CN104408312A - Method for computing maloperation rate of nuclear power station system - Google Patents

Abstract

The invention provides a method for computing the maloperation rate of a nuclear power station system. Based on the MooN architecture of the Markov principle, namely when M components among N components of the nuclear power station are under a normal working condition, the nuclear power station system is capable of working normally, and the state space diagram of the nuclear power station related system and a nuclear power station system failure frequency steady-state expression as shown in the description are established, wherein lambda refers to the maloperation failure rate and mu refers to the repair rate. When a processing and maintenance policy changes, no computational model needs to be re-established and only related parameters are modified to obtain the result after the adjustment of the maintenance policy.

Description

A kind of nuclear power plant system malfunction rate computing method

Technical field

The invention belongs to nuclear power field safe level instrument control technical field, particularly a kind of nuclear power plant system malfunction rate computing method.

Background technology

Malfunction rate, refers at the scene in the normal situation of operating mode, and safe level I&C system performs the frequency (i.e. the parts of safe level I&C system self occur failure conditions and cause system malfunction) of security function because of self random fault by mistake.Once safe level I&C system performs security function, field working conditions is forced to stop, now need to carry out the treatment measures such as a series of investigation, record, recovery, until the reason that security function performs is found out and field working conditions returned to the state that can continue to run, just can restart field working conditions.Therefore, malfunction rate is the important evaluation index that safe level I&C system causes the unexpected stoppage in transit of field working conditions, the accurate response economy of safe level I&C system.

IEEE Std 577 is top layer standards of npp safety level I&C system fail-safe analysis, clearly proposes the requirement of safe level I&C system malfunction rate.But, this standard does not provide the general calculation method of malfunction rate, therefore, at present, the nuclear power instrument control supplier of main flow based on reliability theory, in conjunction with self practical experience, independently be deduced system malfunction rate computing method separately, such as, Mitsubishi application reliability block diagram theory calculate malfunction rate, Westinghouse Electric and AREVA be application and trouble tree theory derivation malfunction rate computing formula then.

General frame due to safe level I&C system is generally MooN type voting system and (that is: gets M voting system in N, as 4 get 2,3 and get 2,2 and get 1 etc., this type systematic is made up of N number of independent identically distributed parts, M or M is only had normally to work with upper-part, system could normally work), belong to repairable system, and maintenance policy is comparatively complicated, for the repairable system of this type of framework, the central principle of no matter malfunction rate algorithm is reliability block diagram or fault tree theory, equal Shortcomings part:

1) for the malfunction rate algorithm based on reliability block diagram,

Reliability block diagram is from the logical diagram between reliability perspectives Study system and parts; it is the avatars of annexation under system unit and reliability meaning thereof; represent that the normal of unit or failure state are on the impact of system state; but the main applicable object due to reliability block diagram is not repairable system; therefore its computation model cannot reflect maintenance policy intuitively; maintenance policy can only be embodied by introducing maintenance parameter in computing formula; which results in computation model and computing formula is not mated, the correctness of model and formula is difficult to be guaranteed.

Its producing cause is: the main applicable object of reliability block diagram is not repairable system, and its computation model cannot reflect maintenance policy intuitively, can only embody maintenance policy by introducing maintenance parameter in computing formula.

2) for the malfunction rate algorithm based on fault tree theory,

Fault tree passes through the various factors of thrashing may be caused (to comprise hardware in system design process, software, environment, human factor) analyze, draw logic diagram (fault tree), thus the various possibility array modes of certainty annuity failure cause or its probability of happening, computing system failure probability, take corresponding corrective action, to improve a kind of Design and analysis methods of system reliability, it is the tree-shaped logic cause-effect relationship figure of a kind of special handstand, it uses event notation, cause-effect relationship in logic gate symbol and transition symbols descriptive system between various event.The incoming event of logic gate be export thing " because of ", the outgoing event of logic gate is incoming event " really ", as can be seen here, although model can reflect maintenance policy intuitively, but a model can only embody a kind of maintenance policy, when needing to compare different maintenance policies, then need to re-establish several different model and just can carry out assessment and compare, the system that this is huge for element number, framework is complicated, will produce workload hugely.

Its producing cause is: although model can reflect maintenance policy intuitively, and a model can only embody a kind of maintenance policy, when needing to compare different maintenance policies, then needs to re-establish several different fault tree models and just can carry out assessment and compare

Summary of the invention

Because nuclear power relevant criterion does not provide general malfunction rate computing method, main flow instrument control supplier derive MooN class framework repairable system malfunction rate computing method and disunity, and the weak point all existed in various degree, therefore, for above-mentioned technology Problems existing, the object of the invention is to introduce a kind of malfunction rate computing method based on Markov Theory, the method can either take into full account the maintenance policy of MooN architecture system, when maintenance policy changes, can greatly improve the efficiency of modeling again again.

The technical solution adopted for the present invention to solve the technical problems is: a kind of nuclear power plant system malfunction rate computing method, comprise the following steps:

S1: set up described nuclear power plant system state space graph according to Markovian process,

Described state space graph comprises: when in the N number of parts belonging to described nuclear power plant system, and have M parts to be in normal operating conditions, described nuclear power plant system can normally work, otherwise described nuclear power plant system is in malfunction; Wherein, M>0, N>M;

S2: according to described nuclear power plant system state space graph, by setting probability matrix and the calculating to described probability matrix, obtains described nuclear power plant system failure-frequency stable state expression formula:

$F=\frac{\mathrm{\μ}}{(M-1)!}\frac{1}{\underset{M}{\overset{N}{\mathrm{\Σ}}}\frac{1}{i!}{\left(\frac{\mathrm{\μ}}{\mathrm{\λ}}\right)}^{i-M+1}}$

Wherein, F is described nuclear power plant system failure-frequency; λ is malfunction crash rate, given by system; μ is repair rate.

Described state space graph also comprises: described nuclear power plant system has N-M+2 different conditions, and described probability matrix is N-M+2 rank square formations:

Wherein, when the parts broken down are greater than 1, parts can only be had to be in service mode, and other trouble units are in state to be repaired; And 0 state to N-M state is described nuclear power plant system normal operating condition, and N-M+1 state belongs to described nuclear power plant system malfunction;

By setting probability matrix and to the computation process of described probability matrix be:

1) according to described N-M+2 rank square formation T, a State Equation Coefficients matrix A is obtained:

Wherein, U is N-M+2 rank unit matrixs;

2) equation of state is obtained according to described State Equation Coefficients matrix A: wherein, P is the column vector of each state, for the column vector of each state probability inverse;

3) by step 2) described equation of state launch to obtain:

4) by described step 3) in equation launch, and carry out pull-type conversion and obtain the stable state of nuclear power plant system failure-frequency described in described step S2 expression formula;

Preferably, described repair rate μ=1/MTTR, wherein MTTR is average time for repair of breakdowns, given by system.

A kind of nuclear power plant system of the present invention is the Reactor trip subsystem RTS of nuclear power station;

The state space graph of described Reactor trip subsystem RTS comprises: when in 4 the identical escape ways belonging to described Reactor trip subsystem RTS, 2 escape ways are had at least to be in normal operating conditions, then described Reactor trip subsystem RTS normally works, otherwise described Reactor trip subsystem RTS is in malfunction;

Preferably, the malfunction of described Reactor trip subsystem RTS is malfunction state;

Preferably, when having at least the Output rusults of 2 escape ways then to perform Reactor trip function for " triggering ", otherwise then non-toggle state is maintained.

The escape way of described Reactor trip subsystem RTS comprises: analog input AI module, Main Processor Unit MPU module and digital output DO module;

Malfunction crash rate (passage)=malfunction crash rate (AI)+malfunction crash rate (the MPU)+malfunction crash rate (DO) of described Reactor trip subsystem RTS;

Preferably, described malfunction crash rate (AI)=4.37E-5;

Described malfunction crash rate (MPU)=1.22E-4;

Described malfunction crash rate (DO)=3.13E-5;

Described malfunction crash rate (passage)=2.07E-4;

Preferably, the average time for repair of breakdowns MTTR=72 hour of described Reactor trip subsystem RTS; Repair rate μ=the 0.014h of described Reactor trip subsystem RTS.

According to nuclear power plant system failure-frequency stable state expression formula in described step S2: by M=2, N=4; λ=2.07E-4; μ=0.014 brings the failure-frequency stable state expression formula obtaining described Reactor trip subsystem RTS into: F=1.02E-6 (h ^-1); Wherein, h ^-1for unit, represent the probability of described generation malfunction per hour.

The state of described Reactor trip subsystem RTS comprises:

State 0: all escape ways normally run;

State 1:1 escape way is in service mode, and all the other escape ways normally run;

State 2:1 escape way is in service mode, and 1 escape way is to be repaired, remains 2 escape ways and normally runs;

State 3:1 escape way is in service mode, and 2 escape ways are to be repaired, remains 1 escape way and normally runs;

Wherein, when described Reactor trip subsystem RTS be in state 0, state 1 or state 2 any one time, described Reactor trip subsystem RTS normally works; When described Reactor trip subsystem RTS is in state 3, described Reactor trip subsystem RTS is in malfunction state.

Due to, described nuclear power plant system is under the condition that the state residing for the t_0 moment is known, the state that the condition distribution of process moment t > t_0 status is residing before moment t_0 with process has nothing to do, therefore described nuclear power plant system meets described Markovian process, wherein the t_0 moment is state known moment, namely the state before the t_0 moment is known, and t is the arbitrary process moment.

The invention has the beneficial effects as follows, MooN framework based on Markov Theory can keep in repair safe level I&C system malfunction rate computing method, when the vicissitudinous situation of process maintenance policy, without the need to re-establishing computation model, only need to modify to the maintenance parameter in state space graph and state equation, the accurate computation model after maintenance policy adjustment can be obtained.This huge for number of components, baroque repairable system, can save the time of lower a large amount of modeling again.

Accompanying drawing explanation

Be specifically described of the present invention below in conjunction with accompanying drawing.

Fig. 1 is the present invention's 1 parts for maintenance resource MooN framework repairable system state space graph;

Fig. 2 is based on certain nuclear power station Reactor trip subsystem (RTS) framework of FirmSys platform;

The RTS malfunction state space graph of Fig. 3 mono-redundant channel Maintenance Resource.

Embodiment

The present invention is based on Markov Theory, set up the computing method of MooN repairable system malfunction rate, mainly comprise workflow and example of engineering calculation, the following content of the present invention will be described in detail to workflow and application example respectively.

1, workflow

Workflow of the present invention follows general research work flow process, comprises following three steps:

A) applicability proves: the applicability first determining inventive method, judges whether practical application meets the constraint condition of invention;

B) set up state space graph (Markov chain): meeting under prerequisite a), applying markov is theoretical, according to system malfunction inactive logic, sets up system state space figure;

C) derivation system malfunction rate expression formula (solving characteristic quantity): according to state space graph b) obtained, application matrix opinion and theory of probability set up state equation, and then obtain stable state malfunction rate expression formula, known parameters is brought into the malfunction rate getting final product calculation system.

1.1, applicability checking

The present invention is based on Markov Theory, therefore before application computing method of the present invention, should judge whether the failure mechanism of research object meets Markovian process, criterion is for: process (or system) is under the condition that the state residing for the t_0 moment is known, and the state that the condition distribution of process moment t > t_0 status should be residing before moment t_0 with process has nothing to do.If the failure mechanism of research object does not belong to Markovian process, then computing method of the present invention are inapplicable.

1.2, state space graph

For MooN framework repairable system, M parts should be had at least in N number of parts to be in normal operating conditions, otherwise system is in malfunction, if the malfunction crash rate of parts and repair rate are respectively λ and μ (μ=1/MTTR), wherein, malfunction was lost efficacy and was referred to the malfunction caused by the component failure in system or system; MTTR (Mean Time To Repair) is average time for repair of breakdowns;

And Maintenance Resource is limited, when multiple fault occurs multiple parts, parts can only be had to be in service mode, and other trouble units are in state to be repaired, then system has N-M+2 different conditions:

0 state: all parts normally run;

1 state: 1 parts is in service mode, and remaining part normally runs;

2 states: 1 parts is in service mode, 1 parts is to be repaired, and remaining part normally runs;

……；

N-M state: 1 parts is in service mode, N-M-1 parts are to be repaired, and remaining part normally runs;

N-M+1 state: 1 parts is in service mode, N-M parts are to be repaired;

Obviously, 0 state ~ N-M state is system normal operating condition, and N-M+1 state belongs to system fault condition.State space as shown in Figure 1.

1.3, malfunction rate calculates

State space graph according to Fig. 1, the state that can obtain is write in probability matrix T (N-M+2 rank square formation):

Specify a new matrix A, be called State Equation Coefficients matrix, A is defined as:

Wherein, U is N-M+2 rank unit matrixs.

Finally can obtain equation of state:

$\stackrel{\·}{P}=\mathrm{AP}$ (formula 3)

In (formula 3), P is the column vector of each state, for the column vector of each state probability inverse, (formula 3) is launched to obtain:

(formula 4) is carried out, and utilizes pull-type conversion, system failure frequency stable state expression formula can be tried to achieve:

$F=\frac{\mathrm{\μ}}{(M-1)!}\frac{1}{\underset{M}{\overset{N}{\mathrm{\Σ}}}\frac{1}{i!}{\left(\frac{\mathrm{\μ}}{\mathrm{\λ}}\right)}^{i-M+1}}$ (formula 5)

Malfunction crash rate and repair rate are respectively into λ and μ substitutes into (formula 5), system malfunction rate occurrence can be obtained.

2, example of engineering calculation

2.1, example of engineering calculation introduction

The practical engineering application being used as example of the present invention is the Reactor trip subsystem (RTS that nuclear power station is built; Reactor Trip System); its framework is 4 heavy redundancy protecting passages; form 2oo4 voting logic; namely 42 voting frameworks are got; when two or more protection channel sends the instruction of jumping heap; RTS performs shutdown function; namely; have at least 2 redundant channels working properly; Reactor trip subsystem RTS normally works, otherwise described Reactor trip subsystem RTS is in malfunction.

Its functional block diagram as shown in Figure 2, wherein, the heavy redundant channel of RTS configuration 4, each passage is by AI (Analogue Input analog input) module, MPU (Main Processing Unit Main Processor Unit) module and DO (Digital Output digital output) module composition, the wherein analog signals that passes over of AI module acquires spot sensor, MPU module processes it, and DO module converts contact signal to MPU result and exports.The Output rusults of 4 heavy redundant channels is carried out the voting of 2oo4 logic by on-the-spot actuator, if voting result is " triggering ", performs Reactor trip function, otherwise then maintains non-toggle state.

The crash rate information of the modules shown in Fig. 2 is as shown in the table:

Module	Product type	Invalid cost	Malfunction crash rate (unit: 1/h)
				AI	Electrical/electronic/programmable electronic	Exponential distribution	4.37E-5
MPU	Electrical/electronic/programmable electronic	Exponential distribution	1.22E-4
				DO	Electrical/electronic/programmable electronic	Exponential distribution	3.13E-5
Redundant channel	Electrical/electronic/programmable electronic	Exponential distribution	2.07E-4

Table 1 each Module Fail rate information table

Wherein, the malfunction crash rate of whole passage is upper table: the malfunction crash rate of redundant channel; Its computing method are: malfunction crash rate (redundant channel)=malfunction crash rate (AI)+malfunction crash rate (MPU)+malfunction crash rate (DO); Here malfunction crash rate (AI), malfunction crash rate (MPU) and malfunction crash rate (DO) are given by system;

The maintenance policy of above-mentioned three generic modules is: once find fault, change immediately, average time for repair of breakdowns MTTR (Mean Time To Repair) is not more than 72h, i.e. repair rate μ=0.014.

2.2, applicability checking

For based on electrical/electronic/programmable electronic technology, system architecture is the RTS system of 2oo4,4 redundant channels are separate, and failure mechanism obedience crash rate is the exponential distribution of 2.07E-4, according to mathematical statistics, can prove that the failure mechanism of this RTS belongs to Poisson process, the Markovian process that namely time contact status is discrete.Therefore, malfunction rate computing method of the present invention have applicability for the RTS system that system architecture is 2oo4.

2.3, state space graph

According to the information that example of engineering calculation provides, and the modeling method of 1.2 joints, the malfunction state space graph of RTS can be obtained:

State 0: all parts normally run;

State 1:1 redundant channel is in service mode, and remaining part normally runs;

State 2:1 redundant channel is in service mode, and 1 redundant channel is to be repaired, remains 2 redundancies and normally runs;

State 3:1 redundant channel is in service mode, and 2 redundant channels are to be repaired, remains 1 redundant channel and normally runs;

Wherein, state 3 is RTS malfunction state.

2.4, malfunction rate calculates

Malfunction state space graph according to Fig. 3, set up state equation, be shown below:

$\left[\begin{array}{c}{\stackrel{\·}{P}}_0\left(t\right)\\ {\stackrel{\·}{P}}_1\left(t\right)\\ {\stackrel{\·}{P}}_2\left(t\right)\\ {\stackrel{\·}{P}}_3\left(t\right)\end{array}\right]=\left[\begin{array}{cccc}-4\mathrm{\λ}& 4\mathrm{\λ}& 0& 0\\ \mathrm{\μ}& -[\mathrm{\μ}+3\mathrm{\λ}]& 3\mathrm{\λ}& 0\\ 0& \mathrm{\μ}& -[\mathrm{\μ}+2\mathrm{\λ}]& 2\mathrm{\λ}\\ 0& 0& \mathrm{\μ}& -[\mathrm{\μ}+\mathrm{\λ}]\end{array}\right]\left[\begin{array}{c}{P}_0\left(t\right)\\ P_1\left(t\right)\\ P_2\left(t\right)\\ P_3\left(t\right)\end{array}\right]$ (formula 6)

Solving state equation, can obtain malfunction rate expression formula as follows

$F=\mathrm{\μ}\frac{1}{\underset{2}{\overset{4}{\mathrm{\Σ}}}\frac{1}{i!}{\left(\frac{\mathrm{\μ}}{\mathrm{\λ}}\right)}^{i-1}}$ (formula 7)

(formula 6) will be substituted into for λ=2.07E-5 and μ=0.014, can obtain:

F=1.02E-6 (h ^-1) (formula 8)

Wherein, h ^-1for unit, represent the probability of generation malfunction per hour.

The above is only preferred embodiment of the present invention, not any pro forma restriction is done to the present invention, although the present invention discloses as above with preferred embodiment, but and be not used to limit the present invention, any technician being familiar with this patent is not departing within the scope of technical solution of the present invention, make a little change when the technology contents of above-mentioned prompting can be utilized or be modified to the Equivalent embodiments of equivalent variations, in every case be the content not departing from technical solution of the present invention, according to any simple modification that technical spirit of the present invention is done above embodiment, equivalent variations and modification, all still belong in the scope of the present invention program.

Claims (8)

1. nuclear power plant system malfunction rate at steady state computing method, is characterized in that,

S1: set up described nuclear power plant system state space graph according to Markovian process,

Described state space graph comprises: when in the N number of parts belonging to described nuclear power plant system, and have M parts to be in normal operating conditions, described nuclear power plant system can normally work, and is in steady state (SS), otherwise described nuclear power plant system is in malfunction; Wherein, M>0, N>M;

S2: according to described nuclear power plant system state space graph, by setting probability matrix and the calculating to described probability matrix, obtains described nuclear power plant system malfunction rate at steady state expression formula:

Wherein, F is described nuclear power plant system malfunction rate at steady state expression formula; λ is malfunction crash rate, given by system; μ is repair rate.

2. a kind of nuclear power plant system according to claim 1 malfunction rate at steady state computing method, it is characterized in that, described state space graph also comprises: described nuclear power plant system has N-M+2 different conditions, and described probability matrix is N-M+2 rank square formations:

Wherein, when the parts broken down are greater than 1, parts can only be had to be in service mode, and other trouble units are in state to be repaired; And 0 state to N-M state is described nuclear power plant system normal operating condition, and N-M+1 state belongs to described nuclear power plant system malfunction.

3. a kind of nuclear power plant system malfunction rate at steady state computing method according to any one of claim 1-2, is characterized in that, by setting probability matrix and to the computation process of described probability matrix are:

1) according to described N-M+2 rank square formation T, a State Equation Coefficients matrix A is obtained:

Wherein, U is N-M+2 rank unit matrixs;

2) equation of state is obtained according to described State Equation Coefficients matrix A: wherein, P is the column vector of each state, for the column vector of each state probability inverse;

3) by step 2) described equation of state launch to obtain:

4) by described step 3) in equation launch, and carry out pull-type conversion and obtain the stable state of nuclear power plant system failure-frequency described in described step S2 expression formula;

Preferably, described repair rate μ=1/MTTR, wherein MTTR is average time for repair of breakdowns, given by system.

4. a kind of nuclear power plant system malfunction rate at steady state computing method according to any one of claim 1-3, is characterized in that, described a kind of nuclear power plant system is the Reactor trip subsystem RTS of nuclear power station; N number of parts of described Reactor trip subsystem RTS are: 4 identical escape ways;

The state space graph of described Reactor trip subsystem RTS comprises: when in 4 the identical escape ways belonging to described Reactor trip subsystem RTS, 2 escape ways are had at least to be in normal operating conditions, then described Reactor trip subsystem RTS normally works, otherwise described Reactor trip subsystem RTS is in malfunction;

Preferably, the malfunction of described Reactor trip subsystem RTS is malfunction state;

Preferably, when having at least the Output rusults of 2 escape ways then to perform Reactor trip function for " triggering ", otherwise then non-toggle state is maintained.

5. a kind of nuclear power plant system according to claim 4 malfunction rate at steady state computing method, it is characterized in that, the escape way of described Reactor trip subsystem RTS comprises: analog input AI module, Main Processor Unit MPU module and digital output DO module;

Malfunction crash rate (passage)=malfunction crash rate (AI)+malfunction crash rate (the MPU)+malfunction crash rate (DO) of described Reactor trip subsystem RTS;

Preferably, described malfunction crash rate (AI)=4.37E-5;

Described malfunction crash rate (MPU)=1.22E-4;

Described malfunction crash rate (DO)=3.13E-5;

Described malfunction crash rate (passage)=2.07E-4;

Preferably, the average time for repair of breakdowns MTTR=72 hour of described Reactor trip subsystem RTS; Repair rate μ=the 0.014h of described Reactor trip subsystem RTS.

6. a kind of nuclear power plant system malfunction rate at steady state computing method according to any one of claim 4-5, is characterized in that, according to nuclear power plant system failure-frequency stable state expression formula in described step S2: by M=2, N=4; λ=2.07E-4; μ=0.014 brings the failure-frequency stable state expression formula obtaining described Reactor trip subsystem RTS into: F=1.02E-6 (h ^-1); Wherein, h ^-1for unit, represent the probability of described generation malfunction per hour.

7. a kind of nuclear power plant system according to claim 4 malfunction rate at steady state computing method, is characterized in that, the state of described Reactor trip subsystem RTS comprises:

State 0: all escape ways normally run;

State 1:1 escape way is in service mode, and all the other escape ways normally run;

State 2:1 escape way is in service mode, and 1 escape way is to be repaired, remains 2 escape ways and normally runs;

State 3:1 escape way is in service mode, and 2 escape ways are to be repaired, remains 1 escape way and normally runs;

Wherein, when described Reactor trip subsystem RTS be in state 0, state 1 or state 2 any one time, described Reactor trip subsystem RTS normally works; When described Reactor trip subsystem RTS is in state 3, described Reactor trip subsystem RTS is in malfunction state.

8. a kind of nuclear power plant system according to claim 1 malfunction rate at steady state computing method, it is characterized in that, described nuclear power plant system is under the condition that the state residing for the t_0 moment is known, and the state that the condition distribution of process moment t > t_0 status is residing before moment t_0 with process has nothing to do.