the r-th reference level of the n-th input, and outputs yj,t+oThe set of reference values of (a) is:
Dj＝{Di j|j＝1,2,...,J；i＝1,2,…,N} (2)
wherein D1 j<D2 j<…<Di j<…<DN j，Di jIs the reference value of the ith reference level of the output, N>1 is the number of output reference values, and a rule base BRBj is constructed based on the number of output reference values;
(3-2) the rule base BRBj constructed by K rules, wherein the value of K is BRBjProduct of reference value numbers of all inputs in the model, wherein the k-th rule RkIs described as
Figure BDA0003053727290000074
Wherein the content of the first and second substances,
Figure BDA0003053727290000075
the nth input fault characteristic variable value x of the model is expressed in the kth rulenCorresponding reference value, mi,kCorresponding to D under the k rulei jAnd satisfies the k rule
Figure BDA0003053727290000076
(3-3) obtaining a sampling sequence f at the time tj,t-l+1，...，fj,t-1，fj,tThen, the input x of the BRBj model can be obtained1＝fj,t-l+1，x2＝fj,t-l+2，...，xl＝fj,tAnd calculating the matching degree of each input corresponding reference value, which comprises the following specific steps:
(a) when in use
Figure BDA0003053727290000077
Or
Figure BDA00030537272900000716
When xnTo pair
Figure BDA0003053727290000078
And
Figure BDA0003053727290000079
degree of matching of (a)n,1And alphan,RValues are all 1, and the matching degrees of other reference values are all 0;
(b) when in use
Figure BDA00030537272900000710
When p is 2,3, …, R-1, xnFor the
Figure BDA00030537272900000711
And
Figure BDA00030537272900000712
respectively has a matching degree of
Figure BDA00030537272900000713
Figure BDA00030537272900000714
At this time, the model inputs xnThe matching degrees for other reference values are all 0；
(3-4) calculating each input x of the BRBj model according to the matching degree of the input corresponding to the reference value obtained in the step (3-3)1,x2,...,xlActivated activation weight corresponding to kth rule
Figure BDA00030537272900000715
Is composed of
Figure BDA0003053727290000081
Wherein
Figure BDA0003053727290000082
Inputting x for the modelnCorresponding reference value under the kth rule
Figure BDA0003053727290000083
The degree of matching of (a) to (b),
Figure BDA0003053727290000084
is the weight of the kth rule, λ is more than or equal to 0nThe reliability of the nth input of the model is less than or equal to 1;
(3-5) obtaining the activation weight of the kth rule according to the step (3-4)
Figure BDA0003053727290000085
Then, the obtained product is subjected to correspondence D under the k rulei jConfidence m ofi,kFusing all the rules to obtain support Di jHas a confidence of
Figure BDA0003053727290000086
(3-6) calculating the future t + o time fj,t+oPredicted value y ofj,t+oIs composed of
Figure BDA0003053727290000087
For ease of understanding, step (3) is illustrated here as the fault signature variable f1Taking the value of a fault characteristic variable f as an example1,t-1And f1,tAs a fault characteristic variable f1Corresponding BRB1Input x of the model1And x2The reference value sets corresponding to the two inputs are respectively A1＝{0,0.2000,0.4000}，A2＝{0,0.2000,0.4000}，BRB1The model output is f1,t+1Set of reference values as D1And (5) establishing 9 rules, wherein the rules are shown in table 2. To simplify the explanation of the problem, the weight of each rule is set
Figure BDA0003053727290000088
Both set to 1, reliability of two inputs λ1And λ2Are also all set to 1.
TABLE 2 Fault feature variables f1Rule base
Figure BDA0003053727290000089
Figure BDA0003053727290000091
Sequencing the collected fault characteristic variable values according to a time sequence, and acquiring x by assuming that the current time is t and the t + o time is t +11＝f1,t-1＝0.0826，x2＝f1,tBRB can be calculated according to step (3-3) at 0.04651Input x in the model1And x2Respectively corresponding to the matching degrees of the reference values to obtain alpha1,1＝0.413,α1,2＝0.587,α1,3＝0,α2,1＝0.2325,α2,2＝0.7675,α2,3When the rule is 0, it is seen that four rules in the rule base are activated, namely, the 1 st rule, the 2 nd rule, the 4 th rule, and the 5 th rule. Based on the set rule weight and the input reliability, each excited can be calculated by the formula (5)The live rule weights are respectively
Figure BDA0003053727290000092
After the confidence of all rules of fusion activation is calculated according to the formula (6), the result is m1＝0.705,m2＝0.245,m30.05, time t +1, time f is obtained from equation (7)1,t+1Predicted value y of1,t+1＝0.069。
(4) For each fault signature variable fjThe corresponding BRB can be obtained according to the step (3)jModel, and obtaining predicted values y of J fault characteristic variables on linej,t+o；
For ease of understanding, the variable f is assigned to each fault signaturejCorresponding BRBj models are established, wherein a total of 5 motor rotor fault characteristic variables, respectively denoted as f, are illustrated here1,f2,f3,f4,f5According to the method in the step (3), another four BRB models are continuously established, and are respectively expressed as BRB1,BRB2,BRB3,BRB4,BRB5Setting the t + o moments of all models to be t +1 moments, obtaining the predicted values of all fault characteristic variables at the t +1 moments in total, and respectively expressing the predicted values as y1,t+1,y2,t+1,y3,t+1,y4,t+1,y5,t+1These values are expressed as a vector of prediction samples as input to a subsequent fault information fusion decision model.
(5) Constructing a fault information fusion decision model, which comprises the following specific steps:
(5-1) setting a fault characteristic variable fjStill follow the reference value set D in equation (2)i jIs marked as Aj＝{Aj,iJ | (1, 2.. J); 1,2, …, N }, wherein aj,1＝Di j,A1,2＝D2 j,...,Aj,i＝Di j,Aj,N＝DN j，Aj,iFor the jth fault signature variable fjThe corresponding ith reference level is obtained from the fault characteristic variable samples collected in the steps (1) to (3)The fault type corresponding to the fault type is obtained as a set of 'sample pairs', and is marked as U { (f)j,t,Fh)}；
For the convenience of understanding the "sample pair" set, the example is briefly described here. Set at time t, fault type F1Under the condition, the sample values of the fault characteristics collected by 5 sensors are respectively f1,t＝0.0465，f2,t＝0.0309，f3,t＝0.0137，f4,t＝0.0150，f5,t0.0445, these sample values can be associated with the corresponding fault type F1Record as a sample pair, (0.0465,0.0309,0.0137,0.0150,0.0445, F1). Similarly, in failure type F2In the case, 5 fault characteristic variable sampling values at the time t are taken, and then the fault type F is considered at the time2The sample pairs of (D) are expressed as (0.1935,0.1636,0.0092,0.0153,0.0253, F2). At different time, sample pairs of the fault characteristic variable values corresponding to the fault types are obtained respectively.
(5-2) establishing a fault characteristic variable f according to the sample pair set UjCorresponding reference value set AjAnd fault type FhReference Evidence Matrix (REM) of mapping relationshipsj) See Table 1
TABLE 1 fjReference evidence matrix of
Figure BDA0003053727290000101
Wherein the content of the first and second substances,
Figure BDA0003053727290000102
is the jth fault signature variable fjSupported fault type F corresponding to ith reference levelhAnd it supports the sum of the reliabilities of all fault types
Figure BDA0003053727290000103
Each column confidence in REMj is recorded as the sum of the reference value Aj,iCorresponding reference evidence
Figure BDA0003053727290000104
For each fault signature variable fjAll the corresponding REMj are established, and J are established in total;
for ease of understanding, REMj is illustrated here, giving two fault signature variables f1And f2The reference evidence matrix of (a), as shown in tables 3 and 4 below.
TABLE 3 f1Reference evidence matrix of
Figure BDA0003053727290000105
TABLE 4 f2Reference evidence matrix of
Figure BDA0003053727290000106
Figure BDA0003053727290000111
Wherein for f1Table 3 reference evidence, evidence
Figure BDA0003053727290000118
Variable f representing fault characteristics1Corresponding to reference value 0, fault type F is supported1The confidence of (1) is 1, and the confidence of supporting the other four fault types is 0. Evidence (evidence)
Figure BDA0003053727290000112
Variable f representing fault characteristics2Corresponding to a reference value of 0.2000, fault type F is supported10.7843, supporting failure type F20.2035, supporting failure type F3Has a confidence of 0.0098, supports the fault type F4Confidence of 0.0024, supporting failure type F5The confidence of (c) is 0. Evidence (evidence)
Figure BDA0003053727290000119
Supporting various fault types F1,F2,F3,F4,F50.0126,0.4006,0.3525, 0.2334 and 0.0009 respectively.
For the same reason, for f2Reference evidence matrix table 4, evidence
Figure BDA0003053727290000113
And
Figure BDA0003053727290000114
the confidence level supporting each fault type can be clearly obtained.
(5-3) comparing the fault characteristic variable f in the step (4)jPredicted value y ofj,t+oActivating evidence e as input to a fault information fusion decision modeljThe specific process is as follows:
(a) when y isj,t+o≤Aj,1Or yj,t+o≥Aj,NWhen y isj,t+oTo Aj,1And Aj,NDegree of similarity ηj,1And ηj,NValues are all 1, and the similarity of other reference values is all 0;
(b) when A isj,q≤yj,t+o≤Aj,q+1When q is 2,3, …, N-1, xnFor Aj,qAnd Aj,q+1Respectively has a matching degree of
ηj,q＝(Aj,q+1-yj,t+o)/(Aj,q+1-Aj,q) (8a)
ηj,q+1＝(yj,t+o-Aj,q)/(Aj,q+1-Aj,q) (8b)
At this time, yj,t+oThe matching degrees for other reference values are all 0;
(c) for the input predicted value yj,t+oIt will fall within an interval [ A ] formed by some two reference valuesj,i,Aj,i+1]When the two reference values correspond to evidence
Figure BDA0003053727290000115
And
Figure BDA0003053727290000116
is activated, then yj,t+oCan be verified by the reference value
Figure BDA00030537272900001110
And
Figure BDA0003053727290000117
obtained as a weighted sum
ej＝{(Fh,ph,j),h＝1,...,H} (9a)
Figure BDA0003053727290000121
To facilitate the pairing of the activation evidence ejIt is understood that this example is briefly described here. Still following tables 3 and 4 with respect to the fault signature variable f1And f2For the sake of simplicity of explanation, activate evidence ejThe two fault characteristic variables are selected for simple calculation. At a certain time t, the fault characteristic variable f obtained in the step (4)1And f2Respectively is y1,t+10.1000 and y2,t+1As can be seen from table 3, y is 0.18001,t+10.1000 proof of activation
Figure BDA0003053727290000122
And
Figure BDA0003053727290000123
the corresponding reference values are 0 and 0.2000, respectively. As can be seen from Table 4, y2,t+10.1800 proof of activation
Figure BDA0003053727290000124
And
Figure BDA0003053727290000125
corresponding reference values are 0.1500 and 0.3500, respectively. It can be calculated from the formula (8a) and the formula (8b) that the predicted value y is1,t+10.1000 relative to a reference valueDegree of matching η of 01,10.5, the degree of matching is η with respect to a reference value of 0.20001,20.5. Predicting value y in the same way2,t+1The matching degree of 0.1800 to the reference value 0.1500 is η2,20.8500, and a matching degree with respect to a reference value of 0.3500 η2,3＝0.1500。
And y is obtained from the equations (9a) and (9b)1,t+1Supporting failure type F at 0.10001Confidence of (p)1,10.5 × 1.000+0.5 × 0.7843 ═ 0.8921, fault type F is supported2Confidence of (p)2,10.5 × 0+0.5 × 0.2035 ═ 0.1018, fault type F is supported3Confidence of (p)3,10.5 × 0+0.5 × 0.0098 ═ 0.0049, fault type F is supported4Confidence of (p)4,10.0012 for 0.5 × 0.0024, and fault type F is supported5Confidence of (p)5,10.5 × 0+0.5 × 0 ═ 0. For y in the same way2,t+1Supported fault type F can be obtained 0.18001Confidence of (p)1,20.85 × 0.2237+0.15 × 0 ═ 0.1901, fault type F is supported2Confidence of (p)2,20.85 × 0.6779+0.15 × 0.1706 ═ 0.6018, fault type F is supported3Confidence of (p)3,20.1131, supported fault type F, 0.85 × 0.0547+0.15 × 0.44414Confidence of (p)4,20.85 × 0.0437+0.15 × 0.3775 ═ 0.0938, fault type F is supported5Confidence of (p)5,20.85 × 0+0.15 × 0.0078 is 0.0012. Thus, the predicted value y can be obtained1,t+10.1000 proof e1＝{(F1,0.8921)(F2,0.1018)(F3,0.0049)(F4,0.0012)(F50), predicted value y2,t+10.1800 evidence e2＝{(F1,0.1901)(F2,0.6018)(F3,0.1131)(F4,0.0938)(F5,0.0012)}。
(5-4) obtaining J pieces of evidence together according to the step (5-3), taking the fault set theta in the step (1) as an identification frame, taking the power set of the fault set theta as P (theta), and taking the fault set as the set of all subsets of the set theta, wherein the power set of the fault set is P (theta), and the power set is the set of all subsets of the set theta
Figure BDA0003053727290000131
Setting an evidence importance factor omegajAnd reliability factor r of evidencejBoth are equal, r is more than or equal to 0j≤1，0≤ωj≤1，
Figure BDA0003053727290000132
One piece of evidence in the Evidence Reasoning (ER) rule is expressed as
Figure BDA0003053727290000133
Wherein the degree of confidence
Figure BDA0003053727290000134
Representing while taking into account riAnd ωjIn case of (e)jTo proposition
Figure BDA0003053727290000136
Is defined as
Figure BDA0003053727290000137
Wherein m isθ,j＝ωjpθ,j，crω,j＝1/(1+ωj-rj) Is a normalization factor;
(5-5) fusing the J evidences by utilizing an ER rule to obtain a fusion result
Z(f(t+o))＝{(Fh,ph,e(J))|h＝1,2,...,H} (12)
Figure BDA0003053727290000138
Wherein J is 1,2h,e(J)After all J evidences are fused, supporting a fault type FhThe union of (a) supports the confidence level, f (t + o) ═ f1,t+o,f2,t+o...,fj,t+o...,fJ,t+o) For J BRB models, corresponding to the predicted value vectors at the moment of J fault characteristic variables t + o, the vector is represented by Z (f (t)+ o)) to make final decision, and determining the fault type supported by the maximum reliability as the fault type to which the sample vector f (t + o) belongs.
To facilitate an understanding of fusing all evidence, a brief explanation of examples is provided herein. Still taking two fault characteristic variables as examples, the evidence e obtained from step (5-3)1And e2Additionally, an evidence importance factor ω is setj1, reliability factor of evidence rjAs 1, the fusion evidence e can be calculated from the equations (10) to (13)1And e2As a result, Z (f (t +1)) ═ Z (f))1,t+1,,f2,t+1)＝{(F1,0.7861)(F2,0.1532)(F2,0.0325)(F2,0.0175)(F20.0107) }, since it corresponds to the failure type F1The probability of occurrence is the highest, 0.7861, so that the fault type F at the moment of t +1 can be predicted1Will occur.
Embodiments of the method of the present invention are described in detail below with reference to the accompanying drawings:
the main flow chart of the method of the invention is shown in fig. 1, and the main contents are as follows:
the corresponding BRB model can be established according to different fault characteristic variable values acquired by vibration acceleration sensors arranged at different positions of the motor rotor, and different fault characteristic variable values at future time can be predicted respectively. Similarly, a reference evidence matrix of the corresponding fault characteristic variable can be obtained from the sampling value of each fault characteristic variable, and the prediction evidence can be obtained by combining the fault characteristic variable value predicted by each BRB model at the future time with the corresponding fault characteristic variable reference evidence matrix. And then all the prediction evidences can be fused according to the fault prediction information fusion decision model, and the fault type at the future moment is predicted.
The relevant detailed steps of the invention are introduced in combination with a ZHS-2 multifunctional motor flexible rotor experimental platform, and the performance of the motor rotor fault prediction method based on confidence rule base reasoning is verified through experimental results.
1. Simulating 5 motor rotor unbalance fault types, and acquiring and installing the motor rotor unbalance fault types at different positions on the experimental platform on lineFault characteristic variable value f of 5 vibration acceleration sensors1,f2,f3,f4And f5Sampling every 3s, 200 per fault type. Each fault type is determined by 5 fault characteristic variable values together, and fig. 2 is a sampling sequence of the fault characteristic variable values collected under the 5 fault types at different times.
2. Establishing a fault characteristic variable f1BRB model BRB1，BRB1The reference value sets corresponding to the two inputs of the model are respectively A1＝{0,0.2,0.4}，A2＝{0,0.2,0.4}，BRB1Set of model output reference values as D1For {0,0.2,0.4}, 9 rules are established, and the weight of each rule is weighted
Figure BDA0003053727290000141
Is set to 1, BRB1Reliability of two inputs of the model λ1And λ2Are also all set to 1. Fault characteristic variable f1The rule base is as follows in table 2.
TABLE 2 Fault feature variables f1Rule base
Figure BDA0003053727290000142
Figure BDA0003053727290000151
And (3) repeating the steps (1) to (3), establishing another BRB models corresponding to 4 fault characteristic variables, and establishing 5 BRB models in total, wherein the current time is t, and the future t + o time is t +1, so that predicted values at the future t +1 time corresponding to the 5 fault characteristic variables can be obtained. Dividing the fault characteristic variable sample value collected in the step (2) and the corresponding fault type into a sample pair set shown in the step (5-1) to obtain a fault characteristic variable f1,f2,f3,f4And f5And combining 5 reference evidence matrixes of the corresponding reference value set and fault type mapping relation with fault characteristic variables given by 5 BRB models at t +1And (5) obtaining a prediction evidence corresponding to the prediction value of each fault characteristic variable according to the prediction value obtained in the step (5-3), and obtaining 5 prediction evidences in total, wherein the prediction evidences are respectively e1、e2、e3、e4And e5. And then fusing the 5 acquired prediction evidences according to the step (5-4) and the step (5-5) to decide the fault type at the future t +1 moment.
The test data obtained at all sampling moments are tested according to the calculation process, and the confusion matrix of the fault prediction result is shown in table 5, so that the average diagnosis rate of 5 fault modes is 96.2%. Fig. 3 is a comparison graph of predicted values and actual values of 5 fault characteristic variables at different times in one experiment, and it can be seen that the BRB model established according to the steps (1) to (3) can more accurately predict future values of the fault characteristic variables, and the effectiveness of the method of the present invention is verified by combining the average diagnosis rate of 5 fault modes.
TABLE 5 confusion matrix of predicted results
Figure BDA0003053727290000152

Claims (1)

1. A motor rotor fault prediction method based on confidence rule base reasoning is characterized by comprising the following steps:
(1) setting a motor rotor unbalance fault set theta ═ F1,F2,...,Fh,...,FH|h＝1,2,...,H}，FhRepresents the H-th fault, H, in the set of faults Θ>3 is the number of fault categories;
(2) j at rotor of electric machine under different classes of unbalance of rotor of electric machine>Collecting vibration acceleration signals at 3 different positions, converting the vibration acceleration signals into frequency domain signals by using a fast Fourier transform method, taking 1 frequency multiplication amplitude as a fault characteristic variable and recording the frequency multiplication amplitude as { f }jJ |, 1,2,., J }, then J fault characteristic variables are obtained;
(3) for J fault characteristic variables, respectively designing corresponding BRB models to predict the characteristic variablesSetting a fault characteristic variable fjIs sampled by fj,tShowing that t epsilon N + is sampling time, N + is a positive integer with the infinite number, and a j fault characteristic variable fjCorresponding BRBjThe input of the model is { fj,t-l+1,...,fj,t-1,fj,t}，l>1 is the number of model inputs, the output variable yj,t+oRepresenting the value f of the fault characteristic variable at the future t + o momentj,t+oPredicted value of (a), here o>0 is the o-th instant after the current instant t;
(3-1) in BRBjIn the model, f isj,t-l+1,...,fj,t-1,fj,tAre respectively recorded as variable x1,x2,...,xn...,xlThe model inputs a set of reference values of
Figure FDA0003053727280000011
Wherein R is>1 is the number of reference values per input, xnIs the value of the fault characteristic variable at the nth input of the model,
Figure FDA0003053727280000012
wherein
Figure FDA0003053727280000013
Is the reference value of the r-th reference level of the n-th input, and outputs yj,t+oIs set as
Dj＝{Di j|j＝1,2,...,J；i＝1,2,…,N} (2)
Wherein D1 j<D2 j<…<Di j<…<DN j，Di jIs the reference value of the ith reference level of the output, N>1 is the number of output reference values, and a rule base BRBj is constructed based on the number of output reference values;
(3-2) the rule base BRBj constructed by K rules, wherein the value of K is BRBjThe product of the numbers of all the input reference values in the model, the first onek rules RkIs described as
Figure FDA0003053727280000014
Wherein the content of the first and second substances,
Figure FDA0003053727280000015
Figure FDA0003053727280000016
indicates the value of the n-th input fault characteristic variable x of the model under the k rulenCorresponding reference value, mi,kCorresponding to D under the k rulei jAnd satisfies the k rule
Figure FDA0003053727280000021
(3-3) obtaining a sampling sequence f at the time tj,t-l+1，...，fj,t-1，fj,tThen, the input x of the BRBj model can be obtained1＝fj,t-l+1，x2＝fj,t-l+2，...，xl＝fj,tAnd calculating the matching degree of each input corresponding reference value, which comprises the following specific steps:
(a) when in use
Figure FDA0003053727280000022
Or
Figure FDA0003053727280000023
When xnTo pair
Figure FDA0003053727280000024
And
Figure FDA0003053727280000025
degree of matching of (a)n,1And alphan,RValues are all 1, and the matching degrees of other reference values are all 0;
(b) when in use
Figure FDA0003053727280000026
When p is 2,3, …, R-1, xnFor the
Figure FDA0003053727280000027
And
Figure FDA0003053727280000028
respectively has a matching degree of
Figure FDA0003053727280000029
Figure FDA00030537272800000210
At this time, the model inputs xnThe matching degrees for other reference values are all 0;
(3-4) calculating each input x of the BRBj model according to the matching degree of the input corresponding to the reference value obtained in the step (3-3)1,x2,...,xlActivated activation weight corresponding to kth rule
Figure FDA00030537272800000211
Is composed of
Figure FDA00030537272800000212
Wherein
Figure FDA00030537272800000213
Inputting x for the modelnCorresponding reference value under the kth rule
Figure FDA00030537272800000214
The degree of matching of (a) to (b),
Figure FDA00030537272800000215
is the weight of the kth rule, λ is more than or equal to 0nThe reliability of the nth input of the model is less than or equal to 1;
(3-5) obtaining the activation weight of the kth rule according to the step (3-4)
Figure FDA00030537272800000218
Then, the obtained product is subjected to correspondence D under the k rulei jConfidence m ofi,kFusing all the rules to obtain support Di jHas a confidence of
Figure FDA00030537272800000216
(3-6) calculating the future t + o time fj,t+oPredicted value y ofj,t+oIs composed of
Figure FDA00030537272800000217
(4) For each fault signature variable fjObtaining corresponding BRB according to the step (3)jModel, and obtaining predicted values y of J fault characteristic variables on linej,t+o；
(5) Constructing a fault information fusion decision model, which comprises the following specific steps:
(5-1) setting a fault characteristic variable fjStill follow the reference value set D in equation (2)i jIs marked as Aj＝{Aj,iJ | (1, 2.. J); 1,2, …, N }, wherein aj,1＝Di j,A1,2＝D2 j,...,Aj,i＝Di j,Aj,N＝DN j，Aj,iFor the jth fault signature variable fjThe corresponding ith reference level is formed by the fault characteristic variable samples collected in the steps (1) to (3) and the corresponding ith reference levelThe corresponding fault type is obtained as a set of 'sample pairs', and is marked as U { (f)j,t,Fh)}；
(5-2) establishing a fault characteristic variable f according to the sample pair set UjCorresponding reference value set AjAnd fault type FhReference Evidence Matrix (REM) of mapping relationshipsj) See Table 1
TABLE 1 fjReference evidence matrix of
Figure FDA0003053727280000031
Wherein the content of the first and second substances,
Figure FDA0003053727280000032
is the jth fault signature variable fjSupported fault type F corresponding to ith reference levelhAnd it supports the sum of the reliabilities of all fault types
Figure FDA0003053727280000033
Each column confidence in REMj is recorded as the sum of the reference value Aj,iCorresponding reference evidence
Figure FDA0003053727280000034
For each fault signature variable fjAll the corresponding REMj are established, and J are established in total;
(5-3) comparing the fault characteristic variable f in the step (4)jPredicted value y ofj,t+oActivating evidence e as input to a fault information fusion decision modeljThe specific process is as follows:
(a) when y isj,t+o≤Aj,1Or yj,t+o≥Aj,NWhen y isj,t+oTo Aj,1And Aj,NDegree of similarity ηj,1And ηj,NValues are all 1, and the similarity of other reference values is all 0;
(b) when A isj,q≤yj,t+o≤Aj,q+1When q is 2,3, …, N-1, xnFor Aj,qAnd Aj,q+1Respectively has a matching degree of
ηj,q＝(Aj,q+1-yj,t+o)/(Aj,q+1-Aj,q) (8a)
ηj,q+1＝(yj,t+o-Aj,q)/(Aj,q+1-Aj,q) (8b)
At this time, yj,t+oThe matching degrees for other reference values are all 0;
(c) for the input predicted value yj,t+oIt will fall within an interval [ A ] formed by some two reference valuesj,i,Aj,i+1]When the two reference values correspond to evidence
Figure FDA0003053727280000041
And
Figure FDA0003053727280000042
is activated, then yj,t+oCan be verified by the reference value
Figure FDA0003053727280000043
And
Figure FDA0003053727280000044
obtained as a weighted sum
ej＝{(Fh,ph,j),h＝1,...,H} (9a)
Figure FDA0003053727280000045
(5-4) obtaining J pieces of evidence together according to the step (5-3), taking the fault set theta in the step (1) as an identification frame, taking the power set of the fault set theta as P (theta), and taking the fault set as the set of all subsets of the set theta, wherein the power set of the fault set is P (theta), and the power set is the set of all subsets of the set theta
Figure FDA0003053727280000046
Setting an evidence importance factor omegajAnd reliability factor r of evidencejBoth are equal, r is more than or equal to 0j≤1，0≤ωj≤1，
Figure FDA0003053727280000047
One piece of evidence in the Evidence Reasoning (ER) rule is expressed as
Figure FDA0003053727280000048
Wherein the degree of confidence
Figure FDA0003053727280000049
Representing while taking into account rjAnd ωjIn case of (e)jTo proposition
Figure FDA00030537272800000410
Is defined as
Figure FDA00030537272800000411
Wherein m isθ,j＝ωjpθ,j，crω,j＝1/(1+ωj-rj) Is a normalization factor;
(5-5) fusing the J evidences by utilizing an ER rule to obtain a fusion result
Z(f(t+o))＝{(Fh,ph,e(J))|h＝1,2,...,H} (12)
Figure FDA00030537272800000412
Figure FDA00030537272800000413
Figure FDA00030537272800000414
Wherein J is 1,2h,e(J)After all J evidences are fused, supporting a fault type FhThe union of (a) supports the confidence level, f (t + o) ═ f1,t+o,f2,t+o...,fj,t+o...,fJ,t+o) And performing final decision on the predicted value vectors of J BRB models corresponding to J fault characteristic variables at the time of t + o by Z (f (t + o)), and determining the fault type supported by the maximum reliability as the fault type to which the sample vector f (t + o) belongs.
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