CN106599352A - Reliability analysis method for aircraft fly-by-wire control system - Google Patents

Abstract

Provided is a reliability analysis method for an aircraft fly-by-wire control system. On the theoretical basis of a dynamic random Petri network, the invention provides a system reliability modeling and reliability calculation method based on a schematic diagram for system functions. The method is used for converting the schematic diagram for system functions into the dynamic random Petri network with a highly uniform topological structure used for system reliability analyses. The Petri network is capable of effectively avoiding interference of subjective factors of modeling personnel and accurately calculating system reliability. Therefore, the reliability analysis method for the aircraft fly-by-wire control system is of great importance in improvement of reliability assessment of a complex engineering system.

Description

A kind of aircraft Flying by wire systems reliability analysis method

Technical field

The invention belongs to engineering system fail-safe analysis field, and in particular to a kind of that aircraft Flying by wire systemic-function is former Reason figure is converted into the System reliability modeling of stochastic Petri net and system dependability computational methods.

Background technology

Reliability is the important technology attribute of complex engineering system effective utilization.High-caliber reliability analysis technology for Screen system weakness in aircraft, Curve guide impeller defect, reduction Life Cycle Cost, raising application of function efficiency etc. to have Important engineering technology is worth and meaning.The core of reliability field work is failure, and the generation of failure not only can have a strong impact on The performance of system itself function, more can cause casualties and property loss.In recent years, with aircraft Flying by wire system synthesis Change constantly development, system design becomes to become increasingly complex, and integrity problem becomes increasingly conspicuous, and the generation of all kinds of accidents is more highlighted The importance and necessity of aircraft Flying by wire systems reliability analysis work.

The defect correction of complex engineering system in aircraft often has the basic feature of " lead and start whole body ", and hiding sets Meter defect will cause the endless future trouble in applying, and be so that system reliability reaches the design requirement of regulation, most basic way Footpath is during system development, just to carry out Reliability modeling comprehensively with analysis work in the design phase so that in system design Stage just gives weaponry good reliability.However, at present in aircraft Flying by wire system design stage, carrying out reliability There is problems with analysis and evaluation work：

(1) efficiency of fail-safe analysis evaluation work.At present in the development process of complex engineering system, system design Used by specialty is professional with reliability is two kinds of technical systems, and system design specialty is only concerned about the work(of system and its element Can, it is not related to the failure of injection system and its element.Specifically, in system design process, how designer will be if paying attention to , into the system for completing specific function ability, after system design terminates, system design specialty will for system components and parts organic assembling Systemic-function schematic diagram obtained by its specialty gives reliability specialty, then the event by reliability specialty to system and its element Barrier impact is analyzed：Reliability specialty is set up according to systemic-function schematic diagram, and there is descriptive system and its element fault logic to close The system reliability model of system, is then analyzed to system reliability according to system reliability model and assesses.However, work as can When finding that reliability is unsatisfactory for design requirement or designs unreasonable by property specialty, need by system design specialty change design, when After the change of design specialist complete design, reliability specialty is given again and re-starts Reliability modeling and reliability assessment, Zhi Daoke Meet by property index and require.

That is, in engineering practice, functional design work is relatively independent successively with fail-safe analysis work to be carried out, and System design work is carried out mainly around functional space, and reliability assessment work is carried out mainly around defective space.Presently, there are System reliability modeling method, its by functional space be converted into equivalence fault logic describe when, topological structure often changes It is very big, and need Reliability modeling personnel that system and composition components and parts are artificially provided on the basis of analysis system schematic diagram of the function Fault impact, reliability assessment inefficiency.It is empty if there is a kind of function that directly can be described systemic-function schematic diagram Between be converted into the method for the highly consistent system failure propagation model of topological structure, then can effectively improve in system design process and be The assessment efficiency of system reliability, so as to finally shorten system development cycle.

(2) correctness problem of reliability model.There is multi-modeling method in fail-safe analysis at present and assessment, these are built Although mould method is somewhat dependent on systemic-function schematic diagram, but remains a need for the technical staff with abundant engineering experience Participate in modeling.Especially in large-scale complicated system modeling process, there will be excessive artificial subjective factor intervention in modeling process, Even if being modeled to same system using same class model, the model that different modelers are set up is likely to different, and modeler holds Easily limited by the level of understanding, analysis level, it is difficult to avoid the cognitive generation with mistake.If can be by reliability assessment Organically combine with functional design so that when the reliability model of foundation is as highly consistent as possible with system principle functional diagram, ability Reflect the objective fact of system to the full extent, it is to avoid the caused error because of the intervention of excessive artificial subjective factor, it is ensured that mould The correctness of type.

(3) the analytical calculation problem of reliability model.The main purpose for setting up system reliability model is effectively to count Calculate system dependability.In addition it is directed to different types of model, the method for the reliability of the system represented for computation model is not yet It is identical.For example, the reliability model set up using failure Bayesian network, needing to be carried out using Bayesian Network Inference technology can Calculate by property；Using the reliability model of Construction of Fault Tree, boolean's Theoretical Calculation system dependability is typically adopted.Therefore, when appoint When a kind of what System reliability modeling method is suggested, corresponding reliability degree calculation method need to be provided, what is otherwise proposed builds Mould method will lose the meaning of presence.

To sum up, it is to solve the problems, such as above three, improves the systems reliability analysis of aircraft Flying by wire and system function design The work of two specialties cooperates with degree, shortens system design and lead time, and need to seek one kind can be directly former by systemic-function Reason figure be converted into the system reliability model highly consistent with its topological structure and can effective computing system reliability method.

The content of the invention

To overcome, reliability assessment efficiency present in prior art is low, model correctness is low and the suitability is poor not Foot, the present invention proposes a kind of aircraft Flying by wire systems reliability analysis method.

The present invention detailed process be：

Step 1, counts element number Num：The statistics element Num numbers are that statistics aircraft Flying by wire systemic-function is former Element number Num in reason figure, and the storehouse for setting up a normal place of expression state and an expression status fault for each element Institute.Specifically, i.e., following operation is performed successively to each element：

It is that element foundation represents that its state is normal for i-th element in aircraft Flying by wire systemic-function schematic diagram Place, and for place numbering P_i.up。P_i.up in, P represents place, and i represents element sequence number, and i meets 1≤i of condition≤Num, Up represents normal.

It is that element foundation represents its status fault for i-th element in aircraft Flying by wire systemic-function schematic diagram Place, and for place numbering P_i.down。P_i.down in, P represents place, and i represents element sequence number, i meet 1≤i of condition≤ Num, down represent failure.

Step 2, sets up contacting for the normal place of each state and corresponding each status fault place.

To represent that the normal place of each element state points to the place for representing each element state failure in step 1.Including：

For the element i that span is 1≤i≤Num, set up a unique time delay and change t_i, and become for the time delay Relevant parameter is moved, the parameter of association is fault rate λ of element i_i.The element i is referred to i-th yuan in systemic-function schematic diagram Part, t_iThe numbering of the time delay transition to set up, λ_iFor the fault rate of element i.

Draw line：Draw the line between element i normal conditions place and the time delay transition of relevant parameter, and the pass Line between the time delay transition of connection parameter and element i failure place states.

Step 3, sets up the place for representing system fault condition.

System is regarded as into an element, place P for representing its malfunction is set up_Num+1.down.In P_Num+1.down in, P Place is represented, down represents malfunction, and Num+1 refers to the numbering of the place of the expression malfunction set up at present.

So far, the place for fail-safe analysis builds and finishes, wherein, the place of the expression malfunction of foundation has Num+ 1, the place of the expression normal condition of foundation has Num.

Step 4, connects the place of each element fault state.

According to the type of attachment of each element, it is P to connect numbering in each element_i.down each place, wherein i's takes Value scope is 1≤i≤Num+1, to set up based on the consistent with systemic-function principle graph structure of stochastic Petri net the Theory Construction Reliability model.

When connecting the place of each element fault state：

With the upstream input element sum that symbol In_N represents i-th element, in static logic form of presentation, i-th The function logic relation of n input element in element and In_N input element of the components upstream is present and or and voting three Plant primitive form, wherein n≤In_N.With symbol j₁、j₂…j_nRepresent n upstream input element of i-th element in systems Numbering, j₁、j₂…j_nMeet 1≤j of condition₁、j₂…j_n≤Num+1.Represent place P of i-th element fault_i.down and represent The place of n element fault of the components upstreamBy the method for attachment of immediate transition according to According to or and voting three kinds of forms be divided into three kinds of situations.

Step 5, using Monte Carlo simulation method solving system reliability.Described solution procedure is as follows：

Setting simulation times Sim_N, Sim_N is set greater than 0 any value.

The variable Sim_n of record emulation course is set up, and initializes Sim_n=1.The Sim_n is be carrying out imitative True number of times, works as Sim_n>During Sim_N, terminate the emulation to set up system reliability model.

Set up array SYS of thrashing time in record simulation process.Element number in array SYS and setting Simulation times Sim_N it is equal, successively record the 1st, 2 ... Sim_N simulation processes in system occur fail time.

Initialization system state.Described system initial state is referred in system initial time, Num element in system It is in normal condition.In the system reliability model that the present invention is set up, the implementation of initialization system state：Set up Represent the variable T of system time_sys=0, and be P in numbering_i.up a Tokken, i spans are sequentially placed in each place For 1≤i≤Num.

By the time delay of all ignitable time delay transition in desampling method successively acquisition system.The time delay transition Whether ignitable determination methods are referring to step 1, described to obtain i-th time delay transition t by desampling method_iX time delay_i Computational methods it is as follows：

I) produce and obey [0,1] equally distributed random number U～U (0,1)；

Ii) X is made_i=-InU/ λ_i, λ_iT is changed for time delay_iParameter.

The operation of the system in the Sim_n time simulation process is promoted by the way that time delay transition are carried out with ignition operation, step is such as Under：

First, X time delay to obtaining_iSequence, takes the corresponding time delay transition of minimum time, uses symbol T_minAnd t ' point Biao Shi not minimum time and its corresponding time delay transition.Secondly, ignition operation is carried out to time delay transition t '：Update system time T_sys=T_sys+T_min, the Tokken for changing the preposition concentrations of t ' is moved in the post set of transition t '.

The operation of the system in the Sim_n time simulation process is promoted by carrying out ignition operation to immediate transition, step is such as Under：

First, determine ignitable immediate transition in system, the whether ignitable determination methods of the immediate transition referring to Step 1.Secondly, ignition operation is carried out to ignitable immediate transition：Tokken is not in the preposition place of ignitable immediate transition Become, a Tokken is placed in each element of ignitable immediate transition post set.

Circulation performs the operation that system in the Sim_n time simulation process is promoted by carrying out ignition operation to immediate transition, Until meeting any one in following two conditions, the operation can be terminated：

Condition 1：There is no ignitable immediate transition in the system reliability model set up；

Condition 2：Place P_Num+1.down there is Tokken.

According to place P_Num+1.down state, judges whether the Sim_n time emulation terminates.Determination methods are as follows：

If P_Num+1.down there is no Tokken, repeat described by all ignitable in desampling method successively acquisition system The time delay of time delay transition, continue executing with the Sim_n time emulation；

If P_Num+1.down there is Tokken, terminate the Sim_n time emulation, and make Sim_n=Sim_n+1, make SYS [Sim_n] =T_sys, repeat initialization system state, start the emulation next time to system.

To process 4.～8. add up perform Sim_N time after, statistical system reliability R.System of the system in the reliability at τ moment Counting formula is：

In formula, whether δ Mk systems break down, when δ=1, system jam；When δ=0, system is not sent out Raw failure.

There is multiple rate gyroscopes, flight control computer, servo actuator, driving cabin in the aircraft Flying by wire system to refer to Make sensor, rudder face displacement transducer and rudder face.Each rate gyroscope, driving cabin instruction sensor and rudder face displacement sensing Device provides respectively rate information, operator command information and rudder face positional information to flight control computer, flight control computer root Calculate effective control signal according to the information for receiving, then control signal be delivered separately to into each servo actuator, finally by Each servo actuator drives rudder face to deflect jointly, so as to control the motion of aircraft.

Described is P for the normal place of expression state that each element is set up_i.up；The expression shape set up for each element The place of state failure is P_i.down。

Described transition firing rule includes：

Time delay changes firing rule：When the preposition collection of time delay transition has Tokken, transition can light a fire.One ignitable to prolong The ignition process of Shi Bianqian is：After a time delay, the Tokken of the preposition concentration of time delay transition is moved out to into post set, Obey exponential described time delay, the parameter of exponential is equal to the parameter of time delay transition.

Immediate transition firing rule：When the preposition collection of immediate transition has Tokken and the rearmounted element that is concentrated with does not have support When willing, transition can light a fire.The ignition process of one ignitable immediate transition is：The preposition concentration Tokken distribution of transition does not occur Change, places a Tokken in each element without Tokken in ignitable immediate transition post set.

The equal function of n input element of described function logic relation "AND" refers to that and if only if i-th element is normal When, the function of i-th element can be performed normally.Described function logic relation "or" is referred to when the n of i-th element is individual defeated To enter have in element any one element function executing normal, then the function of i-th element can be performed normally.Described function is patrolled Volume relation " k/n votings " is referred to when have at least k element function executing in n input element of i-th element normally, then and the The function of i element can be performed normally.

It is described with or and voting three kinds of function logics connected mode, place P_iAnd place .down It is as follows respectively by the method for attachment of immediate transition：

When i-th element be with the function logic relation of n element of the components upstream and when, then foundation and placeOne-to-one n immediate transition, draws n bar directed line segments：By n placeIt is respectively directed to the n immediate transition set up；Continue to draw n bar directed line segments：By institute N immediate transition for stating foundation is respectively directed to place P_i.down。

When i-th element be with the function logic relation of n element of the components upstream or when, then set up an instantaneous change Move, draw n bar directed line segments：By placeIt is respectively directed to the immediate transition set up；After It is continuous to draw directed line segment：Place P is pointed to by the immediate transition of the foundation_i.down。

When i-th element is " k/n votings " with the function logic relation of n input element of the components upstream, then build It is verticalIndividual immediate transition, wherein 1≤k≤n.For the place of n input element Therefrom take n-k+1 place to be combined, number of combinations isForPlant each combination in combination and make following behaviour respectively Make：

I sets up an immediate transition；Ii to combination in each place, respectively draw one by place point to i in instantaneously become The directed line segment for moving；Iii draws one and points to place P by immediate transition in i_i.down directed line segment.

The present invention is in stochastic Petri net theoretical basiss, there is provided one kind is based on aircraft Flying by wire systemic-function schematic diagram System reliability modeling and reliability degree calculation method.Aircraft Flying by wire systemic-function schematic diagram can be converted into and be opened up by the method The consistent stochastic Petri net for systems reliability analysis of structure height is flutterred, the Petri network can be prevented effectively from modeling personnel master The interference of sight factor, can be computed correctly the reliability of static system, for lifting complex engineering Reliability evaluation level With important value.

Compared with prior art, beneficial effects of the present invention are：

(1) ease for operation of model has close ties with the method for expressing of model, generally with system physical structure, function The method for expressing that schematic diagram is close has more preferable maneuverability.Reliability Modeling proposed by the present invention and schematic diagram of the function It is highly consistent, therefore there is good maneuverability in modeling process.

Fig. 8 is the event carried out to the aircraft Flying by wire system in embodiment from traditional fault tree modeling angle in accompanying drawing Barrier propagates description；Corresponding, Fig. 7 is to the aircraft Flying by wire in embodiment according to modeling method proposed by the present invention in accompanying drawing The fault propagation description that system is carried out.Fig. 4 is the schematic diagram of the function of aircraft Flying by wire system in embodiment.Fig. 7 is entered with Fig. 4 Row contrast, Fig. 8 is contrasted with Fig. 4, by two groups of contrasts, using modeling method proposed by the present invention obtain can It is consistent with systemic-function schematic diagram by the structure of property model, and pass through the structure of the fault tree models that traditional modeling method is obtained with There is larger difference in system structure schematic diagram.Therefore relative to traditional modeling method, modeling method proposed by the present invention can be done To highly consistent with systemic-function schematic diagram, therefore there is good operability in modeling process.

(2) the reservation System Working Principle information that modeling method proposed by the present invention can be more complete, to a certain extent " reprocessing " process of systems analyst to product development information is avoided, the description to system is more objective.

The topological structure of contrast Fig. 4 and Fig. 7 understands that both topological structure are on all four.That is, by this The System Working Principle information contained in reservation Fig. 4 that Fig. 7 constructed by modeling method that invention is proposed can be more complete, because This can be avoided " reprocessing " process of systems analyst to product development information in modeling process, thus to the description of system It is more objective, the error that artificial experience is caused in traditional modeling method can be prevented effectively from.

(3) the systemic-function schematic diagram of system design stage directly can be converted into reliability point by method proposed by the present invention Analysis model simultaneously carries out reliability calculating, therefore can effectively improve the analysis efficiency of design phase system reliability, is system design Effective supplementary meanss of stage fail-safe analysis.

Directly the functional space that systemic-function schematic diagram is described can be converted into into topological structure height if there is a kind of The method of consistent system failure propagation model, then can effectively improve the assessment efficiency of system reliability in system design process, So as to finally shorten system development cycle.From the point of view of Fig. 7 and Fig. 8 contrasts, modeling method proposed by the present invention can will will be directly System schematic diagram of the function is converted into the highly consistent fault- traverse technique of topological structure, therefore modeling method of the present invention has raising system The potential quality of system design efficiency.But when any System reliability modeling method is suggested, corresponding reliability need to be provided Degree computational methods, the modeling method for otherwise proposing will lose the meaning of presence.For this purpose, for it is proposed by the present invention can for system By the stochastic Petri net of property analysis, the present invention is supporting to propose the system dependability emulation meter for calculating the Stochastic Petri Net Model Calculation method.Fig. 9 is the comparison diagram of emulation mode acquired results of the present invention and existing Method for Accurate Calculation acquired results.From Fig. 9 Shown curve can be seen that, with the increase of simulation times, the calculated system dependability of foundation the inventive method converges on essence Really solve, this is identical with the law of large numbers in theory of probability, demonstrates the correctness of emulation mode of the present invention.Therefore the present invention is proposed Method not only directly the systemic-function schematic diagram of system design stage can be converted into into reliability analysis model, and can effectively enter Row reliability simulation calculation, for the analysis efficiency for improving design phase system reliability has important value.

Description of the drawings

Fig. 1 be function logic relation be "AND" when, place P_i.down with the connected mode of its preposition collection；

Fig. 2 be function logic relation be "or" when, place P_i.down with the connected mode of its preposition collection；

Fig. 3 be function logic relation be " voting " when, place P_i.down with the connected mode of its preposition collection；

Fig. 4 is the schematic diagram of the function of aircraft Flying by wire system；

Fig. 5 is the stochastic Petri net for fail-safe analysis of aircraft Flying by wire system；

Fig. 6 is the situation after the stochastic Petri net initialization shown in Fig. 5；

Fig. 7 is the fault propagation part of the stochastic Petri net shown in Fig. 5；

Fig. 8 is the fault tree of aircraft Flying by wire system；

Fig. 9 is the reliability curves of aircraft Flying by wire system；

Figure 10 is the flow chart of the present invention.

Specific embodiment

The present embodiment is a kind of aircraft Flying by wire systems reliability analysis method based on stochastic Petri net.

The system refers to that the element with interrelated relation combines, and is configured to complete required spy Determine the organic whole of function.

In the present embodiment, the system is an aircraft Flying by wire system, and Fig. 4 is the schematic diagram of the function of the system.In Fig. 4 In, there are 3 rate gyroscopes, 1 flight control computer, 2 servo actuators, left-hand drive cabin instruction sensor, right driving cabins and refer to Sensor, rudder face displacement transducer and rudder face are made, altogether 10 elements.3 rate gyroscopes provide respectively rate information to winged Control computer, when at least two normal work in 3 rate gyroscopes, flight control computer can receive the speed letter of aircraft Breath；Simultaneously the operational order of pilot can pass to flight control computer by instruction sensor, when the instruction of left or right driving cabin is passed Sensor can normal work when, flight control computer can be properly received the operational order of driver；Flight control computer according to rate information, Pilot operator instruction and the rudder face information from rudder face displacement transducer calculate effective control signal, then will control letter Number be delivered separately to two servo actuators, when two servo actuators any one can normal work when, can driven rudder Deflecting facet；Rudder face can be deflected normally, then imply that the Flying by wire system is normal.Additionally, the fault rate of 3 rate gyroscopes is 3×10^-6, the fault rate of flight control computer is 5 × 10^-6, the fault rate of two servo actuators is 2 × 10^-6, left and right is driven The fault rate for sailing cabin instruction sensor is 0.7 × 10^-6, the fault rate of rudder face displacement transducer is 0.8 × 10^-6, the event of rudder face Barrier rate is 2 × 10^-6。

In the accompanying drawings, 1 is the circle of overstriking, represents the place of malfunction, sequence number P of overstriking circle in figure₁、P₂…P₁₁ The numbering of place represented by circle in stochastic Petri net, i.e. numbering P are collectively formed with " .down "₁.down、P₂.down… P₁₁.down；2 is the circle of non-overstriking, represents the place of element normal condition, sequence number P of non-overstriking circle in figure₁、P₂…P₁₀ The numbering of place represented by circle in stochastic Petri net, i.e. numbering P are collectively formed with " .up "₁.up、P₂.up… P₁₁.up；3 is rectangle, represents time delay transition；4 is vertical line, represents immediate transition；5 is the Tokken in place；6 is using the present invention The reliability of the calculated system shown in Figure 4 of emulation mode, wherein simulation times are 1000；7 is using emulation side of the invention The reliability of the calculated system shown in Figure 4 of method, wherein simulation times are 100000；8 is using convectional reliability analysis side The reliability of the system shown in Figure 4 that method is obtained accurately is solved；The abscissa of figure shown in Fig. 9 be system time, the list of system time Position is hour, and vertical coordinate is system dependability.

With reference to accompanying drawing, the detailed process of the present embodiment is：

Step 1, element number Num in statistics aircraft Flying by wire systemic-function schematic diagram, and set up one for each element The place of the normal place of expression state and an expression status fault.Specifically, i.e., following behaviour is performed successively to each element Make：

1. it is that element foundation is representing its state just for i-th element in aircraft Flying by wire systemic-function schematic diagram Normal place, and for place numbering P_i.up。P_i.up in, P represents place, and i represents element sequence number, i meet 1≤i of condition≤ Num, up represent normal.

2. it is that element foundation represents its state event for i-th element in aircraft Flying by wire systemic-function schematic diagram The place of barrier, and for place numbering P_i.down。P_i.down in, P represents place, and i represents element sequence number, i meet 1≤i of condition≤ Num, down represent failure.

Systemic-function schematic diagram according to Fig. 4, element number Num=10 in this example.

10 normal places are set up, is respectively：P₁.up、P₂.up、P₃.up、P₄.up、P₅.up、P₆.up、P₇.up、P₈.up、 P₉And P .up₁₀.up, 1# rate gyroscopes, 2# rate gyroscopes, 3# rate gyroscopes, flight control computer, 1# in Fig. 4 is represented respectively successively Servo actuator, the work of 2# servo actuators, left-hand drive cabin instruction sensor, right driving cabin instruction sensor, rudder face displacement are passed The normal condition of sensor and rudder face.

Secondly, 10 failure places are set up, is respectively：P₁.down、P₂.down、P₃.down、P₄.down、P₅.down、 P₆.down、P₇.down、P₈.down、P₉And P .down₁₀.down, 1# rate gyroscopes, 2# speed tops in Fig. 4 is represented respectively successively Spiral shell, 3# rate gyroscopes, flight control computer, 1# servo actuators, 2# servo actuators, left-hand drive cabin instruction sensor, right driving The malfunction of cabin instruction sensor, rudder face displacement transducer and rudder face.

The purpose of aircraft Flying by wire system design is from function flow angle, according to element function by the organic company of element Pick up come to realize systemic-function, and ultimately form systemic-function schematic diagram.The systemic-function schematic diagram is referred to from topology The description that structural point is carried out the function flow between system and its element.Systemic-function schematic diagram include expression system and its The node of element, and represent function flow to two kinds of graphic elements of line segment.

The place is referred in stochastic Petri net, represents the graphic element of system and its element state.Institute of the present invention The stochastic Petri net for systems reliability analysis built based on systemic-function schematic diagram stated is 6 tuples：SPN =(P, T, F, K, M₀, λ), SPN is the abbreviation of stochastic Petri net, wherein：

(1) P refers to place set, is represented with circle "○" in the graphic.When having Tokken in the place, library representation Represented state occurs, and when in place without Tokken, the state represented by library representation does not occur.The Tokken is that one kind is in Labelling in place, is represented in the graphic with " "；

(2) T refers to transition set, and transition include two kinds of time delay transition and immediate transition.In the graphic, rectangle is used respectively " " and vertical line " | " represent time delay transition and immediate transition；

(3) F is the oriented stream for connecting place and transition, and directed line segment is shown as in the graphic；

(4) λ is the average excitation rate set of time delay transition.In stochastic Petri net, each time delay transition are flat with one Excitation rate is corresponding, and the speed is referred to as the parameter of time delay transition, represents the point in the ignitable time delay fire transition unit interval Fiery number of times；

(5)M₀For the original state of network, i.e. the Tokken distribution situation of each place of system initial time；

(6)K:P → { 0,1 }, K is the Tokken number that there may be in place in capacity function of the library, i.e. network in network, It is 0 or 1 that P → { 0,1 } refers to the Tokken number of each place in network.

Complete Petri network should have clearly transition firing rule.Transition igniting in stochastic Petri net of the present invention Rule is as follows：

Time delay changes firing rule：When the preposition collection of time delay transition has Tokken, transition can light a fire.One ignitable to prolong The ignition process of Shi Bianqian is：After a time delay, the Tokken of the preposition concentration of time delay transition is moved out to into post set, Obey exponential described time delay, the parameter of exponential is equal to the parameter of time delay transition.

Immediate transition firing rule：When the preposition collection of immediate transition has Tokken and the rearmounted element that is concentrated with does not have support When willing, transition can light a fire.The ignition process of one ignitable immediate transition is：The preposition concentration Tokken distribution of transition does not occur Change, places a Tokken in each element without Tokken in ignitable immediate transition post set.

The preposition collection and post set are defined as follows：

If x ∈ P ∪ T are the either element in SPN, make * x={ y | (y ∈ P ∪ T) ∧ ((y, x) ∈ F) } and x*=y | (y ∈ P ∪ T) ∧ ((x, y) ∈ F) }, claim * x and x* to be respectively the preposition collection and post set of x.

Step 2, sets up contacting for the normal place of each state and corresponding each status fault place.

To represent that the normal place of each element state points to the place for representing each element state failure in step 1.Including：

1. for the element i that span is 1≤i≤Num, set up a unique time delay and change t_i, and for the time delay Transition relevant parameter, the parameter of association is fault rate λ of element i_i.The element i is referred to i-th yuan in systemic-function schematic diagram Part, t_iThe numbering of the time delay transition to set up, λ_iFor the fault rate of element i.

2. line is drawn：The line between element i normal conditions place and the time delay transition of relevant parameter is drawn, and should Line between the time delay transition of relevant parameter and element i failure place states.

In the present embodiment, the operating process described in step 2 is as follows：

1. 1# rate gyroscopes, 2# rate gyroscopes, 3# rate gyroscopes, flight control computer, 1# servo actuators, 2# are watched in Fig. 4 Take actuator, left-hand drive cabin instruction sensor, right driving cabin instruction sensor, rudder face displacement transducer and rudder face 10 elements Sequence number is followed successively by 1,2,3,4,5,6,7,8,9 and 10.Calculate for 1# rate gyroscopes, 2# rate gyroscopes, 3# rate gyroscopes, winged control Machine, 1# servo actuators, 2# servo actuators, left-hand drive cabin instruction sensor, right driving cabin instruction sensor, rudder face displacement are passed Sensor and each element of rudder face set up respectively successively corresponding time delay transition t₁、t₂、t₃、t₄、t₅、t₆、t₇、t₈、t₉And t₁₀, and for 10 Individual time delay transition are respectively associated the fault rate of counter element, and 1# rate gyroscopes, 2# rate gyroscopes, 3# rate gyroscopes, winged control are calculated Machine, 1# servo actuators, 2# servo actuators, left-hand drive cabin instruction sensor, right driving cabin instruction sensor, rudder face displacement are passed The fault rate of sensor and rudder face is followed successively by λ₁=3 × 10^-6、λ₂=3 × 10^-6、λ₃=3 × 10^-6、λ₄=5 × 10^-6、λ₅=2 × 10^-6、λ₆=2 × 10^-6、λ₇=0.7 × 10^-6、λ₈=0.7 × 10^-6、λ₉=0.8 × 10^-6And λ₁₀=2 × 10^-6.Therefore, it is time delay Transition t₁、t₂、t₃、t₄、t₅、t₆、t₇、t₈、t₉And t₁₀The parameter of association is respectively λ₁=3 × 10^-6、λ₂=3 × 10^-6、λ₃=3 × 10^-6、λ₄=5 × 10^-6、λ₅=2 × 10^-6、λ₆=2 × 10^-6、λ₇=0.7 × 10^-6、λ₈=0.7 × 10^-6、λ₉=0.8 × 10^-6With λ₁₀=2 × 10^-6。

2. for 1# rate gyroscopes, draw by place P₁.up transition t is pointed to₁Line, and draw by transition t₁Point to Place P₁.down line.For 2# rate gyroscopes, draw by place P₂.up transition t is pointed to₂Line, and draw by becoming Move t₂Point to place P₂.down line.For 3# rate gyroscopes, draw by place P₃.up transition t is pointed to₃Line, and Draw by transition t₃Point to place P₃.down line.For flight control computer, draw by place P₄.up transition t is pointed to₄Company Line, and draw by transition t₄Point to place P₄.down line.For 1# servo actuators, draw by place P₅.up point to Transition t₅Line, and draw by transition t₅Point to place P₅.down line.For 2# servo actuators, draw by place P₆.up transition t is pointed to₆Line, and draw by transition t₆Point to place P₆.down line.For the instruction of left-hand drive cabin is passed Sensor, draws by place P₇.up transition t is pointed to₇Line, and draw by transition t₇Point to place P₇.down line.It is right In right driving cabin instruction sensor, draw by place P₈.up transition t is pointed to₈Line, and draw by transition t₈Point to place P₈.down line.For rudder face displacement transducer, draw by place P₉.up transition t is pointed to₉Line, and draw by becoming Move t₉Point to place P₉.down line.For rudder face, draw by place P₁₀.up transition t is pointed to₁₀Line, and draw by Transition t₁₀Point to place P₁₀.down line.

Step 3, sets up the place for representing system fault condition.

System is regarded as into an element, place P for representing its malfunction is set up_Num+1.down.In P_Num+1.down in, P Place is represented, down represents malfunction, and Num+1 refers to the numbering of the place of the expression malfunction set up at present.

So far, the place for fail-safe analysis builds and finishes, wherein, the place of the expression malfunction of foundation has Num+ 1, the place of the expression normal condition of foundation has Num.

In the present embodiment, aircraft Flying by wire system is regarded as into an element, sets up and represent aircraft Flying by wire system Place P of malfunction₁₁.down.At present, the place of the expression malfunction set up has 11, represents element normal condition Place have 10,21 places altogether.So far, in the present embodiment, the place for fail-safe analysis builds and finishes.

Step 4, connects the place of each element fault state.

According to the type of attachment of each element, it is P to connect numbering in each element_i.down each place, wherein i's takes Value scope is 1≤i≤Num+1.With the upstream input element sum that symbol In_N represents i-th element, in static logic statement In mode, the function logic relation of n input element in i-th element and In_N input element of the components upstream is present With or and voting three kinds of primitive forms, wherein n≤In_N.With symbol j₁、j₂…j_nRepresent the n upstream input of i-th element Element numbering in systems, j₁、j₂…j_nMeet 1≤j of condition₁、j₂…j_n≤Num+1.Described method of attachment according to or It is divided into following three kinds of situations with three kinds of forms of voting：

1) when i-th element is with the function logic relation of n element of the components upstream and when, then foundation and placeOne-to-one n immediate transition, draws n bar directed line segments：By n placeIt is respectively directed to the n immediate transition set up；Continue to draw n bar directed line segments：By institute N immediate transition for stating foundation is respectively directed to place P_i.down.Fig. 1 gives function logic relation for "AND" and during n=3, storehouse Institute P_i.down with the connected mode of its preposition collection.

The function logic relation is normal for the equal function of n input element of "AND" i-th element that refer to that and if only if When, the function of i-th element can be performed normally.

2) when i-th element is with the function logic relation of n element of the components upstream or when, then set up one instantaneously Transition, draw n bar directed line segments：By placeIt is respectively directed to the immediate transition set up； Continue to draw directed line segment：Place P is pointed to by the immediate transition of the foundation_i.down.Fig. 2 gives function logic relation When "or" and n=3, place P_i.down with the connected mode of its preposition collection.

The function logic relation refers to have any one element in n input element for work as i-th element for "or" Function executing is normal, then the function of i-th element can be performed normally.

3) when i-th element is " k/n votings " with the function logic relation of n input element of the components upstream, then build It is verticalIndividual immediate transition, wherein 1≤k≤n.For the place of n input element Therefrom take n-k+1 place to be combined, number of combinations isForPlant each combination in combination and make following behaviour respectively Make：

I) immediate transition is set up；Ii) to combination in each place, draw respectively one pointed to i) by place in it is instantaneous The directed line segment of transition；Iii) draw one and place P is pointed to by immediate transition in i)_i.down directed line segment.

When Fig. 3 is " 2/3 voting " for function logic relation, place P_i.down with the connected mode of its preposition collection.

The function logic relation is that " k/n votings " refers to have at least k in n input element for work as i-th element Element function executing is normal, then the function of i-th element can be performed normally.

Additionally, as n=1, with or and three kinds of logical equivalences of voting, therefore with or and three kinds of situations of voting described in Three kinds of method of attachment equivalents, can be according to any one in three kinds of situations to i-th element and its upstream input element reality Apply attended operation.

So far, built based on the reliability model consistent with systemic-function principle graph structure of stochastic Petri net the Theory Construction It is vertical to finish.

For the present embodiment, the specific implementation process described in step 4 is as follows：

In the flight control computer systemic-function schematic diagram shown in Fig. 4, flight control computer is input into three in its upstream Elements 1：1# rate sensors, element 2：2# rate sensors and element 3：The function logic relation of 3# rate sensors is 2/3 decides by vote, now n=3, k=2, according to " when i-th element and the function logic relation of n input element of the components upstream When " k/n votings ", then to set upThe principle of individual immediate transition ", must set upIndividual immediate transition.For 3 input units Place P of part₁.down、P₂And P .down₃.down, therefrom take 2 places to be combined, number of combinations is3 kinds combination according to It is secondary to be：{P₂.down、P₃.down}、{P₁.down、P₃} and { P .down₁.down、P₂.down}。

To combine 1 { P₂.down、P₃.down following operation } is made：

I) an immediate transition t is set up₁₁；Ii) to place P₂And P .down₃.down, one is drawn respectively to be pointed to by place Transition t₁₁Directed line segment；Iii a transition t) is drawn₁₁Point to place P₄.down directed line segment.

To combine 2 { P₁.down、P₃.down following operation } is made：

I) an immediate transition t is set up₁₂；Ii) to place P₁And P .down₃.down, one is drawn respectively to be pointed to by place Transition t₁₂Directed line segment；Iii a transition t) is drawn₁₂Point to place P₄.down directed line segment.

To combine 3 { P₁.down、P₂.down following operation } is made：

I) an immediate transition t is set up₁₃；Ii) to place P₁And P .down₂.down, one is drawn respectively to be pointed to by place Transition t₁₃Directed line segment；Iii a transition t) is drawn₁₃Point to place P₄.down directed line segment.

Two input element elements 7 in flight control computer and its upstream：Left-hand drive cabin instruction sensor and element 8：It is right The function logic relation of driving cabin instruction sensor is or, now n=2, according to " as i-th element and n of the components upstream The function logic relation of element be or when, then set up an immediate transition, draw n bar directed line segments " principle, set up instantaneous change Move：Immediate transition t as shown in Figure 5₁₄, draw 2 directed line segments：By the place of expression left-hand drive cabin instruction sensor failure P₇.down transition t is pointed to₁₄Directed line segment and by place P for representing right driving cabin instruction sensor failure₈.down point to Transition t₁₄Directed line segment, continue draw directed line segment：By transition t₁₄Point to the place for representing flight control computer failure P₄.down。

An input element element 9 in flight control computer and its upstream：The function logic relation of rudder face displacement transducer Be with or, 1/1 voting three kinds of logics in any one.Now n=1, according to " as n=1, with or with voting three kinds patrol Volume equivalence " principle, can according to function logic be with or and voting three kinds in the case of any one method of attachment, pass through Set up place P that immediate transition connection represents flight control computer failure₄.down and represent the failure of element 9 place P₉.down.Herein, according to function logic relation be with when method of attachment to place P₄.down with place P₉.down connected Connect.According to " when i-th element be with the function logic relation of n element of the components upstream and when, then foundation and placeThe principle of one-to-one n immediate transition ", must set up and place P₉.down it is right 1 immediate transition answered：Immediate transition t as shown in Figure 5₁₅, draw 1 directed line segment：By place P₉.down point to what is set up Immediate transition t₁₅；Continue to draw 1 directed line segment：By the immediate transition t of the foundation₁₅Point to place P₄.down。

Represent place P of flight control computer failure₄.down Fig. 5 is seen with the connected mode of its preposition collection.

In the diagram, 1# servo actuators only exist 1 input element：Flight control computer, now n=1 is according to described An input element element 9 in flight control computer and its upstream：Rudder face displacement transducer sets up immediate transition and draws line Method, set up an immediate transition t₁₆, draw line：By place P of expression flight control computer failure₄.down transition are pointed to t₁₆, draw line：By transition t₁₆Point to place P for representing 1# servo actuator failures₅.down。

In the diagram, 2# servo actuators only exist 1 input element：Flight control computer, now n=1 is according to described An input element element 9 in flight control computer and its upstream：Rudder face displacement transducer sets up immediate transition and draws line Method, set up an immediate transition t₁₇, draw line：By place P of expression flight control computer failure₄.down transition are pointed to t₁₇, draw line：By transition t₁₇Point to place P for representing 2# servo actuator failures₆.down。

In the diagram, there are 2 input elements in rudder face：1# servo actuators and 2# servo actuators, rudder face and 2 inputs The function logic relation of element is or, now n=2, according to " when i-th element is patrolled with the function of n element of the components upstream Volume relation be or when, then set up an immediate transition, draw n bar directed line segments " principle, set up immediate transition：As shown in Figure 5 Immediate transition t₁₈, draw 2 directed line segments：By place P for representing 1# servo actuator failures₅.down transition t is pointed to₁₈'s Directed line segment and place P by expression 2# servo actuator failures₆.down transition t is pointed to₁₈Directed line segment, continue draw Directed line segment：By transition t₁₈Point to place P for representing rudder face failure₁₀.down。

According to described " rudder face can be deflected normally, then imply that the Flying by wire system is normal ", then when system is regarded After making an element, then system only exists 1 input element：Rudder face, now n=1, according to it is described for flight control computer with thereon An input element element 9 in trip：Rudder face displacement transducer sets up immediate transition and draws the method for line, sets up a wink Shi Bianqian t₁₉, draw line：By place P of expression rudder face failure₁₀.down transition t is pointed to₁₉, draw line：By transition t₁₉Refer to To place P for representing the system failure₁₁.down。

In the diagram, rudder face displacement transducer only exists 1 input element：Rudder face, now n=1, controls according to described for winged An input element element 9 in computer and its upstream：Rudder face displacement transducer sets up immediate transition and draws the side of line Method, sets up an immediate transition t₂₀, draw line：By place P of expression rudder face failure₁₀.down transition t is pointed to₂₀, the company of drafting Line：By transition t₂₀Point to place P for representing rudder face displacement transducer failure₉.down。

So far, built based on the reliability model consistent with systemic-function principle graph structure of stochastic Petri net the Theory Construction It is vertical to finish, as shown in Figure 5.

Step 5, using Monte Carlo simulation method solving system reliability.Described solution procedure is as follows：

1. simulation times Sim_N are set, Sim_N is set greater than 0 any value.

2. the variable Sim_n of record emulation course is set up, and initializes Sim_n=1.The Sim_n is carrying out Simulation times, work as Sim_n>During Sim_N, terminate the emulation to set up system reliability model.

3. array SYS of thrashing time in record simulation process is set up.Element number in array SYS with set Fixed simulation times Sim_N are equal, and the time that system in the 1st, 2 ... Sim_N simulation processes occurs failure is recorded successively.

4. initialization system state.Described system initial state is referred in system initial time, in system Num it is first Part is in normal condition.In the system reliability model that the present invention is set up, the implementation of initialization system state：Build The vertical variable T for representing system time_sys=0, and be P in numbering_i.up a Tokken, i value models are sequentially placed in each place Enclose for 1≤i≤Num.

5. by the time delay of all ignitable time delay transition in desampling method successively acquisition system.The time delay becomes Move whether ignitable determination methods are referring to step 1, it is described that i-th time delay transition t is obtained by desampling method_iTime delay X_iComputational methods it is as follows：

I) produce and obey [0,1] equally distributed random number U～U (0,1)；

Ii) X is made_i=-InU/ λ_i, λ_iT is changed for time delay_iParameter.

6. the operation of the system in the Sim_n time simulation process, step are promoted by the way that time delay transition are carried out with ignition operation It is as follows：

First, X time delay to obtaining_iSequence, takes the corresponding time delay transition of minimum time, uses symbol T_minAnd t ' point Biao Shi not minimum time and its corresponding time delay transition.Secondly, ignition operation is carried out to time delay transition t '：Update system time T_sys=T_sys+T_min, the Tokken for changing the preposition concentrations of t ' is moved in the post set of transition t '.

7. the operation of the system in the Sim_n time simulation process, step are promoted by carrying out ignition operation to immediate transition It is as follows：

First, determine ignitable immediate transition in system, the whether ignitable determination methods of the immediate transition referring to Step 1.Secondly, ignition operation is carried out to ignitable immediate transition：The preposition concentration Tokken distribution of transition does not change, A Tokken is placed in ignitable immediate transition post set in each element without Tokken.

Circulation performs the operation that system in the Sim_n time simulation process is promoted by carrying out ignition operation to immediate transition, Until meeting any one in following two conditions, the operation can be terminated：

Condition 1：There is no ignitable immediate transition in the system reliability model set up；

Condition 2：Place P_Num+1.down there is Tokken.

8. according to place P_Num+1.down state, judges whether the Sim_n time emulation terminates.Determination methods are as follows：

If P_Num+1.down there is no Tokken, repeat described by all ignitable in desampling method successively acquisition system The time delay of time delay transition, continue executing with the Sim_n time emulation；

If P_Num+1.down there is Tokken, terminate the Sim_n time emulation, and make Sim_n=Sim_n+1, make SYS [Sim_n] =T_sys, repeat initialization system state, start the emulation next time to system.

9. to process 4.～8. add up perform Sim_N time after, statistical system reliability R.Reliability of the system at τ moment Statistical formula is：

In formula, whether δ Mk systems break down, when δ=1, system jam；When δ=0, system is not sent out Raw failure.

In the present embodiment, the specific implementation process of step 5 is as follows：

1. simulation times Sim_N=10 are set.

2. the variable Sim_n of record emulation course is set up, and initializes Sim_n=1.

3. array SYS [10] of thrashing time in record simulation process is set up.

4. initialization system state.Set up the variable T for representing system time_sys=0, and in place P₁.up、P₂.up、 P₃.up、P₄.up、P₅.up、P₆.up、P₇.up、P₈.up、P₉And P .up₁₀.up a Tokken is sequentially placed in.It is after initialization System is as shown in Figure 6.

5. by the time delay of all ignitable time delay transition in desampling method successively acquisition system.

For ignitable time delay changes t_i, calculate its time delay of X_iImplementation it is as follows：

I) produce and obey [0,1] equally distributed random number U～U (0,1)；

Ii) X is made_i=-InU/ λ_i, λ_iT is changed for time delay_iParameter.

When the equally distributed random number U～U of obedience [0,1] is produced, (0, when 1), using matlab, C programming softwares can Produce and obey [0,1] equally distributed random number.Random number extraction is carried out using C programming softwares in the present embodiment.Due to this The method of bright proposition is based on stochastic sampling, therefore the random number for obtaining of sampling every time is possible different.In this embodiment, this step Only the method for the present invention is illustrated by taking a kind of possible sampling resultses as an example, described is explanation of the invention rather than limit It is fixed.

According to step 1, the whether ignitable determination methods of time delay transition are：When the preposition collection of time delay transition has support When willing, transition can light a fire.Current system time T_sys=0, time delay transition t_iPreposition collection P_i.up there is Tokken, wherein i successively Value 1,2 ... 10, therefore t₁～t₁₀10 time delay transition altogether can light a fire.

A time delay is extracted respectively for each ignitable time delay transition, it is as a result as follows：

For ignitable time delay changes t₁, the equally distributed random number of obedience [0,1] i) is randomly selected for 0.41368； Ii) X is made₁=-In0.41368/ λ₁=-In0.41368/3 × 10^-6=127778.49；

For ignitable time delay changes t₂, the equally distributed random number of obedience [0,1] i) is randomly selected for 0.725871； Ii) X is made₂=-In0.725871/ λ₂=-In0.725871/3 × 10^-6=46380.18；

For ignitable time delay changes t₃, the equally distributed random number of obedience [0,1] i) is randomly selected for 0.225378； Ii) X is made₃=-In0.225378/ λ₃=-In0.225378/3 × 10^-6=215696.16；

For ignitable time delay changes t₄, the equally distributed random number of obedience [0,1] i) is randomly selected for 0.198322； Ii) X is made₄=-In0.198322/ λ₄=-In0.198322/5 × 10^-6=140525.82；

For ignitable time delay changes t₅, the equally distributed random number of obedience [0,1] i) is randomly selected for 0.829819； Ii) X is made₅=-In0.829819/ λ₅=-In0.829819/2 × 10^-6=40508.31；

For ignitable time delay changes t₆, the equally distributed random number of obedience [0,1] i) is randomly selected for 0.915635； Ii) X is made₆=-In0.915635/ λ₆=-In0.915635/2 × 10^-6=19138.81；

For ignitable time delay changes t₇, the equally distributed random number of obedience [0,1] i) is randomly selected for 0.324589； Ii) X is made₇=-In0.324589/ λ₇=-In0.324589/0.7 × 10^-6=698094.57；

For ignitable time delay changes t₈, the equally distributed random number of obedience [0,1] i) is randomly selected for 0.018562； Ii) X is made₈=-In0.018562/ λ₈=-In0.018562/0.7 × 10^-6=2473393.19；

For ignitable time delay changes t₉, the equally distributed random number of obedience [0,1] i) is randomly selected for 0.637526； Ii) X is made₉=-In0.637526/ λ₉=-In0.637526/0.8 × 10^-6=244377.62；

For ignitable time delay changes t₁₀, the equally distributed random number of obedience [0,1] i) is randomly selected for 0.397021； Ii) X is made₁₀=-In0.397021/ λ₁₀=-In0.397021/2 × 10^-6=200593.26.

6. time delay transition are carried out with the operation that ignition operation promotes the system in the Sim_n=1 time simulation process.

The ignitable minimum time obtained in a time delay is extracted respectively according to for each ignitable time delay transition For 19138.81, the corresponding time delay transition of the minimum time are t₆, to t₆Carry out ignition operation：Update system time T_sys=T_sys+ 19138.81=0+19138.81=19138.81, will change t₆Preposition collection P₆.up the Tokken in moves into transition t₆Post set P₆.down in.

7. the fortune that ignition operation promotes the system in the Sim_n=1 time simulation process is carried out to ignitable immediate transition OK.

The whether ignitable Rule of judgment of immediate transition is：When the preposition collection of immediate transition is present in Tokken and post set When having element to there is no Tokken, transition can light a fire.When process, 6. the ignition operation that carries out to time delay transition is promoted in Sim_n In=1 simulation process after the end of run of system, current T_sys=19138.81, P_i.down only has P in class place₆.down deposit In Tokken, wherein 1≤i≤11, understand, immediate transition t according to the lighted a fire Rule of judgment of immediate transition₁₁～t₂₀Can not point Fire, meets described termination condition 1, that is, there is no ignitable immediate transition in the system reliability model set up, therefore ties Beam carries out the operation that ignition operation promotes the system in the Sim_n=1 time simulation process to ignitable immediate transition.

8. according to place P₁₁.down state, judges whether the 1st emulation terminates.

Current place P₁₁.down there is no Tokken, go to by all ignitable in desampling method successively acquisition system The time delay of time delay transition, the 1st emulation is continued executing with, until place P₁₁When there is Tokken in .down, the Sim_n=1 time Emulation terminates, and the 1st emulation Jia 1 certainly after terminating to Sim_n：Sim_n=Sim_n+1=2, makes SYS [Sim_n]=T_sys.This mistake Journey terminates, and goes to initialization system state, starts the to system the 2nd emulation.

9. repetitive process 4.～8. add up perform Sim_N=10 time after, according to array SYS statistical system reliability.

Using this step process 1.～9., the present embodiment is carried out 10 times emulation after, 10 data in array SYS according to It is secondary for 25792.78,575975.40,483755.57,201469.86,83803.35,60638.59,65332.32, 180655.60,96740.00,1030240.37}。

By system the reliability at τ moment statistical formula：

The reliability that system is obtained at the τ moment is：

Data amount check ÷ emulation total degree Sim_N in R (τ)=1- arrays SYS less than or equal to τ

If τ=100000, in array SYS less than 100000 data be 25792.78,83803.35,60638.59, 65332.32 and 96740.00,5 altogether, therefore R (τ=100000)=1-5 ÷ 10=0.5.

It is more than, with Sim_N=10, as a example by τ=100000, to illustrate public in the statistics of the reliability at τ moment by system The method that formula determines system dependability.

Method proposed by the present invention is based on stochastic sampling, therefore by using Monte Carlo simulation method solving system reliability When spending, different analysts finally give system dependability can slightly have difference.But according to law of great number, with simulation times Sim_N Increase, the system dependability of gained must converge on true solution.Fig. 9 be when Sim_N takes different value, system it is time dependent Reliability curves.

So far, the simulation calculation to aircraft Flying by wire system electricity reliability is completed.

Can be seen that from curve shown in Fig. 9, with the increase of simulation times, can according to the calculated system of the inventive method A stationary value is converged on by degree, the stationary value is true solution.In order to verify the correctness and superiority of the inventive method, herein The present embodiment is analyzed using existing Fault Tree Analysis.

First, according to existing fault tree construction method, to the fax aircraft Flying by wire system structure described in the present embodiment The fault tree built is as shown in Figure 8.In fig. 8, X_iThe bottom event of i-th element failure in expression system, wherein 1≤i≤ 10；G1 represents that the rate gyroscope subsystem that element 1, element 2 and element 3 are constituted occurs the intermediate event of failure；G2 represents element 5 The servo constituted with element 6 makees the intermediate event that subsystem occurs failure；G3 represents the driving cabin that element 7 and element 8 are constituted There is the intermediate event of failure in instruction sensor subsystem；G4 represents the outside crosslinking abnormal signal that flight control computer is received Intermediate event；Top event T represents the fax aircraft Flying by wire thrashing described in the present embodiment.

Essentially, the fault tree shown in Fig. 8 is that the fault propagation process of system is described by gate, right Answer, the stochastic Petri net for systems reliability analysis proposed by the present invention is by P_i.down class place, P_i.down class Immediate transition and directed line segment between place is described to the fault propagation process of system, as shown in Figure 7.

Fig. 7 is contrasted with Fig. 4, Fig. 8 is contrasted with Fig. 4, by two groups of contrasts, carried using the present invention The structure of the reliability model that the modeling method for going out is obtained is consistent with systemic-function schematic diagram, and passes through traditional modeling method and obtain Structure and the system structure schematic diagram of fault tree models there is larger difference.Therefore relative to traditional modeling method, the present invention Propose the Stochastic Petri Net Model for System Reliability Analysis can be more complete reservation System Working Principle information, because This can be avoided " reprocessing " process of systems analyst to product development information in modeling process, thus to the description of system It is more objective, the error that artificial experience is caused in traditional modeling method can be prevented effectively from.

Secondly, according to Fault Tree Analysis, the computing formula of reliability R (τ) of the system in τ is：

R (τ)=R (G2) R (G4) R₄R₁₀

Wherein, R (G2)=1- (1-R₅)(1-R₆), R (G4)=R (G1) R (G3) R₉；R (G3)=1- (1-R₇)(1-R₈)；

Symbol R_iThe reliability of i-th element in system is referred to, its computing formula For：τ is system time, λ_iFor the fault rate of element i.

Using system dependability computing formula R (τ)=R (G2) R (G4) R₄R₁₀, can computing system time instant τ=100, The system dependability at 200 ... 3,000 30 moment of grade, result of calculation is shown in Fig. 9.

Fault Tree Analysis result of calculation in Fig. 9 is understood with the emulation mode result of calculation contrast of the present invention, with The increase of simulation times, reliability model proposed by the present invention can be computed correctly out by emulation mode proposed by the present invention. Therefore the systemic-function schematic diagram of system design stage not only directly can be converted into fail-safe analysis by method proposed by the present invention Model, and can effectively carry out reliability simulation calculation, for the analysis efficiency for improving design phase system reliability have it is important Value.

Claims (6)

1. a kind of aircraft Flying by wire systems reliability analysis method, it is characterised in that detailed process is：

Step 1, counts element number Num：

Statistics element number Num is element number Num in statistics aircraft Flying by wire systemic-function schematic diagram, and for each unit Part sets up the place of a normal place of expression state and an expression status fault；Specifically, i.e., to each element successively Perform following operation：

It is that element foundation represents the normal storehouse of its state for i-th element in aircraft Flying by wire systemic-function schematic diagram Institute, and for place numbering P_i.up；P_i.up in, P represents place, and i represents element sequence number, and i meets 1≤i of condition≤Num, up tables Show normal；

It is that the element sets up the storehouse for representing its status fault for i-th element in aircraft Flying by wire systemic-function schematic diagram Institute, and for place numbering P_i.down；P_i.down in, P represents place, and i represents element sequence number, and i meets 1≤i of condition≤Num, Down represents failure；

Step 2, sets up contacting for the normal place of each state and corresponding each status fault place：

To represent that the normal place of each element state points to the place for representing each element state failure in step 1；Including：

For the element i that span is 1≤i≤Num, set up a unique time delay and change t_i, and close for the time delay transition Connection parameter, the parameter of association is fault rate λ of element i_i；The element i refers to i-th element, t in systemic-function schematic diagram_iFor The numbering of the time delay transition of foundation, λ_iFor the fault rate of element i；

Draw line：Draw the line between element i normal conditions place and the time delay transition of relevant parameter, and the association ginseng Line between several time delay transition and element i failure place states；

Step 3, sets up the place for representing system fault condition：

System is regarded as into an element, place P for representing its malfunction is set up_Num+1.down；In P_Num+1.down in, P is represented Place, down represents malfunction, and Num+1 refers to the numbering of the place of the expression malfunction set up at present；

So far, the place for fail-safe analysis builds and finishes, wherein, the place of the expression malfunction of foundation has Num+1, The place of the expression normal condition of foundation has Num；

Step 4, connects the place of each element fault state；

According to the type of attachment of each element, it is P to connect numbering in each element_i.down each place, the wherein span of i For 1≤i≤Num+1, to set up based on the reliability consistent with systemic-function principle graph structure of stochastic Petri net the Theory Construction Model；

When connecting the place of each element fault state：

With the upstream input element sum that symbol In_N represents i-th element, in static logic form of presentation, i-th element Exist with the function logic relation of n input element in In_N input element of the components upstream and or and three kinds of bases of voting This form, wherein n≤In_N；With symbol j₁、j₂…j_nRepresent n upstream input element of i-th element volume in systems Number, j₁、j₂…j_nMeet 1≤j of condition₁、j₂…j_n≤Num+1；Represent place P of i-th element fault_i.down it is somebody's turn to do with representing The place of n element fault of components upstream By the method for attachment foundation of immediate transition With or and voting three kinds of forms be divided into three kinds of situations；

Step 5, using Monte Carlo simulation method solving system reliability：

Described solution procedure is as follows：

Setting simulation times Sim_N, Sim_N is set greater than 0 any value；

The variable Sim_n of record emulation course is set up, and initializes Sim_n=1；The Sim_n is the emulation time being carrying out Number, works as Sim_n>During Sim_N, terminate the emulation to set up system reliability model；

Set up array SYS of thrashing time in record simulation process；Element number in array SYS is imitative with setting True number of times Sim_N is equal, and the time that system in the 1st, 2 ... Sim_N simulation processes occurs failure is recorded successively；

Initialization system state；Described system initial state is referred in system initial time, and Num element is located in system In normal condition；In the system reliability model that the present invention is set up, the implementation of initialization system state：Set up and represent The variable T of system time_sys=0, and be P in numbering_i.up it is sequentially placed a Tokken in each place, i spans are 1≤ i≤Num；

By the time delay of all ignitable time delay transition in desampling method successively acquisition system；Whether the time delay transition Ignitable determination methods are described to obtain i-th time delay transition t by desampling method referring to step 1_iX time delay_iMeter Calculation method is as follows：

I) produce and obey [0,1] equally distributed random number U～U (0,1)；

Ii) X is made_i=-InU/ λ_i, λ_iT is changed for time delay_iParameter；

The operation of the system in the Sim_n time simulation process is promoted by the way that time delay transition are carried out with ignition operation, step is as follows：

First, X time delay to obtaining_iSequence, takes the corresponding time delay transition of minimum time, uses symbol T_minAnd t ' is represented respectively Minimum time and its corresponding time delay transition；Secondly, ignition operation is carried out to time delay transition t '：Update system time T_sys=T_sys +T_min, the Tokken for changing the preposition concentrations of t ' is moved in the post set of transition t '；

The operation of the system in the Sim_n time simulation process is promoted by carrying out ignition operation to immediate transition, step is as follows：

First, ignitable immediate transition in system is determined, the whether ignitable determination methods of the immediate transition are referring to step 1；Secondly, ignition operation is carried out to ignitable immediate transition：Tokken is constant in the preposition place of ignitable immediate transition, A Tokken is placed in each element of ignitable immediate transition post set；

Circulation performs the operation that system in the Sim_n time simulation process is promoted by carrying out ignition operation to immediate transition,

Until meeting any one in following two conditions, the operation can be terminated：

Condition 1：There is no ignitable immediate transition in the system reliability model set up；

Condition 2：Place P_Num+1.down there is Tokken；

According to place P_Num+1.down state, judges whether the Sim_n time emulation terminates；Determination methods are as follows：

If P_Num+1.down there is no Tokken, repeat described by all ignitable time delays in desampling method successively acquisition system The time delay of transition, continue executing with the Sim_n time emulation；

If P_Num+1.down there is Tokken, terminate the Sim_n time and emulate, and make Sim_n=Sim_n+1, make SYS [Sim_n]= T_sys, repeat initialization system state, start the emulation next time to system；

To process 4.～8. add up perform Sim_N time after, statistical system reliability R；System is public in the statistics of the reliability at τ moment Formula is：

$\begin{array}{cc}R\left(\mathrm{\τ}\right)=1-\frac{\underset{Sim\_n=1}{\overset{Sim\_N}{\Σ}}\mathrm{\δ}}{Sim\_N}& \mathrm{\δ}=\left\{\begin{array}{ccc}1& if& SYS\[Sim\_n\]\≤\mathrm{\τ}\\ 0& if& SYS\[Sim\_n\]>\mathrm{\τ}\end{array}\right.\end{array}$

In formula, whether δ Mk systems break down, when δ=1, system jam；When δ=0, there is no event in system Barrier.

2. aircraft Flying by wire systems reliability analysis method as claimed in claim 1, it is characterised in that the aircraft fax control There is multiple rate gyroscopes, flight control computer, servo actuator, driving cabin instruction sensor, rudder face displacement sensing in system processed Device and rudder face；Each rate gyroscope, driving cabin instruction sensor and rudder face displacement transducer provide respectively rate information, drive , to flight control computer, flight control computer has been calculated according to the information for receiving for the person's of sailing operation instruction information and rudder face positional information The control signal of effect, then control signal is delivered separately to into each servo actuator, finally rudder is driven by each servo actuator jointly Face deflects, so as to control the motion of aircraft.

3. aircraft Flying by wire systems reliability analysis method as claimed in claim 1, it is characterised in that described to build for each element The vertical normal place of expression state is P_i.up；The place of the expression status fault set up for each element is P_i.down。

4. aircraft Flying by wire systems reliability analysis method as claimed in claim 1, it is characterised in that described transition igniting Rule includes：

Time delay changes firing rule：When the preposition collection of time delay transition has Tokken, transition can light a fire；One ignitable time delay becomes The ignition process moved is：After a time delay, the Tokken of the preposition concentration of time delay transition is moved out to into post set, it is described Time delay obey exponential, the parameter of exponential is equal to the parameter of time delay transition；

Immediate transition firing rule：When the preposition collection of immediate transition has Tokken and the rearmounted element that is concentrated with does not have Tokken When, transition can light a fire；The ignition process of one ignitable immediate transition is：The preposition concentration Tokken distribution of transition does not become Change, a Tokken is placed in each element without Tokken in ignitable immediate transition post set.

5. aircraft Flying by wire systems reliability analysis method as claimed in claim 1, it is characterised in that described function logic When the equal function of n input element of relation "AND" refers to that and if only if i-th element is normal, the function of i-th element can It is normal to perform；Described function logic relation "or" refers to have any one element in n input element for work as i-th element Function executing is normal, then the function of i-th element can be performed normally；Described function logic relation " k/n votings " is referred to When there is at least k element function executing normal in n input element of i-th element, then the function of i-th element can be normal Perform.

6. aircraft Flying by wire systems reliability analysis method as claimed in claim 5, it is characterised in that it is described with or and table The certainly connected mode of three kinds of function logics, place P_iAnd place .downBy instantaneous The method of attachment of transition is as follows respectively：

When i-th element be with the function logic relation of n element of the components upstream and when, then foundation and placeOne-to-one n immediate transition, draws n bar directed line segments：By n placeIt is respectively directed to the n immediate transition set up；Continue to draw n bar directed line segments：By institute N immediate transition for stating foundation is respectively directed to place P_i.down；

When i-th element be with the function logic relation of n element of the components upstream or when, then set up an immediate transition, Draw n bar directed line segments：By placeIt is respectively directed to the immediate transition set up；Continue Draw directed line segment：Place P is pointed to by the immediate transition of the foundation_i.down；

When i-th element is " k/n votings " with the function logic relation of n input element of the components upstream, then set upIndividual immediate transition, wherein 1≤k≤n；For the place of n input element From In take n-k+1 place and be combined, number of combinations isForPlant each combination in combination and make following operation respectively：

I sets up an immediate transition；Ii to combination in each place, one is drawn respectively immediate transition in i is pointed to by place Directed line segment；Iii draws one and points to place P by immediate transition in i_i.down directed line segment.