CN110045715A - Minimal cut set method for solving based on Petri network and improvement binary decision graph model - Google Patents
Minimal cut set method for solving based on Petri network and improvement binary decision graph model Download PDFInfo
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- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
- G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
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Abstract
The present invention discloses a kind of minimal cut set method for solving based on Petri network and improvement binary decision graph model, including the with good grounds fault condition of step establishes corresponding failure tree；According to the corresponding Petri net model of the Construction of Fault Tree established；The Boolean logic relationship formula of top layer event is calculated according to the Petri net model established；It is converted into improving binary decision graph model according to the Boolean logic relationship formula of top layer event；Minimal cut set can be more intuitively obtained according to binary decision graph model is improved.Multiple shot array and np problem existing for minimal cut set are solved the beneficial effects of the present invention are: can effectively solve the problem that.
Description
Technical field
It is the invention belongs to failure tree analysis (FTA) technical field, in particular to a kind of based on Petri network and improvement binary decision diagrams (bdds)
The minimal cut set method for solving of model mainly solves complex fault tree minimal cut set Solve problems.
Background technique
Failure tree analysis (FTA) is to study the important method of system reliability, when carrying out failure tree analysis (FTA) to system, is solved most
Small cut set is the basis that system carries out failure tree analysis (FTA).Minimal cut set theory has important meaning for computing system reliability index
Justice constantly has the addition of software systems and hardware system as system equipment becomes increasingly complex, and progress fault tree modeling is caused to be got over
Come more complicated.Fault tree models are analyzed by minimal cut set, the exception also become is difficult, and existing minimal cut set method has minimum
Lu Jifa, ascending method and descending method, non cross link Matrix Calculating minimal cut set etc..
Minimal cut set is solved with Petri network, has become a kind of important means of research Reliability Index, still
Carrying out there are problems that multiple shot array in solution procedure to complex fault tree.Minimal cut set is solved with binary decision diagrams (bdds), it can
Effectively to solve the problems, such as multiple shot array existing for complex fault tree, but itself there is also np problems.In conjunction with two methods
Pros and Cons, by can effectively solve the problem that multiple shot array and NP are asked with Petri network and the method for improving binary decision diagrams (bdds)
Topic.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of based on Petri network and improves binary decision graph model most
Small cut set method for solving, to solve to solve multiple shot array and np problem existing for complex fault tree minimal cut set.
In order to solve the above-mentioned technical problem, the technical solution adopted by the present invention is that: one kind based on Petri network and improve binary
The minimal cut set method for solving of decision graph models, the analysis method are to propose to be based on Petri network on the basis of failure tree analysis (FTA)
With improve binary decision diagrams (bdds) minimal cut set method for solving, method includes the following steps:
1), according to system fault event, fault tree models are established
For system occur event of failure, determine fault tree top layer event, according to cause top layer event occur the reason of,
Further determine that the intermediate event and bottom event of fault tree.It is closed according to the logic of top layer event, intermediate event, bottom event
System, establishes corresponding failure tree-model, as shown in Figure 2.
2), according to fault tree models, Petri net model is established
According to the fault tree models of foundation, determine every in each top layer event, intermediate event, bottom event and Petri network
A corresponding relationship represented between symbol establishes Petri net model, as shown in Figure 3 according to Petri network theoretical knowledge.
3), according to Petri net model, the boolean logical expression of top layer event is calculated
Its top layer event is determined according to each logical relation represented between symbol according to the Petri net model of foundation
Boolean logical expression, wherein G1 is fault tree top layer event, and a, b, c, d, e respectively indicate fault tree bottom event, boolean
Logical expression is as follows:
G1=a+b* (c+d+e)
4) it according to the boolean logical expression of top layer event, establishes and improves binary decision graph model
According to the complexity of the boolean logical expression of top layer event, foundation is correspondingly improved binary decision graph model.
When boolean logical expression is relatively easy, can be directly indicated by improving binary decision diagrams (bdds), as shown in Figure 4.Work as boolean
Logical expression is relative complex, and boolean logical expression is as follows:
Y=[a+b* (c+d)] * [e+f* (g+h)]
Wherein Y is fault tree top layer event, and a, b, c, d, e, f, g, h respectively indicate fault tree bottom event.Boolean is patrolled
It collects expression formula to be decomposed, in the boolean logical expression decomposed, Y1, Y2 are fault tree intermediate event.Its decomposition obtains
Obtained boolean logical expression is as follows:
Y1=a+b* (c+d)；Y2=e+f* (g+h)
It is converted into improving binary decision diagrams (bdds) according to the boolean logical expression of decomposition, improves binary decision diagrams (bdds) such as Fig. 5 institute
Show.
5), according to improvement binary decision graph model, the minimal cut set of computing system
According to binary decision graph model is improved, closed according to the logic for improving binary decision diagrams (bdds) top layer event and bottom event
System, determines the minimal cut set of system.Wherein the minimal cut set of G1 is respectively: single order minimal cut set { a }；Second order minimal cut set b,
C }, { b, d }, { b, e }.Wherein the minimal cut set of Y is respectively: second order minimal cut set { a, e }；Three rank minimal cut sets { a, f, g },
{ a, f, h }, { b, c, e }, { b, d, e }；Quadravalence minimal cut set { b, c, f, g }, { b, c, f, h }, { b, d, f, g }, { b, d, f, h }.
The beneficial effects of the present invention are: the present invention provides a kind of based on Petri network and improves binary decision graph model
Minimal cut set method for solving, the minimal cut set method for solving can effectively avoid multiple shot array problem existing for Petri network, also can
Enough solve np problem existing for binary decision diagrams (bdds).There is certain superiority for solving complex fault tree, it can be quick and precisely
Solving system minimal cut set.
Detailed description of the invention
Fig. 1 is the implementation flow chart of minimal cut set method for solving of the invention；
Fig. 2 is fault tree models figure of the invention；
Fig. 3 is Petri net model figure of the invention；
Fig. 4 is improvement binary decision diagrams (bdds) illustraton of model of the invention；
Fig. 5 is improvement binary decision diagrams (bdds) illustraton of model after decomposition of the invention；
Fig. 6 is the annular power grid system construction drawing of Boeing 787；
Fig. 7 is 270V direct current supply schematic diagram；
Fig. 8 be 270V DC BUS L1 without electricity when fault tree models figure；
Fig. 9 be 235V AC BUS L2 without electricity when fault tree models figure；
Figure 10 is 3 fault tree models figure of combined fault；
Figure 11 be 235V AC BUS R2 without electricity when fault tree models figure；
Figure 12 be 235V AC BUS R1 without electricity when fault tree models figure；
Figure 13 be 270V DC BUS L1 without electricity when Petri net model figure；
Figure 14 be 235V AC BUS L2 without electricity when Petri net model figure；
Figure 15 is combined fault 3Petri pessimistic concurrency control figure；
Figure 16 be 235V AC BUS R2 without electricity when Petri net model figure；
Figure 17 be 235V AC BUS R1 without electricity when Petri net model figure；
Figure 18 is the improvement binary decision diagrams (bdds) illustraton of model of Y1；
Figure 19 is the improvement binary decision diagrams (bdds) illustraton of model of Y2；
Figure 20 is the improvement binary decision diagrams (bdds) illustraton of model of Y3.
Specific embodiment
With reference to the accompanying drawings and detailed description to the present invention is based on the minimal cuts of Petri network and improvement binary decision diagrams (bdds)
Collection method for solving is described in further detail.
The design philosophy based on Petri network and the minimal cut set method for solving for improving binary decision graph model of the invention is
The reason of it leads to the failure is analyzed, fault tree models are established according to the failure that system occurs according to Fault Tree Analysis.
Petri net model is established according to fault tree models, is then expressed according to the Boolean logic that Petri net model calculates top layer event
Formula, when fault tree is more complicated, obtained boolean logical expression just will appear multiple shot array problem.Then by boolean
Logical expression is converted into improving binary decision graph model, finally obtains the minimal cut set of system.
As shown in Figure 1, the minimal cut set method for solving of the invention based on Petri network and improvement binary decision graph model,
It the following steps are included:
1) according to system fault event, fault tree models are established
For system occur event of failure, determine fault tree top layer event, according to cause top layer event occur the reason of,
Further determine that the intermediate event and bottom event of fault tree.It is closed according to the logic of top layer event, intermediate event, bottom event
System, establishes corresponding failure tree-model, as shown in Figure 2.
2) according to fault tree models, Petri net model is established
According to the fault tree models of foundation, determine every in each top layer event, intermediate event, bottom event and Petri network
A corresponding relationship represented between symbol establishes Petri net model, as shown in Figure 3 according to Petri network theoretical knowledge.
3) according to Petri net model, the boolean logical expression of top layer event is calculated
Its top layer event is determined according to each logical relation represented between symbol according to the Petri net model of foundation
Boolean logical expression, the symbol G1 therein that represents indicate fault tree top layer event, and a, b, c, d, e indicate fault tree bottom thing
Part, boolean logical expression are as follows:
G1=a+b* (c+d+e)
4) it according to the boolean logical expression of top layer event, establishes and improves binary decision graph model
According to the complexity of top layer event boolean logical expression, foundation is correspondingly improved binary decision graph model.When
Boolean logical expression is relatively easy, can be directly indicated by improving binary decision diagrams (bdds), as shown in Figure 4.When boolean patrols
Volume expression formula is relative complex, and boolean logical expression is as follows:
Y=[a+b* (c+d)] * [e+f* (g+h)]
Wherein Y indicates fault tree top layer event, and a, b, c, d, e, f, g, h indicate fault tree bottom event.Since boolean patrols
It is more complicated to collect expression formula, boolean logical expression can be decomposed, wherein Y1, Y2 respectively indicate thing among fault tree
Part.It is as follows to decompose obtained boolean logical expression:
Y1=a+b* (c+d)；Y2=e+f* (g+h)
It is converted into improving binary decision diagrams (bdds) according to the boolean logical expression of decomposition, improves binary decision diagrams (bdds) such as Fig. 5 institute
Show.
5) according to improvement binary decision graph model, the minimal cut set of computing system
According to binary decision graph model is improved, closed according to the logic for improving binary decision diagrams (bdds) top layer event and bottom event
System, determines the minimal cut set of system.Wherein the minimal cut set of G1 is respectively: single order minimal cut set { a }；Second order minimal cut set b,
C }, { b, d }, { b, e }.Wherein the minimal cut set of Y is respectively: second order minimal cut set { a, e }；Three rank minimal cut sets { a, f, g },
{ a, f, h }, { b, c, e }, { b, d, e }；Quadravalence minimal cut set { b, c, f, g }, { b, c, f, h }, { b, d, f, g }, { b, d, f, h }.
The present invention realizes based on Petri network and improves the minimal cut set solution of binary decision diagrams (bdds) as a result, meets multiple
In the case of miscellaneous fault tree, existing multiple shot array and np problem during solving minimal cut set can effectively solve the problem that.
Embodiment
Fig. 1 is the implementation flow chart based on Petri network and improvement binary decision minimal cut set method for solving.
The present embodiment is based on the annular power grid of Boeing 787, establishes fault tree models, and Fig. 6 is the annular network system knot of Boeing 787
Composition.
787 annular electro host of Boeing will by 235V AC BUS L1,235V AC BUS L2,235V AC BUS R1,
235V AC BUS R2、Capt Instr BUS、270V DC BUS L1、270V DC BUS L2、270V DC BUS R1、
270V DC BUS R2,115V AC BUS L, 115V AC BUS R buss-bar set at.
By taking 270V DC BUS L1 busbar is without electricity as an example, electric network composition schematic diagram, as shown in Figure 7.According to each thing
Logical relation between part, is attached by AND gate and OR-gate and establishes fault tree models, and fault tree models are divided into seven
A sub- fault tree models, as shown in Fig. 8, Fig. 9, Figure 10, Figure 11, Figure 12.
According to the fault tree models that step 1) is established, the event of failure in fault tree models is met with representative and carries out table
Show, event of failure and represent the corresponding relationship between symbol, as shown in table 1.
1 event of failure of table and Petri network represent symbol corresponding relationship
Corresponding Petri net model is established according to table 1, Petri net model is divided into 7 sub- Petri net models, such as schemes
13, shown in Figure 14, Figure 15, Figure 16, Figure 17.
The Petri net model that step 2) is obtained is converted into logical relation expression formula, and logical relation expression formula is as follows:
P1=P2+P3+P4+P5+P7+ (P12+P13+P14) * { P15+P16+P21+ (P25+P26+P27) * [P28+P29+
(P33+P34+P35)*(P36+P37)]}*[P18+P19+(P40+P41+P42)*(P43+P44+P46+P47)]
It is intermediate event for P46 in above formula, logical relation expression formula is as follows:
P46=(P53+P54+P55) * [P50+P51+P56+ (P60+P61) * (P62+P63+P64)]
The logical relation expression formula obtained according to step 3), and logical expression is turned by improving binary decision diagrams (bdds) theory
Become graphic form, but its logical relation expression formula is more complicated, can be converted into several expression formula phases by decomposition operation
The relationship multiplied, the logical expression being converted to, as follows.
X1=(P12+P13+P14) * { P15+P16+P21+ (P25+P26+P27) * [P28+P29+ (P33+P34+P35) *
(P36+P37)]}
X2=P18+P19+ (P40+P41+P42) * (P43+P44+P46+P47)
For the obtained X1 logical relation expression formula of decomposition, logical relation expression formula or more complicated also needs to continue
It is decomposed, the relational expression decomposed, as follows.
Y1=P28+P29+ (P33+P34+P35) * (P36+P37)
Y2=P25+P26+P27
Y3=P12+P13+P14
According to the logical relation expression formula that step 4) obtains, it is carried out to be converted to improvement binary decision diagrams (bdds), conversion obtains
Improvement binary decision diagrams (bdds), as shown in Figure 18, Figure 19, Figure 20.
The improvement binary decision diagrams (bdds) obtained according to step 5), and according to binary decision diagrams (bdds) principle is improved, entire system can be obtained
The minimal cut set of system, for 270V DC BUS L1 busbar without electricity for, as long as obtaining thirdly rank minimal cut set obtains
To more accurately reliability index, then its single order minimal cut set { P2 }, { P3 }, { P4 }, { P5 }, { P7 }；Three rank minimal cut sets
{P18、P12、P15}、{P18、P12、P16}、{P18、P12、P21}、{P18、P13、P15}、{P18、P13、P16}、{P18、
P13、P21}、{P18、P14、P15}、{P18、P14、P16}、{P18、P14、P21}、{P19、P12、P15}、{P19、P12、
P16}、{P19、P12、P21}、{P19、P13、P15}、{P19、P13、P16}、{P19、P13、P21}、{P19、P14、P15}、
{P19、P14、P16}、{P19、P14、P21}。
The present invention realizes minimal cut set solution procedure as a result, and quick-fried to combination present in minimal cut set solution procedure
Fried problem and NP carry out effective solution, and also infinitely expanding to state space existing for improvement binary decision diagrams (bdds) itself is had
The improvement of effect.
Finally it should be noted that: only illustrate technical solution of the present invention in conjunction with above-described embodiment rather than it limited
System.Those of ordinary skills in the art should understand that arrive: those skilled in the art can carry out embodiments of the present invention
Modification or equivalent replacement, but these modifications or change are being applied within pending claims.
Claims (6)
1. a kind of minimal cut set method for solving based on Petri network and improvement binary decision graph model, which is in event
On the basis of fault tree analysis method, the minimal cut set method for solving of binary decision graph model is proposed based on Petri network and improves, it is special
Sign is, the analysis method the following steps are included:
Step 1) establishes fault tree models according to event of failure；
Step 2) establishes Petri net model according to the fault tree models in step 1)；
Step 3) calculates the Boolean logic relationship formula of top layer event according to the Petri net model in step 2) are as follows:
G1=a+b* (c+d+e) (1)
Or Y=[a+b* (c+d)] * [e+f* (g+h)] (2)
Wherein, the G1 in formula (1) is fault tree top layer event, and a, b, c, d, e respectively indicate fault tree bottom event；In formula (2)
Y be fault tree top layer event, a, b, c, d, e, f, g, h respectively indicate fault tree bottom event；
Boolean logical expression when formula (2) in the step 4) step 3) is more complicated, to boolean logical expression into
Row decomposes, the Boolean logic relationship formula decomposed are as follows:
Y1=a+b* (c+d)；Y2=e+f* (g+h) (3)
Wherein Y1, Y2 are fault tree intermediate event；
The boolean logical expression that step 4) is decomposed is converted into improving binary decision graph model by step 5), according to formula (1) to (3)
The minimal cut set of computing system:
The minimal cut set of G1 is respectively: single order minimal cut set { a }；Second order minimal cut set { b, c }, { b, d }, { b, e }；The minimum of Y
Cut set is respectively: second order minimal cut set { a, e }；Three rank minimal cut sets { a, f, g }, { a, f, h }, { b, c, e }, { b, d, e }；Quadravalence
Minimal cut set { b, c, f, g }, { b, c, f, h }, { b, d, f, g }, { b, d, f, h }.
2. a kind of minimal cut set solution side based on Petri network and improvement binary decision graph model according to claim 1
Method, it is characterized in that: fault tree models described in step 1) are the logical relation for indicating bottom event and top layer event being caused to occur.
3. a kind of minimal cut set solution side based on Petri network and improvement binary decision graph model according to claim 1
Method, it is characterized in that: Petri net model described in step 2) is logical relation expression-form corresponding with fault tree models.
4. a kind of minimal cut set solution side based on Petri network and improvement binary decision graph model according to claim 1
Method, it is characterized in that: formula described in step 3) (1) is corresponding according to the logic of Petri net model with the boolean logical expression of formula (2)
Relationship is established.
5. a kind of minimal cut set solution side based on Petri network and improvement binary decision graph model according to claim 1
Method, it is characterized in that: the boolean logical expression of formula described in step 4) (3) is that the Boolean logic decomposed to formula (2) is expressed
Formula.
6. a kind of minimal cut set solution side based on Petri network and improvement binary decision graph model according to claim 1
Method, it is characterized in that: improving the figure that binary decision graph model is the Boolean logic relationship formula after decomposing after decomposing described in step 5)
Shape expression-form.
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