CN109657797B - Fault diagnosis capability analysis method based on hybrid diagnosis Bayesian network - Google Patents

Fault diagnosis capability analysis method based on hybrid diagnosis Bayesian network Download PDF

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CN109657797B
CN109657797B CN201811580885.1A CN201811580885A CN109657797B CN 109657797 B CN109657797 B CN 109657797B CN 201811580885 A CN201811580885 A CN 201811580885A CN 109657797 B CN109657797 B CN 109657797B
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连光耀
孙江生
闫鹏程
李会杰
连云峰
张西山
梁伟杰
张连武
代冬升
李雅峰
王凯
邱文浩
杨金鹏
陈然
李宝晨
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32181 Troops of PLA
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Abstract

The invention discloses a fault diagnosis capability analysis method based on a hybrid diagnosis Bayesian network, and relates to the technical field of fault diagnosis methods. The method comprises the following steps: and (3) fault probability correlation correction: performing fault probability correlation correction on the component based on two criteria of whether reliability data is deficient and whether fault probability credibility of the fault mode is higher than functional fault probability; establishing and reasoning a hybrid diagnosis Bayesian network model: selecting a construction mode of the hybrid diagnosis Bayesian network model based on the fault probability correlation correction result, and carrying out modeling and reasoning on the hybrid diagnosis Bayesian network model; and calculating a fault diagnosis capability index. The method improves the accuracy of fault diagnosis analysis modeling and the reliability of the prediction result of the testability index.

Description

Fault diagnosis capability analysis method based on hybrid diagnosis Bayesian network
Technical Field
The invention relates to the technical field of fault diagnosis methods, in particular to a fault diagnosis capability analysis method based on a hybrid diagnosis Bayesian network.
Background
At present, due to the lack of consideration of uncertainty factors in fault propagation and test processes in information flow models, multi-signal flow diagram models and the like, the deviation between the expected value and the actual value of many current testability indexes based on fault diagnosis models is large, and the quantitative evaluation of the actual fault diagnosis capability level of products is not facilitated.
Disclosure of Invention
The invention aims to solve the technical problem of how to provide a method capable of improving the accuracy of fault diagnosis analysis modeling and the reliability of a testability index prediction result.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a fault diagnosis capability analysis method based on a hybrid diagnosis Bayesian network is characterized by comprising the following steps:
and (3) fault probability correlation correction: performing fault probability correlation correction on the component based on two criteria of whether reliability data is deficient and whether fault probability credibility of the fault mode is higher than functional fault probability;
establishing and reasoning a hybrid diagnosis Bayesian network model: selecting a construction mode of the hybrid diagnosis Bayesian network model based on the fault probability correlation correction result, and carrying out modeling and reasoning on the hybrid diagnosis Bayesian network model;
and (3) calculating a fault diagnosis capability index: and performing fault diagnosis capability index calculation based on a hybrid diagnosis Bayesian network model based on the generated root node-test dependency matrix, root node-test detection-false alarm probability matrix and fault probability correlation correction result, generating a component fault diagnosis capability index prediction report, and completing the fault diagnosis capability analysis of the hybrid diagnosis Bayesian network.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: according to the method, firstly, fault probability correlation correction is carried out, then a hybrid diagnosis Bayesian network model is established and inferred, and finally fault diagnosis capability index calculation is carried out, so that the accuracy of fault diagnosis analysis modeling and the reliability of a testability index prediction result are improved.
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The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a diagram of four dependencies between a fault source and a test in an embodiment of the invention;
FIG. 2 is a diagram of the dependency relationship between the fault and the test under the non-false-alarm asymmetric test condition in the embodiment of the present invention;
FIG. 3 is a diagram illustrating the dependency between faults and tests under symmetric false alarm testing in an embodiment of the present invention;
FIG. 4 is a diagram of the dependency between failure and test under deterministic testing in an embodiment of the present invention;
FIG. 5 is a state transition diagram for four cases in an embodiment of the present invention;
FIG. 6 is a diagram of a Bayesian network fault diagnosis model in an embodiment of the present invention;
FIG. 7 is a fault composition diagram of an LRU component in an embodiment of the present invention;
FIG. 8 is a flow chart of failure mode and functional association identification in an embodiment of the present invention;
FIG. 9 is a graph of membership function in an embodiment of the invention;
FIG. 10 is a bipartite graphical representation of a failure mode versus functional association in an embodiment of the invention;
FIG. 11 is a graph representing failure modes and raw values of functional failure probability in an embodiment of the present invention;
FIG. 12 is a mixed dependency graph between test, failure mode, function, LRU in an embodiment of the present invention;
FIGS. 13 a-13 c are three segmented subgraphs in accordance with embodiments of the present invention;
FIG. 14 is a graph of the graph theoretic information fusion of HDBN, BN and HDM in an embodiment of the invention;
FIGS. 15 a-15 b are two representational form diagrams of a hybrid diagnostic Bayesian network model in an embodiment of the present invention;
FIG. 16 is a HDBN graph with functional hidden layers culled in accordance with an embodiment of the invention;
FIG. 17 is a diagram of a Bayesian network fault diagnosis model conversion form of the HDBN in an embodiment of the invention;
FIG. 18 is a flow chart of a method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
The traditional fault and test correlation model ignores uncertainty information and cannot describe potential fault false alarm and missing detection problems in the model, and the problems may bring significant risks to development and use of PHM (fault diagnosis and prediction), so that description of the uncertainty test information needs to be considered as much as possible when modeling the product fault and test correlation. A method for modeling the correlation between a fault and a test based on uncertainty test information will be given below.
Let S be { S ═ S for fault set1,s2,...,smRepresents that it can take values as a product function set F or a failure mode set FM. For the sake of description, assume the test is a binary test, for fault siAnd test tjThe values of (a) are assumed qualitatively as follows.
Figure BDA0001917807930000031
Figure BDA0001917807930000032
siAnd tjThere are four possible dependency states shown in FIG. 1, where PdijDenotes siWhen there is a fault, tjProbability of failing, also known as tjTo siThe detection probability of (1). PfijDenotes siIn the absence of a fault, tjProbability of failing, also known as tjTo siThe false alarm probability of.
Let Pr (t) be based on mathematical logic and Bayesian theoryj) Is tjThe probability of not passing through is determined,
Figure BDA0001917807930000034
is tjProbability of passing, Pr(s)i) Is s isiThe probability of a failure is determined by the probability of a failure,
Figure BDA0001917807930000035
is s isiProbability of no failure, then
Pdij＝Pr(tj|si) (3)
Figure BDA0001917807930000033
In fig. 1, four edges correspond to the following four dependencies, respectively.
The relationship is: siFailure, tjFail, for correct pass indication, the corresponding probability is Pdij；
The relationship (c): siFailure, tjThe corresponding probability is 1-Pd for missed diagnosis and incorrect indicationij；
Relationship (c): siNormal, tjFail, false alarm, incorrect indication, probability of correspondence Pfij；
Relationship iv: siNormal, tjBy, for a correct fail indication, the corresponding probability is 1-Pfij。
In the process of fault diagnosis design and analysis, the method can be divided into four conditions of false alarm asymmetric test, false alarm symmetric test and false alarm symmetric test according to the completeness of detection probability and false alarm probability data.
The following conditions are: there is a false alarm asymmetry test. At this time, Pfij≠0，PdijNot equal to 1, the relationship between fault and test is shown in fig. 1.
Case two: and carrying out non-false-alarm asymmetric testing. At this time, Pfij＝0，PdijNot equal to 1, the relationship between fault and test is shown in fig. 2.
Case (c): there is a false alarm symmetry test. At this time, Pfij≠0，PdijThe relationship between failure and test is shown in fig. 3 as 1.
Case four: symmetric tests without false alarms are also called deterministic tests. At this time, Pfij＝0，PdijThe relationship between failure and test is shown in fig. 4 as 1.
The state transition diagram for the four cases is shown in fig. 5, and the corresponding fault diagnosis modeling method should be selected according to the completeness of the detection probability and the false alarm probability data.
Let tjCannot detect siWhen is Pdij＝PfijWith detection-false alarm probability pair (Pd) of 0ij,Pfij) Represents tjTo siTest uncertainty of (2). PFIijRepresents tjTo siGiving probability of erroneous judgement
Figure BDA0001917807930000041
PTIijRepresents tjTo siGiving the probability of correct judgement, also called tjTo siThe accuracy of the test.
Figure BDA0001917807930000042
If n tests in T are independent of each other, siIs erroneously indicated as
Figure BDA0001917807930000043
PdijAnd PfijData can be specified by experts, but data given based on expert specification methods tend to deviate significantly from actual data. A relatively scientific approach is to learn Pd through sample data trainingijAnd PfijAlso known as data driving method. The data driving method can be divided into a complete data set driving method and an incomplete data set driving method according to the actual observation condition of data. Each test in the complete data set driving method has complete actual observation data, and the incomplete data set driving method refers to the phenomenon that the actual observation data of some tests have partial deletion or abnormity. Imperfect data-driven methods include monte carlo methods, gaussian approximations, expectation maximization methods, maximum posterior probability methods, and the like. The complete data driving method mainly comprises a maximum likelihood estimation method and a Bayes method, wherein the maximum likelihood estimation method is easy to master. The maximum likelihood estimation considers the mean of the samples to be close to the expected value for large sample data, under the assumption that PdijCan be represented by the formula (8)
Figure BDA0001917807930000051
PfijCan also be similarly defined as
Figure BDA0001917807930000052
Fault diagnosis modeling based on Bayesian network
Fault diagnosis models such as an information flow model and a multi-signal flow diagram model are constructed under the assumption of deterministic test, the existence of uncertain information is ignored, and the deviation of the provided fault detection rate and fault isolation rate index prediction result from the real situation is large. Therefore, a fault diagnosis model capable of describing uncertain test information needs to be designed, and the reliability of prediction of the testability index is improved.
The bayesian network is considered as a main technology and an excellent tool for uncertainty knowledge representation and reasoning in artificial intelligence research, is increasingly widely used in the field of uncertainty modeling of complex systems, is one of research hotspots in the aspect of current diagnosis modeling, and a fault diagnosis modeling method based on the bayesian network is provided below.
Bayesian network model:
the Bayesian network is also called Bayesian belief network, is directed graphic description based on a network structure, and is a product combining artificial intelligence, probability theory and graph theory. The Bayesian network expresses the incidence relation and influence degree between the information elements by using a directed graph with a network structure, expresses the information elements by using node variables, expresses the incidence relation between the information elements by using directed edges connecting the nodes, and expresses the influence degree between the information elements by using conditional probability.
A bayesian network is a directed acyclic graph showing the dependency relationship between variables, and can be represented by a ternary directed graph BN ═ V, E, P, where V is a set of nodes, the nodes represent random variables, and the random variables can be abstractions of any problem, such as product components, test results, failure phenomena, etc.; e is a directed edge set, and the directed edges represent the association relationship between nodes, usually the causal relationship; p is a weight matrix, and each node has a Conditional Probability Table (CPT) for quantitatively representing the effect of all its parent nodes on the node, which is the causal influence strength between nodes.
The bayesian network is based on the conditional independence assumption, in which the independence relationship is basically divided into the following three types:
(1) the root node is condition independent;
(2) nodes with a plurality of father nodes are independent in condition when no incidence relation exists among the nodes and the states of the father nodes are given;
(3) for any node, given the state of all its parents (direct parents), the node is conditionally independent from all ancestor nodes.
Let V be { V ═ V1,V2,...,Vn}，A(Vi) Denotes non-ViAny subset of nodes, pi (V), formed by descendant nodesi) Represents ViThe parent node of (1), node ViThe conditional probability of (a) is:
Pr(Vi|A(Vi),Π(Vi))＝Pr(Vi|π(Vi)) (10)
under the above conditional independence assumption, the joint distribution probability of the variables is:
Figure BDA0001917807930000061
according to the nodes, the mutual relation of the nodes and the conditional probability table, the Bayesian network can express the joint probability of all the nodes in the system Bayesian network model, and can calculate the probability information of any other node according to the prior probability information or the values of some nodes.
And (3) Bayesian network fault diagnosis modeling:
the bayesian network fault diagnosis model is an abbreviation of "fault-test conclusion" bayesian network model and can be represented by a quaternary directed graph BNT ═ S (S, T, E, P), which divides V in the bayesian network BN ═ S (V, E, P) into two subsets of a fault set S and a test set T, V ═ S ═ T, S ≡ T ═ Φ, P ═ PS ═ PDF, PS ═ PDF ═ Φ, and a fault occurrence probability set PS ═ Pr (S, T, E, P1＝1),Pr(s2＝1),...,Pr(sm1) covering all root node condition probability tables in the bayesian network fault diagnosis model; PDF { [ PD, PF } { [ PD } ]ij],[Pfij]And represents a detection-false alarm probability set that can be interconverted with all sub-node conditional probability tables in the bayesian network fault diagnosis model.
FIG. 6 is a model of Bayesian network fault diagnosis under a typical binary test scenario.
Since v (bnt) ═ ssut, S ═ T ═ Φ, and the tail of each edge in the bayesian network fault diagnosis model is in S and the head is in T, the bayesian network fault diagnosis model is a two-part directed graph.
Let dependency matrix D ═ Dij]Representing the dependency between S and T if T is testedjDetecting a source of failure siThen d isij1, otherwise d ij0, D is equivalent to the two-part directed-graph boolean adjacency matrix of the bayesian network fault diagnosis model. The expression of D is as follows.
Figure BDA0001917807930000071
Based on the condition independent assumption, for any two different variables S in Si，sjIs provided with
Pr(si|sj)＝Pr(si)i≠j (12)
Similarly, for any two different variables T in Ti，tjIs provided with
Pr(ti|tj)＝Pr(ti)i≠j (13)
In the case of binary testing, Pr (t)j) Is calculated by
Figure BDA0001917807930000072
Due to si，tjAre all Boolean values, and the Bayesian network is a directed bipartite graph, so
Figure BDA0001917807930000079
And pi (t)j)＝{si|dij1} so there are
Figure BDA0001917807930000074
Substituting equation (15) into equation (14) to obtain test tjIs not communicated withThe probability of passing is
Figure BDA0001917807930000075
Test tjThe probability of passing is
Figure BDA0001917807930000076
Will detect the probability PdijCalculating formula (5) and false alarm probability PfijSubstituting calculation formula (6) into formulas (16) and (17) has
Figure BDA0001917807930000077
Figure BDA0001917807930000078
Pdij，PfijValue of and dijIs taken as equivalent
Figure BDA0001917807930000081
If d isij1, then siIs tjA parent node of siFor tjThe causal influence strength of (a) can be represented by a conditional probability table shown in table 1.
TABLE 1siAnd tjConditional probability table of
Figure BDA0001917807930000082
If and all d ij1 corresponding detection-false alarm probability pair (Pd)ij,Pfij) If known, all sub-node condition probability tables in the bayesian network fault diagnosis model can be described. Figure 6 pairThe conditional probability table for the corresponding bayesian network is shown in table 2.
Table 2 conditional probability table of fig. 6
Figure BDA0001917807930000083
Basic object information required to be input in Bayesian network fault diagnosis modeling comprises two parts:
(1) the deterministic information part comprises a fault set S, a test set T and a dependency matrix D;
(2) and the uncertainty information part comprises a fault occurrence probability set PS and a detection-false alarm probability set PDF.
The method for acquiring the information of each element in the Bayesian network fault diagnosis model comprises the following steps:
s can be obtained by functional division and fault mode division in reliability analysis;
t may be obtained based on fault diagnosis design information;
d can be obtained based on historical experience, a fault diagnosis model, a simulation test conclusion, fault mode influence analysis, a fault dictionary, a fault tree, a Petri network model and the like, and can also be obtained through Bayesian network structure learning;
the PS can be obtained by reliability analysis, fault tolerance analysis, monte carlo analysis, and the like;
the PDF can be obtained by a data driving method or the like.
The Bayesian network fault diagnosis model can achieve good effects in the testability modeling field under the uncertainty test condition, but has the following main problems:
the method has the advantages that a feedback loop cannot be processed, the feedback loop often appears in the fault propagation process, and the Bayesian network fault diagnosis model is a two-part directed acyclic graph;
the accessibility analysis capability is not strong, and the failure mode propagation mechanism analysis is difficult to be carried out based on a Bayesian network failure diagnosis model;
the definition of a fault source is fuzzy, the definition of a fault source set S is fuzzy, the S comprises functions, components, fault modes and the like, and the functions, the components and the fault modes have an incidence relation.
Fault mode and function dependency relationship analysis based on hybrid diagnosis model
Hybrid diagnostic model:
the hybrid diagnosis model is short for a fault mode-function-test hybrid diagnosis model, is the fusion of a fault mode-test correlation model and a function-test correlation model, and achieves the goal of uniformly modeling the fault mode and the function in the same correlation model. The hybrid diagnosis model can intervene in the design and analysis of the fault diagnosis capability in the initial development and design stages of the product, and is a fault diagnosis model for the whole life cycle of the product. The basic element composition of the hybrid diagnosis model is obtained by deeply analyzing the modeling mechanism of the hybrid diagnosis model:
set of components C ═ C1,c2,…,cL}；
Function set F ═ F1,f2,…,fJ}；
Failure mode set FM ═ FM1,fm2,…,fmI}；
Test set T ═ T1,t2,…,tn}；
Failure mode fmiEver-influencing function sets
Figure BDA0001917807930000091
affmi＝|AFFM(fmi)|；
Failure mode fmiSometimes affected function sets
Figure BDA0001917807930000092
sffmi＝|SFFM(fmi)|；
Component ciAssociated function set
Figure BDA0001917807930000101
fc＝|FC(ci)|；
Component ciSet of failure modes
Figure BDA0001917807930000102
fmc＝|FMC(ci)|；
Function fjSet of associated components
Figure BDA0001917807930000103
cf＝|CF(fj)|；
Function(s)
Figure BDA0001917807930000104
Associated FMC (c)i) Failure mode subset
Figure BDA0001917807930000105
Failure mode
Figure BDA0001917807930000106
Associated FC (c)i) Subset of functions
Figure BDA0001917807930000107
Component failure rate set λ (C) { λ (C) }1),λ(c2),...,λ(cL)}；
Function fjAt component ciFailure rate of upper distribution
Figure BDA0001917807930000108
Failure mode fmjAt component ciFailure rate of upper distribution
Figure BDA0001917807930000109
Function(s)
Figure BDA00019178079300001010
Corrected functional failure probability of original failure probability
Figure BDA00019178079300001011
Failure mode
Figure BDA00019178079300001012
Original failure probability of
Figure BDA00019178079300001013
Modified failure mode failure probability
Figure BDA00019178079300001014
Coloring directed graph HDM (C, F, FM, T, E), wherein V ═ C ═ F ═ FM @ u @,
Figure BDA00019178079300001015
v is a node set, and E is a directed edge set between nodes of the hybrid diagnostic model.
The hybrid diagnosis model gives specific attribute information (such as cost, test type, importance and the like) to each node and directed edge in the color directed graph HDM (C, F, FM, T, E) based on an object-oriented idea so as to meet the requirements of system fault diagnosis design and analysis.
Fuzzy recognition of the fault mode and the functional dependence relationship:
in the bayesian network fault diagnosis model, the fault set S may include component, function, fault mode faults, etc., and causal dependencies often exist among the components, the function, and the fault modes. FIG. 7 illustrates a fault configuration for an LRU component, including a set of fault patterns FM ═ FM1,fm2,fm3F and F1,f2,f3}. When all of the LRU components, failure modes, and functions are considered as failures, the failure set S ═ fm1,fm2,fm3,f1,f2,f3LRU, S must be divided because there is no independence between sub-elements in S. The hybrid diagnostic model divides the fault source into a component set C, a function set F and a fault mode set FM according to the assumption of independence of faults, and fuzzily divides the dependency relationship between the fault mode and the function into No influence (No effect, NA), Sometimes influence (someimes effect, SA), Always influence (Always effect,AA) three classes. There is currently no clear canonical way to determine which class the dependency between failure modes and functions belongs to.
From the perspective of fuzzy pattern recognition, the problem of identifying the dependency relationship between the failure mode and the function belongs to the problem of single-mode recognition, and the determination may be performed based on the principle of maximum membership degree, where a specific determination flow is shown in fig. 8.
The principle of maximum membership for single pattern recognition is as follows.
(1) Maximum membership rule 1: let A1,A2,...,AmAre m fuzzy subsets on U, U is a fixed element in U, if there is i e {1,2
Figure BDA0001917807930000111
Then u is considered to be relatively subordinate to Ai。
(2) Maximum membership rule 2: defining a threshold value lambda epsilon (0, 1) and recording
Figure BDA0001917807930000112
If alpha is less than lambda, making 'rejection' judgment, and otherwise analyzing the reason to be searched, if alpha is more than or equal to lambda, considering that the identification is feasible, and making judgment according to the maximum membership rule 1. The maximum membership rule 2 can avoid that the maximum membership rule makes a decision which deviates far from the actual decision because the membership is all very small.
Let the relation of no influence on NA, sometimes influence on SA and always influence on AA correspond to fuzzy set A respectively1,A2,A3The threshold λ is 0.55. For each failure mode fm in FIG. 81,fm2,fm3When N is 100 simulation injections, the domain X is 0,100]Corresponding membership function of
Figure BDA0001917807930000113
Figure BDA0001917807930000114
Figure BDA0001917807930000121
The membership function curve is shown in fig. 9.
Respectively to fm1,fm2,fm3Statistics f after 100 times of simulation fault injection1,f2,f3The number of failures is shown in table 3.
TABLE 3 statistical table of functional failures
Figure BDA0001917807930000122
Let the elements in Table 3 use NfmfijExpressing, solving based on the principle of maximum membership
Ak(Nfmfij)＝max{A1(Nfmfij),A2(Nfmfij),A3(Nfmfij)}，k∈{1,2,3} (26)
Determination of NfmfijRelative membership to Ak. Derived set of failure modes { fm1,fm2,fm3And function set f1,f2,f3The qualitative influence relationship is shown in Table 4.
TABLE 4 relationship between failure modes and qualitative functional impact
Figure BDA0001917807930000123
FIG. 10 shows a failure mode { fm }1,fm2,fm3And function { f }1,f2,f3A bipartite graph representation of dependencies, where solid lines represent always influencing relationships and dashed lines represent sometimes influencing relationships. Hybrid diagnostics to avoid failure modes or isolation of functional informationIn the model, the single failure mode or function is usually set as a virtual function or a virtual function is associated with the single failure mode by default, so that the dependency relationship between all failure modes and functions is constructed, and the failure modes and the functions in the component are relatively independent.
And (3) correcting the association between the fault mode and the functional fault probability based on the hybrid diagnosis model:
in the hybrid diagnosis model, the fault probability is the relative probability of fault occurrence, is the expansion of the fault rate, and is important input data for calculating the fault detection rate, the fault isolation rate and the fault false alarm rate.
The functional fault probability can be obtained by the fault rate distribution of the upper-layer components and the fault rate accumulation of the lower-layer components; the failure mode failure probability is typically calculated as a proportional distribution of component failure rates. Due to the different data sources of the functional failure probability and the failure mode failure probability, the failure rate prediction for the same component based on the functional failure probability and the failure mode failure probability may not be consistent. On one hand, reliability data provided in the system cannot completely reflect the reliability of the system, and reliability indexes are evaluated by only depending on the functional fault probability or the fault mode fault probability, so that the reliability of the system cannot be objectively expressed; on the other hand, in the system modeling process, as new failure modes of the components are added, the failure mode failure probability is changed, and the change causes the functional failure probability to be redistributed.
In response to the above problems, the failure probability data must be modified or updated by correlating the functional failure probability with the failure mode failure probability in a manner. In order to solve the problem, three fault probability correlation correction methods based on a hybrid diagnosis model are provided, namely a fault mode fault probability average distribution method, a functional fault probability priority distribution method and a fault mode fault probability priority distribution method.
(1) Failure mode failure probability average distribution method
The failure probability average distribution method of the failure modes is suitable for the condition of functional reliability data shortage which is neglectedFunctional reliability data, direct failure mode failure probability
Figure BDA0001917807930000131
Distributed evenly among the functions it affects, component ciFailure mode of
Figure BDA0001917807930000132
Evenly distributed to functions associated therewith
Figure BDA0001917807930000133
Has a fault probability of
Figure BDA0001917807930000134
Corrected functional failure probability
Figure BDA0001917807930000135
Is calculated by the formula
Figure BDA0001917807930000136
(2) Functional failure probability priority distribution method
When the data reliability of the functional fault probability is higher than the fault probability of the fault mode, the fault probability of the fault mode is corrected by adopting a functional fault probability priority method, and the specific calculation steps are as follows:
STEP1 calculation of component c using equation (29)iFailure mode of
Figure BDA0001917807930000141
Fault probability of
Figure BDA0001917807930000142
Based on
Figure BDA0001917807930000143
Each function fault probability proportion of distributing to the fault of the related functionProbability of being
Figure BDA0001917807930000144
STEP2 calculation will be performed using equation (30)
Figure BDA0001917807930000145
Fault probability of
Figure BDA00019178079300001422
Based on the result of equation (29)
Figure BDA00019178079300001423
Each failure mode in (1)
Figure BDA0001917807930000148
Is distributed to
Figure BDA0001917807930000149
Distribution of fault probability ratio to
Figure BDA00019178079300001410
Has a fault probability of
Figure BDA00019178079300001411
STEP3 calculation of the value obtained by equation (31)
Figure BDA00019178079300001412
Each function in (1)
Figure BDA00019178079300001424
Is distributed to
Figure BDA00019178079300001414
The fault probability ratio of the above is accumulated to obtain the corrected fault mode fault probability of
Figure BDA00019178079300001415
(3) Failure probability priority distribution method for failure mode
When the data reliability of the fault probability of the fault mode is higher than the functional fault probability, the functional fault probability is corrected by adopting a fault probability priority method of the fault mode, and the specific calculation steps are as follows:
STEP1 calculation of component c using equation (32)iFunction of (2)
Figure BDA00019178079300001416
Fault probability of
Figure BDA00019178079300001425
Based on
Figure BDA00019178079300001418
The fault probability of each fault mode is proportionally distributed to the fault probability of the relevant fault mode
Figure BDA00019178079300001419
STEP2 calculation will be performed using equation (33)
Figure BDA00019178079300001420
Fault probability of
Figure BDA00019178079300001421
Based on the result of equation (32)
Figure BDA0001917807930000151
Each function in (1)
Figure BDA0001917807930000152
Is distributed to
Figure BDA0001917807930000153
Distribution of fault probability ratio to
Figure BDA0001917807930000154
Has a fault probability of
Figure BDA0001917807930000155
STEP3 calculation of the value obtained by equation (34)
Figure BDA0001917807930000156
Each failure mode in (1)
Figure BDA0001917807930000157
Is distributed to
Figure BDA0001917807930000158
The fault probability ratio is accumulated to obtain the corrected functional fault probability of
Figure BDA0001917807930000159
(4) Failure rate correlation correction example
The original values of the failure modes and the functional failure probabilities of the LRUs shown in fig. 10 are shown in fig. 11. The fault probability correction is performed on the LRU by using a fault pattern fault probability average distribution method (method a), a functional fault probability priority method (method b), and a fault pattern fault probability priority method (method c), and the obtained fault probability correction results are shown in table 5.
TABLE 5 failure modes and functional probability correction results
Figure BDA00019178079300001510
For electronic products, component ciFailure rate λ (c)i) Two methods can be adopted for prediction, one method is a function counting method which is suitable for the situation of preferential distribution of the probability of the functional fault, and the calculation method is
Figure BDA00019178079300001511
The second method is a failure mode counting method which is suitable for the conditions of failure mode failure probability average distribution and failure mode failure probability priority distribution, and the calculation method is
Figure BDA0001917807930000161
Hybrid diagnostic Bayesian network fault diagnosis capability analysis
Comprehensive analysis of fault diagnosis modeling problems based on uncertainty information:
let T ═ T be the test set for the example LRU given in fig. 111,t2,t3,t4Divide T into function test set TF＝{t1,t2And failure mode test set TFM＝{t3,t4}. The mixed dependencies between test, failure mode, function, LRU are shown in fig. 12.
Fig. 12 can be divided into two bayesian network models and one hybrid diagnostic model as shown in fig. 13a, 13b, 13c, respectively.
If the Bayesian network is used for fault diagnosis modeling, the incidence relation between the fault mode and the function is ignored, and if the hybrid diagnosis model is used for modeling, the testing uncertainty is ignored. In order to enable the fault diagnosis model to reflect the dependency relationship between the fault and the test more accurately, a fault diagnosis model capable of modeling the uncertainty test information and the fault mode and function fuzzy dependency relationship simultaneously needs to be designed.
Hybrid diagnostic bayesian network model:
based on the directed graph definition, the hybrid diagnostic model HDM (C, F, FM, T, E) can be simplified to be represented as HDM (V, E), where V ═ C ═ F ═ FM ═ T is the set of nodes. Similarly, a Bayesian network fault diagnosis model BNT (V, E, P) derived from the directed graph can be naturally combined with the hybrid diagnosis model to realize Bayesian uncertainty inference based on the hybrid diagnosis model, and form advantage complementation of the hybrid diagnosis model and the Bayesian network fault diagnosis model.
By fusing the hybrid diagnosis model and the bayesian network fault diagnosis model on the basis of considering the description of the uncertainty test information, the designed hybrid diagnosis bayesian network model can be represented by a directed graph HDBN ═ C, F, FM, T, E, P. Wherein, V ═ C ═ F { [ F } { [ T ]) is a set of nodes,
Figure BDA0001917807930000162
e represents the directed edge set between the system nodes, and P is the weight matrix. The graph theory information fusion relationship between the hybrid diagnosis bayesian network model and the hybrid diagnosis bayesian network and bayesian network fault diagnosis model is shown in fig. 14.
The source of each element information in HDBN ═ C, F, FM, T, E, P) is as follows:
set of components C ═ C1,c2,…,cLDerived from a mixed diagnostic model HDM (C, F, FM, T, E);
function set F ═ F1,f2,…,fJDerived from a mixed diagnostic model HDM (C, F, FM, T, E);
failure mode set FM ═ FM1,fm2,…,fmIDerived from a mixed diagnostic model HDM (C, F, FM, T, E);
test set T ═ T1,t2,…,tnDerived from a mixed diagnostic model HDM (C, F, FM, T, E);
the directed edge set E is derived from a hybrid diagnostic model HDM (C, F, FM, T, E);
the probability of the faults of each fault mode, function and component is derived from the hybrid diagnosis model reasoning;
the weight matrix P information is derived from the fusion of the hybrid diagnostic model HDM (C, F, FM, T, E) and the bayesian network fault diagnosis model BNT ═ information (V, E, P). The fault mode and test directly related to the fault mode and the conditional probability information of the test, the function and the test can be obtained based on a Bayesian network fault diagnosis model; although conditional probability information between the fault mode and the function is derived from the analysis of the dependency relationship between the fault mode and the function based on the hybrid diagnostic model, the conditional probability information is only obtained by the existing inference method of the hybrid diagnostic model, and a related algorithm and an inference rule need to be further designed on the basis of the analysis of the dependency relationship between the fault mode and the function based on the hybrid diagnostic model.
For any one component, the hybrid diagnostic bayesian network model can be represented in two forms: one is in the form of a function root node, which is suitable for the case of priority assignment of probability of function failure, as shown in fig. 15 a; the other is in the form of a failure mode as a root node, which is suitable for the case of failure mode failure probability average distribution and failure mode failure probability priority distribution as shown in fig. 15 b. The hybrid diagnostic bayesian network comprises three layers: the top layer is a root node layer, the middle layer is a hidden layer, and the bottom layer is a test layer.
Hybrid diagnostic Bayesian network model inference:
due to the existence of the hidden layer, the hybrid diagnosis Bayesian network model cannot be directly used for prediction of fault diagnosis capability quantitative indexes. In order to predict the fault diagnosis capability index, a hidden layer needs to be removed based on the node propagation rule of the directed graph, and conditional probability information between a root node and all tests needs to be analyzed. The inference process of the hybrid diagnostic bayesian network model is as follows.
(1) Removing hidden layers
ROOT for the element set of the ROOT node layer ═ ROOT1,root2,...,rootmDenotes that the element set of the hidden layer is HID ═ HID { (HID) }1,hid2,...,hidwDenotes that the element set of the test layer is T ═ T1,t2,...,tnThe fuzzy dependency relationship between each element of the root node layer and each element of the hidden layer is represented by a matrix RH ═ RHij]Is represented by (1), wherein rhijE to { NA, SA, AA }, and the matrix HT for the incidence relation between each element of the hidden layer and each element of the test layer is [ HT [ [ HT ]jk]Matrix for representing and eliminating direct incidence relation between root node layer and test layer added after hidden layer is eliminated
Figure BDA0001917807930000181
And (4) showing. Hidden layer rejection is given to node propagation law based on directed graphIs of the formula
Figure BDA0001917807930000182
The reliability of the fault probability data of the fault mode of the LRU shown in fig. 12 is higher than the functional fault probability, and if the fault rate is corrected in a correlated manner by using a fault probability priority allocation method of the fault mode, the LRU adopts a mixed diagnosis bayesian network model designed in a form of taking the fault mode as a root node. The functional hidden layer of fig. 15b is culled based on equation (37), as shown in fig. 16.
(2) Conditional probability information calculation
Since the relationship between the root node and the hidden node is a qualitative fuzzy relationship, it is also necessary to provide conditional probability information between the root node and the hidden node on the basis of the analysis result of the functional dependency relationship and the failure mode based on the hybrid diagnostic model. The following conditional probability information calculation rule between the root node and the hidden node is defined.
Rule 1: if root node rootiAnd hidden node hidjIf the root node is a permanent influence relation, the hidden node is also generated when the root node is generated; when the root node does not occur, the hidden node does not occur. The corresponding mathematical description is: if rhijAA, then
Figure BDA0001917807930000186
Rule 2: if root node rootiAnd hidden node hidjIs always an influence relationship between them, rootiAnd hidjThe solution method of the conditional probability is
Figure BDA0001917807930000183
Figure BDA0001917807930000184
Among them, Pr' (hid)j) To hide nodes hidjCorrected failure probability; pr' (root)i) Root node rootiCorrected failure probability.
Figure BDA0001917807930000185
Rule 3: if root node rootiAnd hidden node hidjDo not influence rh mutuallyijWhen being NA, then
Figure BDA0001917807930000187
(3) Removing heavy edges
The heavy edges between two nodes often cause diagnostic reasoning conflicts, and therefore, a mechanism for solving the conflicts needs to be constructed. It has been proven in probability theory that the probability of occurrence of two sets of union a ∪ B is greater than the probability of occurrence of either set a or B alone
Pr(A∪B)≥max{Pr(A),Pr(B)} (41)
Therefore, the maximum value of the detection rate and the false alarm rate in the heavy edges between the root node and the test node can be approximately taken as the detection-false alarm probability between the root node and the test node, so as to reduce the error of the prediction of the fault diagnosis capability index.
Rule 4: based on each rootiAnd tkPath between pathsijkFunction sets F and TFDetection of (2) -false alarm probability matrix, failure mode set FM and TFMRespectively computing the false alarm probability matrix
Figure BDA0001917807930000191
And combining the heavy edge detection-false alarm probabilities based on the following formula
Figure BDA0001917807930000192
After the hybrid diagnostic bayesian network model inference is completed, the hybrid diagnostic bayesian network model shown in fig. 15b will be converted into the bayesian network fault diagnosis model form shown in fig. 17.
In summary, as shown in fig. 18, an embodiment of the present invention discloses a fault diagnosis capability analysis method based on a hybrid diagnosis bayesian network, including the following steps:
1): and (3) fault probability correlation correction: selecting a method for performing fault probability correlation correction on the component based on two criteria of whether reliability data is deficient and whether the fault probability credibility of the fault mode is higher than the functional fault probability;
2): establishing a modeling and reasoning model of the hybrid diagnosis Bayesian network model: selecting a construction mode of the hybrid diagnosis Bayesian network model based on the fault probability correlation correction result, and carrying out modeling and reasoning on the hybrid diagnosis Bayesian network model;
3): and (3) calculating a fault diagnosis capability index: and performing fault diagnosis capability index calculation based on a hybrid diagnosis Bayesian network model based on the generated root node-test dependency matrix, root node-test detection-false alarm probability matrix and fault probability correlation correction result to generate a component fault diagnosis capability index prediction report.
The specific method of the above steps 1) and 2) is described in detail below with reference to the foregoing description and step 3.
Although the IEEE STD 1522 provides a design framework of quantitative indexes based on AI-ESTATE, a specific fault diagnosis capability index calculation method based on different models is not provided, and therefore the problem is to design a fault diagnosis capability quantitative index calculation method based on a hybrid diagnosis Bayesian network model by referring to a fault diagnosis capability quantitative index information model provided by the IEEE STD 1522.
After the hybrid diagnosis Bayesian network reasoning, the obtained dependency matrix between the root node and the test node is
Figure BDA0001917807930000201
The detection-false alarm probability matrix between the root node and the test node is
Figure BDA0001917807930000202
According toDefining an EPoD information model, and giving an EPoD calculation formula based on a hybrid diagnosis Bayesian network fault diagnosis model as
Figure BDA0001917807930000203
Wherein, EPoDiTo a fault siProbability of being possibly detected, if t existsjSo that d ij1, then siMay be detected, otherwise, siAnd cannot be detected. When d isijWhen 1 is true
Figure BDA0001917807930000204
EPoDiIs calculated by the formula
Figure BDA0001917807930000205
Wherein the expected isolation rate is defined by an incremental expected isolation rate IEPoI (IEPoI) as the ratio of the total failure rate of a fuzzy group of a particular size correctly isolated using a test set given by the model to the total failure rate of detected failures within a particular diagnostic model framework. The cumulative expected fault isolation rate CEPoI (CEPoI) is defined as the ratio of the total fault rate of fuzzy groups correctly isolated to within a certain size using a test set given by a model to the total fault rate of detected faults within a specific diagnostic model framework. Within the framework of a hybrid diagnostic Bayesian network fault diagnosis model, the relationship between IEPoI and CEPoI is
IEPoI(g)＝CEPoI(g)-CEPoI(g-1) (46)
Figure BDA0001917807930000211
Before calculating IEPoI, first, ROOT is divided into a plurality of mutually independent fault isolation fuzzy groups, each fault isolation fuzzy group contains l fault elements, and l belongs to {1, 2., | ROOT | }.
A fault ambiguity set refers to a subset of faults consisting of faults having the same characteristics. In the case of a single fault assumption, the fault isolation fuzzy set may be based on the dependency matrix D*And (6) calculating. Is provided with
Figure BDA0001917807930000212
And
Figure BDA0001917807930000213
is any two row vectors in D, and i ≠ j, if
Figure BDA0001917807930000214
Namely, it is
Figure BDA0001917807930000215
Description of rootiOr rootjWhen a fault occurs, at tkThe information presented above is the same, so rootiAnd rootjTo inseparable faults, they belong to the same fuzzy group, and similarly multiple faults can be grouped into one fuzzy group. Root calculation based on hybrid diagnosis Bayesian network modeliThe method for isolating the fuzzy group by the fault is
Figure BDA0001917807930000216
rootiThe size of the fault isolation fuzzy group is AGi|。
Single failure assumption requires rootiIn case of failure, all detection rootsiNone of the tests (2) pass, it can be isolated.
For calculation convenience, a single expected performance of isolation (SEPoI) definition is added in the framework of the hybrid diagnostic Bayesian network model. SEPoI is defined as using a test set given by a model to enable a single fault within a specific diagnostic model frameworkA ratio of the isolated failure rate to a total failure rate of the detected failures. root (R)iThe SEPoI calculation formula is
Figure BDA0001917807930000217
The formula for IEPoI is
Figure BDA0001917807930000218
Isolation to fuzzy group size max { | AGiThe CEPoI within | } has the calculation formula of
Figure BDA0001917807930000219
The CEPoI isolated to within the fuzzy set size L is calculated as
Figure BDA0001917807930000221
The expected aggregate size (EAGS) of the fault isolation fuzzy group is defined as the average fault rate size of the fault isolation fuzzy group correctly isolated by using the test set given by the model in a specific diagnosis model framework. The EAGS has the calculation formula of
Figure BDA0001917807930000222
The hybrid diagnosis Bayesian network model has the potential of fault false alarm rate prediction, one of the important functions of the PHM is to inhibit false alarms, and a fault false alarm rate calculation formula based on the hybrid diagnosis Bayesian network model is designed. The fault false alarm rate based on the hybrid diagnosis Bayesian network model is synthetically calculated by two independent formulas of single expected fault rate of fault alarm (SEFROA) and cumulative expected fault rate of fault alarm (CEPoA).
SEFRoA is defined as the false alarm rate of a single fault detection within a specific diagnostic model framework using the test set given by the model. The formula for calculating SEFROA is as follows
Figure BDA0001917807930000223
It can be seen from the calculation formula of the SEFRoA that the more the correlation tests are, the higher the probability of the false alarm is when the same fault is detected.
The calculation formula of the accumulated expected failure rate of failure alarm (CEFRoA) is as follows:
Figure BDA0001917807930000224
CEPoA is defined as the ratio of the cumulative fault expected false alarm fault rate calculated using the test set given by the model to the sum of the cumulative fault expected false alarm fault rate and the expected weighted detection rate within a particular diagnostic model framework. CEPoA is calculated by the formula
Figure BDA0001917807930000225

Claims (1)

1. A fault diagnosis capability analysis method based on a hybrid diagnosis Bayesian network is characterized by comprising the following steps:
and (3) fault probability correlation correction: performing fault probability correlation correction on the component based on two criteria of whether reliability data is deficient and whether fault probability credibility of the fault mode is higher than functional fault probability;
establishing and reasoning a hybrid diagnosis Bayesian network model: selecting a construction mode of the hybrid diagnosis Bayesian network model based on the fault probability correlation correction result, and carrying out modeling and reasoning on the hybrid diagnosis Bayesian network model;
and (3) calculating a fault diagnosis capability index: performing fault diagnosis capability index calculation based on the hybrid diagnosis Bayesian network model on a root node-test dependence matrix, a root node-test detection-false alarm probability matrix and a fault probability correlation correction result generated based on the hybrid diagnosis Bayesian network model, generating a component fault diagnosis capability index prediction report, and completing fault diagnosis capability analysis of the hybrid diagnosis Bayesian network;
the method for generating the component fault diagnosis capability index prediction report and completing the fault diagnosis capability analysis of the hybrid diagnosis Bayesian network comprises the following steps:
after the hybrid diagnosis Bayesian network reasoning, the obtained dependency matrix between the root node and the test node is
Figure FDA0002942014960000011
D is a dependency matrix between the root node and the test node after the hybrid diagnosis Bayesian network inference,
Figure FDA0002942014960000012
for the elements of the matrix, it is,
Figure FDA0002942014960000013
indicating that the ith root node and the kth test node have a dependency relationship, otherwise, not;
the detection-false alarm probability matrix between the root node and the test node is
Figure FDA0002942014960000014
The EPoD calculation formula based on the hybrid diagnosis Bayesian network fault diagnosis model is given as follows:
Figure FDA0002942014960000015
wherein EPoD represents a fault detection rate obtained based on the fault diagnosis model,
Figure FDA0002942014960000016
representing the passing of hidden nodes hid*The detection probability of the kth test node to the ith root node,
Figure FDA0002942014960000017
representing the passing of hidden nodes hid*The false alarm probability of the kth test node to the ith root node is measured; ROOT is the set of elements of the ROOT node layeriIs the ith root node, rootjIs the jth root node; pr (root)i) Root node root representationiProbability of failure;
EPoDito a fault siProbability of being detected, if t existsjSo that dij1, then siCan be detected, otherwise, siCan not be detected, tjRepresenting the jth test node; when d isijWhen the value is 1:
Figure FDA0002942014960000021
wherein
Figure FDA0002942014960000022
Representing the dependency relationship between the ith test node and the jth fault; t is tkIs the kth test node; by using
Figure FDA0002942014960000023
Indicating overall the ability to detect a fault siAll of the test nodes of (a) are,
Figure FDA0002942014960000024
indicating a fault siThe probability that it can be detected;
Figure FDA0002942014960000025
indicating a fault siProbability of failing to be detected;
EPoDithe calculation formula of (2) is as follows:
Figure FDA0002942014960000026
within the framework of a hybrid diagnostic bayesian network fault diagnosis model, the relationship between the incremental expected isolation rate IEPoI and the cumulative expected fault isolation rate CEPoI is:
IEPoI(g)＝CEPoI(g)-CEPoI(g-1)
Figure FDA0002942014960000027
wherein g and h represent the sizes of fault isolation fuzzy groups; iepoi (g) represents the incremental expected isolation rate isolated to fuzzy group g, CEPoI (g) represents the cumulative expected fault isolation rate isolated to fuzzy group g, CEPoI (g-1) represents the cumulative expected fault isolation rate isolated to fuzzy group g-1, iepoi (h) represents the incremental expected isolation rate isolated to fuzzy group h;
before calculating IEPoI, dividing ROOT into a plurality of mutually independent fault isolation fuzzy groups, wherein each fault isolation fuzzy group contains l fault elements, and l belongs to {1, 2., | ROOT | };
a fault fuzzy set refers to a fault subset consisting of faults having the same characteristics; in the case of a single fault assumption, the fault isolation fuzzy set may be based on the dependency matrix D*Calculating to obtain; is provided with
Figure FDA0002942014960000028
And
Figure FDA0002942014960000029
is any two row vectors in D, and i ≠ j, if
Figure FDA00029420149600000210
Namely, it is
Figure FDA00029420149600000211
(k is 1,2, …, n) for rootiOr rootjWhen a fault occurs, at tkThe information presented above is the same, so rootiAnd rootjTo inseparable faults, they belong to the same fuzzy group, to group a plurality of faults into one fuzzy group,
Figure FDA0002942014960000031
indicating that the ith root node and the kth test node have a dependency relationship,
Figure FDA0002942014960000032
representing that the jth root node and the kth test node have a dependency relationship; root calculation based on hybrid diagnosis Bayesian network modeliThe method for isolating the fuzzy group by the fault comprises the following steps:
Figure FDA0002942014960000033
rootithe size of the fault isolation fuzzy group is AGi|；
Wherein, AGiRoot node rootiThe fault isolation fuzzy group is located;
single failure assumption requires rootiIn case of failure, all detection rootsiCan not be isolated until the test of (1) fails;
in a hybrid diagnosis Bayesian network model framework, adding a single fault expected isolation rate SEPoI, wherein the SEPoI is defined as the ratio of the isolated fault rate of a single fault to the total fault rate of detected faults in a specific diagnosis model framework by using a test set given by a model; root (R)iThe SEPoI calculation formula is as follows:
Figure FDA0002942014960000034
wherein: pr (root)j) Root node root representationjProbability of failure;
the formula for IEPoI is:
Figure FDA0002942014960000035
wherein Pr (t)k|rooti) Representing the probability that the ith root node can be detected by the kth test node t; EPoDjIndicates the probability that the jth fault can be detected; IEPoI is the incremental expected isolation rate; l is the fault isolation fuzzy group size, iepoi (L) is the incremental expected isolation rate isolated to the fuzzy group size of L;
isolation to fuzzy group size max { | AGiThe formula for CEPoI within | } is:
Figure FDA0002942014960000036
the CEPoI isolated to within the fuzzy set size L is calculated as
Figure FDA0002942014960000037
Wherein max { | AGi| represents the maximum value of the cardinality in the fault isolation fuzzy set of all the root nodes;
the expected fault isolation fuzzy group size EAGS is defined as the average fault rate of a fault fuzzy group correctly isolated by using a test set given by a model in a specific diagnosis model framework; the calculation formula of EAGS is:
Figure FDA0002942014960000041
the fault false alarm rate based on the hybrid diagnosis Bayesian network model is synthesized and calculated by two independent formulas of single fault expected false alarm rate SEFROA and cumulative expected false alarm rate CEPoA, and the fault false alarm rate calculation formula based on the hybrid diagnosis Bayesian network model;
the formula for calculating SEFRoA is:
Figure FDA0002942014960000042
SEFROA represents the false alarm rate of single fault detection in a specific diagnosis model framework by using a test set given by a model; it can be seen from the calculation formula of the SEFRoA that, when the same fault is detected, the more the correlation test is, the higher the probability of the false alarm is;
Figure FDA0002942014960000043
representing the ith root node rootiNo fault, kth test node tkThe probability of passing the test;
Figure FDA0002942014960000044
representing the product of the false alarm rates of all root nodes capable of being tested and the difference value of 1;
Figure FDA0002942014960000045
representing the ith root node rootiNo fault, kth test node tkThe product of the probabilities of passing the test; sefroa (i) represents the expected false alarm rate for the ith root node;
the calculation formula of the expected false alarm rate CEFRoA of the accumulated faults is as follows:
Figure FDA0002942014960000046
CEPoA is defined as the sum ratio of the accumulated fault expected false alarm fault rate, the accumulated fault expected false alarm fault rate and the expected weighted detection rate calculated by using a test set given by a model in a specific diagnosis model frame; the formula for CEPoA is:
Figure FDA0002942014960000047
the fault probability correlation correction method comprises the following steps:
failure mode failure probability average distribution method:
the failure probability average distribution method of the failure mode is suitable for the condition of lacking functional reliability data, ignores the functional reliability data and directly uses the failure probability of the failure mode
Figure FDA0002942014960000051
Distributed evenly among the functions it affects, component ciFailure mode of
Figure FDA0002942014960000052
Evenly distributed to functions associated therewith
Figure FDA0002942014960000053
Has a fault probability of
Figure FDA0002942014960000054
Wherein
Figure FDA0002942014960000055
Indicating failure modes
Figure FDA0002942014960000056
The associated function set; corrected functional failure probability
Figure FDA0002942014960000057
Is calculated by the formula
Figure FDA0002942014960000058
Wherein
Figure FDA0002942014960000059
Representing a component ciThe kth function of (1);
Figure FDA00029420149600000510
representation of belonging to component ciFailure mode of
Figure FDA00029420149600000511
The failure probability of (2);
Figure FDA00029420149600000512
indicating function
Figure FDA00029420149600000513
A set of associated failure modes;
the fault probability correlation correction method comprises the following steps:
function failure probability priority allocation method:
when the data reliability of the functional fault probability is higher than the fault probability of the fault mode, the fault probability of the fault mode is corrected by adopting a functional fault probability priority method, and the specific calculation steps are as follows:
STEP1 calculation of component c using equation (3)iFailure mode of
Figure FDA00029420149600000514
Fault probability of
Figure FDA00029420149600000515
Based on
Figure FDA00029420149600000516
The probability of failure of each function is proportionally distributed to the probability of failure of the related function
Figure FDA00029420149600000517
Figure FDA00029420149600000518
Representing a component ciThe h function of (1);
Figure FDA00029420149600000519
and
Figure FDA00029420149600000520
respectively representing functions
Figure FDA00029420149600000521
And function
Figure FDA00029420149600000522
Probability of failure; STEP2 adopting the formula (4) according to
Figure FDA00029420149600000523
Middle function
Figure FDA00029420149600000524
Set of associated failure modes, derived to be
Figure FDA00029420149600000525
Fault probability of
Figure FDA00029420149600000526
Is proportionally distributed to
Figure FDA00029420149600000527
The failure probability of (1) is:
Figure FDA00029420149600000528
Figure FDA00029420149600000529
representing a component ciThe jth function of (1);
Figure FDA00029420149600000530
indicating function
Figure FDA00029420149600000531
A set of associated failure modes;
STEP3 according to equation (5)
Figure FDA0002942014960000061
Medium failure mode
Figure FDA0002942014960000062
The associated function set, the probability of failure mode failure that can be corrected is:
Figure FDA0002942014960000063
the fault probability correlation correction method comprises the following steps:
failure mode failure probability priority assignment method:
when the data reliability of the fault probability of the fault mode is higher than the functional fault probability, the functional fault probability is corrected by adopting a fault probability priority method of the fault mode, and the specific calculation steps are as follows:
STEP1 calculation of component c using equation (6)iFunction of (2)
Figure FDA0002942014960000064
Fault probability of
Figure FDA0002942014960000065
Based on
Figure FDA0002942014960000066
The fault probability of each fault mode is proportionally distributed to the fault probability of the relevant fault mode
Figure FDA0002942014960000067
Figure FDA0002942014960000068
Representing a component ciThe kth failure mode of (1);
Figure FDA0002942014960000069
representing a component ciThe h-th failure mode of (1);
STEP2 according to equation (7)
Figure FDA00029420149600000610
Medium failure mode
Figure FDA00029420149600000611
Associated function set, derived to be
Figure FDA00029420149600000612
Fault probability of
Figure FDA00029420149600000613
Is proportionally distributed to
Figure FDA00029420149600000614
The failure probability of (1) is:
Figure FDA00029420149600000615
STEP3 adopting the formula (8) according to
Figure FDA00029420149600000616
Middle function
Figure FDA00029420149600000617
The probability of a functional failure that can be corrected for the set of associated failure modes is:
Figure FDA00029420149600000618
the method for establishing the hybrid diagnosis Bayesian network model comprises the following steps:
based on the directed graph definition, the hybrid diagnostic model HDM (C, F, FM, T, E) can be simplified as HDM (V, E); a bayesian network fault diagnosis model derived from a directed graph, BNT ═ (V, E, P);
on the basis of considering the description of the uncertainty test information, by fusing the hybrid diagnosis model and the Bayesian network fault diagnosis model, the designed hybrid diagnosis Bayesian network model can be represented by a directed graph HDBN ═ C, F, FM, T, E and P; wherein, V ═ C ═ F { [ F } { [ T ]) is a set of nodes,
Figure FDA0002942014960000071
e represents a directed edge set among system nodes, and P is a weight matrix;
the source of each element information in HDBN ═ C, F, FM, T, E, P) is as follows:
set of components C ═ C1,c2,…,cLFrom a mixed diagnostic model HDM (C, F, FM, T, E), CLDenotes the lth component;
function set F ═ F1,f2,…,fJ(iii) from the mixed diagnostic model HDM (C, F, FM, T, E); f. ofJRepresents the jth function;
failure mode set FM ═ FM1,fm2,…,fmI(iii) from the mixed diagnostic model HDM (C, F, FM, T, E); fmIIndicating an ith failure mode;
test set T ═ T1,t2,…,tnFrom the hybrid diagnostic model HDM (C, F, FM, T, E), TnRepresenting the nth test node;
directed edge set E, derived from the hybrid diagnostic model HDM (C, F, FM, T, E);
the probability of the faults of each fault mode, function and component is derived from the hybrid diagnosis model reasoning;
the weight matrix P information is derived from the fusion of a hybrid diagnosis model HDM (C, F, FM, T, E) and a Bayesian network fault diagnosis model BNT ═ information (V, E, P);
for any one component, the hybrid diagnostic bayesian network model can be represented in two forms: one is in the form of a function root node, which is adapted to the case of priority assignment of the probability of a functional failure; the other is in the form of taking a fault mode as a root node, and is suitable for the conditions of mean distribution of fault probability of the fault mode and preferential distribution of fault probability of the fault mode;
the method for reasoning the hybrid diagnosis Bayesian network model comprises the following steps:
removing a function hidden layer in the hybrid diagnosis Bayesian network model;
calculating conditional probability information between the root node and the hidden node;
taking the maximum value of the detection rate and the false alarm rate in the heavy edges between the root node and the test node as the detection-false alarm probability between the root node and the test node;
the method for eliminating the function hidden layer in the hybrid diagnosis Bayesian network model comprises the following steps:
ROOT for the element set of the ROOT node layer ═ ROOT1,root2,...,rootmDenotes that the element set of the hidden layer is HID ═ HID { (HID) }1,hid2,...,hidwDenotes that the element set of the test layer is T ═ T1,t2,...,tnDenotes, tnRepresenting the nth test node, the fuzzy dependency relationship between each element of the root node layer and each element of the hidden layer is represented by a matrix RH ═ RHij]Is represented by (1), wherein rhijE { NA, SA, AA }, wherein NA represents that the dependency between the fault mode and the function is not influenced, SA represents that the fault mode is influenced sometimes, and AA represents that the fault mode is influenced constantly; root (R)mIs the m-th root node, hidwIs the w-th hidden node, rhijFor the elements in the matrix RH, the ith root node is representedThe dependency of a layer element on the jth hidden layer element;
the matrix HT ═ HT for the correlation between each element of the hidden layer and each element of the test layerjk]Representation, htjk1 means that the jth hidden layer element has a dependency relationship with the kth test layer element; matrix for direct incidence relation between root node layer and test layer added after hidden layer elimination
Figure FDA0002942014960000081
It is shown that,
Figure FDA0002942014960000082
representing that the ith root node layer element has a dependency relationship with the kth test layer element; the formula for hidden layer rejection based on the node propagation rule of the directed graph is as follows:
Figure FDA0002942014960000083
the method for calculating the conditional probability information between the root node and the hidden node comprises the following steps:
defining a conditional probability information calculation rule between the following root node and hidden node:
rule 1: if root node rootiAnd hidden node hidjIf the root node fails, the hidden node also fails; when the root node does not have a fault, the hidden node does not have a fault; the corresponding mathematical description is: if rhijAA, then
Figure FDA0002942014960000084
Figure FDA0002942014960000085
Representing the probability that the hidden node hidj does not have a fault when the root node rooti does not have a fault;
rule 2: if root node rootiAnd hidden node hidjCan influenceRelation, rootiAnd hidjThe solving method of the conditional probability comprises the following steps:
Figure FDA0002942014960000086
Figure FDA0002942014960000087
Pr′(hidk) Representing hidden nodes hidkCorrected failure probability; pr' (root)k) Root node root representationkCorrected failure probability;
Figure FDA0002942014960000088
representing the sum of the failure probabilities of all hidden nodes having a dependency relationship with the ith root node,
Figure FDA0002942014960000089
representing the sum of the failure probabilities of all root nodes which have dependency relationship with the kth hidden node;
among them, Pr' (hid)j) To hide nodes hidjCorrected failure probability; pr' (root)i) Root node rootiCorrected failure probability; pr (hid)j|rooti) Root node root representationiFailed, hidden node hidjProbability of failure also; pr (root)i|hidj) Representing hidden nodes hidjFailed, root node rootiProbability of failure also; rh ofikRepresenting the dependency of the ith root node on the kth hidden node, rhkjRepresenting the dependency relationship between the kth root node and the jth hidden node;
Figure FDA0002942014960000091
Figure FDA0002942014960000092
root node root representationiFail-free, hidden node hidjProbability of failure;
Figure FDA0002942014960000093
root node root representationiThe probability that a failure does not occur,
Figure FDA0002942014960000094
representing hidden nodes hidjFailed, root node rootiProbability of no failure;
rule 3: if root node rootiAnd hidden node hidjDo not influence rh mutuallyijWhen being NA, then
Figure FDA0002942014960000095
The method for taking the maximum value of the detection rate and the false alarm rate in the heavy edges between the root node and the test node as the detection-false alarm probability between the root node and the test node comprises the following steps:
the probability of occurrence of two sets of union A ^ B is greater than the probability of occurrence of any set A or B alone
Pr(A∪B)≥max{Pr(A),Pr(B)}
Taking the maximum value of the detection rate and the false alarm rate in the heavy edges between the root node and the test node as the detection-false alarm probability between the root node and the test node;
rule 4: root based on each root nodeiAnd tkPath between pathsijkFunction sets F and TFDetection of (2) -false alarm probability matrix, failure mode set FM and TFMRespectively computing the false alarm probability matrix
Figure FDA0002942014960000096
Combining the heavy edge detection and false alarm probability based on the following formula;
Figure FDA0002942014960000097
rootiis the ith root node, rootjIs the jth root node; t is tkRepresenting the kth test node; t isFA functional test set; t isFMA failure mode test set;
Figure FDA0002942014960000098
indicating the passage of the jth hidden node hidjThe detection probability of the kth test node to the ith root node,
Figure FDA0002942014960000099
indicating the passage of the jth hidden node hidjThe false alarm probability of the kth test node to the ith root node is measured; PATHikRepresents the set of paths, path, between the ith root node and the kth test nodejRepresenting the path through the root node and the test node of the jth hidden node.
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