CN104850750B - A kind of nuclear power plant reactor protects systems reliability analysis method - Google Patents
A kind of nuclear power plant reactor protects systems reliability analysis method Download PDFInfo
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Abstract
The present invention provides a kind of nuclear power plant reactor protection systems reliability analysis method, including protects the structure and functional cohesion of system to determine its fault tree models according to nuclear power plant reactor；Solve the minimal cut set for triggering top event；Obtain the historical failure data that nuclear power plant reactor protects system；Calculate nuclear power plant reactor protection system lifetim statistic；The entropy model that nuclear power plant reactor protects lifetime of system distribution probability density function is set up, the life-span distribution probability density function of nuclear power plant reactor protection system optimal, failure probability, the nuclear power plant reactor of nuclear power plant reactor protection system is solved and protects system dependability, the dynamic crash rate of nuclear power plant reactor protection system.The present invention life-span distribution overall to system according to a small amount of reliability test data is made prediction with dynamic crash rate; it is consistent with the Monte Carlo simulation result based on large sample, is that nuclear power plant reactor protection lifetime of system prediction in the case of small failure probability and dynamic crash rate are assessed and provide technical method.
Description
Technical field
The invention belongs to systems reliability analysis and design field, and in particular to a kind of nuclear power plant reactor protection system
System analysis method for reliability.
Background technology
System reliability represents ability of the system with completion predetermined function in the defined time under the conditions of defined.From whole
The visual angle of individual Life cycle sees that can system, which can complete expectation function, multiple measurement indexs：For repairable system and setting
Standby, measurement index includes reliability, MTBF (Mean Time Between Failure, MTBF), averagely repaiied
Multiple time (Mean Time To Repair, MTTR), availability, useful life etc.；For not repairable system or product, including
The technical indicators such as reliability, Q-percentile life, fault rate, average life span (Mean Time To Failure, MTTF).
Product design is needed after terminating by strict Material Physics experiment and the work of stress screening, production and manufacturing process
Skill is controlled, and the link such as strict quality testing, and the reliability that at this moment product has is referred to as " inherent reliability ".Reliably
Property experiment be product development unit and using unit understand product reliability, obtain reliability data Basic Ways.Due to production
Product life test has destructiveness, and design and producing unit typically leads to too small amount of test data prediction product overall life-span can
By property level and all kinds of reliability indexs, this needs a kind of foundation System in Small Sample Situation can be to system reliability level and dynamic crash rate
Make correctly estimated high precision technology method.
The failure event of nuclear power plant reactor protection system has serious influence consequence, influence time length, coverage big
Etc. excessive risk the characteristics of, so each workpiece of system and reliability of structure standard require very high, failure probability typically exists
The level of 100000 times one chances or million times one chances.Using convectional reliability method of estimation, every million times reliable is needed in theory
Property experiment could obtain a fail data sample, necessarily lead to the cost consumptions such as huge human and material resources and financial resources.If energy
It is enough to provide a kind of based on hundreds of times or thousand System in Small Sample Situation reliability tests, result in 10-5~10-6Level-systems failure probability
Accurate estimation technique method, undoubtedly there is important engineering to anticipate the evaluation problem for solving the small failure probability of complex electromechanical systems
Justice.
The content of the invention
The problem of existing for prior art, the present invention provides a kind of nuclear power plant reactor protection systems reliability analysis side
Method.
The technical scheme is that：
A kind of nuclear power plant reactor protects systems reliability analysis method, comprises the following steps：
Step 1, according to nuclear power plant reactor protect system structure and functional cohesion determine its fault tree models；
Step 2, solved with descending method and trigger top event to be the minimal cut set that nuclear power station emergency shut-down failure occurs, i.e. bottom thing
The combination for then causing top event to occur occurs simultaneously for part；
Step 3, obtain nuclear power plant reactor protection system historical failure data be each bottom event break down when
Between statistics sample；
Step 4, pass through minimal cut set calculate nuclear power plant reactor protect system lifetim statistic, i.e. nuclear power plant reactor
The time run during protection system jam；
Step 5, the entropy model for setting up nuclear power plant reactor protection lifetime of system distribution probability density function, solve core
The optimal life-span distribution probability density function of power station reactor protection system；
Step 6, utilize nuclear power plant reactor protection lifetime of system distribution probability density function to solve nuclear power plant reactor to protect
The probability that the failure probability of protecting system, i.e. nuclear power plant reactor protection system break down before t；
Step 7, utilize nuclear power plant reactor protection lifetime of system distribution probability density function to solve nuclear power plant reactor to protect
Protecting system reliability, i.e. nuclear power plant reactor protect system still probability of normal work after time t；
Step 8, utilize nuclear power plant reactor protection lifetime of system distribution probability density function to solve nuclear power plant reactor to protect
Protecting system dynamic crash rate, i.e., nuclear power plant reactor protection system work to moment t when not yet fail, the list after moment t
The probability failed in the time of position.
The step 1 comprises the following steps：
Step 1.1, the secondary event for determining top event and causing top event to occur；
Top event fails for nuclear power station emergency shut-down；
Cause top event secondary event include the failure of voltage-stablizer pressure low signal, shutdown breaker refuse out, at least three beams
Control rod is blocked；
Any secondary event occurs to cause top event；
Step 1.2, the three-level event for determining to cause in fault tree secondary event to occur；
The event for causing voltage-stablizer pressure low signal failure event to occur include the failure of voltage-stablizer pressure sensor, three it is steady
Depressor pressure sensor threshold value relay definite value mistake；
The event for causing shutdown breaker to refuse out event generation is two shutdown breaker common cause failures；
At least three beams control rod, which blocks event and is considered as bottom event, causes what nuclear power station emergency shut-down failed can not divide again
Event；
Step 1.3, determination cause the Possible event i.e. level Four event that three-level event occurs；
The event for causing voltage-stablizer pressure sensor to fail includes related voltage-stablizer pressure sensor failure；It is wherein any
Two events occur then cause the generation of voltage-stablizer pressure sensor failure event simultaneously；
Three voltage-stablizer pressure sensor threshold value relay definite value mistakes, two shutdown breaker common cause failures are bottom thing
Part；
Step 1.4, determination cause the Possible event i.e. Pyatyi event that level Four event occurs；
Step 1.5, determination cause the Possible event i.e. six grade event that Pyatyi event occurs, until the event can not be further divided into
Only, it is that all Possible event searches that nuclear power station emergency shut-down failure event occurs are finished to trigger top event, obtains bottom event.
Nuclear power plant reactor protection lifetime of system distribution probability density function is set up as follows described in step 5：
Step 5.1, introducing Maximum entropy estimation method, set up the entropy model that nuclear power plant reactor protects system；
Step 5.2, the constraints for determining nuclear power plant reactor protection system information entropy optimization model, including nuclear power station are anti-
Heap is answered to protect the foundation of the fraction square of lifetime of system statistic, nuclear power plant reactor protection lifetime of system distribution probability density function
The integrated value of estimation is 1；
Step 5.3, introducing Lagrange's equation solve nuclear power plant reactor protection system maximum entropy constrained optimization problem, make
Lagrange's equation seeks partial derivative to nuclear power plant reactor protection lifetime of system distribution probability density estimation amount, makes its value be equal to 0,
Obtain the analytic expression estimation of nuclear power plant reactor protection lifetime of system distribution probability density function；
Step 5.4, introducing K-L distance methods, set up and solve nuclear power plant reactor protection lifetime of system distribution probability density
The unconstrained optimization model of function parameter；
Step 5.5, utilize historical failure data solve nuclear power plant reactor protection lifetime of system distribution probability density function
Lagrange multiplier λ and fraction square index α；
Step 5.6, the nuclear power plant reactor for substituting into Lagrange multiplier λ and fraction square index α in step 5-3 are protected and are
The analytic expression estimation of the probability density function of system, obtains nuclear power plant reactor protection lifetime of system distribution probability density function.
Beneficial effect：
The present invention breaches dependence of the conventional method to a large amount of observation samples, according to a small amount of reliability test data to system
Overall life-span distribution is made prediction with dynamic crash rate, result of calculation and the Monte Carlo simulation result phase based on large sample
Symbol, is that nuclear power plant reactor protection system lifetim prediction in the case of small failure probability and dynamic crash rate are assessed and provide technical side
Method.
Brief description of the drawings
Fig. 1 is the nuclear power plant reactor protection systems reliability analysis method flow diagram of the specific embodiment of the invention；
Fig. 2 is the nuclear power plant reactor protection system failure tree-model of the specific embodiment of the invention；
Fig. 3 is the fault tree models after the simplification of the specific embodiment of the invention；
Fig. 4 is that the nuclear power plant reactor protection lifetime of system distribution probability density function of the specific embodiment of the invention is set up
Flow chart；
Fig. 5 is the nuclear power plant reactor protection lifetime of system distribution probability density function of the specific embodiment of the invention；
Fig. 6 is the nuclear power plant reactor protection System failure probability prediction curve of the specific embodiment of the invention；
Fig. 7 is the nuclear power plant reactor protection system dependability prediction curve of the specific embodiment of the invention；
Fig. 8 is the dynamic crash rate prediction curve of nuclear power plant reactor protection system of the specific embodiment of the invention.
Embodiment
The embodiment to the present invention elaborates below in conjunction with the accompanying drawings.
By taking the fail-safe analysis that certain nuclear power plant reactor protects system as an example, the implementation of the inventive method is described in detail
Journey, nuclear power plant reactor protection systems reliability analysis method, as shown in figure 1, comprising the following steps：
Step 1, according to nuclear power plant reactor protect system structure and functional cohesion determine its fault tree models；
Step 1.1, the secondary event for determining top event and causing top event to occur；
Top event is nuclear power station emergency shut-down failure (RCPS000)；
Cause the secondary event of top event to include voltage-stablizer pressure low signal failure (RCPS001), shutdown breaker to refuse out
(RCPS002), at least three beams control rod is blocked (RCPS003)；
Any secondary event occurs to cause top event (RCPS000) to occur；
Step 1.2, the three-level event for determining to cause in fault tree secondary event to occur；
The event that voltage-stablizer pressure low signal failure event (RCPS001) occurs is caused to be lost including voltage-stablizer pressure sensor
Imitate (RCPS004), three voltage-stablizer pressure sensor threshold value relay definite value mistakes (PCF005-013)；
It is two shutdown breaker common cause failures to cause the event that the shutdown breaker event of refusing out (RCPS002) occurs
(RPA300JA-RO)；
At least three beams control rod block event (RCPS003) be considered as bottom event cause nuclear power station emergency shut-down failure not
The event that can divide again；
Step 1.3, determination cause the Possible event i.e. level Four event that three-level event occurs；
Cause the event of voltage-stablizer pressure sensor failure (RCPS004) to include related voltage-stablizer pressure sensor to lose
Effect, specifically voltage-stablizer pressure sensor RCP005MP failures (RCPS005), voltage-stablizer pressure sensor RCP006MP failures
(RCPS006) and voltage-stablizer pressure sensor RCP007MP failure (RCPS007)；Any two of which event occurs then simultaneously
Cause the generation of voltage-stablizer pressure sensor failure (RCPS004) event；
Three voltage-stablizer pressure sensor threshold value relay definite value mistakes (PCF005-013), two shutdown breakers altogether because
Failure (RPA300JA-RO) is bottom event；
Step 1.4, determination cause the Possible event i.e. Pyatyi event that level Four event occurs；
The event for causing voltage-stablizer pressure sensor RCP005MP failure (RCPS005) events to occur has voltage-stablizer pressure biography
Sensor RCP005MP demand expirations (RCPS005-MP), voltage-stablizer pressure sensor RCP005MP threshold value relay failures
(RCPS005-RC), wherein any one occurrence occurs cause voltage-stablizer pressure sensor RCP005MP failure (RCPS005) things
Part occurs.
The event for causing voltage-stablizer pressure sensor RCP006MP failure (RCPS006) events to occur has voltage-stablizer pressure biography
Sensor RCP006MP demand expirations (RCPS006-MP) and voltage-stablizer pressure sensor RCP006MP threshold value relay failures
(RCPS006-RC), wherein any one occurrence occurs cause voltage-stablizer pressure sensor RCP006MP failure (RCPS006) things
Part occurs.
The event for causing voltage-stablizer pressure sensor RCP007MP failure (RCPS007) events to occur has voltage-stablizer pressure biography
Sensor RCP007MP demand expirations (RCPS007-MP) and voltage-stablizer pressure sensor RCP007MP threshold value relay failures
(RCPS007-RC), wherein any one occurrence occurs cause voltage-stablizer pressure sensor RCP007MP failure (RCPS007) things
Part occurs.
Step 1.5, determination cause the Possible event i.e. six grade event that Pyatyi event occurs, until the event can not be further divided into
Only, it is that all Possible event searches that nuclear power station emergency shut-down failure event occurs are finished to trigger top event, obtains bottom event.
Voltage-stablizer pressure sensor RCP005MP demand expirations (RCPS005-MP), voltage-stablizer pressure sensor RCP005MP
Threshold value relay failure (RCPS005-RC), voltage-stablizer pressure sensor RCP006MP demand expirations (RCPS006-MP), voltage stabilizing
Device pressure sensor RCP006MP threshold values relay failure (RCPS006-RC), voltage-stablizer pressure sensor RCP007MP demands are lost
It is bottom event to imitate (RCPS007-MP) and voltage-stablizer pressure sensor RCP007MP threshold values relay failure (RCPS007-RC).
So far it is all Possible event searches that nuclear power station emergency shut-down failure (RCPS000) event occurs to trigger top event
Finish.The fault tree models of the system can be set up according to its set membership, as shown in Figure 2.
Step 2, with descending method solve trigger top event be nuclear power station emergency shut-down failure (RCPS000) occur minimal cut
The combination for then causing top event to occur occurs simultaneously for collection, i.e. bottom event；
To simplify calculating, event nuclear power station emergency shut-down failure (RCPS000) is represented with T, the low letter of event voltage-stablizer pressure
Number failure (RCPS001) represent that event shutdown breaker is refused out (RCPS002) and represented with G2 with G1, event at least three beams control
Rod blocks (RCPS003) and represented with A, and event voltage-stablizer pressure sensor failure (RCPS004) is represented with G3, three voltage stabilizings of event
Device pressure sensor threshold value relay definite value mistake (PCF005-013) represents with B, two event shutdown purpose of breaker failure
(RPA300JA-RO) represented respectively with C and D, G4 tables are used in event voltage-stablizer pressure sensor RCP005MP failures (RCPS005)
Show, event voltage-stablizer pressure sensor RCP006MP failures (RCPS006) are represented with G5, event voltage-stablizer pressure sensor
RCP007MP failure (RCPS007) represented with G6, event voltage-stablizer pressure sensor RCP005MP demand expirations (RCPS005-
MP) represented with E, event voltage-stablizer pressure sensor RCP005MP threshold values relay failure (RCPS005-RC) is represented with F, event
Voltage-stablizer pressure sensor RCP006MP demand expirations (RCPS006-MP) are represented with G, event voltage-stablizer pressure sensor
RCP006MP threshold values relay failure (RCPS006-RC) is represented with H, event voltage-stablizer pressure sensor RCP007MP demands are lost
Imitate (RCPS007-MP) to be represented with I, event voltage-stablizer pressure sensor RCP007MP threshold values relay failure (RCPS007-RC)
Represented with J, the fault tree models after simplifying are as shown in Figure 3.
The process for solving the minimal cut set of fault tree is as follows：
The first step：Door below top event T is OR gate (any one event occurs, and top event is to occur), therefore by the defeated of it
Enter G1, G2, A (displacement T) arranged in columns；
Second step：Elementary event A is no longer decomposed, under G1 events be OR gate, be inputted G3, B form a line displacement G1；G2
Under event be with door (all events all occur, and top event just occurs), be inputted C, D and be in line, displacement G2；
3rd step：Elementary event B, C, D are no longer decomposed, and (have two or two in subevent under G3 events for 2/3 voting door
More than occur, top event occurs), be inputted after G4, G5, G6 combination of two embarks on journey, line up column permutation G3；
4th step：Under G4 events be OR gate, be inputted E, F form a line displacement G4,；It is OR gate under G5 events, by it
Input G, H, which form a line, replaces G5；Under G6 events be OR gate, be inputted I, J form a line displacement G6；
5th step：Obtain 15 cut sets that a row are all represented by elementary event：{ A }, { CD }, { B }, { EG }, { EH },
{ FG }, { FH }, { EI }, { EJ }, { FI }, { FJ }, { GI }, { GJ }, { HI }, { HJ } is shown in Table 1.
The nuclear power plant reactor of table 1 protects fault Tree descending development
To sum up, the minimum bottom event combination for causing nuclear power station emergency shut-down to fail (RCPS000) generation can be obtained.
Step 3, obtain nuclear power plant reactor protection system historical failure data be each bottom event (A, B, C, D, E, F,
G, H, I, J) the time statistics sample that breaks down：
Wherein, the time normally run when t represents to break down, subscript represents different samples, and N is sample number
Amount, subscript represents different events.
Step 4, pass through minimal cut set calculate nuclear power plant reactor protect system lifetim statistic, i.e. nuclear power plant reactor
The time run during protection system jam
I-th of time statistics sampleFor the working time minimum in minimal cut set, contain two or more
The working time of bottom event element is the maximum of which working time.It is specifically：From i-th of time statistics sample,
Find out the time that at least three beams control rod blocks (RCPS003) i.e. event A generations, three voltage-stablizer pressure sensor threshold value relays
Device definite value mistake (PCF005-013) is the time that event B occurs, and shutdown purpose of breaker failure (RPA300JA-RO) is event C and D
The greater of the time of generation, voltage-stablizer pressure sensor RCP005MP demand expirations (RCPS005-MP) and voltage-stablizer pressure are passed
Sensor RCP006MP demand expirations (RCPS006-MP) are the greater of event E and event G time of origins, voltage-stablizer pressure sensing
Device RCP005MP demand expirations (RCPS005-MP) and voltage-stablizer pressure sensor RCP006MP threshold value relay failures
(RCPS006-RC) be event E and H time of origin the greater, voltage-stablizer pressure sensor RCP005MP threshold value relay failures
And voltage-stablizer pressure sensor RCP006MP demand expirations (RCPS006-MP) are time F and G time of origin (RCPS005-RC)
The greater, voltage-stablizer pressure sensor RCP005MP threshold values relay failure (RCPS005-RC) and voltage-stablizer pressure sensor
RCP006MP threshold values relay failure (RCPS006-RC) is the greater of event F and H time of origin, voltage-stablizer pressure sensor
RCP005MP demand expirations (RCPS005-MP) and voltage-stablizer pressure sensor RCP007MP demand expirations (RCPS007-MP) are
The greater of event E and I time of origin, voltage-stablizer pressure sensor RCP005MP demand expirations (RCPS005-MP) and voltage-stablizer
Pressure sensor RCP007MP threshold values relay failure (RCPS007-RC) is the greater of event E and J time of origin, voltage-stablizer
Pressure sensor RCP005MP threshold values relay failure (RCPS005-RC) and voltage-stablizer pressure sensor RCP007MP demands are lost
Effect (RCPS007-MP) is the greater of event F and I time of origin, and voltage-stablizer pressure sensor RCP005MP threshold values relay loses
It is event F and J to imitate (RCPS005-RC) and voltage-stablizer pressure sensor RCP007MP threshold values relay failure (RCPS007-RC)
The greater of time of origin, voltage-stablizer pressure sensor RCP006MP demand expirations (RCPS006-MP) and voltage-stablizer pressure sensing
Device RCP007MP demand expirations (RCPS007-MP) are the greater of event G and I time of origin, voltage-stablizer pressure sensor
RCP006MP demand expirations (RCPS006-MP) and voltage-stablizer pressure sensor RCP007MP threshold value relay failures (RCPS007-
RC) be event G and J time of origin the greater, voltage-stablizer pressure sensor RCP006MP threshold value relay failures (RCPS006-
RC) and voltage-stablizer pressure sensor RCP007MP demand expirations (RCPS007-MP) are the greater of event H and I time of origin,
Voltage-stablizer pressure sensor RCP006MP threshold values relay failure (RCPS006-RC) and voltage-stablizer pressure sensor RCP007MP
Threshold value relay failure (RCPS007-RC) is the greater of event H and J time of origin, and the time of minimum is taken from the above time
The working time of as i-th time statistics sample.
It can specifically be calculated by following formula：
Thus system lifetim statistic can be drawn successively
Step 5, the entropy model for setting up nuclear power plant reactor protection lifetime of system distribution probability density function, solve core
The optimal life-span distribution probability density function of power station reactor protection system；
As shown in figure 4, nuclear power plant reactor protection lifetime of system distribution probability density function is set up as follows：
Step 5.1, introducing Maximum entropy estimation method, set up the entropy model that nuclear power plant reactor protects system；
In order to determine fraction square index α and Lagrange multiplier λ in life-span distribution, then need to introduce Maximum entropy estimation side
Method.
Known life-span distribution probability density function fT(t), its entropy model is defined as：
H [f]=- ∫TfT(t)log[fT(t)]dt
Step 5.2, the constraints for determining nuclear power plant reactor protection system information entropy optimization model, including nuclear power station are anti-
Heap is answered to protect the foundation of the fraction square of lifetime of system statistic, nuclear power plant reactor protection lifetime of system distribution probability density function
The integrated value of estimation is 1；
Stochastic variable T is part (or system) life-span stochastic variable, and its α rank fraction square is defined as：
Wherein α is any real number.
It should be noted that：The sufficient and necessary condition that life-span stochastic variable fraction square is present is fraction square integrationConvergence, it is equivalent to the presence of k rank integer squares, and and if only if | α | during≤kIn the presence of.
For mathematic(al) expectation distribution probability density function fT (t) estimatorThen need to apply maximum entropy theory.Pass through
Each rank fraction square of life-span statistic is introduced, the constraints of comentropy Optimized model is：
WithWherein m is fraction square number of times, is verified through multiple practical application, takes three rank fraction squares to constrain (i.e. m=3) i.e.
It can reach acquisition and be satisfied with computational accuracy；α j are the fraction square index of correspondence order；Lifetime of system is protected for nuclear power plant reactor
That is the fraction moments estimation of failure, MTTF,N is the time statistics sample size of system.This
When, it is only necessary to make information entropy estimateMaximization.
Its comentropy Optimized model can be expressed as：
Step 5.3, introducing Lagrange's equation solve nuclear power plant reactor protection system maximum entropy constrained optimization problem, make
Lagrange's equation seeks partial derivative to nuclear power plant reactor protection lifetime of system distribution probability density estimation amount, makes its value be equal to 0,
Obtain the analytic expression estimation of nuclear power plant reactor protection lifetime of system distribution probability density function；
Introduce Lagrange's equation and solve the maximum entropy constrained optimization problem：
Wherein λ=[λ0,λ1,…,λm]TFor Lagrange multiplier, α=[α0,α1,…,αm]TFor fraction square index.
To obtain Maximum entropy estimation, Lagrange's equation need to be only made to ask Multilayer networks amount partial derivative to make it be equal to 0
.I.e.：Order
Obtain the fraction square information entropy estimate expression formula of unknown life-span probability density function：
ConsiderTry to achieve Lagrange multiplier λ0Expression formula be：
In order to simplify comentropy Optimized model, the Lagrange that K-L distances solve life-span distribution probability density function is introduced
Multiplier λ and fraction square index α.
Step 5.4, introducing K-L distance methods, set up and solve nuclear power plant reactor protection lifetime of system distribution probability density
The unconstrained optimization model of function parameter；
K-L distance definitions are the difference between true entropy and estimation entropy, and its is smaller to show estimation entropy closer to true entropy, just
It is more accurate.Its formula is：
When the expression formula of Given Life distribution probability estimation of density function amountK-L distances can be further represented as：
Because the theoretical value that H [f] is the comentropy being distributed in the life-span is usually real constant.Therefore the changing unit of K-L distances
It can be expressed as：
So far, the unconstrained optimization model for solving life-span distribution probability density function parameter can be set up：
Above-mentioned unconstrained optimization solution to model can be using quasi-Newton method, simplex method etc. without constrained nonlinear systems problem
Solve.Obtain optimal Lagrange multiplier λ=[λ0,λ1,…,λm]TWith optimal fraction square index α=[α0,α1,…,αm]T.Using
Fminsearch functions in MATLAB tool boxes are solved, and its advantage is using simplex method without calculating mesh
The gradient information of scalar functions, programming and numerical solution are convenient.
Step 5.5, utilize historical failure data solve nuclear power plant reactor protection lifetime of system distribution probability density function
Lagrange multiplier λ and fraction square index α；
Step 5.6, by Lagrange multiplier λ=[λ0,λ1,…,λm]TWith fraction square index α=[α0,α1,…,αm]TSubstitute into
The analytic expression estimation of the probability density function of nuclear power plant reactor protection system in step 5-3, obtains nuclear power plant reactor guarantor
Protecting system life-span distribution probability density function, as shown in Figure 5.
Wherein,
Step 6, utilize nuclear power plant reactor protection lifetime of system distribution probability density function to solve nuclear power plant reactor to protect
Probability (the nuclear power plant reactor that the failure probability of protecting system, i.e. nuclear power plant reactor protection system break down before t
Lifetime of system distribution probability density function is protected in integrated value of the time 0 to t to t), as shown in Figure 6.
I.e.：
Step 7, utilize nuclear power plant reactor protection lifetime of system distribution probability density function to solve nuclear power plant reactor to protect
Protecting system reliability, i.e. nuclear power plant reactor protect system still probability of normal work after time t, as shown in Figure 7.Can
By spending the failure probability complementation with system.
I.e.：
Step 8, utilize nuclear power plant reactor protection lifetime of system distribution probability density function to solve nuclear power plant reactor to protect
Protecting system dynamic crash rate, i.e., nuclear power plant reactor protection system work to moment t when not yet fail, the list after moment t
The probability failed in the time of position, as shown in Figure 8.
I.e.：
It is pointed out that MCS represents 10 in Fig. 5, Fig. 6, Fig. 7, Fig. 86Secondary Monte Carlo numerical value sampling results, ME-FM
For based on 103The fraction square maximum entropy optimum results of individual sample.It can be seen that the application present invention's is maximum based on fraction square
The analysis method for reliability of entropy optimization, only with 103Lifetime of system probability distribution, reliability obtained by individual lifetime data sample is with moving
State crash rate computational accuracy i.e. and 106Secondary Monte Carlo random effect precision is identical, embodies the inventive method and is based on small data
Advantage and use value in terms of the distribution of sample reconfiguration system life-span and dynamic crash rate calculating.
Claims (2)
1. a kind of nuclear power plant reactor protects systems reliability analysis method, it is characterised in that comprise the following steps：
Step 1, according to nuclear power plant reactor protect system structure and functional cohesion determine its fault tree models；
Step 2, solved with descending method and trigger top event to be the minimal cut set that nuclear power station emergency shut-down failure occurs, be i.e. bottom event is same
Shi Fasheng then causes the combination that top event occurs；
Step 3, the historical failure data of acquisition nuclear power plant reactor protection system are the time system that each bottom event breaks down
Count sample；
Step 4, pass through minimal cut set calculate nuclear power plant reactor protect system lifetim statistic, i.e., nuclear power plant reactor protect
The time run during system jam；
Step 5, the entropy model for setting up nuclear power plant reactor protection lifetime of system distribution probability density function, set up nuclear power station
The optimal life-span distribution probability density function of reactor protection system；
The nuclear power plant reactor protection lifetime of system distribution probability density function is set up as follows：
Step 5.1, introducing Maximum entropy estimation method, set up the entropy model that nuclear power plant reactor protects system；
Known life-span distribution probability density function fT(t), its entropy model H [f] is defined as：
H [f]=- ∫TfT(t)log[fT(t)]dt
Step 5.2, the constraints for determining nuclear power plant reactor protection system information entropy optimization model, including nuclear power plant reactor
Protect foundation, the nuclear power plant reactor protection lifetime of system distribution probability estimation of density function of the fraction square of lifetime of system statistic
Integrated value be 1；
Step 5.3, introducing Lagrange's equation solve nuclear power plant reactor protection system maximum entropy constrained optimization problem, make glug
Bright day equation seeks partial derivative to nuclear power plant reactor protection lifetime of system distribution probability density estimation amount, makes its value be equal to 0, obtains
The analytic expression estimation of nuclear power plant reactor protection lifetime of system distribution probability density function；
Step 5.4, introducing K-L distance methods, set up and solve nuclear power plant reactor protection lifetime of system distribution probability density function
The unconstrained optimization model of parameter；
Step 5.5, the drawing using historical failure data solution nuclear power plant reactor protection lifetime of system distribution probability density function
Ge Lang multipliers λ and fraction square index α；
Step 5.6, the nuclear power plant reactor for substituting into Lagrange multiplier λ and fraction square index α in step 5-3 protect system
The analytic expression estimation of probability density function, obtains nuclear power plant reactor protection lifetime of system distribution probability density function；
Step 6, nuclear power plant reactor protection lifetime of system distribution probability density function is utilized to solve nuclear power plant reactor protection system
The probability that the failure probability of system, i.e. nuclear power plant reactor protection system break down before t；
Step 7, nuclear power plant reactor protection lifetime of system distribution probability density function is utilized to solve nuclear power plant reactor protection system
Unite reliability, i.e. nuclear power plant reactor protects system still probability of normal work after time t；
Step 8, nuclear power plant reactor protection lifetime of system distribution probability density function is utilized to solve nuclear power plant reactor protection system
Not yet failed, in the unit after moment t when the dynamic crash rate of system, the i.e. work of nuclear power plant reactor protection system are to moment t
The interior probability failed.
2. nuclear power plant reactor according to claim 1 protects systems reliability analysis method, it is characterised in that the step
Rapid 1 comprises the following steps：
Step 1.1, the secondary event for determining top event and causing top event to occur；
Top event fails for nuclear power station emergency shut-down；
Cause top event secondary event include voltage-stablizer pressure low signal failure, shutdown breaker refuse out, at least three beams control
Rod is blocked；
Any secondary event occurs to cause top event；
Step 1.2, the three-level event for determining to cause in fault tree secondary event to occur；
The event for causing voltage-stablizer pressure low signal failure event to occur includes the failure of voltage-stablizer pressure sensor, three voltage-stablizers
Pressure sensor threshold value relay definite value mistake；
The event for causing shutdown breaker to refuse out event generation is two shutdown breaker common cause failures；
At least three beams control rod block event be considered as bottom event cause nuclear power station emergency shut-down fail the event that can not divide again；
Step 1.3, determination cause the Possible event i.e. level Four event that three-level event occurs；
The event for causing voltage-stablizer pressure sensor to fail includes related voltage-stablizer pressure sensor failure；Any two of which
Event occurs then cause the generation of voltage-stablizer pressure sensor failure event simultaneously；
Three voltage-stablizer pressure sensor threshold value relay definite value mistakes, two shutdown breaker common cause failures are bottom event；
Step 1.4, determination cause the Possible event i.e. Pyatyi event that level Four event occurs；
Step 1.5, determination cause the Possible event i.e. six grade event that Pyatyi event occurs, until the event can not be further divided into only,
It is that all Possible event searches that nuclear power station emergency shut-down failure event occurs are finished to trigger top event, obtains bottom event.
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| CN107301884B (en) * | 2017-07-24 | 2019-07-16 | 哈尔滨工程大学 | A kind of hybrid nuclear power station method for diagnosing faults |
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