CN104850750B - A kind of nuclear power plant reactor protects systems reliability analysis method - Google Patents
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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 the technical field of system reliability analysis and design, and particularly relates to a method for analyzing the reliability of a nuclear power station reactor protection system.
Background
System reliability refers to the ability of a system to perform a specified function under specified conditions and for a specified time. From the perspective of the entire full lifecycle, there are a number of metrics for whether the system can perform the intended function: for repairable systems and devices, the metrics include reliability, Mean Time Between Failure (MTBF), Mean Time To Repair (MTTR), availability, useful life, and the like; for an unrepairable system or product, technical indexes such as reliability, reliable service life, Failure rate and Mean Time To Failure (MTTF) are included.
After the product design is finished, strict links such as material physical test, stress screening, process control of production and manufacturing processes, strict quality detection and the like need to be carried out, and the reliability of the product is called as 'inherent reliability'. The reliability test is a basic way for a product development unit and a use unit to know the reliability of the product and obtain reliability data. Because the product life test is destructive, design and production units generally predict the overall life reliability level and various reliability indexes of the product through a small amount of test data, and a high-precision technical method capable of correctly predicting the system reliability level and the dynamic failure rate according to small samples is needed.
The failure event of the nuclear power station reactor protection system has the characteristics of high risk of serious influence effect, long influence time, large influence range and the like, so that the reliability standard requirement of each working component and structure of the system is very high, and the failure probability is generally at the level of one hundred thousand times or one million times. By applying the traditional reliability estimation method, theoretically, one failure data sample can be obtained only by reliability tests of millions of times, and huge cost consumption of manpower, material resources, financial resources and the like is inevitably generated. If a reliability test based on hundreds or thousands of small subsamples could be provided, 10 could be obtained-5～10-6The accurate estimation technical method of the failure probability of the level system undoubtedly has important engineering significance for solving the evaluation problem of the small failure probability of the complex electromechanical system.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for analyzing the reliability of a reactor protection system of a nuclear power station.
The technical scheme of the invention is as follows:
a method for analyzing the reliability of a reactor protection system of a nuclear power station comprises the following steps:
step 1, determining a fault tree model of a nuclear power plant reactor protection system according to the structural and functional relation of the nuclear power plant reactor protection system;
step 2, solving a minimal cut set which causes a top event, namely the occurrence of the emergency shutdown failure of the nuclear power station, by using a downlink method, namely a combination which causes the top event when a bottom event occurs simultaneously;
step 3, obtaining historical fault data of the nuclear power plant reactor protection system, namely time statistical data samples of faults of all bottom events;
step 4, calculating the service life statistic of the nuclear power station reactor protection system through the minimum cut set, namely the running time of the nuclear power station reactor protection system when the nuclear power station reactor protection system fails;
step 5, establishing an information entropy model of the life distribution probability density function of the nuclear power plant reactor protection system, and solving the optimal life distribution probability density function of the nuclear power plant reactor protection system;
step 6, solving the failure probability of the nuclear power plant reactor protection system by using the life distribution probability density function of the nuclear power plant reactor protection system, namely the probability of the nuclear power plant reactor protection system failing before the time t;
step 7, solving the reliability of the nuclear power plant reactor protection system by using the life distribution probability density function of the nuclear power plant reactor protection system, namely the probability that the nuclear power plant reactor protection system still normally works after time t;
and 8, solving the dynamic failure rate of the nuclear power plant reactor protection system by using the life distribution probability density function of the nuclear power plant reactor protection system, namely the probability that the nuclear power plant reactor protection system is not failed when working to the moment t and fails in unit time after the moment t.
The step 1 comprises the following steps:
step 1.1, determining a top event of a fault tree and a secondary event causing the top event to occur;
the top event of the fault tree is the failure of the emergency shutdown of the nuclear power station;
secondary events leading to a top event include a low voltage regulator signal failure, a shutdown breaker rejection, and at least three control rod sticks;
any secondary event occurrence results in a top event occurrence;
step 1.2, determining a tertiary event causing a secondary event in a fault tree;
events causing the occurrence of the low-pressure signal failure event of the voltage stabilizer comprise the failure of a pressure sensor of the voltage stabilizer and the fixed value error of a threshold relay of three pressure sensors of the voltage stabilizer;
the event causing the shutdown breaker opening refusing event is the common cause failure of two shutdown breakers;
at least three control rod jamming events are regarded as bottom events, namely irreparable events which cause the emergency shutdown failure of the nuclear power station;
step 1.3, determining a possible event causing a third-level event, namely a fourth-level event;
events that cause failure of a regulator pressure sensor include failure of the associated regulator pressure sensor; any two events occur simultaneously, which can cause the failure event of the pressure sensor of the voltage stabilizer;
setting value errors of threshold relays of the three voltage stabilizer pressure sensors and common cause failures of the two shutdown circuit breakers are bottom events;
step 1.4, determining a possible event causing the occurrence of a four-level event, namely a five-level event;
and step 1.5, determining a possible event causing the occurrence of a fifth-level event, namely a sixth-level event, until the event can not be subdivided, finishing searching all possible events causing a top event, namely the emergency shutdown failure event of the nuclear power station, and obtaining a bottom event.
Step 5, the probability density function of the life distribution of the reactor protection system of the nuclear power station is established according to the following steps:
step 5.1, introducing a maximum entropy estimation method, and establishing an information entropy model of a reactor protection system of a nuclear power station;
step 5.2, determining constraint conditions of the information entropy optimization model of the nuclear power plant reactor protection system, wherein the constraint conditions comprise the establishment of a fractional moment of the life statistic of the nuclear power plant reactor protection system and the estimation of an integral value of a life distribution probability density function of the nuclear power plant reactor protection system, and the integral value is 1;
step 5.3, introducing a Lagrange equation to solve the maximum entropy constraint optimization problem of the nuclear power plant reactor protection system, and enabling the Lagrange equation to solve a partial derivative of the life distribution probability density estimator of the nuclear power plant reactor protection system, wherein the value of the partial derivative is equal to 0, so as to obtain an analytic expression estimation of the life distribution probability density function of the nuclear power plant reactor protection system;
step 5.4, introducing a K-L distance method, and establishing an unconstrained optimization model for solving the service life distribution probability density function parameters of the nuclear power plant reactor protection system;
step 5.5, solving a Lagrange multiplier lambda and a fraction moment index alpha of a life distribution probability density function of the nuclear power plant reactor protection system by using historical fault data;
and 5.6, substituting the Lagrange multiplier lambda and the fraction moment index alpha into the analytic expression estimation of the probability density function of the nuclear power station reactor protection system in the step 5-3 to obtain the life distribution probability density function of the nuclear power station reactor protection system.
Has the advantages that:
the method breaks through the dependence of the traditional method on a large number of observation samples, predicts the overall service life distribution and dynamic failure rate of the system according to a small amount of reliability test data, and provides a technical method for service life prediction and dynamic failure rate evaluation of the nuclear power station reactor protection system under the condition of small failure probability, wherein the calculation result is consistent with the Monte Carlo simulation result based on a large sample.
Drawings
FIG. 1 is a flow chart of a method for analyzing the reliability of a nuclear power plant reactor protection system in accordance with an embodiment of the present invention;
FIG. 2 is a nuclear power plant reactor protection system fault tree model according to an embodiment of the present invention;
FIG. 3 is a simplified fault tree model of an embodiment of the present invention;
FIG. 4 is a flow chart of a nuclear power plant reactor protection system life distribution probability density function establishment in accordance with an embodiment of the present invention;
FIG. 5 is a probability density function of life distribution for a nuclear power plant reactor protection system in accordance with an embodiment of the present invention;
FIG. 6 is a nuclear power plant reactor protection system failure probability prediction curve according to an embodiment of the present invention;
FIG. 7 is a graph illustrating a predicted reliability of a nuclear power plant reactor protection system in accordance with an embodiment of the present invention;
fig. 8 is a dynamic failure rate prediction curve of a reactor protection system of a nuclear power plant according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings.
Taking reliability analysis of a reactor protection system of a certain nuclear power station as an example, the implementation process of the method is described in detail, and the reliability analysis method of the reactor protection system of the nuclear power station, as shown in fig. 1, comprises the following steps:
step 1, determining a fault tree model of a nuclear power plant reactor protection system according to the structural and functional relation of the nuclear power plant reactor protection system;
step 1.1, determining a top event of a fault tree and a secondary event causing the top event to occur;
the top event of the fault tree is a nuclear power station scram failure (RCPS 000);
secondary events leading to top events include a potentiostat low pressure signal failure (RCPS001), shutdown breaker rejection (RCPS002), at least three control rod jamming (RCPS 003);
any secondary event occurrence results in the occurrence of a top event (RCPS 000);
step 1.2, determining a tertiary event causing a secondary event in a fault tree;
events that caused the occurrence of a regulator pressure low signal failure event (RCPS001) include a regulator pressure sensor failure (RCPS004), three regulator pressure sensor threshold relay misvaluing (PCF 005-013);
the event causing the shutdown breaker rejection event (RCPS002) to occur is two shutdown breaker common cause failures (RPA300 JA-RO);
at least three bundles of control rod sticking events (RCPS003) are considered as bottom events, i.e. events that cannot be subdivided that lead to a nuclear power plant scram failure;
step 1.3, determining a possible event causing a third-level event, namely a fourth-level event;
events that lead to a failure of the potentiostat pressure sensor (RCPS004) include associated potentiostat pressure sensor failures, specifically, a potentiostat pressure sensor RCP005MP failure (RCPS005), a potentiostat pressure sensor RCP006MP failure (RCPS006), and a potentiostat pressure sensor RCP007MP failure (RCPS 007); any two of these events occurring simultaneously may result in the occurrence of a regulator pressure sensor failure (RCPS004) event;
three voltage stabilizer pressure sensor threshold relay setting errors (PCF005-013) and two trip breaker common cause failures (RPA300JA-RO) are bottom events;
step 1.4, determining a possible event causing the occurrence of a four-level event, namely a five-level event;
events that lead to the occurrence of a regulator pressure sensor RCP005MP failure (RCPs005) event are regulator pressure sensor RCP005MP demand failure (RCPs005-MP), regulator pressure sensor RCP005MP threshold relay failure (RCPs005-RC), any of which can lead to the occurrence of a regulator pressure sensor RCP005MP failure (RCPs 005).
Events that lead to a regulator pressure sensor RCP006MP failure (RCPs006) event are regulator pressure sensor RCP006MP demand failure (RCPs006-MP) and regulator pressure sensor RCP006MP threshold relay failure (RCPs006-RC), any of which can lead to a regulator pressure sensor RCP006MP failure (RCPs006) event.
Events that caused the regulator pressure sensor RCP007MP failure (RCPs007) event were regulator pressure sensor RCP007MP demand failure (RCPs007-MP) and regulator pressure sensor RCP007MP threshold relay failure (RCPs007-RC), any of which caused the regulator pressure sensor RCP007MP failure (RCPs007) event.
And step 1.5, determining a possible event causing the occurrence of a fifth-level event, namely a sixth-level event, until the event can not be subdivided, finishing searching all possible events causing a top event, namely the emergency shutdown failure event of the nuclear power station, and obtaining a bottom event.
Regulator pressure sensor RCP005MP demand failure (RCPS005-MP), regulator pressure sensor RCP005MP threshold relay failure (RCPS005-RC), regulator pressure sensor RCP006MP demand failure (RCPS006-MP), regulator pressure sensor RCP006MP threshold relay failure (RCPS006-RC), regulator pressure sensor RCP007MP demand failure (RCPS007-MP), and regulator pressure sensor RCP007MP threshold relay failure (RCPS007-RC) are bottom events.
All possible events causing the top event, i.e., the occurrence of a nuclear power plant emergency shutdown failure (RCPS000) event, are searched. The fault tree model of the system may be built based on its parent-child relationships, as shown in FIG. 2.
Step 2, solving a minimal cut set which causes a top event, namely the occurrence of the nuclear power station emergency shutdown failure (RCPS000), by using a downlink method, namely a combination of top events caused by the simultaneous occurrence of bottom events;
for simplicity of calculation, an incident nuclear power plant scram failure (RCPS000) is denoted by T, an incident regulator pressure low signal failure (RCPS001) is denoted by G1, an incident shutdown breaker rejection (RCPS002) is denoted by G2, an incident at least three control rod stuck (RCPS003) is denoted by A, an incident regulator pressure sensor failure (RCPS004) is denoted by G3, an incident three regulator pressure sensor threshold relay set error (PCF005-013) is denoted by B, two incident shutdown breaker failures (RPA300JA-RO) are denoted by C and D, respectively, an incident regulator pressure sensor RCP005MP failure (RCPS005) is denoted by G4, an incident regulator pressure sensor RCP006MP failure (RCPS006) is denoted by G5, an incident regulator pressure sensor RCP007MP failure (RCPS007) is denoted by G6, an incident regulator pressure sensor RCP005MP demand failure (RCE 005-MP) is denoted by RCE, an incident regulator pressure sensor RCP 005-78 is denoted by RCF relay threshold Relay (RCF) is denoted by RCF 005MP, the event regulator pressure sensor RCP006MP demand failure (RCPs006-MP) is denoted by G, the event regulator pressure sensor RCP006MP threshold relay failure (RCPs006-RC) is denoted by H, the event regulator pressure sensor RCP007MP demand failure (RCPs007-MP) is denoted by I, the event regulator pressure sensor RCP007MP threshold relay failure (RCPs007-RC) is denoted by J, and the simplified fault tree model is shown in fig. 3.
The process of solving the minimal cut set of the fault tree is as follows:
the first step is as follows: the gate below the top event T is an or gate (either event occurs, the top event occurs), thus its inputs G1, G2, a are arranged in columns (permutation T);
the second step is that: the basic event A is not decomposed any more, the G1 event is an OR gate, and the inputs G3 and B are arranged into a column to replace G1; g2 event is and gate (all events happen, top event happens), aligns its inputs C, D, permutes G2;
the third step: the basic event B, C, D is not decomposed, the G3 event is 2/3 voting gates (two or more sub-events occur, and the top event occurs), and the inputs G4, G5 and G6 are combined into rows in pairs and then arranged into columns to replace G3;
the fourth step: the G4 event is an or gate, which arranges its input E, F in a column permutes G4; the G5 event is an or gate, which arranges its input G, H into a column permutation G5; the G6 event is an or gate, which arranges its input I, J into a column permutation G6;
the fifth step: a list of 15 cut sets, all represented by base events, is obtained: { A }, { CD }, { B }, { EG }, { EH }, { FG }, { FH }, { EI }, { EJ }, { FI }, { FJ }, { GI }, { GJ }, { HI }, { HJ }, see Table 1.
TABLE 1 Down method deployment of reactor protection System Fault Tree for Nuclear Power plants
In summary, a minimal combination of bottom events that cause a nuclear power plant scram failure (RCPS000) to occur may be obtained.
Step 3, obtaining historical fault data of the nuclear power plant reactor protection system, namely time statistical data samples of faults of all bottom events (A, B, C, D, E, F, G, H, I and J):
where t represents the time that has been operating normally when a fault occurs, the superscript represents the different samples, N is the number of samples, and the subscript represents the different events.
Step 4, calculating the service life statistic of the reactor protection system of the nuclear power station through the minimum cut set, namely the time of the reactor protection system of the nuclear power station which has been operated when the reactor protection system of the nuclear power station has a fault
Ith time statistic sampleThe minimum working time in the minimal cut set, and the working time containing two or more bottom event elements is the maximum working time. The method specifically comprises the following steps: from the ith time statistics sample, find out the time of occurrence of at least three bundles of control rod stuck (RCPS003), event A, the time of occurrence of three regulator pressure sensor threshold relay definite value errors (PCF005-013), event B, trip breaker failure (RPA300JA-RO), the greater of the times of occurrence of events C and D, the greater of the times of occurrence of event E and event G, the greater of the events of regulator pressure sensor RCP005 demand failure (RCPS005-MP) and regulator pressure sensor RCP006MP threshold relay failure (RCPS006-RC), the greater of the times of occurrence of event E and H, the greater of the times of occurrence of event F and G, the greater of the times of event G and of event G, regulator pressure sensor RCP005MP threshold relay failure (RCPS005-RC) and regulator pressure sensor RCP006MP threshold relay failure (RCPS006-RC), i.e., the greater of the times at which events F and H occur, regulator pressure sensor RCP005MP demand failure (RCPS005-MP) and regulator pressure sensor RCP007MP demand failure (RCPS007-MP), i.e., the greater of the times at which events E and I occur, regulator pressure sensor RCP005MP demand failure (RCPS005-MP) and regulator pressure sensor RCP007MP threshold relay failure (RCPS007-RC), i.e., the greater of the times at which events E and J occurFurther, the greater of the regulator pressure sensor RCP005MP threshold relay failure (RCPs005-RC) and regulator pressure sensor RCP007MP demand failure (RCPs007-MP), event F and I occurrence time, the greater of the regulator pressure sensor RCP005MP threshold relay failure (RCPs005-RC) and regulator pressure sensor RCP007MP threshold relay failure (RCPs007-RC), event F and J occurrence time, the greater of the event G and I occurrence time, the greater of the regulator pressure sensor RCP006MP demand failure (RCPs006-MP) and regulator pressure sensor RCP007MP demand failure (RCPs007-MP), the greater of the event G and I occurrence time, the greater of the regulator pressure sensor RCP006MP demand failure (RCPs 006-006) and regulator pressure sensor RCP MP threshold relay failure (RCPs006-RC 007), event G007 and J occurrence time, the threshold pressure sensor RCP MP threshold relay failure (RCPs006-RC) and regulator pressure sensor RCP007 RCp MP demand relay failure (RCP 007-RC) The greater of the generation times, the greater of the occurrence times of the regulator pressure sensor RCP006MP threshold relay failure (RCPs006-RC) and the regulator pressure sensor RCP007MP threshold relay failure (RCPs007-RC), i.e., the events H and J, the smallest of the above times is the working time of the ith time statistic sample.
It can be calculated specifically by the following formula:
from which in turn life statistics for the system can be derived
Step 5, establishing an information entropy model of the life distribution probability density function of the nuclear power plant reactor protection system, and solving the optimal life distribution probability density function of the nuclear power plant reactor protection system;
as shown in fig. 4, the probability density function of life distribution of the reactor protection system of the nuclear power plant is established as follows:
step 5.1, introducing a maximum entropy estimation method, and establishing an information entropy model of a reactor protection system of a nuclear power station;
in order to determine the fractional moment index α and the lagrangian multiplier λ in the lifetime distribution, a maximum entropy estimation method needs to be introduced.
Probability density function f of known lifetime distributionT(t), the information entropy model of which is defined as:
H[f]＝-∫TfT(t)log[fT(t)]dt
step 5.2, determining constraint conditions of the information entropy optimization model of the nuclear power plant reactor protection system, wherein the constraint conditions comprise the establishment of a fractional moment of the life statistic of the nuclear power plant reactor protection system and the estimation of an integral value of a life distribution probability density function of the nuclear power plant reactor protection system, and the integral value is 1;
the random variable T is a random variable of the service life of a component (or a system), and the alpha-order fractional moment of the random variable T is defined as:
where alpha is any real number.
It should be noted that: a sufficient prerequisite for the existence of a life time random variable fractional moment is the fractional moment integralConvergence, which is equivalent to the presence of an integer moment of order k, if and only if | α | ≦ kAre present.
For calculating an estimate of the lifetime distribution probability density function ft (t)Then maximum entropy needs to be appliedTheory. By introducing each order fractional moment of the service life statistics, the constraint conditions of the information entropy optimization model are as follows:andwherein m is the number of times of fractional moment, and the satisfactory calculation precision can be obtained by taking the third-order fractional moment constraint (i.e. m is 3) through multiple practical application verification, and α j is the fractional moment index of the corresponding order;for the estimation of the fraction moment of the life of the reactor protection system of a nuclear power plant, i.e. the working time before failure,and N is the time statistic data sample number of the system. At this time, only the information entropy needs to be estimatedAnd (4) maximizing.
The information entropy optimization model can be expressed as:
step 5.3, introducing a Lagrange equation to solve the maximum entropy constraint optimization problem of the nuclear power plant reactor protection system, and enabling the Lagrange equation to solve a partial derivative of the life distribution probability density estimator of the nuclear power plant reactor protection system, wherein the value of the partial derivative is equal to 0, so as to obtain an analytic expression estimation of the life distribution probability density function of the nuclear power plant reactor protection system;
introducing a Lagrange equation to solve the maximum entropy constraint optimization problem:
wherein λ ═ λ0,λ1,…,λm]TFor lagrange multiplier, α ═ α0,α1,…,αm]TIs a fractional moment index.
To obtain the maximum entropy estimation, the lagrangian equation is only required to solve the partial derivative of the probability density estimator so that the partial derivative is equal to 0. Namely: order to
Obtaining a fractional moment information entropy estimation expression of an unknown life probability density function:
in view ofSolving lagrange multiplier lambda0The expression of (a) is:
in order to simplify an information entropy optimization model, a Lagrange multiplier lambda and a fraction moment index alpha of a service life distribution probability density function are solved by introducing K-L distance.
Step 5.4, introducing a K-L distance method, and establishing an unconstrained optimization model for solving the service life distribution probability density function parameters of the nuclear power plant reactor protection system;
the K-L distance is defined as the difference between the true entropy and the estimated entropy, with smaller values indicating that the estimated entropy is closer to the true entropy, and more accurate. The formula is as follows:
expression of probability density function estimator when given lifetime distributionThe K-L distance may be further expressed as:
the theoretical value of the information entropy is usually a real constant since hf is the lifetime distribution. The portion of the K-L distance that varies can therefore be expressed as:
so far, an unconstrained optimization model for solving the service life distribution probability density function parameters can be established:
the solution of the unconstrained optimization model can be solved by applying a unconstrained nonlinear optimization problem such as a quasi-Newton method, a simplex method and the like. Obtaining the optimal Lagrange multiplier lambda ═ lambda0,λ1,…,λm]TAnd the best fractional moment index α ═ α0,α1,…,αm]T. The fminsearch function in the MATLAB toolbox is applied to solve, and the method has the advantages that a simplex method is applied without calculating gradient information of an objective function, and programming and numerical value solving are convenient.
Step 5.5, solving a Lagrange multiplier lambda and a fraction moment index alpha of a life distribution probability density function of the nuclear power plant reactor protection system by using historical fault data;
step 5.6, changing lagrange multiplier lambda to [ lambda ]0,λ1,…,λm]TAnd fractional moment index α ═ α0,α1,…,αm]TAnd 5, substituting the probability density function of the nuclear power plant reactor protection system in the step 5-3 into an analytic expression estimation to obtain a probability density function of the life distribution of the nuclear power plant reactor protection system, as shown in fig. 5.
Wherein,
step 6, solving the failure probability of the reactor protection system of the nuclear power station by using the life distribution probability density function of the reactor protection system of the nuclear power station, namely the probability of the reactor protection system of the nuclear power station failing before the time t (the integral value of the life distribution probability density function of the reactor protection system of the nuclear power station to t from the time 0 to the time t), as shown in fig. 6.
Namely:
and 7, solving the reliability of the nuclear power plant reactor protection system by using the life distribution probability density function of the nuclear power plant reactor protection system, namely the probability that the nuclear power plant reactor protection system still normally works after time t, as shown in fig. 7. The reliability is complementary to the probability of failure of the system.
Namely:
and 8, solving the dynamic failure rate of the reactor protection system of the nuclear power station by using the life distribution probability density function of the reactor protection system of the nuclear power station, namely the probability that the reactor protection system of the nuclear power station is not failed when working to the moment t and fails in unit time after the moment t, as shown in fig. 8.
Namely:
it is to be noted that MCS representation 10 in fig. 5, 6, 7, and 86The result of sampling the sub-Monte Carlo values, ME-FM is based on 103And (4) optimizing the result of the maximum entropy of the fractional moments of the samples. It can be seen that the reliability analysis method based on the maximum entropy optimization of the fractional moments, which is applied to the invention, is only 103The system life probability distribution, reliability and dynamic failure rate calculation accuracy obtained by each life data sample are 106The sub-Monte Carlo random results have the same precision, and represent the advantages and the use value of the method in the aspects of system life distribution and dynamic failure rate calculation based on small data sample reconstruction.
Claims (2)
1. A method for analyzing the reliability of a nuclear power station reactor protection system is characterized by comprising the following steps:
step 1, determining a fault tree model of a nuclear power plant reactor protection system according to the structural and functional relation of the nuclear power plant reactor protection system;
step 2, solving a minimal cut set which causes a top event, namely the occurrence of the emergency shutdown failure of the nuclear power station, by using a downlink method, namely a combination which causes the top event when a bottom event occurs simultaneously;
step 3, obtaining historical fault data of the nuclear power plant reactor protection system, namely time statistical data samples of faults of all bottom events;
step 4, calculating the service life statistic of the nuclear power station reactor protection system through the minimum cut set, namely the running time of the nuclear power station reactor protection system when the nuclear power station reactor protection system fails;
step 5, establishing an information entropy model of the life distribution probability density function of the nuclear power plant reactor protection system, and establishing an optimal life distribution probability density function of the nuclear power plant reactor protection system;
the nuclear power station reactor protection system life distribution probability density function is established according to the following steps:
step 5.1, introducing a maximum entropy estimation method, and establishing an information entropy model of a reactor protection system of a nuclear power station;
probability density function f of known lifetime distributionT(t) its information entropy model H [ f]Is defined as:
H[f]＝-∫TfT(t)log[fT(t)]dt
step 5.2, determining constraint conditions of the information entropy optimization model of the nuclear power plant reactor protection system, wherein the constraint conditions comprise the establishment of a fractional moment of the life statistic of the nuclear power plant reactor protection system and the estimation of an integral value of a life distribution probability density function of the nuclear power plant reactor protection system, and the integral value is 1;
step 5.3, introducing a Lagrange equation to solve the maximum entropy constraint optimization problem of the nuclear power plant reactor protection system, and enabling the Lagrange equation to solve a partial derivative of the life distribution probability density estimator of the nuclear power plant reactor protection system, wherein the value of the partial derivative is equal to 0, so as to obtain an analytic expression estimation of the life distribution probability density function of the nuclear power plant reactor protection system;
step 5.4, introducing a K-L distance method, and establishing an unconstrained optimization model for solving the service life distribution probability density function parameters of the nuclear power plant reactor protection system;
step 5.5, solving a Lagrange multiplier lambda and a fraction moment index alpha of a life distribution probability density function of the nuclear power plant reactor protection system by using historical fault data;
step 5.6, substituting the Lagrange multiplier lambda and the fraction moment index alpha into the analytic expression estimation of the probability density function of the nuclear power station reactor protection system in the step 5-3 to obtain a life distribution probability density function of the nuclear power station reactor protection system;
step 6, solving the failure probability of the nuclear power plant reactor protection system by using the life distribution probability density function of the nuclear power plant reactor protection system, namely the probability of the nuclear power plant reactor protection system failing before the time t;
step 7, solving the reliability of the nuclear power plant reactor protection system by using the life distribution probability density function of the nuclear power plant reactor protection system, namely the probability that the nuclear power plant reactor protection system still normally works after time t;
and 8, solving the dynamic failure rate of the nuclear power plant reactor protection system by using the life distribution probability density function of the nuclear power plant reactor protection system, namely the probability that the nuclear power plant reactor protection system is not failed when working to the moment t and fails in unit time after the moment t.
2. The method for analyzing the reliability of the nuclear power plant reactor protection system according to claim 1, wherein the step 1 comprises the following steps:
step 1.1, determining a top event of a fault tree and a secondary event causing the top event to occur;
the top event of the fault tree is the failure of the emergency shutdown of the nuclear power station;
secondary events leading to a top event include a low voltage regulator signal failure, a shutdown breaker rejection, and at least three control rod sticks;
any secondary event occurrence results in a top event occurrence;
step 1.2, determining a tertiary event causing a secondary event in a fault tree;
events causing the occurrence of the low-pressure signal failure event of the voltage stabilizer comprise the failure of a pressure sensor of the voltage stabilizer and the fixed value error of a threshold relay of three pressure sensors of the voltage stabilizer;
the event causing the shutdown breaker opening refusing event is the common cause failure of two shutdown breakers;
at least three control rod jamming events are regarded as bottom events, namely irreparable events which cause the emergency shutdown failure of the nuclear power station;
step 1.3, determining a possible event causing a third-level event, namely a fourth-level event;
events that cause failure of a regulator pressure sensor include failure of the associated regulator pressure sensor; any two events occur simultaneously, which can cause the failure event of the pressure sensor of the voltage stabilizer;
setting value errors of threshold relays of the three voltage stabilizer pressure sensors and common cause failures of the two shutdown circuit breakers are bottom events;
step 1.4, determining a possible event causing the occurrence of a four-level event, namely a five-level event;
and step 1.5, determining a possible event causing the occurrence of a fifth-level event, namely a sixth-level event, until the event can not be subdivided, finishing searching all possible events causing a top event, namely the emergency shutdown failure event of the nuclear power station, and obtaining a bottom event.
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