CN105373700B - A kind of mechanical failure diagnostic method based on comentropy and evidence theory - Google Patents
A kind of mechanical failure diagnostic method based on comentropy and evidence theory Download PDFInfo
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Abstract
The present invention relates to a kind of mechanical failure diagnostic method based on comentropy and evidence theory, step 1：Using four kinds of typical machine fault types come conformation identification framework；Step 2：Using four kinds of comentropies of vibration signal as fault signature；Step 3：By analogue simulation, the fault signature reference value for obtaining four kinds of typical machine fault types is calculated；Step 4：The fault vibration signal that sensor receives is obtained, its fault eigenvalue is calculated by comentropy；Step 5：Using the fault signature extracting method based on Weighted information entropy, the basic probability assignment function that sensor vibration signal distributes to four kinds of typical machine fault types is obtained；Step 6：Using based on the improvement Evidence to conflict between amendment evidence, combining evidences are carried out to obtained basic probability assignment function, obtain composite result；Step 7：According to decision rule, the final result of fault diagnosis is obtained.
Description
Technical field
The present invention relates to mechanical fault diagnosis signal processing technology field, more particularly to one kind to be managed based on comentropy and evidence
The mechanical failure diagnostic method of opinion.
Background technology
With the rapid development of science and technology and modern industry, machinery, the energy, petrochemical industry, delivery and the national defence of national economy
Etc. industry plant equipment maximize increasingly, high speed, it is integrated and automation, how to ensure that plant equipment safe operation turns into
Current research emphasis.The accurate mechanical fault diagnosis that carries out targetedly can carry out timely processing to failure, to ensureing
Plant equipment safe operation is of great importance.Fault diagnosis is using reliability theory, information theory, cybernetics and systematology as theory
Basis, using modern testing equipment and computer as technological means, gradually formed with reference to the particular law of various diagnosis phenomenons
One new branch of science.
Because the noise jamming of measuring environment, the measurement accuracy of sensor are limited to so that the vibration signal that sensor obtains
Certain error is had, simultaneously as the factor for producing mechanical oscillation is a lot, a kind of failure can be retouched with different features
State, it is jointly caused that same feature is likely to be several failures.So the diversity of failure, uncertainty and various failures
Between the complexity that contacts constitute the difficult point of mechanical fault diagnosis.Therefore, want correctly to carry out mechanical fault diagnosis to be just badly in need of
Using information fusion, multiple features fault diagnosis is carried out.
In the prior art, Publication No. CN102928231A patent proposes a kind of equipment based on D-S evidence theory
Method for diagnosing faults, independent diagnostics are carried out to equipment using a variety of diagnostic methods, then using evidence theory to multiple diagnosis sides
The result of method is integrated, and obtains the final result of fault diagnosis, still, while a variety of diagnostic methods enters guild's increase algorithm
Amount of calculation, it is impossible to realize the real-time of fault diagnosis.《IEEE 7th International Workshop on
Computational Intelligence and Applications》In meeting, " the Engine that is write by Yao Zhuting
In the texts of fault diagnosis based on the weighted DS evidence theory " one, it is contemplated that tradition card
According to the limitation of theory, it is proposed that weighted evidence is theoretical, applied to mechanical fault diagnosis；《Machine science and technology》The phase of periodical the 6th
In volume 25, " rotary machinery fault diagnosis method based on comentropy approach degree and evidence theory " one write by Geng Junbao is literary
In, comentropy approach degree is proposed to establish the basic probability assignment function of evidence theory, then row information is entered using evidence theory and melted
Close；《Electronic surveying and instrument journal》In the 7th phase of periodical volume 23, " grey correlation and evidence theory are based on by what Lin Yun write
Method for diagnosing faults " in a text, the basic probability assignment function of evidence theory is established using grey correlation theory, then use
Evidence theory carries out information fusion.Above-mentioned three kinds of methods directly carry out information fusion using evidence theory, in noisy environment and biography
In the case of sensor limited precision, the diagnostic result of mistake may be produced.
The content of the invention
It is an object of the invention to provide a kind of mechanical failure diagnostic method based on comentropy and evidence theory, Neng Gou
Fault signature is properly and efficiently extracted in the case that noisy environment and sensor accuracy are limited, in the uncertain of evidence itself
Property may cause conflict in the case of carry out fault diagnosis exactly.
Realize the technical scheme of the object of the invention：
A kind of mechanical failure diagnostic method based on comentropy and evidence theory, it is characterised in that：
Step 1：Using four kinds of typical machine fault types come conformation identification framework, described four kinds of typical machine fault types
Refer to imbalance, axle crackle, misalign and pedestal looseness；
Step 2：Using four kinds of comentropies of vibration signal as fault signature, described four kinds of comentropies refer to singular spectrum entropy,
Power Spectral Entropy, wavelet energy entropy and wavelet space state characteristic spectrum entropy；
Step 3：By analogue simulation, the fault signature reference value for obtaining four kinds of typical machine fault types is calculated；
Step 4：The fault vibration signal that sensor receives is obtained, its fault eigenvalue is calculated by comentropy；
Step 5：Using the fault signature extracting method based on Weighted information entropy, obtain sensor vibration signal and distribute to four
The basic probability assignment function of kind typical machine fault type；
Step 6：Using based on the improvement Evidence that conflicts between amendment evidence, to obtained Basic Probability As-signment letter
Number carries out combining evidences, obtains composite result；
Step 7：According to decision rule, the final result of fault diagnosis is obtained.
In step 5, specifically comprise the following steps,
Step 5.1：The fault signature reference of fault eigenvalue and typical machine fault type to sensor vibration signal
Value carries out numeric ratio pair, according to different weight calculation sensor vibration signals and four kinds of typical machine fault types apart from letter
Number, constructive formula are as follows
Wherein, k=1,2,3,4 represent the kth kind comentropy of fault signature, wkRepresent the weight of kth kind comentropy, wk∈
[0,1], assignment, H are carried out according to concrete applicationikThe kth kind comentropy of i-th of sensor is represented,Represent jth kind typical case's machine
The kth kind comentropy of tool fault type；
Step 5.2：The similarity of sensor vibration signal and four kinds of typical machine fault types is calculated using exponential function；
Constructive formula is as follows,
Wherein, e is the truth of a matter of natural logrithm in exponential function；
Step 5.3：Similarity is normalized, the substantially general of each typical machine fault type is distributed to as sensor
Rate assignment function, constructive formula is as follows,
In formula, M represents the sum of sensor.
In step 6, specifically comprise the following steps,
Step 6.1：The distance function between evidence two-by-two is calculated according to Ming Shi distances；
mi,mj(i, j=1,2 ..., M) it is identification framework Θ={ R1,R2,R3,R4Two BPA, R1,R2,R3,R4Point
Other four kinds of typical machine fault types of table, constructive formula is as follows,
M is obtained according to Ming Shi distancesi,mjDistance function between evidence, constructive formula is as follows,
Wherein, dBPADistance function between evidence, l=1,2,3,4 be l kind typical machine fault types, plFor evidence
miTo the basic probability assignment function apportioning cost of l kind typical machine fault types, qlFor evidence mjTo the event of l kinds typical machine
Hinder the basic probability assignment function apportioning cost of type；
Step 6.2：According to the distance function between evidence, the similarity and evidence support between evidence are calculated；
Step 6.3：Screening amendment is carried out to evidence according to the distribution of Distance support；
Step 6.4：Corrected evidence support will be screened to be normalized to obtain Certainty Factor；
Step 6.5：The weighted sum that evidence is carried out using Certainty Factor as weighted factor averagely obtains correcting evidence；
Step 6.6：M-1 evidence fusion is carried out using DS composition rules, obtains composite resultRepresent sensor
Vibration signal distributes to the basic probability assignment function of four kinds of typical machine fault types, and the constructive formula of DS composition rules is such as
Under,
Wherein, Rj1,Rj2,...,RjnRespectively evidence m1,m2,...,mnIn jth kind typical machine fault type this
Event, Φ are empty set, represent this event of indeterminate fauit.
In step 7, the building method of decision rule is as follows,
If meet：
The device have the advantages that：
The present invention is first with the fault signature extracting method based on Weighted information entropy, with reference to four kinds of comentropies, including it is strange
Different spectrum entropy, Power Spectral Entropy, wavelet energy entropy and wavelet space state characteristic spectrum entropy, consider time domain, frequency domain and time-frequency domain three
Aspect, accurately extract fault signature, so as to get fault signature there is more preferable integrality and accuracy；Then using being based on
The improvement Evidence to conflict between amendment evidence, on the basis of DS composition rules, Ming Shi distances are introduced, to evidence support
It is modified, it is possible to increase the validity and reliability of composite result.The present invention can have in noisy environment and sensor accuracy
Fault signature is properly and efficiently extracted in the case of limit, in the case where the uncertainty of evidence itself may cause conflict
Fault diagnosis is carried out exactly, reaches the purpose for ensureing plant equipment safe operation.
Brief description of the drawings
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is the method for building up of fault signature.
Embodiment
As shown in figure 1, the mechanical failure diagnostic method of the invention based on comentropy and evidence theory, method flow diagram include
Following steps：
Step 1：The construction of identification framework.Using four kinds of typical mechanical breakdown types come conformation identification framework Θ={ R1,
R2,R3,R4, wherein, Θ represents identification framework, R1,R2,R3,R4Imbalance, axle crackle are represented respectively, are misaligned and pedestal looseness
Four kinds of typical machine fault types.
Step 2：The foundation of fault signature.Fault signature F using four kinds of comentropies of vibration signal as the vibration signal
=[H1,H2,H3,H4], specific acquisition methods are as shown in Figure 2.Wherein, H1,H2,H3,H4Singular spectrum entropy, power spectrum are represented respectively
Entropy, wavelet energy entropy and wavelet space state characteristic spectrum entropy.
Four kinds of comentropies are calculated as follows：
Singular spectrum entropy：The component time series X=[x received to sensor1,x2,...,xN], using the embedding sunken skill that is delayed
Signal is mapped to embedded space by art, the track matrix A of a M rows N row is obtained, shown in building method such as formula (1).
Wherein, M is the length of the embedded space, and N is the length of time series.
Singular value decomposition is carried out to track matrix A, obtains singular value δ1≥δ2≥...≥δM, then singular spectrum { δ1,δ2,...,
δMIt is that the one kind of vibration signal in time domain is divided, the singular spectrum entropy of vibration signal is defined, shown in building method such as formula (2).
Wherein, n=1,2 ..., M,For n-th of singular value proportion shared in whole singular spectrum, lg is
Denary logarithm function.
Power Spectral Entropy：It is X (f) by the discrete Fourier transform for calculating component time series, obtains its power spectrum P (f),
Shown in building method such as formula (3)
Wherein, f is the frequency of time series.
Signal transforms to the conservation of energy in Frequency domain procedures by time domain, then power spectrum { P1,P2,...,PMIt is to vibration signal
Divided in one kind of frequency domain, the Power Spectral Entropy of vibration signal is defined, shown in building method such as formula (4).
Wherein,For n-th of power spectral value proportion shared in whole power spectrum.
Wavelet energy entropy：Time series with finite energy conservation of energy before and after wavelet transformation, by wavelet transformation,
The wavelet energy E (a) under different scale is obtained, shown in building method such as formula (5).
Wherein, a is the yardstick of wavelet transformation, is positive number, b is displacement, can just can be born, Wf(a, b) is the width of wavelet transformation
Value.
Wavelet Energy Spectrum { E1,E2,...,EMIt is that one kind of signal energy is divided in scale domain, define wavelet energy
Entropy is composed, shown in building method such as formula (6).
Wherein,For n-th of wavelet energy proportion shared in whole Wavelet Energy Spectrum.
Wavelet space state characteristic spectrum entropy：The Energy distribution matrix of 2-d wavelet after wavelet transformation spatially is carried out unusual
Value is decomposed, and singular spectrum isAs the feature of time series, similar to the singular spectrum entropy of time domain.Define time-frequency
The wavelet space state characteristic spectrum entropy in domain, shown in building method such as formula (7).
Wherein,For n-th of characteristic value proportion shared in whole characteristic spectrum.
Step 3：The fault eigenvalue that four kinds of typical machine fault types are obtained by analogue simulation is used as fault signature ginseng
Examine value.
Simulate four kinds of typical machine fault type Ri(i=1,2,3,4) fault signature reference value when producingI=1,2,3,4, wherein, i represents i-th kind of typical machine fault type, RiRepresent i-th kind of typical case
This event of mechanical breakdown type,Four kinds of comentropies of i-th kind of typical fault type are represented respectively：It is unusual
Entropy, Power Spectral Entropy, wavelet energy entropy and wavelet space state characteristic spectrum entropy are composed,I-th kind of typical machine fault type of expression
Fault signature reference value.
Step 4：The fault vibration signal that sensor receives is obtained, its fault signature is calculated by comentropy.
The vibration signal that sensor is received carries out the calculating of comentropy, obtains sensor vibration signal Sj(j=1,
2 ..., M) fault signature Fj=[Hj1,Hj2,Hj3,Hj4], j=1,2 ..., M, wherein, j represents j-th of sensor, and M is represented
The sum of sensor, SjRepresent j-th of sensor vibration signal, Hj1,Hj2,Hj3,Hj4J-th of sensor vibration letter is represented respectively
Number four kinds of comentropies：Singular spectrum entropy, Power Spectral Entropy, wavelet energy entropy and wavelet space state characteristic spectrum entropy, FjRepresent j-th
The fault signature of sensor vibration signal；
Step 5：The acquisition of basic probability assignment function.Obtained using the fault signature extracting method based on Weighted information entropy
Basic probability assignment function of the sensor vibration signal with respect to four kinds of typical machine fault types.Specifically comprise the following steps：
Step 5.1：The fault signature reference of fault eigenvalue and typical machine fault type to sensor vibration signal
Value carries out numeric ratio pair, according to different weight calculation sensor vibration signals and four kinds of typical machine fault types apart from letter
Number, shown in building method such as formula (8)；
Wherein, k=1,2,3,4 represent the kth kind comentropy of fault signature, wkRepresent the weight of kth kind comentropy, wk∈
[0,1], assignment, H are carried out according to concrete applicationikThe kth kind comentropy of i-th of sensor is represented,Represent jth kind typical case's machine
The kth kind comentropy of tool fault type.
Step 5.2：The similarity of sensor vibration signal and four kinds of typical machine fault types is calculated using exponential function；
Shown in building method such as formula (9)；
Wherein, e is the truth of a matter of natural logrithm in exponential function.
Step 5.3：Similarity is normalized, the substantially general of each typical machine fault type is distributed to as sensor
Rate assignment function, shown in building method such as formula (10).
Step:6：Combining evidences.It is basic to what is obtained using based on the improvement Evidence that conflicts between amendment evidence
Probability assignment function carries out combining evidences, obtains composite result.Specifically comprise the following steps：
Step 6.1：The distance function between evidence two-by-two is calculated according to Ming Shi distances；
mi,mj(i, j=1,2 ..., M) it is identification framework Θ={ R1,R2,R3,R4Two BPA, building method is as public
Shown in formula (11).
M is obtained according to Ming Shi distancesi,mjDistance function between evidence, shown in building method such as formula (12).
Wherein, dBPADistance function between evidence, l=1,2,3,4 be l kind typical machine fault types, plFor evidence
miTo the basic probability assignment function apportioning cost of l kind typical machine fault types, qlFor evidence mjTo the event of l kinds typical machine
Hinder the basic probability assignment function apportioning cost of type.Ming Shi distances are that one kind in theorem in Euclid space is estimated, and are Euclidean distances and graceful
The popularization of Hatton's distance, it is manhatton distance as m=1 in Ming Shi distances；It is Euclidean distance as m=2；As m → ∞
When, it is Chebyshev's distance.
Step 6.2：According to the distance function between evidence, the similarity and evidence support between evidence, building method are calculated
Respectively as shown in formula (13) and formula (14)；
sim(mi,mj)=1-dBPA(mi,mj) (13)
Wherein, sim is writing a Chinese character in simplified form for similarity, represents the similarity between evidence, and sup is writing a Chinese character in simplified form for support, is represented
Evidence support.
Step 6.3：Screening amendment is carried out to evidence according to the distribution of Distance support, wherein, the average of evidence support
With the building method of standard deviation respectively as shown in formula (15) and formula (16), the method such as formula of evidence support is corrected in screening
(17) shown in；
Wherein,ε is predetermined threshold value.As ρ >=σ and ρ >=ε, represent that evidence is supported
Degree and evidence support average differ greatly, it is believed that the evidence is unreasonable, therefore makes sup'(mi)=0.
Step 6.4：Corrected evidence support will be screened to be normalized to obtain Certainty Factor, building method such as public affairs
Shown in formula (18)；
Crd is writing a Chinese character in simplified form for credibility, represents Certainty Factor.WhenWhen, represent evidence between mutually not
Support,When, represent to support completely between evidence, this season
Step 6.5：The weighted sum that Certainty Factor carries out evidence as weighted factor averagely obtains correcting evidence, construction side
Shown in method such as formula (19).
Wherein,
Step 6.6：M-1 evidence fusion is carried out using DS composition rules, obtains composite resultRepresent sensor
Vibration signal distributes to the basic probability assignment function of four kinds of typical machine fault types, the building method such as public affairs of DS composition rules
Shown in formula (20).
Wherein, Rj1,Rj2,...,RjnRespectively evidence m1,m2,...,mnIn jth kind typical machine fault type this
Event, Φ are empty set, represent this event of indeterminate fauit.
Step 7：Merge decision-making.According to decision rule, the final result of fault diagnosis, the building method of decision rule are obtained
It is as follows.
If meet：
Then the result of decision is Ri, otherwise, result of decision Φ.
Shown herein as when composite result meets：The final result of fault diagnosis is the maximum in combining evidences result；Therefore
Hinder the final result of diagnosis and the difference of other diagnostic result maximums is more than threshold value set in advance；Fault diagnosis it is final
As a result it is more than threshold value set in advance, the final result of fault diagnosis is typical fault type Ri, otherwise fault diagnosis is most
Termination fruit is indeterminate fauit.
With reference to specific embodiment, beneficial effects of the present invention are further illustrated.
Embodiment 1：Assuming that measuring environment is good, the precision of sensor is good.Under MATLAB simulated conditions, one is simulated
The failure misaligned, it is assumed that the number M=4 of sensor, comentropy weight w1=w2=0.1, w3=w4=0.4, preset door
Limit value ε=0.03, ε1=0.15, ε2=0.4, emulation experiment is carried out to beneficial effects of the present invention：
The fault signature reference value of typical machine fault typeThe concrete numerical value such as institute of table 1
Show, the fault signature F for the vibration signal that sensor receivesj=[Hj1,Hj2,Hj3,Hj4] concrete numerical value as shown in table 2
The fault signature reference value of 1 four kinds of typical machine fault types of table
The fault signature of 2 four sensor vibration signals of table
Sensor distributes to the basic probability assignment function m of typical machine fault typei(Rj) the concrete numerical value such as institute of table 3
Show.
The sensor of table 3 distributes to the basic probability assignment function of each typical machine fault type
From table 3 it is observed that four sensors judge mechanical breakdown type to misalign failure using maximum trust,
Now conflict between evidence low.
Certainty Factor crd (mi) concrete numerical value it is as shown in table 4, composite resultConcrete numerical value is as shown in table 5.
The Certainty Factor of table 4
The combining evidences result of table 5
It can further be proved from table 4, be mutual trust between evidence.
According to decision rule, the final result for obtaining fault diagnosis is：Mechanical breakdown type is to misalign failure.
Embodiment 2：Assuming that measuring environment is severe, the precision of sensor is poor.Under MATLAB simulated conditions, one is simulated
The failure misaligned, the setting of design parameter and embodiment 1 are identical, and emulation experiment is carried out to beneficial effects of the present invention：
Obtain the fault signature F of sensor vibration signalj=[Hj1,Hj2,Hj3,Hj4], concrete numerical value is as shown in table 6.
The fault signature of 6 four sensor vibration signals of table
Sensor distributes to the basic probability assignment function m of typical machine fault typei(Rj) the concrete numerical value such as institute of table 7
Show.
The sensor of table 7 distributes to the basic probability assignment function of each typical machine fault type
As can be seen from Table 7, present sensor S1、S2、S3Judge mechanical breakdown type to be not right using maximum trust
Middle failure, and sensor S4But mechanical breakdown type is judged as axle crack fault using maximum trust, rather than misaligns failure, this
When evidence between conflict it is higher.
Certainty Factor crd (mi) concrete numerical value it is as shown in table 8, composite resultConcrete numerical value is as shown in table 9.
The Certainty Factor of table 8
The combining evidences result of table 9
As can be seen from Table 8, by conflicting between amendment evidence, the present invention can be with debug sensor S4Influence.
According to decision rule, the final result for obtaining fault diagnosis is：Mechanical breakdown type is to misalign failure.
The result of embodiment 1 and embodiment 2 shows that the present invention can not only measure in good environment and compared with low sensor
Fault diagnosis is correctly carried out in the case of error, can also correctly be carried out in the case where noisy environment and sensor accuracy are limited
Fault diagnosis.
Claims (2)
- A kind of 1. mechanical failure diagnostic method based on comentropy and evidence theory, it is characterised in that：Step 1：Referred to using four kinds of typical machine fault types come conformation identification framework, described four kinds of typical machine fault types Imbalance, axle crackle, misalign and pedestal looseness；Step 2：Refer to singular spectrum entropy, power using four kinds of comentropies of vibration signal as fault signature, described four kinds of comentropies Compose entropy, wavelet energy entropy and wavelet space state characteristic spectrum entropy；Step 3：By analogue simulation, the fault signature reference value for obtaining four kinds of typical machine fault types is calculated；Step 4：The fault vibration signal that sensor receives is obtained, its fault eigenvalue is calculated by comentropy；Step 5：Using the fault signature extracting method based on Weighted information entropy, obtain sensor vibration signal and distribute to four kinds of allusion quotations The basic probability assignment function of type mechanical breakdown type；Step 6：Using based on the improvement Evidence to conflict between amendment evidence, obtained basic probability assignment function is entered Row combining evidences, obtain composite result；Step 7：According to decision rule, the final result of fault diagnosis is obtained；In step 5, specifically comprise the following steps,Step 5.1：The fault signature reference value of fault eigenvalue and typical machine fault type to sensor vibration signal is entered Line number value compares, according to different weight calculation sensor vibration signals and the distance function of four kinds of typical machine fault types, Constructive formula is as followsWherein, k=1,2,3,4 represent the kth kind comentropy of fault signature, wkRepresent the weight of kth kind comentropy, wk∈[0, 1], assignment, H are carried out according to concrete applicationikThe kth kind comentropy of i-th of sensor is represented,Represent jth kind typical machine The kth kind comentropy of fault type；Step 5.2：The similarity of sensor vibration signal and four kinds of typical machine fault types is calculated using exponential function；Construction Formula is as follows,Wherein, e is the truth of a matter of natural logrithm in exponential function；Step 5.3：Similarity is normalized, the elementary probability that each typical machine fault type is distributed to as sensor is assigned Value function, constructive formula is as follows,In formula, M represents the sum of sensor；In step 6, specifically comprise the following steps,Step 6.1：The distance function between evidence two-by-two is calculated according to Ming Shi distances；mi,mjIt is identification framework Θ={ R1,R2,R3,R4Two BPA, i, j=1,2 ..., M, R1,R2,R3,R4Table four respectively Kind typical machine fault type, constructive formula is as follows,M is obtained according to Ming Shi distancesi,mjDistance function between evidence, constructive formula is as follows,Wherein, dBPADistance function between evidence, l=1,2,3,4 be l kind typical machine fault types, plFor evidence miIt is right The basic probability assignment function apportioning cost of l kind typical machine fault types, qlFor evidence mjTo l kind typical machine failure classes The basic probability assignment function apportioning cost of type；Step 6.2：According to the distance function between evidence, the similarity and evidence support between evidence are calculated；Step 6.3：Screening amendment is carried out to evidence according to the distribution of Distance support；Step 6.4：Corrected evidence support will be screened to be normalized to obtain Certainty Factor；Step 6.5：The weighted sum that evidence is carried out using Certainty Factor as weighted factor averagely obtains correcting evidence；Step 6.6：M-1 evidence fusion is carried out using DS composition rules, obtains composite resultRepresent sensor vibration Signal distributes to the basic probability assignment function of four kinds of typical machine fault types, and the constructive formula of DS composition rules is as follows,Wherein, Rj1,Rj2,...,RjnRespectively evidence m1,m2,...,mnIn jth kind typical machine fault type this event, Φ is empty set, represents this event of indeterminate fauit.
- 2. the mechanical failure diagnostic method according to claim 1 based on comentropy and evidence theory, it is characterised in that：Step In rapid 7, the building method of decision rule is as follows,Wherein i=1,2,3,4, j=1,2,3,4, if meeting：Then the result of decision is Ri, otherwise, result of decision Φ；When composite result meets：The final result of fault diagnosis is the maximum in combining evidences result；Fault diagnosis it is final As a result the difference with other diagnostic result maximums is more than threshold value set in advance；The final result of fault diagnosis is more than advance The threshold value of setting, then the final result of fault diagnosis is typical fault type Ri, otherwise the final result of fault diagnosis is not Determinate fault.
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