CN106021647A - A cut sequence set-based dynamic fault tree Monte-Carlo simulation quantitative calculation method - Google Patents
A cut sequence set-based dynamic fault tree Monte-Carlo simulation quantitative calculation method Download PDFInfo
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Abstract
The invention provides a cut sequence set-based dynamic fault tree Monte-Carlo simulation quantitative calculation method and relates to the technical field of reliability and safety (safe system engineering). The method comprises the steps of performing left-to-right depth-first traversal on different dynamic logic gates, and acquiring the minimum cut sequence set of a dynamic fault tree according to the cut sequence conversion rules of dynamic logic gates; employing the Monte-Carlo simulation method and comparing the sample failure time of events with the minimum cut sequence set, and recording a failure once if the time meets the occurrence order of events in the minimum cut sequence set and the occurrence time of the last event is within set system operation time. The method can provide important information for reliability design, improvement, enhancement and troubleshooting in engineering. The Monte-Carlo simulation is performed based on cut sequence sets, so that secondary conversion of a DFT, for example, to Markov, the Bayesian network or a failure time tree, is avoided and the quantitative calculation procedures are optimized.
Description
Technical field
The invention belongs to reliability and safety (safety system engineering) technical field, be specifically related to a kind of based on cutting the dynamic of sequence collection
Fault tree Monte Carlo simulation quantitative calculation method.
Background technology
Along with progress and the development of science and technology in epoch, sorts of systems just by initially simple series parallel structure to synthesization, networking,
Complicating development, the scale of system constantly increases, and the 26S Proteasome Structure and Function of system is also the most complicated.The fault of these complication systems is not
Only being embodied in connection in series-parallel aspect, the fault of system exists and influences each other, relies on and sequential relationship etc..Traditional fault tree,
Reliability block diagram etc. point analysis method can not meet the most far away the fail-safe analysis of this kind of system.To this, scholar is had to propose for tool
There is the dynamic fault tree model (DFT) of complex time sequence relation, backup relation, dependence.
Mainly have based on Markov model, based on Bayes, based on ladder currently for DFT typical quantitative calculation and analysis method
Shape computing formula, correlation technique based on Monte Carlo.There is the problem of multiple shot array in Markov model, based on Bayesian network
There is again bigger error in the method for network and trapezoidal computing formula.Although method based on Monte Carlo also has phantom error, but can
With by Multi simulation running by error control within certain confidence range.DFT is mainly converted by monte carlo method at present
For out-of-service time tree, emulate based on out-of-service time tree.Out-of-service time tree can not react different event groups in DFT intuitively
Close impact on top event, these be then during DFT analyzes to reliability design, improve, improve and troubleshooting plays an important role
Result.
Summary of the invention
What during the present invention is to solve Dynamic fault tree quantitative Analysis, existing method existed is not suitable for large system analysis, combination
The defect problems such as blast, propose a kind of based on the Dynamic fault tree Monte Carlo simulation quantitative calculation method cutting sequence collection.According to DFT
Cut sequence collection transformation rule and merge rule, draw the minimal cut sequence collection of top event, can be reliability design in engineering, improvement,
Raising, troubleshooting etc. provide important information.It is simultaneously based on and cuts sequence collection and carry out Monte Carlo simulation, it is to avoid the twice transformation to DFT,
Such as it is converted into Ma Erke, Bayesian network or out-of-service time tree etc., optimizes quantitative Analysis flow process.
It is a kind of based on cutting the Dynamic fault tree Monte Carlo simulation quantitative calculation method of sequence collection that the present invention provides, concrete steps flow process
As follows:
The dynamic logic gate that step one, from left to right depth-first traversal are different, cuts sequence transformation rule according to dynamic logic gate,
Draw the minimal cut sequence collection of Dynamic fault tree.
Step 2, the method using Monte Carlo simulation, emulation sampling draws the inefficacy time of origin of different event, to event
Inefficacy time of origin sorts, and contrasts minimal cut sequence collection, if meeting minimal cut sequence to concentrate the order of occurrence of event, and last event
Time of origin set system operation time within, then remember and once lost efficacy, through Multi simulation running sample, and then calculate DFT
The reliability of top event, unreliable degree, mean down time MTTF etc..Defer to corresponding classical assumption: i.e. dynamically former herein
In barrier tree, corresponding event is all dimorphism, respectively serviceable condition or failure state, and can not repair after inefficacy.
The present invention gives a kind of illiteracy based on the Dynamic fault tree cutting sequence level and block emulation quantitative calculation method, its advantage is:
(1) present invention is incorporated into cutting sequence collection in the Monte Carlo simulation quantitative Analysis of Dynamic fault tree, compared to based on Markov
Model, the Dynamic fault tree computational methods of Bayesian network, it is conducive to Dynamic fault tree extensive to big system to carry out quantitative scoring
Calculate.
(2) compared to Monte Carlo simulation quantitative calculation method based on out-of-service time tree, it is not necessary to DFT is carried out twice transformation,
And cut sequence collection can as system reliability design, improve, improve and the important references of troubleshooting.
Accompanying drawing explanation
Fig. 1 is preferential and door.
Fig. 2 is order dependent door.
Fig. 3 is cold standby part door.
Fig. 4 is temperature spare part door.
Fig. 5 is hot spare door.
Fig. 6 is function trigger gate.
Fig. 7 is and door.
Fig. 8 is or door.
Fig. 9 is k/n door.
Figure 10 is AFDX network data transmission time wrong Dynamic fault tree in embodiment.
Detailed description of the invention
Below in conjunction with drawings and Examples, the present invention is described in further details.
The present invention provides a kind of and covers card emulation quantitative calculation method based on the Dynamic fault tree cutting sequence level, specifically includes following steps:
The dynamic logic gate that step one, from left to right depth-first traversal are different, cuts sequence transformation rule according to dynamic logic gate,
Draw the minimal cut sequence collection of Dynamic fault tree.
Cut sequence to refer to cause that top event in Dynamic fault tree occurs and contain the basic thing occurred according to order of certain out-of-service time
Part combines, and cutting sequence collection is multiple set cutting sequence, cuts and refers to cause elementary event or the base that in Dynamic fault tree, top event occurs
Present event combines, and cut set is multiple set cut.Cut sequence and traditional cutting is distinguished and be that the bottom event cutting in sequence inefficacy also exists elder generation
The ordering relation of rear generation.Symbolization in the present invention "-> " show this ordering relation, with symbol "-> " connect 2 events, table
The event on the bright symbol left side first lost efficacy, and lost efficacy after the event on the right of symbol.Such as cut sequence " A-> B " represent event A and
Event B lost efficacy, and event A lost efficacy prior to event B, and top event lost efficacy, and cuts sequence " (A, B-> C) " and represents event A, B, C
All occurring, and event B lost efficacy prior to event C, top event lost efficacy.And for cut sequence, cut sequence collection, cut, cut set.Simple act
Example, as cut sequence (A-> B-> C) or cutting sequence (D, E-> F);Cut sequence collection (A-> B-> C), (D, E-> F);Cut (A) and
Cut (B, C);Cut set (A), (B, C).
Step one is divided into again four detailed execution steps, illustrates as follows:
(1st) step, from left to right depth-first traversal, search the gate of the bottom in DFT, according to different logic classes
Cutting sequence or cutting corresponding to type, is given and traverses corresponding the cutting sequence or cut of gate in DFT, as shown in Fig. 1-Fig. 9, described
Logic gate types have preferential with door, order dependent door, cold standby part door, warm spare part door, hot spare door, function trigger gate and door,
Or door, k/n door.Preferential and door represents A and B order of occurrence no requirement (NR), but when only A occurs prior to B, top event occurs,
The sequence of cutting of its correspondence is (A-> B);Order dependent door represents that event occurs successively only in the order of A, B, C, and all sends out
After life, top event occurs, and corresponding sequence of cutting is A-> B-> C;Cold standby part door represents that main part A first works, and after inefficacy, spare part is successively
Entering duty, after all losing efficacy, top event occurred, and will not lose efficacy during spare part storage, and corresponding cuts sequence (A-> B-> C);Wen Bei
Part door represents that main part A first works, and after inefficacy, spare part sequentially enters duty, and after all losing efficacy, top event occurred, and spare part is being deposited
Storage state has crash rate, less than duty crash rate, although therefore bottom event enter job order and have successively, but lost efficacy and occurred
Order is the most successively, and corresponding is segmented into (A, B, C).Hot spare door represents that main part A first works, after inefficacy, and spare part
Entering duty according to this, after all losing efficacy, top event occurred, and spare part is identical with duty crash rate in storage state, although therefore
Bottom event enters job order to be had successively, but inefficacy order of occurrence is less than successively, and corresponding is segmented into (A, B, C);Function
After trigger gate represents that trigger event A occurs, its event B that is triggered also lost efficacy.Meanwhile, event B also can independent failure, corresponding
Cut (A), (B);Representing that bottom event all occurs with door, top event occurs, and corresponding is segmented into (A, B);Or door represents
Bottom event any one event occurs, and top event occurs, and corresponding is segmented into (A), (B);K/n door represents that in bottom event, k event occurs,
Top event occurs, it is assumed that is 2/3 and corresponding is segmented into (A, B), (A, C), (B, C).
(2nd) step, traversal search obtains whether event above gate is top event, if it is, perform (4th) step, if
Not, (3rd) step is performed.
(3rd) step, from left to right depth-first traversal, continue up search on the basis of upper once traversal search, search
First level logical door.If being bottom event below this gate, then provide cutting sequence or cutting of its correspondence;If being middle below this gate
Event, according to the door type of this gate, will cut sequence corresponding to intermediate event below this gate, or cuts ordered sets also, close
And be divided into and cutting and merging of cutting, cutting sequence and merging of cutting, cut sequence and merging of cutting sequence, specific rules is as follows, turns simultaneously
To (2nd) step.
(3.1). cut with merging of cutting and be divided into merge or merge, k/n merges, order merges.
(3.1.1) with merge: with door compatible rule merging in illustrating according to accompanying drawing, case (A) and (B), amalgamation result (A, B).
(3.1.2) or merge: in illustrating according to accompanying drawing or door compatible rule merging, case (A) or (B), amalgamation result (A), (B).
(3.1.3) k/n merges: according to accompanying drawing middle k/n door compatible rule merging is described, case (A), (B), in (C) 2/3, merges knot
Really (A, B), (A, C), (B, C).
(3.1.4) order merges: order dependent door compatible rule merging in illustrating according to accompanying drawing, case (A)-> (B), amalgamation result (A-> B).
(3.2). cut sequence with merging of cutting and be divided into merge or merge, k/n merges, order merges.
(3.2.1) with merge: with door compatible rule merging in illustrating according to accompanying drawing, case (A) and (B-> C), amalgamation result (A, B-> C).
(3.2.2) or merge: in illustrating according to accompanying drawing or door compatible rule merging, case (A) or (B-> C), amalgamation result (A),
(B->C)。
(3.2.3) k/n merges: according to accompanying drawing middle k/n door compatible rule merging is described, case (A), (B), in (C-> D) 2/3, closes
And result (A, B), (A, C-> D), (B, C-> D).
(3.2.4) order merges: will cut before being connected to cut sequence with sequence number, as an amalgamation result;And be moved back by according to this
Move and cut, often move an event, increase an amalgamation result, until cutting before cutting last event of sequence.Case (A)->
(B-> C), amalgamation result (A-> B-> C), (B-> A-> C).
(3.3). cut sequence with merging of cutting sequence and be divided into merge or merge, k/n merges, order merges.
(3.3.1) with merge: with door compatible rule merging in illustrating according to accompanying drawing, case (A-> B) and (C-> D), amalgamation result (A-> B,
C->D)。
(3.3.2) or merge: in illustrating according to accompanying drawing or door compatible rule merging, case (A-> B) or (C-> D), amalgamation result (A-> B),
(C->D)。
(3.3.3) k/n merges: according to accompanying drawing, middle k/n door compatible rule merging, case (A-> B) being described, (C-> D), in (E-> F)
2/3, amalgamation result (A-> B, C-> D), (A-> B, E-> F), (C-> D, E-> F).
(3.3.4) order merges: last event and the later of cutting sequence by first are cut sequence and synthesized according to the order cutting and cutting sequence,
First event cutting sequence of traversal the most forward, according to cutting and cut the composition rule of sequence, until the event of traversal is in its initial cutting
In sequence before later event.Case (A-> B)-> (C-> D), amalgamation result (A-> B-> C-> D), (A-> C-> B-> D),
(C->A->B->D)。
All sequence collection that cut of top event are carried out deduplication, draw minimal cut sequence collection by (4th) step, and minimal cut sequence is concentrated with k
Cut sequence.By cut sequence collection solve minimal cut sequence collection time, use set operation absorption law rule simplify.If i.e. existing and cutting sequence collection
{ { B-> C}, then minimal cut sequence collection is { B-> C} to A-> B-> C-> D} with cutting sequence collection.
Step 2, step one give and can cause top event that all minimal cut sequences lost efficacy occur, and step 2 mainly uses dynamic event
The method of barrier tree Monte Carlo simulation, emulation sampling draws the sampling out-of-service time of different event, the sampling out-of-service time to event
Sequence, contrasts minimal cut sequence collection, if meeting minimal cut sequence to concentrate the order of occurrence of event, and when the sampling of last event was lost efficacy
Between within the system operation time set, then remember and once lost efficacy, sample through Multi simulation running, and then calculate DFT top event
Reliability, unreliable degree, mean down time MTTF etc..Defer to corresponding classical assumption: i.e. phase in Dynamic fault tree herein
The event answered is all dimorphism, respectively serviceable condition or failure state, and can not repair after inefficacy.
Dynamic fault tree Monte Carlo simulation concretely comprises the following steps:
2.1., total simulation times M, the system operation time T of the analyzed setting of Dynamic fault tree, Dynamic fault tree all ends thing are set
Part invalid cost q1,q2,…,qn, and variable m, n, fm.Wherein, m represents current simulation times, and n represents at the bottom of Dynamic fault tree
Event number, fmFor judging whether the m time emulation top event in the system operation time T set lost efficacy.Top event lost efficacy,
fm=1, top event did not lose efficacy, then fm=0.Initial condition m=0, fm=0;
2.2. simulation times m adds 1, i.e. m=m+1, it is judged that whether the simulation times after adding 1 is more than M.If so, knot is emulated
Bundle, goes to the 2.9th step;Otherwise, the 2.3rd step is carried out.
2.3. according to the invalid cost q of the bottom event of Dynamic fault tree1,q2,…,qn, when emulation sampling obtains the sampling inefficacy of each bottom event
Between be t1, t2..., tii..., tn.1,2 ..., ii ..., n one bottom event of uniquely tagged respectively.
2.4. require owing to different event being entered the order of occurrence of duty and inefficacy by dynamic logic gate, and the 2.3rd
In step, it is the direct sampling to the bottom event out-of-service time, does not accounts for timing requirements, therefore will be to imitating under Different Dynamic gate
The true sample time specifically processes.And below static logic gates event occur without timing requirements, therefore need not process.Traversal
All gates, if a certain dynamic logic gate, then process according to the process rule of this gate is concrete.
(2.4.1) the order dependent door sampling out-of-service time processes: it is suitable that order dependent door requires bottom event only in from left to right
Sequence lost efficacy successively, i.e. the generation of later event was lost efficacy always after previous event lost efficacy, therefore to the sampling out-of-service time
Process then need successively in sampling out-of-service time of later event plus sampling out-of-service time of previous event.That is:
Determining the bottom event under order dependent door, the bottom event sampling out-of-service time be given according to the 2.3rd step, search obtains successively
Below order dependent door, the sampling out-of-service time of bottom event isS is the individual of event below a certain dynamic logic gate
Number, gate is order dependent door herein,For the i-th i event in the 2.3rd step that the c event under this dynamic logic gate is corresponding
Sampling out-of-service time (it should be noted that correspondence herein is with concrete event as correspondence).When the sampling of order dependent door was lost efficacy
Between process, from the beginning of second event, the most from left to right, plus previous event on the sampling out-of-service time of this event
Sampling out-of-service time, and sequential iteration renewal, it is:
(2.4.2) the cold standby part door sampling out-of-service time processes: cold standby part door requires that main part first works, and after inefficacy, spare part enters successively
Entering duty, until all losing efficacy, and spare part is in storage state no-failure rate.Therefore substantially bottom event be also according to from a left side to
Right order occurs, the most order dependent door of process to this.Except for the difference that s is the number of event below a certain dynamic logic gate,
It is the number of event below cold standby part door in this case.
(2.4.3) the function trigger gate sampling out-of-service time processes: after function trigger gate requires that trigger event occurs, its thing that is triggered
Part also lost efficacy.Meanwhile, the event that is triggered also can independent failure, then after sampling, if the trigger event sampling out-of-service time is more than quilt
The trigger event sampling out-of-service time, then illustrate that the event that is triggered lost efficacy prior to trigger event, then need not process;Otherwise,
Then explanation trigger event is prior to the stale event that is triggered, and now, the event of being triggered should lose efficacy simultaneously, therefore uses trigger event
The sampling out-of-service time replace being triggered sampling out-of-service time of event.In function trigger gate, the trigger event sampling out-of-service time is
Event sampling out-of-service time that is triggered isThe most concrete process is:
(2.4.4) the hot spare door sampling out-of-service time processes: in hot spare door, main part and spare part simultaneously enter duty, until
After main part and spare part all lost efficacy, thrashing, therefore below hot spare door, event is in the most not requirement of losing efficacy, story part is corresponding
The sampling out-of-service time be not required to process.
(2.4.5) the temperature spare part door sampling out-of-service time processes: temperature spare part door requires that main part first works, and after inefficacy, spare part enters successively
Enter duty, until all inefficacy and spare part are less than the crash rate of spare part running status in storage state.The most right during sampling for the first time
All bottom events are sampled successively according to the crash rate under its duty, if there is also temperature spare part door in fault tree, then it is right to need
In temperature spare part door, the spare part out-of-service time in the storage position is sampled toRegulation has 2 spare parts herein, and c represents this sampling
Out-of-service time is the sampling out-of-service time under Reserve State.
Specifically, the main part sampling out-of-service time is found to be t from the 2.3rd stepiiIf,SimultaneouslyMain part is described
The sampling out-of-service time samples the out-of-service time more than all spares reserves, and the most all spare parts lost efficacy prior to main part, it is not necessary to lose sampling
The effect time processes.Otherwise, need to process.If the main part sampling out-of-service timeIllustrate when main part lost efficacy, the 1st
Spare part in storage state and did not lose efficacy, and the 1st spare part subsequently enters duty, finds the 1st spare part to exist from the 2.3rd step
The sampling out-of-service time under duty isIts sampling out-of-service time be processed as into2nd spare part sampling is lost
The effect time processes, ifIllustrating that the 1st spare part of cut-off lost efficacy, the 2nd spare part did not the most lose efficacy under Reserve State,
Therefore after the 1st spare part lost efficacy, the 2nd spare part enters duty, is processed as, finds the 2nd spare part to exist from the 2.3rd step
The sampling out-of-service time under duty isIts sampling out-of-service time is processed as
(2.4.6) the preferential and door sampling out-of-service time processes: preferential and door requires that the event of this lower section is according to the most successively
During inefficacy, preferential with door above event lost efficacy, if while this lower section event not according to this Sequence Fault, then go up
Side's event will not lose efficacy.Therefore the inefficacy of its event order does not has sequential relationship, simply has sequential relationship when judging and losing efficacy.
2.5., after the sampling out-of-service time having been processed, corresponding event in the 2.3rd step is replaced with the sampling out-of-service time after process successively
The sampling out-of-service time.
2.6. the sampling out-of-service time after the process in the 2.5th is sorted according to order from small to large, when the sampling after sequence was lost efficacy
Between order be t '1, t'2..., t 'ii..., t'n.1,2 ..., ii ..., n one bottom event of uniquely tagged respectively.
In contrast step one, minimal cut sequence is concentrated and is cut bottom event that sequence represents and the order of occurrence that bottom event lost efficacy and emulation the most according to this
The sampling out-of-service time order of the corresponding bottom event that obtains of sampling and bottom event.In step one, obtain k cut sequence.
If i-th cuts multiple bottom event inefficacies order that sequence represents, the sampling out-of-service time of the plurality of bottom event obtained with sampling from
Little to big sequence consensus, then remember this cut sequence sampling the out-of-service time be ti=tmax, tmax are that this cuts last bottom event in sequence
The sampling out-of-service time.The sampling out-of-service time t of system is to cut sequence to concentrate all sampling out-of-service times cutting sequence minimum, i.e. system to imitate
True sampling out-of-service time t=minti (i=1,2 ..., k).
2.8. t is madem=t, tmIt is the m time analogue system sampling out-of-service time, if tm> T, then the system that explanation emulation sampling draws
The time lost efficacy is longer than the system operation time T of initial setting, and in the system operation time T i.e. set, fault tree top event does not has
There is generation, then fm=0, fmFor judging whether the m time analogue system lost efficacy within the operation time set;Otherwise, top event
Lost efficacy in T time, then fm=1 goes back to step 2.2.
2.9. emulation terminates, then run, in the system set, the probability that top event occurs in T time, namely top event is unreliable
DegreeUnreliable degree is(tiFor each analogue system
Out-of-service time).
Embodiment
The specification of avionic full-duplex switched-type Ethernet (AFDX) ARINC 664 is given the standard of propagation delay time and determines
Justice.The overall delay setting end system comprises technology time delay and configuration time delay, and wherein technology time delay is independent of flow load, during technology
Prolonging and be defined as not having other tasks to process when, end system receives and processes application data, and when starting to send required
Between, and configure time delay and depend on configuration and the flow load of transmitting terminal, can be because of the difference of configuration and how many generations of flow load
The time delays such as shake, wherein shake can be different because concrete condition is different.
Need forward through transmitting terminal ES, transmission, switch storage and connect during AFDX data transmission in network
In the stages such as receiving end ES, therefore from the latency issue of these phase analysis data, the event causing the transmission time excessive is respectively
Transmitting terminal ES processes that data delay is excessive, switch processes data delay is excessive, channel transmission time delay is excessive and at receiving terminal ES
Reason data delay is excessive.In transmission, arbitrary link occurs time delay to cross mostly will affect whole net transmission data generation time delay.Set up the time
Wrong Dynamic fault tree is as shown in Figure 10.
The bottom event of described Dynamic fault tree is followed successively by:
Transmitting terminal cpu data processing delay is excessive, represents with symbol A, and invalid cost is exponential, and crash rate is
0.017×10-6/h。
The storage of DPRAM data and Forwarding Delay are excessive, represent with symbol B, and invalid cost is exponential, and crash rate is
0.107×10-6/h。
Transmitting terminal FPGA data processing delay is excessive, represents with symbol C, and invalid cost is exponential, and crash rate is
0.048×10-6/h。
VL configuration is improper causes shake time delay excessive, represents with symbol D, and invalid cost is exponential, and crash rate is 1 × 10-5/h。
Flow load is excessive causes time delay excessive, represents with symbol E, and invalid cost is exponential, and crash rate is 1 × 10-5/h。
Channel A transmission is congested causes time delay excessive, represents with symbol F, and invalid cost is exponential, and crash rate is 1 × 10-6/h。
Channel B transmission is congested causes time delay excessive, represents with symbol G, and invalid cost is exponential, and crash rate is 1 × 10-6/h。
Filtering frames control causes time delay excessive, represents with symbol H, and invalid cost is exponential, and crash rate is 5 × 10-5/h。
Frame scheduling causes time delay excessive, represents with symbol I, and invalid cost is exponential, and crash rate is 5 × 10-5/h。
Frame forwards and causes time delay excessive, represents with symbol J, and invalid cost is exponential, and crash rate is 5 × 10-5/h。
SSRAAM cached configuration is improper causes time delay excessive, represents with symbol K, and invalid cost is exponential, and crash rate is
5×10-5/h。
DPRAAM cached configuration is improper causes time delay excessive, represents with symbol L, and invalid cost is exponential, and crash rate is
5×10-5/h。
Receiving terminal FPGA data processing delay is excessive, represents by symbol M, and invalid cost is exponential, and crash rate is
0.017×10-6/h。
The storage of DPRAM data and Forwarding Delay are excessive, represent with symbol N, and invalid cost is exponential, and crash rate is
0.107×10-6/h。
Receiving terminal cpu data processing delay is excessive, represents with symbol O, and invalid cost is exponential, and crash rate is
0.017×10-6/h。
SKEWMAX arranges excessive, represents with symbol P, and invalid cost is exponential, and crash rate is 1 × 10-5/h。
VL buffer configuration is improper, represents with symbol Q, and invalid cost is exponential, and crash rate is 1 × 10-5/h。
Gate above ABC event is order dependent door, and corresponding upper strata intermediate event is that transmitting terminal technology time delay is excessive, DE
The gate of top is or door, and corresponding upper strata intermediate event is that transmitting terminal configuration time delay is excessive;Patrol above the two intermediate event
Collecting door is or door that corresponding upper strata intermediate event is that transmitting terminal time delay is excessive.
Gate above FG event is and door, and corresponding upper strata intermediate event is that channel transmission time delay is excessive.
Gate above HJI event is order dependent door, and corresponding upper strata intermediate event is that exchange data processing delay is excessive,
Gate above KL is or door, and corresponding upper strata intermediate event is that memorizer configuration is improper causes time delay excessive;In the middle of the two
Above event, gate is or door, and corresponding upper strata intermediate event is that switch time delay is excessive.
Gate above MNO event is order dependent door, and corresponding upper strata intermediate event is that receiving terminal technology time delay is excessive, PQ
The gate of top is or door, and corresponding upper strata intermediate event is that receiving terminal configuration time delay is excessive;Patrol above the two intermediate event
Collecting door is or door that corresponding upper strata intermediate event is that receiving terminal time delay is excessive.
Above-mentioned for being discussed in detail the case of Dynamic fault tree.Be described in detail below the present invention provide based on cutting the dynamic of sequence collection
Fault tree Monte Carlo simulation quantitative calculation method, in the enforcement of this case, concretely comprises the following steps:
Step one: the dynamic logic gate that depth-first traversal is different from left to right, cuts sequence transformation rule according to dynamic logic gate,
Draw the minimal cut sequence collection of Dynamic fault tree.
(1) travel through gate for the first time: depth-first traversal from left to right, search the gate of the bottom, root in DFT
According to cutting sequence or cutting corresponding to door type different in Fig. 1-Fig. 9, according to Figure 10, depth-first traversal from left to right, time
Going through the bottom gate of Dynamic fault tree, the bottom gate of described case is followed successively by order dependent door or door, sequentially
Associated gate or door, order dependent door or door, according to different logic gate types, provide event below described gate
Cut sequence or cut.It is as follows,
Order dependent door: corresponding cuts sequence for (A-> B-> C).
Or door: corresponding is segmented into (D), (E).
Order dependent door: corresponding cuts sequence for (H-> I-> J)
Or door: corresponding is segmented into (K), (L).
Order dependent door: corresponding cuts sequence for (M-> N-> O)
Or door: corresponding is segmented into (P), (Q).
(2) traversal search obtains event above gate for the first time is not top event, proceeds second time and travels through gate.From a left side
Depth-first to the right is upwards searched for, and searches for last layer logic gate types, patrolling of described case depth-first upper layer from left to right
Volume door is followed successively by or door and door or door or door.Synthesizing sequence of cutting or cut below according to this, result is:
Or door: should or door below be not bottom event, be one cut sequence with cut according to or the synthesis of door, according to its composition rule,
The result going out synthesis is: (A-> B-> C), (D), (E).
With door: being bottom event below this and door, according to the rule with door, directly give this is segmented into (F, G).
Or door: should or door below be not bottom event, be one cut sequence with cut according to or the synthesis of door, according to its composition rule,
The result going out synthesis is: (H-> I-> J), (K), (L).
Or door: should or door below be not bottom event, be one cut sequence with cut according to or the synthesis of door, according to its composition rule,
The result going out synthesis is: (M-> N-> O), (P), (Q).
(3) traversal search obtains event above gate for the second time is not top event, third time traversal gate: from left to right time
Go through after gate for or door, or door above event be top event, according to or the merging rule of door, draw and cut sequence collection for (A-> B-> C),
(D), (E), (H-> I-> J), (K), (L), (M-> N-> O), (P), (Q), (F, G).
(4) cut ordered sets also by all, draw minimal cut sequence collection.By cut sequence collection solve minimal cut sequence collection time, use set
Computing absorption law rule simplifies.Sequence collection is cut it can be seen that cut sequence and concentrate and do not deposit by the second time traversal top event that draws of gate
There iing the sequence of cutting of polyisomenism, therefore need not absorb simplification.Its obtained result is minimal cut sequence collection.
The minimal cut sequence collection finally drawing top event is: (A-> B-> C), (D), (E), (H-> I-> J), (K), (L), (M-> N-> O),
(P), (Q), (F, G).
Step 2:
When top event according to minimal cut sequence set representations breaks down, different bottom events and out-of-service time sequential combination thereof, use and cover
The method of special Carlow emulation, draws according to emulation the sampling out-of-service time of different event, as the case may be to the sampling out-of-service time
Process, to the sequence of sampling out-of-service time after process, contrast minimal cut sequence collection, if meeting the order of occurrence that minimal cut sequence is concentrated,
Then remember inefficacy.Detailed process is as follows:
1. total simulation times M, the system operation time T of the analyzed setting of Dynamic fault tree, Dynamic fault tree all ends thing are set
Part invalid cost qA,qB,…,qQ, and variable m, n, fm.Wherein, m represents current simulation times, and n represents Dynamic fault tree
Bottom event number, bottom event is A-Q totally 17 herein, therefore n=17.fmFor judging that the m time emulation is in the system set
In running time T, whether top event lost efficacy.Top event lost efficacy, fm=1, top event did not lose efficacy, then fm=0.Initial condition
M=0, fm=0.Make M=1000000, T=1000h.
2. make simulation times m be incremented by m+1, it is judged that whether m+1 is more than M.If so, emulation terminates, and goes to the 9th step;No
Then, the 3rd step is carried out.
3. according to the bottom event invalid cost q of Dynamic fault treeA,qB,…,qQ, emulation sampling obtains each bottom event sampling out-of-service time
It is respectively tA, tB..., tQ。
4. needing dynamic logic gate to be processed in present case is order dependent door, therefore the process of associated gate is regular in order, to order
Under associated gate, the sampling out-of-service time of event processes.
Under first order dependent door, bottom event is tri-events of A, B, C from left to right, and the sampling out-of-service time is respectively tA、tB、
tC, specifically it is processed as the described sampling out-of-service time is updated to t respectivelyA'=tA;tB'=tB+tA';tC'=tC+tB'。
Under second order dependent door, bottom event is tri-events of H, I, J, and the sampling out-of-service time is respectively tH、tI、tJ, tool
Body is processed as the described sampling out-of-service time is updated to t respectivelyH'=tH;tI'=tI+tH';tJ'=tJ+tI'。
Under 3rd order dependent door, bottom event is tri-events of M, N, O, and the sampling out-of-service time is respectively tM、tN、tO,
Specifically it is processed as the described sampling out-of-service time is updated to t respectivelyM'=tM;tN'=tN+tM';tO'=tO+tN'。
Wherein tA', tB', tC', tH', tI', tJ', tM', tN', tO' it is the sampling out-of-service time after processing.
5. after pair the sampling out-of-service time processed, successively with the taking out of correspondence event in sampling out-of-service time replacement the 3rd step after processing
The sample out-of-service time.
6. the sampling out-of-service time after the process in pair the 5th step sorts according to order from small to large, and the out-of-service time after sequence is suitable
Sequence is t '1, t'2..., t '17。
In contrast step one, minimal cut sequence is concentrated the bottom event and the order of occurrence of bottom event inefficacy that cut sequence and represent, is emulated and take out the most according to this
The sampling out-of-service time order of corresponding bottom event that sample obtains and bottom event.
The sequence of cutting cutting sequence concentration obtained in step one is:
(A-> B-> C), (D), (E), (H-> I-> J), (K), (L), (M-> N-> O), (P), (Q), (F, G) is total to
10.
For (A-> B-> C), if sampling out-of-service time order meets tA< tB< tC, then record this and cut sequence out-of-service time t1=tC;
If do not met, do not note down.
For (D), record this and cut sequence out-of-service time t2=tD。
For (E), record this and cut sequence out-of-service time t3=tE。
For (H-> I-> J), if sampling out-of-service time order meets tH< tI< tJ, then record this and cut sequence out-of-service time t4=tJ;
If do not met, do not note down.
For (K), record this and cut sequence out-of-service time t5=tK。
For (L), record this and cut sequence out-of-service time t6=tL。
For (M-> N-> O), if sampling out-of-service time order meets tM< tN< tO, then record this and cut sequence out-of-service time t7=tO;
If do not met, do not note down.
For (P), record this and cut sequence out-of-service time t8=tP。
For (Q), record this and cut sequence out-of-service time t9=tQ。
For (F, G), record this and cut sequence out-of-service time t10=max (tF,tG)。
System is t=min t in this emulation out-of-service timei(i=1,2 ..., 10).
8. make tm=t, tmIt is the m time analogue system sampling out-of-service time, if tm> T, then the system that explanation emulation sampling draws is lost
The time of effect is longer than the system operation time T of initial setting, and in the system operation time T i.e. set, fault tree top event does not has
Occur, then fm=0, fmFor judging whether the m time analogue system lost efficacy within the operation time set;Otherwise, top event is at T
Lost efficacy in time, then fm=1 goes back to step 2, proceeds emulation.
9. emulation terminates, then the probability that top event occurs in the system operation time T set, namely the unreliable degree of top eventUnreliable degree is(tiMistake for each analogue system
The effect time).
Programming realization show that Dynamic fault tree quantitative analysis results is as follows:
F (1000)=0.8694;R (1000)=0.1306;MTTF=7054.6h.
Claims (4)
1. one kind based on the Dynamic fault tree Monte Carlo simulation quantitative calculation method cutting sequence collection, it is characterised in that:
The dynamic logic gate that step one, from left to right depth-first traversal are different, cuts sequence transformation rule according to dynamic logic gate,
Draw the minimal cut sequence collection of Dynamic fault tree;Particularly as follows:
(1st) step, from left to right depth-first traversal, search the gate of the bottom in DFT, according to different logic classes
Cutting sequence or cutting corresponding to type, is given and traverses corresponding the cutting sequence or cut of gate in DFT;
(2nd) step, traversal search obtains whether event above gate is top event, if it is, perform (4th) step, if
Not, (3rd) step is performed;
(3rd) step, from left to right depth-first traversal, continue up search on the basis of upper once traversal search, search
First level logical door;If being bottom event below this gate, then provide cutting sequence or cutting of its correspondence;If being middle below this gate
Event, according to the door type of this gate, by cutting sequence or cutting ordered sets also corresponding to intermediate event below this gate, merges
It is divided into again and cutting and merging of cutting, cut sequence and merging of cutting, cut sequence and merging of cutting sequence, go to (2nd) step simultaneously;
All sequence collection that cut of top event are carried out deduplication, draw minimal cut sequence collection by (4th) step, and minimal cut sequence is concentrated with k
Cut sequence;
Step 2, the method using Monte Carlo simulation, draw the sampling out-of-service time of different event, and the sampling to event was lost efficacy
Time-sequencing, contrasts minimal cut sequence collection, if meeting minimal cut sequence to concentrate the order of occurrence of event, and the sampling of last event is lost
The effect time within the system operation time set, is then remembered and once lost efficacy, and samples through Multi simulation running, and then it is useful to calculate DFT
The reliability of part, unreliable degree and mean down time MTTF;Particularly as follows:
2.1., total simulation times M, the system operation time T of the analyzed setting of Dynamic fault tree, Dynamic fault tree all ends thing are set
Part invalid cost q1,q2,…,qn, and variable m, n, fm, wherein, m represents current simulation times, and n represents at the bottom of Dynamic fault tree
Event number, fmFor judging whether the m time emulation top event in the system operation time T set lost efficacy, top event lost efficacy,
Then fm=1, top event did not lose efficacy, then fm=0;Initial condition m=0, fm=0;
2.2. simulation times m adds 1, i.e. m=m+1, it is judged that the simulation times after adding 1, whether more than M, if so, emulates knot
Bundle, goes to the 2.9th step;Otherwise, the 2.3rd step is carried out;
2.3. according to the invalid cost q of the bottom event of Dynamic fault tree1,q2,…,qn, when emulation sampling obtains the sampling inefficacy of each bottom event
Between be t1, t2..., tii..., tn;1,2 ..., ii ..., n one bottom event of uniquely tagged respectively;
2.4. travel through all gates, if a certain dynamic logic gate, then specifically process sampling according to the process rule of this gate
Out-of-service time;
2.5., after the sampling out-of-service time having been processed, corresponding event in the 2.3rd step is replaced with the sampling out-of-service time after process successively
The sampling out-of-service time;
2.6. the sampling out-of-service time after the process in the 2.5th is sorted according to order from small to large, when the sampling after sequence was lost efficacy
Between order be t '1, t'2..., t 'ii..., t'n;1,2 ..., ii ..., n one bottom event of uniquely tagged respectively;
Contrast minimal cut sequence is concentrated and is cut bottom event that sequence represents and the order of occurrence that bottom event lost efficacy obtains with emulating sampling the most successively
Corresponding bottom event and bottom event the sampling out-of-service time order;If i-th cuts multiple bottom event inefficacies order that sequence represents, and take out
The plurality of bottom event that sample obtains sampling out-of-service time sequence consensus from small to large, then remember this cut sequence sampling the out-of-service time be
ti=tmax, tmax are that this cuts sampling out-of-service time of last bottom event in sequence;The sampling out-of-service time t of system is for cutting sequence
Concentrate all cutting the sampling out-of-service time that sequence is minimum, i.e. system emulation sampling out-of-service time t=minti(i=1,2 ..., k);
2.8. t is madem=t, tmIt is the m time analogue system sampling out-of-service time, if tm> T, then the system that explanation emulation sampling draws
The time lost efficacy is longer than the system operation time T of initial setting, and in the system operation time T i.e. set, fault tree top event does not has
There is generation, then fm=0, fmFor judging whether the m time analogue system lost efficacy within the operation time set;Otherwise, top event
Lost efficacy in T time, then fm=1 goes back to step 2.2.
2.9. emulation terminates, then run, in the system set, the probability that top event occurs in T time, namely top event is unreliable
DegreeUnreliable degree istiFor each analogue system
Out-of-service time.
The most according to claim 1 a kind of based on cutting the Dynamic fault tree Monte Carlo simulation quantitative calculation method of sequence collection, its feature exists
In: described logic gate types has preferential and door, order dependent door, cold standby part door, temperature spare part door, hot spare door, function triggering
Door and door or door, k/n door;Preferential and door represents A and B order of occurrence no requirement (NR), but pushes up when only A occurs prior to B
Event occurs, and the sequence of cutting of its correspondence is (A-> B);Order dependent door represents that event occurs successively only in the order of A, B, C,
And top event occurs after all occurring, corresponding sequence of cutting is A-> B-> C;Cold standby part door represents that main part A first works, after inefficacy, and spare part
Sequentially entering duty, after all losing efficacy, top event occurred, and will not lose efficacy during spare part storage, and corresponding cuts sequence (A-> B-> C);Temperature
Spare part door represents that main part A first works, and after inefficacy, spare part sequentially enters duty, and after all losing efficacy, top event occurred, and spare part is being deposited
Storage state has crash rate, less than duty crash rate, although therefore bottom event enter job order and have successively, but lost efficacy occur suitable
Sequence is less than successively, and corresponding is segmented into (A, B, C);Hot spare door represents that main part A first works, and after inefficacy, spare part enters according to this
Enter duty, after all losing efficacy top event occur, spare part storage state identical with duty crash rate, although therefore bottom event enter
Entering job order to have successively, but inefficacy order of occurrence is less than successively, corresponding is segmented into (A, B, C);Function trigger gate represents
After trigger event A occurs, its event B that is triggered also lost efficacy;Meanwhile, event B also can independent failure, corresponding has cut (A),
(B);Representing that bottom event all occurs with door, top event occurs, and corresponding is segmented into (A, B);Or door represents bottom event any one event
Occurring, top event occurs, and corresponding is segmented into (A), (B);K/n door represents that in bottom event, k event occurs, and top event occurs, false
It is set to 2/3 and corresponding is segmented into (A, B), (A, C), (B, C).
The most according to claim 1 a kind of based on cutting the Dynamic fault tree Monte Carlo simulation quantitative calculation method of sequence collection, its feature exists
In:
Described cut with merging of cutting and be divided into merge or merge, k/n merges, order merges;
(3.1.1) with merge: according to door compatible rule merging, case (A) and (B), amalgamation result (A, B);
(3.1.2) or merge: according to or door compatible rule merging, case (A) or (B), amalgamation result (A), (B);
(3.1.3) k/n merges: according to k/n door compatible rule merging, case (A), (B), in (C) 2/3, and amalgamation result (A, B), (A, C),
(B,C);
(3.1.4) order merges: associated gate compatible rule merging in order, case (A)-> (B), amalgamation result (A-> B);
Described cut sequence with merging of cutting and be divided into merge or merge, k/n merges, order merges;
(3.2.1) with merge: according to door compatible rule merging, case (A) and (B-> C), amalgamation result (A, B-> C)
(3.2.2) or merge: according to or door compatible rule merging, case (A) or (B-> C), amalgamation result (A), (B-> C)
(3.2.3) k/n merges: according to k/n door compatible rule merging, case (A), (B), in (C-> D) 2/3, and amalgamation result (A, B),
(A,C->D),(B,C->D);
(3.2.4) order merges: will cut before being connected to cut sequence with sequence number, as an amalgamation result;And be moved back by according to this
Move and cut, often move an event, increase an amalgamation result, until cutting before cutting last event of sequence;Case (A)->
(B-> C), amalgamation result (A-> B-> C), (B-> A-> C);
Described cut sequence with merging of cutting sequence and be divided into merge or merge, k/n merges, order merges;
(3.3.1) with merge: according to door compatible rule merging, case (A-> B) and (C-> D), amalgamation result (A-> B, C-> D);
(3.3.2) or merge: according to or door compatible rule merging, case (A-> B) or (C-> D), amalgamation result (A-> B), (C-> D);
(3.3.3) k/n merges: according to k/n door compatible rule merging, case (A-> B), (C-> D), in (E-> F) 2/3, merges knot
Really (A-> B, C-> D), (A-> B, E-> F), (C-> D, E-> F);
(3.3.4) order merges: last event and the later of cutting sequence by first are cut sequence and synthesized according to the order cutting and cutting sequence,
First event cutting sequence of traversal the most forward, according to cutting and cut the composition rule of sequence, until the event of traversal is in its initial cutting
In sequence before later event;Case (A-> B)-> (C-> D), amalgamation result (A-> B-> C-> D), (A-> C-> B-> D),
(C->A->B->D)。
The most according to claim 1 a kind of based on cutting the Dynamic fault tree Monte Carlo simulation quantitative calculation method of sequence collection, its feature
It is: the emulation sampling out-of-service time under Different Dynamic gate processes, and specifically includes,
(2.4.1) the order dependent door sampling out-of-service time processes: it is suitable that order dependent door requires bottom event only in from left to right
Sequence lost efficacy successively, i.e. the generation of later event was lost efficacy always after previous event lost efficacy, therefore when sampling was lost efficacy
Between process then need successively in sampling out-of-service time of later event plus sampling out-of-service time of previous event;That is:
Determining the bottom event under order dependent door, sample the out-of-service time according to bottom event, search obtains below order dependent door successively
The sampling out-of-service time of bottom event isS is the number of event, herein gate below a certain dynamic logic gate
For order dependent door,The sampling out-of-service time for the i-th i event corresponding to the c event under this dynamic logic gate;Order dependent door
The sampling out-of-service time processes, and from the beginning of second event, the most from left to right, adds and go forward on the sampling out-of-service time of this event
The sampling out-of-service time of one event, and sequential iteration renewal, it is:
(2.4.2) the cold standby part door sampling out-of-service time processes: cold standby part door requires that main part first works, and after inefficacy, spare part enters successively
Entering duty, until all losing efficacy, and spare part is in storage state no-failure rate;Therefore substantially bottom event be also according to from a left side to
Right order occurs, the most order dependent door of process to this;Except for the difference that s is the number of event below a certain dynamic logic gate,
It is the number of event below cold standby part door in this case;
(2.4.3) the function trigger gate sampling out-of-service time processes: after function trigger gate requires that trigger event occurs, its thing that is triggered
Part also lost efficacy;Meanwhile, the event that is triggered also can independent failure, then after sampling, if the trigger event sampling out-of-service time is more than quilt
The trigger event sampling out-of-service time, then illustrate that the event that is triggered lost efficacy prior to trigger event, then need not process;Otherwise,
Then explanation trigger event is prior to the stale event that is triggered, and now, the event of being triggered should lose efficacy simultaneously, therefore uses trigger event
The sampling out-of-service time replace being triggered sampling out-of-service time of event;In function trigger gate, the trigger event sampling out-of-service time is
Event sampling out-of-service time that is triggered isThe most concrete process is:
(2.4.4) the hot spare door sampling out-of-service time processes: in hot spare door, main part and spare part simultaneously enter duty, until
After main part and spare part all lost efficacy, thrashing, therefore below hot spare door, event is in the most not requirement of losing efficacy, story part is corresponding
The sampling out-of-service time be not required to process;
(2.4.5) the temperature spare part door sampling out-of-service time processes: temperature spare part door requires that main part first works, and after inefficacy, spare part enters successively
Enter duty, until all inefficacy and spare part are less than the crash rate of spare part running status in storage state;The most right during sampling for the first time
All bottom events are sampled successively according to the crash rate under its duty, if there is also temperature spare part door in fault tree, then it is right to need
In temperature spare part door, the spare part out-of-service time in the storage position is sampled toRegulation has 2 spare parts herein, and c represents that this is taken out
The sample out-of-service time is the sampling out-of-service time under Reserve State;
Specifically, finding the main part sampling out-of-service time is tiiIf,SimultaneouslyIllustrate when main part sampling was lost efficacy
Between sample the out-of-service time more than all spares reserves, the most all spare parts lost efficacy prior to main part, it is not necessary to the sampling out-of-service time is done and located
Reason;Otherwise, need to process;If the main part sampling out-of-service timeIllustrating when main part lost efficacy, the 1st spare part is in storage
State and not inefficacy, the 1st spare part subsequently enters duty, and the sampling under finding the 1st spare part in working order was lost efficacy
Time isIts sampling out-of-service time be processed as into2nd spare part sampling out-of-service time is processed, if
Illustrating that the 1st spare part of cut-off lost efficacy, the 2nd spare part did not the most lose efficacy under Reserve State, therefore after the 1st spare part lost efficacy,
2nd spare part enters duty, is processed as, and the sampling out-of-service time under finding the 2nd spare part in working order isIts
The sampling out-of-service time is processed as iteration and updates the sampling out-of-service time
(2.4.6) the preferential and door sampling out-of-service time processes: preferential and door requires that the event of this lower section is according to the most successively
During inefficacy, preferential with door above event lost efficacy, if while this lower section event not according to this Sequence Fault, then go up
Side's event will not lose efficacy;Therefore the inefficacy of its event order does not has sequential relationship, simply has sequential relationship when judging and losing efficacy.
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