CN109657797A - Trouble diagnosibility analysis method based on hybrid diagnosis Bayesian network - Google Patents
Trouble diagnosibility analysis method based on hybrid diagnosis Bayesian network Download PDFInfo
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Abstract
The invention discloses a kind of trouble diagnosibility analysis methods based on hybrid diagnosis Bayesian network, are related to method for diagnosing faults technical field.Described method includes following steps: probability of malfunction association amendment: based on reliability data, whether deficient and fault mode probability of malfunction confidence level is higher than the two criterion selections of functional fault probability, carries out probability of malfunction association amendment to component；Hybrid diagnosis Bayesian network model is established and reasoning: being associated with the forming types of correction result selection hybrid diagnosis Bayesian network model based on probability of malfunction, is carried out the modeling of hybrid diagnosis Bayesian network model and reasoning；Trouble diagnosibility index calculates.The method improves the accuracy of Analysis on Fault Diagnosis modeling and the confidence level of testability index intended result.
Description
Technical field
The present invention relates to method for diagnosing faults technical field more particularly to a kind of events based on hybrid diagnosis Bayesian network
Hinder diagnosis capability analysis method.
Background technique
Currently, since information flow model, multi-signal flow graph model etc. lack to uncertain in fault propagation, test process
The considerations of factor, causes current many testability index predicted values and actual value deviation based on fault diagnosis model very big, no
It is horizontal conducive to product physical fault diagnosis capability is quantitatively evaluated.
Summary of the invention
The technical problem to be solved by the present invention is to how to provide it is a kind of can be improved Analysis on Fault Diagnosis modeling it is accurate
The method of the confidence level of degree and testability index intended result.
In order to solve the above technical problems, the technical solution used in the present invention is: a kind of be based on hybrid diagnosis Bayesian network
The trouble diagnosibility analysis method of network, it is characterised in that include the following steps:
Probability of malfunction association amendment: based on reliability data, whether deficient and fault mode probability of malfunction confidence level is high
In the two criterion selections of functional fault probability, probability of malfunction association amendment is carried out to component；
Hybrid diagnosis Bayesian network model is established and reasoning: being associated with correction result selection hybrid diagnosis based on probability of malfunction
The forming types of Bayesian network model carry out the modeling of hybrid diagnosis Bayesian network model and reasoning；
Trouble diagnosibility index calculates: the root node based on generation-test relies on matrix, root node-test inspection
Survey-false-alarm probability matrix, probability of malfunction association correction result carry out the fault diagnosis based on hybrid diagnosis Bayesian network model
Capacity index calculates, formation component trouble diagnosibility index prediction address, completes hybrid diagnosis Bayesian network fault diagnosis
Capability analysis.
The beneficial effects of adopting the technical scheme are that the method is repaired by probability of malfunction association first
Just, the foundation of hybrid diagnosis Bayesian network model and reasoning then are being carried out, is finally carrying out the calculating of trouble diagnosibility index, mentions
The high accuracy of Analysis on Fault Diagnosis modeling and the confidence level of testability index intended result.
Detailed description of the invention
The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
Fig. 1 is four kinds of dependence graphs in the embodiment of the present invention between the source of trouble and test；
Fig. 2 is in the embodiment of the present invention without the dependence graph between failure under the asymmetric test case of false-alarm and test；
Fig. 3 is the dependence graph having under the symmetrical test case of false-alarm between failure and test in the embodiment of the present invention；
Fig. 4 is the dependence graph in the embodiment of the present invention in the case of Determinate test between failure and test；
Fig. 5 is the state transition graph of four kinds of situations in the embodiment of the present invention；
Fig. 6 is Bayesian network fault diagnosis model figure in the embodiment of the present invention；
Fig. 7 is the failure composition figure of certain LRU component in the embodiment of the present invention；
Fig. 8 is fault mode and functional association relation identification process figure in the embodiment of the present invention；
Fig. 9 is subordinating degree function curve graph in the embodiment of the present invention；
Figure 10 is the bigraph (bipartite graph) expression figure of fault mode and functional association relation in the embodiment of the present invention；
Figure 11 is fault mode and functional fault probability original value expression figure in the embodiment of the present invention；
Figure 12 is test in the embodiment of the present invention, fault mode, function, the mixed dependence relational graph between LRU；
Figure 13 a- Figure 13 c is three kinds of segmentation subgraphs in the embodiment of the present invention；
Figure 14 is the graph theory information syncretic relation figure of HDBN in the embodiment of the present invention, BN and HDM；
Figure 15 a- Figure 15 b is two kinds of representation figures of hybrid diagnosis Bayesian network model in the embodiment of the present invention；
Figure 16 is the HDBN figure of removing function hidden layer in the embodiment of the present invention；
Figure 17 is the Bayesian network fault diagnosis model reformulations figure of HDBN in the embodiment of the present invention；
Figure 18 is the flow chart of the method for the invention.
Specific embodiment
With reference to the attached drawing in the embodiment of the present invention, technical solution in the embodiment of the present invention carries out clear, complete
Ground description, it is clear that described embodiment is only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to facilitate a full understanding of the present invention, but the present invention can be with
Implemented using other than the one described here other way, those skilled in the art can be without prejudice to intension of the present invention
In the case of do similar popularization, therefore the present invention is not limited by the specific embodiments disclosed below.
Traditional failure and test correlation models has ignored unascertained information, can not describe potential event in a model
Hindering false-alarm and missing inspection problem, these problems may be developed to PHM (fault diagnosis and fault prediction) and bring material risk with use,
It needs to consider the description to uncertain test information as far as possible in product failure and test correlation modeling thus.It will give below
It has failure and test correlation modeling method based on uncertain test information.
Enable fault set S={ s1,s2,...,smIndicate, it can be using value as product function collection F or fault mode collection FM.
It is assumed for convenience of description that test is that binary is tested, to failure siWith test tjValue make following qualitative hypothesis.
siWith tjBetween there are four kinds shown in FIG. 1 may rely on state, wherein PdijIndicate siIn the event of failure, tjDo not lead to
The probability crossed, also known as tjTo siDetection probability.PfijIndicate siWhen fault-free, tjUnsanctioned probability, also known as tjTo siFalse-alarm
Probability.
Based on mathematical logic and bayesian theory, Pr (t is enabledj) it is tjUnacceptable probability,For tjBy it is general
Rate, Pr (si) it is siFaulty probability,For siTrouble-free probability, then have
Pdij=Pr (tj|si) (3)
In Fig. 1, four edges respectively correspond following four kinds of dependences.
Relationship is 1.: siFailure, tjDo not pass through, to be correct by instruction, corresponding probability is Pdij；
Relationship is 2.: siFailure, tjPass through, is incorrect instruction to fail to pinpoint a disease in diagnosis, corresponding probability is 1-Pdij；
Relationship is 3.: siNormally, tjDo not pass through, be false-alarm, be incorrect instruction, corresponding probability is Pfij；
Relationship is 4.: siNormally, tjPass through, to be correct not by instruction, corresponding probability is 1-Pfij。
In Fault diagnosis design and analytic process, according to the completeness of detection probability and false-alarm probability data, Ke Yifen
To there is the test of false-alarm asymmetry, without the test of false-alarm asymmetry, there is false-alarm symmetrically to test, symmetrically test four kinds of situations without false-alarm.
Situation is 1.: having the asymmetric test of false-alarm.At this point, Pfij≠ 0, Pdij≠ 1, relationship such as Fig. 1 institute between failure and test
Show.
Situation is 2.: without the asymmetric test of false-alarm.At this point, Pfij=0, Pdij≠ 1, relationship such as Fig. 2 institute between failure and test
Show.
Situation is 3.: having false-alarm symmetrically to test.At this point, Pfij≠ 0, Pdij=1, relationship such as Fig. 3 institute between failure and test
Show.
Situation is 4.: no false-alarm symmetrically tests also known as Determinate test.At this point, Pfij=0, Pdij=1, between failure and test
Relationship it is as shown in Figure 4.
The state transition graph of four kinds of situations is as shown in figure 5, should be according to the complete situation of detection probability and false-alarm probability data
Select corresponding fault diagnosis modeling method.
Enable tjS cannot be detectediWhen, Pdij=Pfij=0, with detection-false-alarm probability to (Pdij,Pfij) indicate tjTo si's
Test is uncertain.PFIijIndicate tjTo siProvide the probability of false judgment
PTIijIndicate tjTo siProvide the probability correctly judged, also known as tjTo siTest accuracy.
If n mutually indepedent to each other, the s of test in TiIt is by the probability of error indication
PdijAnd PfijData can be specified by expert, but the data for specifying method to provide based on expert often with real data
Deviation is larger.Scientific method is to learn Pd by sample data training relativelyijAnd Pfij, also known as data-driven method.Data
Driving method can be divided into complete data collection driving method and Incomplete data set driving method according to the actual observation situation of data.It is complete
Each test in data set driving method, all has complete actual observation data, and Incomplete data set driving method refers to certain
The actual observation data of test have the phenomenon of excalation or exception.It includes Monte Carlo method, Gauss that incomplete data, which drives method,
Approximatioss, expectation maximization method, maximum a posteriori probability method etc..It mainly includes Maximum Likelihood Estimation Method and shellfish that complete data, which drives method,
Ye Sifa, wherein Maximum Likelihood Estimation Method is easy to grasp.Maximum-likelihood estimation thinks that for big-sample data sample average be to become
It is bordering on desired value, under this hypothesis, PdijIt can be indicated with formula (8)
PfijCan also be similarly defined for
Fault diagnosis modeling based on Bayesian network
The fault diagnosis models such as information flow model, multi-signal flow graph model are constructed under Determinate test hypothesis,
The presence for having ignored unascertained information, the fault detection rate provided, Percent Isolated index intended result and truth are inclined
Difference is larger.For this reason, it may be necessary to design a kind of fault diagnosis model that can describe uncertain test information, testability index is improved
It is expected that confidence level.
Bayesian network be considered as uncertainty knowledge in artificial intelligence study indicate and the major technique of reasoning and
Excellent tool is more widely deployed for complication system uncertainties model field, is the research heat of current diagnosis modeling aspect
One of point, is presented below the fault diagnosis modeling method based on Bayesian network.
Bayesian network model:
Bayesian network is also known as bayesian belief networks, is a kind of oriented diagram description based on network structure, is artificial
The product that intelligence, probability theory, graph theory combine.Bayesian network is wanted with each information of oriented graph expression with network structure
Incidence relation and influence degree between element express each information element with node variable, with the directed edge between link node
The incidence relation between each information element is expressed, expresses the influence degree between each information element with conditional probability.
One Bayesian network is the directed acyclic graph for showing dependence between variable, can use ternary digraph B N=
(V, E, P) is indicated, wherein V is nodal set, and node represents stochastic variable, and stochastic variable can be the abstract of any problem, such as produce
Product component, test result, phenomenon of the failure etc.；E is directed edge collection, and directed edge represents the incidence relation between node, usually cause and effect
Relationship；P is weight matrix, the causal influence intensity between node, and each node has a conditional probability table (Conditional
Probability Table, CPT), its effect of all father nodes to the node for quantificational expression.
Bayesian network is based on conditional independence assumption, and independence therein is divided into following three kinds substantially:
(1) root node is conditional sampling；
(2) with the node of multiple father nodes, when there is no incidence relation, father node state given between them, then they
Conditional sampling；
(3) to any node, when the state for giving its all father node (direct parents), then the node and all ancestors are tied
Point is all conditional sampling.
Enable V={ V1,V2,...,Vn, A (Vi) indicate non-ViAny node subset that consequent node is constituted, π (Vi) indicate Vi
Father node, then node ViConditional probability are as follows:
Pr(Vi|A(Vi),Π(Vi))=Pr (Vi|π(Vi)) (10)
Under above-mentioned condition independence assumption, the Joint Distribution probability of variable are as follows:
According to node and its correlation, conditional probability table, Bayesian network can expression system Bayesian network mould
The joint probability of all nodes in type, and can be according to any other node of exploitation of priori probability information or certain nodes
Probabilistic information.
The modeling of Bayesian network fault diagnosis:
Bayesian network fault diagnosis model is the abbreviation of " failure-test result " Bayesian network model, can use four
First digraph B NT=(S, T, E, P) indicates, the V in Bayesian network BN=(V, E, P) is divided into fault set S and test
Collect two subsets of T, V=S ∪ T, S ∩ T=φ, P=PS ∪ PDF, PS ∩ PDF=φ, fault rate integrates as PS={ Pr
(s1=1), Pr (s2... ,=1) Pr (sm=1) whole root node items in Bayesian network fault diagnosis model }, are covered
Part probability tables；PDF={ PD, PF }={ [Pdij],[Pfij] indicate detection-false-alarm probability collection, it can be with Bayesian network
Whole child node conditional probability tables in fault diagnosis model mutually convert.
Fig. 6 is the Bayesian network fault diagnosis model under a typical binary test case.
Because of V (BNT)=S ∪ T, S ∩ T=φ, and in Bayesian network fault diagnosis model each edge tail portion all in S
In, head all in T, so Bayesian network fault diagnosis model is two digraphs.
It enables and relies on matrix D=[dij] indicate S and T between dependence, wherein if test tjDetect source of trouble si, then
dij=1, otherwise dij=0, D are equivalent to two digraph boolean's adjacency matrix of Bayesian network fault diagnosis model.The table of D
Show that form is as follows.
Based on conditional independence assumption, for any two difference variable s in Si, sjHave
Pr(si|sj)=Pr (si)i≠j (12)
Equally, for any two difference variable t in Ti, tjHave
Pr(ti|tj)=Pr (ti)i≠j (13)
In the case where binary test, Pr (tj) calculation method be
Due to si, tjIt is all boolean's value, and Bayesian network is oriented bigraph (bipartite graph), soAnd π (tj)=
{si|dij=1 }, therefore have
Formula (15) are substituted into formula (14), acquire test tjUnacceptable probability is
Test tjBy probability be
It will test probability P dijCalculation formula (5) and false-alarm probability PfijCalculation formula (6) substitutes into formula (16) and (17),
Then have
Pdij, PfijValue and dijValue exist such as equivalence
If dij=1, then siFor tjA father node, siTo tjCausal influence intensity can use condition shown in table 1
Probability tables indicate.
1 s of tableiWith tjConditional probability table
If with whole dij=1 corresponding detection-false-alarm probability is to (Pdij,Pfij) it is known that can then describe pattra leaves
Whole child node conditional probability tables in this network fault diagnosis model.The conditional probability table of the corresponding Bayesian network of Fig. 6 is such as
Shown in table 2.
The conditional probability table of 2 Fig. 6 of table
It includes two parts that the modeling of Bayesian network fault diagnosis, which needs the basic object information inputted:
(1) certainty information part includes fault set S, test set T, relies on matrix D；
(2) unascertained information part includes fault rate collection PS, detection-false-alarm probability collection PDF.
The acquisition methods of each element information are as follows in Bayesian network fault diagnosis model:
S can pass through the function division and fault mode division acquisition in fail-safe analysis；
T can be based on Fault diagnosis design information acquisition；
D can be based on historical experience, fault diagnosis model, emulation testing conclusion, Failure Mode Effective Analysis, faulty word
Allusion quotation, fault tree, Petri net model etc. obtain, and can also be obtained by bayesian network structure learning；
PS can be obtained by fail-safe analysis, fault tolerance analysis, Monte Carlo analysis etc.；
PDF can be obtained by data-driven method etc..
Testability modeling field of the Bayesian network fault diagnosis model under uncertain test case can obtain good
Good effect, but it there are following main problems:
Feedback loop cannot be handled, often occurs feedback loop in fault propagation process, and Bayesian network fault diagnosis model
It is two directed acyclic graphs；
Approachability analysis is indifferent, it is difficult to carry out the fault mode mechanism of transmission based on Bayesian network fault diagnosis model
Analysis；
Source of trouble ambiguity in definition, the definition of source of trouble collection S is more fuzzy, includes function, component, fault mode failure in S
Deng, and there is incidence relations in itself between function, component, fault mode.
Fault mode and function dependence based on hybrid diagnosis model are analyzed
Hybrid diagnosis model:
Hybrid diagnosis model is the abbreviation of " fault mode-function-test " hybrid diagnosis model, it is " failure mould
The fusion of formula-test " correlation models and " function-test " correlation models, realizes fault mode and function same
The target of unified Modeling in one correlation models.Hybrid diagnosis model can intervene the failure of product initial development and design phase
Diagnosis capability design and analysis is a kind of fault diagnosis model towards product life cycels.By to hybrid diagnosis model
Modeling mechanism carry out going deep into parsing, obtain hybrid diagnosis model basic element composition are as follows:
Component set C={ c1,c2,…,cL}；
Function collection F={ f1,f2,…,fJ}；
Fault mode collection FM={ fm1,fm2,…,fmI}；
Test set T={ t1,t2,…,tn}；
Fault mode fmiThe function collection always affectedaffmi=|
AFFM(fmi)|；
Fault mode fmiSometimes the function collection influencedsffmi=|
SFFM(fmi)|；
Component ciAssociated function collectionFc=| FC (ci)|；
Component ciFault mode collectionFmc=| FMC (ci)|；
Function fjAssociated component setCf=| CF (fj)|；
FunctionAssociated FMC (ci) fault mode subset
Fault modeAssociated FC (ci) function subset
Component faults rate collection λ (C)={ λ (c1),λ(c2),...,λ(cL)}；
Function fjIn component ciThe failure rate of upper distribution
Fault mode fmjIn component ciThe failure rate of upper distribution
FunctionThe modified functional fault probability of primary fault probability
Fault modePrimary fault probabilityModified fault mode probability of malfunction
It colours digraph HDM (C, F, FM, T, E), wherein V=C ∪ F ∪ FM ∪ T,V is knot
Point set, directed edge collection of the E between hybrid diagnosis model node.
Hybrid diagnosis model based on the thought of object-oriented to coloring digraph HDM (C, F, FM, T, E) in each node and
Directed edge assigns particular community information (such as expense, test-types, different degree) to meet system fault diagnosis design and analysis
Demand.
Fault mode and the fuzzy diagnosis of function dependence:
In Bayesian network fault diagnosis model, component, function, fault mode failure etc., group may include in fault set S
Part, function are frequently present of cause and effect dependence between fault mode.Fig. 7 is that the failure of certain LRU component is constituted, including
Fault mode collection FM={ fm1,fm2,fm3And function collection F={ f1,f2,f3}.When LRU component, fault mode, function are all examined
When worry is failure, fault set S={ fm1,fm2,fm3,f1,f2,f3, LRU }, due to not independent between daughter element each in S, so necessary
S is divided.Hybrid diagnosis model according to failure independence assumption, by the source of trouble be divided into component set C, function collection F and
Fault mode collection FM, and by the dependence fuzzy division between fault mode and function be do not influence (No Affect, NA),
Sometimes it influences (Sometimes Affect, SA), always affect (Always Affect, AA) three classes.Currently without explicitly sentencing
Determine the method for normalizing which kind of dependence between fault mode and function belongs to.
From the perspective of Fuzzy Pattern Recognition, fault mode and function dependence identification problem belong to single mode knowledge
Other problem can determine that specific determination flow is as shown in Figure 8 based on maximum membership grade principle.
The maximum membership grade principle of single mode identification is as follows.
(1) maximum membership grade principle 1: A is set1,A2,...,AmIt is m fuzzy subset on U, u is the fixed element in U,
I ∈ { 1,2 ..., m } makes if it exists
Then think that u is opposite and is under the jurisdiction of Ai。
(2) maximum membership grade principle 2: one threshold value λ ∈ of regulation (0,1], note
If α < λ, makees " rejection " judgement, reason should be searched and separately performed an analysis, if α >=λ, then it is assumed that identification is feasible, presses
It is adjudicated according to maximum membership grade principle 1.Maximum membership grade principle 2 can to avoid due to degree of membership all very littles by maximum membership grade principle
Make the practical farther away judgement of deviation.
Order does not influence NA, influences SA sometimes and always affect AA three classes relationship and correspond respectively to fuzzy set A1,A2,A3, threshold value
λ=0.55.Each fault mode fm in Fig. 81,fm2,fm3In the case where carrying out N=100 emulation injection respectively, domain X=
[0,100], corresponding subordinating degree function are
Subordinating degree function curve is as shown in Figure 9.
Respectively to fm1,fm2,fm3F is counted after carrying out 100 simulated fault injections1,f2,f3The number to break down such as table 3
It is shown.
3 functional fault statistical form of table
Enable the element Nfmf in table 3ijIt indicates, is solved based on maximum membership grade principle
Ak(Nfmfij)=max { A1(Nfmfij),A2(Nfmfij),A3(Nfmfij), k ∈ { 1,2,3 } (26)
Determine NfmfijIt is opposite to be under the jurisdiction of Ak.Fault mode collection { the fm acquired1,fm2,fm3And function collection { f1,f2,f3?
Qualitative effect relationship is as shown in table 4.
4 fault mode of table and function qualitative effect relationship
Figure 10 is fault mode { fm1,fm2,fm3And function { f1,f2,f3Dependence bigraph (bipartite graph) representation,
Middle solid line expression always affects relationship, and dotted line expression influences relationship sometimes.In order to avoid fault mode or functional information are isolated, mix
Close diagnostic model in usually by individual fault mode or function all default setting one virtual function or fault mode therewith
One-to-one association thus constructs the dependence between whole fault modes and function, and each fault mode of component internal
Between, it is relatively independent between each function.
Fault mode and functional fault probabilistic correlation based on hybrid diagnosis model are corrected:
In hybrid diagnosis model, probability of malfunction is the relative probability that failure occurs, and is the expansion of failure rate, is based on
Calculate fault detection rate, the important input data of Percent Isolated, failure false alarm rate.
Functional fault probability can be distributed to obtain by the failure rate of upper component, can also lower layer components failure rate it is cumulative
It arrives；Fault mode probability of malfunction is then usually calculated with the proportional assignment of component faults rate.Due to functional fault probability and event
The data source for hindering mode fault probability is different, based on functional fault probability with based on fault mode probability of malfunction to same group
Part carries out the estimated result that provides of failure rate may be inconsistent.On the one hand, the reliability data provided in system cannot react completely
The unfailing performance of system itself, simple refers to by functional fault probability or fault mode probability of malfunction to evaluate reliability
Mark, is unable to objectively give expression to the unfailing performance of system；On the other hand, during system modelling, with component newly event
The addition of barrier mode will lead to fault mode probability of malfunction and change, this to change the weight that also cause functional fault probability
New distribution.
In view of the above-mentioned problems, must correlation function probability of malfunction and fault mode probability of malfunction in one way, to failure
Probability data is corrected or is updated.In order to solve this problem, fault mode probability of malfunction average distribution system, function are provided
Probability of malfunction of three kinds of the preferential distribution method of the preferential distribution method of probability of malfunction, fault mode probability of malfunction based on hybrid diagnosis model closes
Join modification method.
(1) fault mode probability of malfunction average distribution system
Fault mode probability of malfunction average distribution system is adapted to the situation of functional reliability data scarcity, and ignoring function can
By property data, directly by fault mode probability of malfunctionIt is evenly distributed in each function that it is influenced, component ciEvent
Barrier modeIt is evenly distributed to the function being associatedOn probability of malfunction be
Revised functional fault probabilityCalculation formula is
(2) functional fault preference for probability distribution method
When the data reliability of functional fault probability is higher than fault mode probability of malfunction, using functional fault preference for probability
Method carries out the amendment of fault mode probability of malfunction, and steps are as follows for specific calculating:
STEP1: using formula (29), calculates component ciFault modeProbability of malfunctionIt is based onEach functional fault probability proportion be assigned to the probability of malfunction on correlation function and be
STEP2: using formula (30), and calculating willProbability of malfunctionBased on what is obtained by formula (29)In each fault modeIt is assigned toOn probability of malfunction pro rate arriveOn event
Hindering probability is
STEP3: what calculating was obtained by formula (31)In each functionIt is assigned toOn probability of malfunction ratio cumulative obtain modified fault mode probability of malfunction and be
(3) the preferential distribution method of fault mode probability of malfunction
When the data reliability of fault mode probability of malfunction is higher than functional fault probability, using fault mode probability of malfunction
Precedence method carries out the amendment of functional fault probability, and steps are as follows for specific calculating:
STEP1: using formula (32), calculates component ciFunctionProbability of malfunctionIt is based on
Each fault mode probability of malfunction pro rate to dependent failure mode on probability of malfunction be
STEP2: using formula (33), and calculating willProbability of malfunctionBased on what is obtained by formula (32)In each functionIt is assigned toOn probability of malfunction pro rate arriveOn failure
Probability is
STEP3: what calculating was obtained by formula (34)In each fault modeIt is assigned toOn probability of malfunction ratio cumulative obtain modified functional fault probability and be
(4) failure rate association amendment example
Each fault mode of LRU shown in Figure 10 and each functional fault probability original value are as shown in figure 11.Failure is respectively adopted
((method b), fault mode probability of malfunction are preferential for method a), functional fault preference for probability method for mode fault probability average distribution system
(the method c) LRU carries out probability of malfunction amendment to method, and obtained probability of malfunction correction result is as shown in table 5.
5 fault mode of table and function probability correction result
For electronic product, component ciFailure rate λ (ci) two methods can be used, it is expected that method one is function counting method,
Suitable for functional fault preference for probability distribution condition, calculation method is
Method two is fault mode counting method, and it is general to be suitable for fault mode probability of malfunction mean allocation, fault mode failure
The case where rate is preferentially distributed, calculation method are
The analysis of hybrid diagnosis Bayesian network trouble diagnosibility
Fault diagnosis modeling problem comprehensive analysis based on unascertained information:
Assuming that providing the corresponding test set of example LRU in Figure 11 is T={ t1,t2,t3,t4, T points are functional test collection TF=
{t1,t2And fault mode test set TFM={ t3,t4}.Test, fault mode, function, the mixed dependence relationship between LRU are such as
Shown in Figure 12.
Figure 12 can be divided into two Bayesian network models and a hybrid diagnosis model, respectively as Figure 13 a, 13b,
Shown in 13c.
If carrying out fault diagnosis modeling using Bayesian network merely, it is ignored as the pass between fault mode and function
Connection relationship ignores that the uncertainty of test if modeled using hybrid diagnosis model merely.In order to make fault diagnosis
Model can more accurately faults and test between dependence, need to design one kind can simultaneously to uncertainty
The fault diagnosis model that test information and fault mode and indistinct usage dependence are modeled.
Hybrid diagnosis Bayesian network model:
It being defined based on digraph, hybrid diagnosis model HDM (C, F, FM, T, E), which can simplify, is expressed as HDM (V, E),
In, V=C ∪ F ∪ FM ∪ T is nodal set.It is also derived from the Bayesian network fault diagnosis model BNT=(V, E, P) of digraph
Nature can get up with hybrid diagnosis models coupling, realize that the Bayes's uncertainty established on the basis of hybrid diagnosis model pushes away
Reason forms the mutual supplement with each other's advantages of hybrid diagnosis model and Bayesian network fault diagnosis model.
On the basis of consideration uncertain test information description, pass through fusion hybrid diagnosis model and Bayesian network event
Hinder diagnostic model, the hybrid diagnosis Bayesian network model of design can be indicated with digraph HDBN=(C, F, FM, T, E, P).
Wherein, V=C ∪ F ∪ FM ∪ T is nodal set,E indicates that the directed edge collection between system node, P are power
Matrix.Graph theory letter between hybrid diagnosis Bayesian network model and hybrid diagnosis model, Bayesian network fault diagnosis model
It is as shown in figure 14 to cease syncretic relation.
The source of each element information is as follows in HDBN=(C, F, FM, T, E, P):
Component set C={ c1,c2,…,cLIt is derived from hybrid diagnosis model HDM (C, F, FM, T, E)；
Function collection F={ f1,f2,…,fJIt is derived from hybrid diagnosis model HDM (C, F, FM, T, E)；
Fault mode collection FM={ fm1,fm2,…,fmIIt is derived from hybrid diagnosis model HDM (C, F, FM, T, E)；
Test set T={ t1,t2,…,tnIt is derived from hybrid diagnosis model HDM (C, F, FM, T, E)；
Directed edge collection E is derived from hybrid diagnosis model HDM (C, F, FM, T, E)；
Each fault mode, function, component failure probability be derived from hybrid diagnosis model reasoning；
Weight matrix P information is derived from hybrid diagnosis model HDM (C, F, FM, T, E) and Bayesian network fault diagnosis model BNT
The fusion of=(V, E, P) information.Wherein, the fault mode of direct correlation and the conditional probability information of test, function and test can
To be obtained based on Bayesian network fault diagnosis model；It is based on although the conditional probability information between fault mode and function is derived from
The fault mode and function dependence of hybrid diagnosis model are analyzed, but only base oneself upon existing hybrid diagnosis model reasoning side
Method is unable to get, and is needed on the basis of the fault mode based on hybrid diagnosis model is analyzed with function dependence into one
Step design related algorithm and inference rule.
For any one component, hybrid diagnosis Bayesian network model can be expressed as two kinds of forms: one is with function
It can be the form of root node, the case where distribution it is suitable for functional fault preference for probability, such as Figure 15 a；Another kind is with failure mould
Formula is the form of root node, and it is suitable for fault mode probability of malfunction mean allocation, fault mode probabilities of malfunction preferentially to distribute
Situation such as Figure 15 b.Hybrid diagnosis Bayesian network includes three layers: top layer is root node layer, and middle layer is hidden layer, and bottom is to survey
Try layer.
Hybrid diagnosis Bayesian network model reasoning:
Due to the presence of hidden layer, it is quantitative that hybrid diagnosis Bayesian network model cannot be used directly to trouble diagnosibility
Index expects.In order to carry out trouble diagnosibility index, it is expected that needing the node propagation law based on digraph, rejects and hide
Layer, and analyze the conditional probability information between root node and all test.The reasoning process of hybrid diagnosis Bayesian network model
It is as follows.
(1) hidden layer is rejected
The element set of root node layer ROOT={ root1,root2,...,rootmIndicate, the element set of hidden layer is used
HID={ hid1,hid2,...,hidwIndicate, the element set T={ t of test layer1,t2,...,tnIndicate, root node layer is each
Fuzzy dependency relationship matrix RH=[rh between element and hidden layer each elementij] indicate, wherein rhij∈ { NA, SA, AA },
Incidence relation matrix H T=[ht between hidden layer each element and test layer each elementjk] indicate, increase after rejecting hidden layer
Root node layer and test layer be directly linked relationship matrixIt indicates.Node propagation law based on digraph is given
The formula of hidden layer rejecting is out
The fault mode probability of malfunction data reliability of LRU shown in Figure 13 is higher than functional fault probability, using fault mode
The preferential distribution method of probability of malfunction is associated amendment to failure rate, then the LRU using using fault mode as root node in the form of set
Count hybrid diagnosis Bayesian network model.The function hidden layer of Figure 15 b is rejected based on formula (37), as shown in figure 16.
(2) conditional probability information calculates
Since the relationship between root node and hiding node is qualitative fuzzy relation, so also needing to examine based on mixing
The condition between root node and hiding node is provided on the basis of the fault mode and function dependence analysis result of disconnected model
Probabilistic information.The conditional probability information computation rule being defined as follows between root node and hiding node.
Rule 1: if root node rootiWith hiding node hidjBetween be to always affect relationship, then it is assumed that root node occur
When, it hides node and also occurs；When root node does not occur, hides node and also do not occur.Corresponding mathematical description are as follows: if rhij=
AA, then
Rule 2: if root node rootiWith hiding node hidjBetween be to always affect relationship, then rootiWith hidjIt
Between the method for solving of conditional probability be
Wherein, Pr ' (hidj) it is to hide node hidjRevised probability of malfunction；Pr'(rooti) it is root node rootiIt repairs
Probability of malfunction after just.
Rule 3: if root node rootiWith hiding node hidjBetween be independent of each other rhij=NA, then
(3) weight side is removed
Heavy side between two nodes often will lead to diagnostic reasoning conflict, need to construct the mechanism for solving conflict thus.General
The probability that verified two set union A ∪ B has occurred in rate opinion is greater than the probability that any one set A or B individually occur
Pr(A∪B)≥max{Pr(A),Pr(B)} (41)
So root node and the maximum value tested between node in weight side in verification and measurement ratio and false alarm rate approximate can be taken to make
For root node and detection-false-alarm probability between node is tested, to reduce the estimated error of trouble diagnosibility index.
Rule 4: it is based on every rootiWith tkBetween path pathijk, function collection F and TFDetection-false-alarm probability matrix,
Fault mode collection FM and TFMDetection-false-alarm probability matrix, calculate separatelyAnd formula based on following merges weight
Frontier inspection survey-false-alarm probability
After completing the reasoning of hybrid diagnosis Bayesian network model, hybrid diagnosis Bayesian network model shown in Figure 15 b will
It is converted into Bayesian network fault diagnosis model form shown in Figure 17.
To sum up, as shown in figure 18, the embodiment of the invention discloses a kind of failures based on hybrid diagnosis Bayesian network to examine
Cutting capacity analysis method, includes the following steps:
1): probability of malfunction association amendment: based on reliability data, whether deficient and fault mode probability of malfunction confidence level is
It is no to be higher than the two criterion selections of functional fault probability to the modified method of component progress probability of malfunction association；
2): the foundation modeling of hybrid diagnosis Bayesian network model is with reasoning: being associated with correction result choosing based on probability of malfunction
The forming types of hybrid diagnosis Bayesian network model are selected, the modeling of hybrid diagnosis Bayesian network model and reasoning are carried out；
3): trouble diagnosibility index calculates: " root node-test " based on generation relies on matrix, " root node-survey
Examination " detection-false-alarm probability matrix, probability of malfunction association correction result carry out the event based on hybrid diagnosis Bayesian network model
Hinder diagnosis capability index to calculate, the estimated report of formation component trouble diagnosibility index.
Above step 1) and the specific method of step 2) please refer to foregoing teachings, the content of step 3 is carried out below detailed
It describes in detail bright.
Although IEEE STD 1522 gives the design framework of the quantitative target based on AI-ESTATE, but does not give
It is specifically given out for this this project with reference to IEEE STD 1522 based on the trouble diagnosibility index calculating method of different models
Trouble diagnosibility quantitative target information model out devises the fault diagnosis energy based on hybrid diagnosis Bayesian network model
Power quantitative target calculation method.
After hybrid diagnosis Bayesian Network Inference, the dependence matrix between obtained root node and test node isRoot node and the detection-false-alarm probability matrix tested between node areAccording to
The definition of EPoD information model, providing the EPoD calculation formula based on hybrid diagnosis Bayesian network fault diagnosis model is
Wherein, EPoDiFor failure siThe probability that may be detected, if there is tjSo that dij=1, then siIt may be detected,
Otherwise, siIt cannot be detected.Work as dijWhen=1
EPoDiCalculating method formula be
Wherein, it is expected that isolation rate it is expected isolation rate IEPoI (incremental expected percentage by increment
Of isolation, IEPoI) be defined as in a specific diagnostic model frame, the test set provided using model correctly every
From to particular size ambiguity group total failare rate and the ratio between the total failare rate of failure that detects.Accumulation expectation Fault Isolation
Rate CEPoI (cumulative expected percentage of isolation, CEPoI) is defined as specifically examining at one
In disconnected model framework, the total failare rate and inspection of the ambiguity group within particular size are correctly isolated using the test set that model provides
The ratio between total failare rate of the failure measured.In hybrid diagnosis Bayesian network fault diagnosis model frame, IEPoI and CEPoI
Between relationship be
IEPoI (g)=CEPoI (g)-CEPoI (g-1) (46)
It before calculating IEPoI, first has to for ROOT to be divided into multiple mutually independent Fault Isolation ambiguity groups, each event
Phragma includes l failure element from ambiguity group, l ∈ { 1,2 ..., | ROOT | }.
One failure ambiguity group refers to the failure subset being made of the failure with same characteristic features.Assume in single fault
In the case where, Fault Isolation ambiguity group can be based on dependence matrix D*It calculates and obtains.IfWithFor any two row in D to
Amount, and i ≠ j, ifI.e.Illustrate to work as rootiOr rootjWhen breaking down, in tk
On the information that is showed be the same, therefore rootiWith rootjFor inseparable failure, they belong to the same ambiguity group, similar
Multiple failures can be classified as an ambiguity group by ground.Root is calculated based on hybrid diagnosis Bayesian network modeliThe failure at place
Isolation ambiguity group method be
rootiThe size of the Fault Isolation ambiguity group at place is | AGi|。
Single fault hypothesis requires rootiWhen breaking down, all detection rootiTest do not pass through, could by every
From.
For ease of calculation, in hybrid diagnosis Bayesian network model frame, increase a single fault expectation isolation rate
(single expected percentage of isolation, SEPoI) definition.SEPoI is defined as in a specific diagnosis
In model framework, total event of the segregate failure rate of single failure with the failure detected is made using the test set that model provides
The ratio between barrier rate.rootiSEPoI calculation formula be
The calculation formula of IEPoI is
Be isolated to ambiguity group size be max | AGi| within the calculation formula of CEPoI be
Being isolated to the calculation formula that ambiguity group size is the CEPoI within L is
It is expected that Fault Isolation ambiguity group size (expected ambiguity group size, EAGS) is defined as one
In a specific diagnostic model frame, the failure rate for the failure ambiguity group being correctly isolated using the test set that model provides is big
It is small.The calculation formula of EAGS is
Hybrid diagnosis Bayesian network model has the potentiality of failure false alarm rate prediction, and one of critical function of PHM is just
It is to inhibit false-alarm, the application devises the failure false alarm rate calculation formula based on hybrid diagnosis Bayesian network model.Based on mixed
The failure false alarm rate for closing diagnosis Bayesian network model it is expected false alarm rate (single expected failure by single fault
Rate of false alarm, SEFRoA) and accumulation expectation false alarm rate (cumulative expected percentage of
False alarm, CEPoA) two independent formula composite calulations.
SEFRoA is defined as in a specific diagnostic model frame, carries out single failure using the test set that model provides
The false alarm rate of detection.The calculation formula of SEFRoA is
It can be seen that from the calculation formula of SEFRoA when being detected for the same failure, more, false-alarm is tested in association
Probability it is bigger.
The failure that adds up expectation false alarm rate (cumulative expected failure rate of false alarm,
CEFRoA calculation formula) are as follows:
CEPoA is defined as in a specific diagnostic model frame, is calculated using the test set that model provides tired
Add failure expectation false-alarm failure rate and cumulative failure expectation false-alarm failure rate and the ratio for it is expected weight detection rate adduction.CEPoA
Calculation formula be
Claims (10)
1. a kind of trouble diagnosibility analysis method based on hybrid diagnosis Bayesian network, it is characterised in that including walking as follows
It is rapid:
Probability of malfunction association amendment: based on reliability data, whether deficient and fault mode probability of malfunction confidence level is higher than function
The two criterions selections of energy probability of malfunction carry out probability of malfunction association amendment to component；
Hybrid diagnosis Bayesian network model is established and reasoning: being associated with correction result selection hybrid diagnosis pattra leaves based on probability of malfunction
The forming types of this network model carry out the modeling of hybrid diagnosis Bayesian network model and reasoning；
Trouble diagnosibility index calculates: the root node generated based on hybrid diagnosis Bayesian network model-test relies on square
Battle array, root node-test detection-false-alarm probability matrix, probability of malfunction association correction result are carried out based on hybrid diagnosis Bayes
The trouble diagnosibility index of network model calculates, formation component trouble diagnosibility index prediction address, completes hybrid diagnosis
The analysis of Bayesian network trouble diagnosibility.
2. as described in claim 1 based on the trouble diagnosibility analysis method of hybrid diagnosis Bayesian network, feature exists
In it is as follows that the probability of malfunction is associated with modified method:
Fault mode probability of malfunction average distribution system:
Fault mode probability of malfunction average distribution system is adapted to the situation of functional reliability data scarcity, ignores functional reliability
Data, directly by fault mode probability of malfunctionIt is evenly distributed in each function that it is influenced, component ciFailure mould
FormulaIt is evenly distributed to the function being associatedOn probability of malfunction be
Revised functional fault probabilityCalculation formula is
3. as described in claim 1 based on the trouble diagnosibility analysis method of hybrid diagnosis Bayesian network, feature exists
In it is as follows that the probability of malfunction is associated with modified method:
Functional fault preference for probability distribution method:
When the data reliability of functional fault probability be higher than fault mode probability of malfunction when, using functional fault preference for probability method into
The amendment of row fault mode probability of malfunction, steps are as follows for specific calculating:
STEP1: using formula (3), calculates component ciFault modeProbability of malfunctionIt is based onEach functional fault probability proportion be assigned to the probability of malfunction on correlation function and be
STEP2: using formula (4), and calculating willProbability of malfunctionBased on what is obtained by formula (3)In
Each fault modeIt is assigned toOn probability of malfunction pro rate arriveOn probability of malfunction be
STEP3: what calculating was obtained by formula (5)In each functionIt is assigned toOn
Probability of malfunction ratio is cumulative to be obtained modified fault mode probability of malfunction and is
4. as described in claim 1 based on the trouble diagnosibility analysis method of hybrid diagnosis Bayesian network, feature exists
In it is as follows that the probability of malfunction is associated with modified method:
The preferential distribution method of fault mode probability of malfunction
It is preferential using fault mode probability of malfunction when the data reliability of fault mode probability of malfunction is higher than functional fault probability
Method carries out the amendment of functional fault probability, and steps are as follows for specific calculating:
STEP1: using formula (6), calculates component ciFunctionProbability of malfunctionIt is based onIt is each therefore
Hindering the probability of malfunction that mode fault probability proportion is assigned in dependent failure mode is
STEP2: using formula (7), and calculating willProbability of malfunctionBased on what is obtained by formula (6)
In each functionIt is assigned toOn probability of malfunction pro rate arriveOn probability of malfunction be
STEP3: what calculating was obtained by formula (8)In each fault modeIt is assigned toOn
Probability of malfunction ratio cumulative obtain modified functional fault probability and be
5. as described in claim 1 based on the trouble diagnosibility analysis method of hybrid diagnosis Bayesian network, feature exists
In the method for building up of the hybrid diagnosis Bayesian network model is as follows:
It is defined based on digraph, hybrid diagnosis model HDM (C, F, FM, T, E), which can simplify, is expressed as HDM (V, E)；Derived from oriented
The Bayesian network fault diagnosis model BNT=(V, E, P) of figure；
On the basis of considering uncertain test information description, examined by fusion hybrid diagnosis model and Bayesian network failure
The hybrid diagnosis Bayesian network model of disconnected model, design can be indicated with digraph HDBN=(C, F, FM, T, E, P)；Wherein,
V=C ∪ F ∪ FM ∪ T is nodal set,E indicates the directed edge collection between system node, and P is weight matrix；
The source of each element information is as follows in HDBN=(C, F, FM, T, E, P):
Component set C={ c1,c2,…,cL, it is derived from hybrid diagnosis model HDM (C, F, FM, T, E)；
Function collection F={ f1,f2,…,fJ, it is derived from hybrid diagnosis model HDM (C, F, FM, T, E)；
Fault mode collection FM={ fm1,fm2,…,fmI, it is derived from hybrid diagnosis model HDM (C, F, FM, T, E)；
Test set T={ t1,t2,…,tn, it is derived from hybrid diagnosis model HDM (C, F, FM, T, E)；
Directed edge collection E is derived from hybrid diagnosis model HDM (C, F, FM, T, E)；
Each fault mode, function, component failure probability be derived from hybrid diagnosis model reasoning；
Weight matrix P information is derived from hybrid diagnosis model HDM (C, F, FM, T, E) and Bayesian network fault diagnosis model BNT=
The fusion of (V, E, P) information；
For any one component, hybrid diagnosis Bayesian network model can be expressed as two kinds of forms: one is be with function
The case where form of root node, it is suitable for functional fault preference for probability distribution；Another kind is using fault mode as root node
Form, the case where preferentially distribution it is suitable for fault mode probability of malfunction mean allocation, fault mode probability of malfunction.
6. as described in claim 1 based on the trouble diagnosibility analysis method of hybrid diagnosis Bayesian network, feature exists
In the method made inferences to hybrid diagnosis Bayesian network model is as follows:
Reject the function hidden layer in hybrid diagnosis Bayesian network model；
Calculate the conditional probability information between root node and hiding node；
The maximum value for taking root node and testing between node in weight side in verification and measurement ratio and false alarm rate is tied as root node and test
Detection-false-alarm probability between point.
7. as claimed in claim 6 based on the trouble diagnosibility analysis method of hybrid diagnosis Bayesian network, feature exists
In the method for rejecting the function hidden layer in hybrid diagnosis Bayesian network model is as follows:
The element set of root node layer ROOT={ root1,root2,...,rootmIndicate, the element set HID=of hidden layer
{hid1,hid2,...,hidwIndicate, the element set T={ t of test layer1,t2,...,tnIndicate, root node layer each element with
Fuzzy dependency relationship matrix RH=[rh between hidden layer each elementij] indicate, wherein rhij∈ { NA, SA, AA }, wherein NA
Indicate the dependence between fault mode and function be do not influence, SA indicates to influence sometimes, AA expression always affects；
Incidence relation matrix H T=[ht between hidden layer each element and test layer each elementjk] indicate, after rejecting hidden layer
Increased root node layer and test layer are directly linked relationship matrixIt indicates；Node based on digraph propagates rule
Rule provides the formula of hidden layer rejecting are as follows:
8. as claimed in claim 7 based on the trouble diagnosibility analysis method of hybrid diagnosis Bayesian network, feature exists
In the method for calculating the conditional probability information between root node and hiding node is as follows:
The conditional probability information computation rule being defined as follows between root node and hiding node:
Rule 1: if root node rootiWith hiding node hidjBetween be to always affect relationship, then it is assumed that root node breaks down
When, it hides node and also breaks down；When root node does not break down, hides node and also do not break down；Corresponding mathematical description
If are as follows: rhij=AA, then
Rule 2: if root node rootiWith hiding node hidjBetween be to always affect relationship, then rootiWith hidjBetween condition
The method for solving of probability is
Wherein, Pr ' (hidj) it is to hide node hidjRevised probability of malfunction；Pr'(rooti) it is root node rootiAfter amendment
Probability of malfunction；
Rule 3: if root node rootiWith hiding node hidjBetween be independent of each other rhij=NA, then
9. as claimed in claim 8 based on the trouble diagnosibility analysis method of hybrid diagnosis Bayesian network, feature exists
In the maximum value taken between root node and test node in weight side in verification and measurement ratio and false alarm rate is as root node and test
Detection-false-alarm probability method between node is as follows:
The probability that two set union A ∪ B occur is greater than probability P r (A ∪ B) >=max that any one set A or B individually occur
{Pr(A),Pr(B)}
Approximation takes the maximum value between root node and test node in weight side in verification and measurement ratio and false alarm rate as root node and surveys
Try detection-false-alarm probability between node；
Rule 4: it is based on every root node rootiWith tkBetween path pathijk, function collection F and TFDetection-false-alarm probability square
Battle array, fault mode collection FM and TFMDetection-false-alarm probability matrix, calculate separatelyAnd formula based on following merges
Weight frontier inspection survey-false-alarm probability
10. as described in claim 1 based on the trouble diagnosibility analysis method of hybrid diagnosis Bayesian network, feature exists
In the formation component trouble diagnosibility index prediction address completes hybrid diagnosis Bayesian network trouble diagnosibility point
The method of analysis is as follows:
After hybrid diagnosis Bayesian Network Inference, the dependence matrix between obtained root node and test node isRoot node and the detection-false-alarm probability matrix tested between node areIt provides
EPoD calculation formula based on hybrid diagnosis Bayesian network fault diagnosis model are as follows:
Wherein, EPoDiFor failure siThe probability that may be detected, if there is tjSo that dij=1, then siIt may be detected, it is no
Then, siIt cannot be detected；Work as dijWhen=1:
EPoDiCalculating method formula be
In hybrid diagnosis Bayesian network fault diagnosis model frame, it is expected that isolation rate by increment expectation isolation rate IEPoI with
Accumulation it is expected that the relationship between Percent Isolated CEPoI is
IEPoI (g)=CEPoI (g)-CEPoI (g-1)
Before calculating IEPoI, first have to for ROOT to be divided into multiple mutually independent Fault Isolation ambiguity groups, each failure every
It include l failure element from ambiguity group, l ∈ { 1,2 ..., | ROOT | }；
One failure ambiguity group refers to the failure subset being made of the failure with same characteristic features；In the feelings that single fault is assumed
Under condition, Fault Isolation ambiguity group can be based on dependence matrix D*It calculates and obtains；IfWithFor any two row vector in D,
And i ≠ j, ifI.e.Illustrate to work as rootiOr rootjWhen breaking down, in tkOn
The information showed is the same, therefore rootiWith rootjFor inseparable failure, they belong to the same ambiguity group, similarly
Multiple failures can be classified as to an ambiguity group；Root is calculated based on hybrid diagnosis Bayesian network modeliThe failure at place every
Method from ambiguity group is
rootiThe size of the Fault Isolation ambiguity group at place is | AGi|；
Single fault hypothesis requires rootiWhen breaking down, all detection rootiTest do not pass through, can just be isolated；
In hybrid diagnosis Bayesian network model frame, increases a single fault and it is expected that isolation rate SEPoI, SEPoI are defined as
In a specific diagnostic model frame, makes the segregate failure rate of single failure using the test set that model provides and detect
The ratio between the total failare rate of failure；rootiSEPoI calculation formula are as follows:
The calculation formula of IEPoI are as follows:
Be isolated to ambiguity group size be max | AGi| within CEPoI calculation formula are as follows:
Being isolated to the calculation formula that ambiguity group size is the CEPoI within L is
It is expected that Fault Isolation ambiguity group size EAGS is defined as in a specific diagnostic model frame, the survey provided using model
The failure rate size for the failure ambiguity group that examination collection is correctly isolated；The calculation formula of EAGS are as follows:
It is expected based on the failure false alarm rate of hybrid diagnosis Bayesian network model by single fault expectation false alarm rate SEFRoA and accumulation
False alarm rate CEPoA two independent formula composite calulations, the failure false alarm rate based on hybrid diagnosis Bayesian network model calculate public
Formula；
SEFRoA is defined as in a specific diagnostic model frame, carries out single fault detection using the test set that model provides
False alarm rate；The calculation formula of SEFRoA are as follows:
Can be seen that from the calculation formula of SEFRoA when being detected for the same failure, association test is more, false-alarm it is general
Rate is bigger；
The calculation formula of cumulative failure expectation false alarm rate CEFRoA are as follows:
CEPoA is defined as in a specific diagnostic model frame, the cumulative event being calculated using the test set that model provides
Barrier expectation false-alarm failure rate and cumulative failure expectation false-alarm failure rate and the ratio for it is expected weight detection rate adduction；The meter of CEPoA
Calculate formula are as follows:
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| CN115358281B (en) * | 2022-10-21 | 2023-01-13 | 深圳市耐思特实业有限公司 | Machine learning-based cold and hot all-in-one machine monitoring control method and system |
| CN116881675A (en) * | 2023-09-07 | 2023-10-13 | 南京中鑫智电科技有限公司 | Power equipment state monitoring method based on Bayesian algorithm |
| CN116881675B (en) * | 2023-09-07 | 2023-12-08 | 南京中鑫智电科技有限公司 | Power equipment state monitoring method based on Bayesian algorithm |
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