KR102166116B1 - Method and apparatus for calculation of failure event probabilities from partially correlated combination probabilities for seismic probabilistic safety assessment of nuclear power plants - Google Patents

Abstract

The method for calculating the probability of device failure events for the probabilistic safety evaluation of an earthquake event of a nuclear power plant according to an embodiment of the present invention is a predetermined method in the method of calculating the failure combination probability for the probabilistic stability evaluation of an earthquake event of a nuclear power plant. The step of calculating a plurality of failure combination probabilities corresponding to the logical combination of N (N is a natural number) in the nuclear power plant, and failure tree consisting of device failure events corresponding to each of the plurality of failure combination probabilities. The plurality of device failure events based on the step of calculating, calculating a minimum interruption set corresponding to the fault tree, and a plurality of minimum interruption sets corresponding to each of the plurality of failure combination probability and the plurality of failure combination probability And calculating each probability.

Description

METHOD AND APPARATUS FOR CALCULATION OF FAILURE EVENT PROBABILITIES FROM PARTIALLY CORRELATED COMBINATION PROBABILITIES FOR SEISMIC PROBABILIST SAFETY ASSESSMENT OF NUCLEAR POWER PLANTS}

The present invention relates to a method and apparatus for calculating the probability of equipment failure events from the failure combination probabilities of equipment having partial correlation for the probabilistic safety evaluation of an earthquake event of a nuclear power plant, and more specifically, to a partial correlation due to an earthquake event. The present invention relates to a method and apparatus for individually calculating the probability of equipment failure events from the failure combination probability of equipment.

Probabilistic Safety Assessment (PSA) for nuclear power plants was first developed in the 1970s and is currently used as important information to identify risks when operating nuclear power plants worldwide.

These PSA models consist of a full power/stop low power model according to the power plant operation status, an internal/external event (earthquake, fire, flooding, etc.) model according to the type of disaster, and Levels 1, 2, and 3 according to the final risk ending. Has been.

Using the model developed based on the data reflecting the unique information of the power plant, the final risk is derived as a quantitative number, such as the core damage frequency (CDF) and the mass early release frequency (LERF).

In particular, in the probabilistic safety evaluation of an internal event, the device sensitivity analysis can be performed by a relatively simple method, and the system reliability can be improved using the device sensitivity analysis result.

However, in the case of an earthquake event, the probability of failure combination of devices with partial correlation due to the earthquake event is directly calculated as an integral, so unlike internal event probabilistic safety evaluation, it is impossible to create a minimum disconnected set consisting of device failure events. Since it is not possible to perform device sensitivity analysis, there is a need for technology related to this.

Korean Patent Application Publication No. 10-2015-0032040 (2015.03.25)

An object of the present invention is to provide a method and apparatus for calculating the probability of each equipment failure event by combining relational expressions related to the probability of a plurality of failure combinations and the probability of each equipment failure event in a nuclear power plant having partial correlation due to an earthquake event.

The problem to be solved by the present invention is not limited to the problem(s) mentioned above, and another problem(s) not mentioned will be clearly understood by those skilled in the art from the following description.

The method for calculating the probability of equipment failure events for probabilistic safety evaluation of an earthquake event of a nuclear power plant according to an embodiment of the present invention is, in the method of calculating the probability of equipment failure events for the probabilistic stability evaluation of an earthquake event of a nuclear power plant, in advance. Calculating a plurality of failure combination probabilities corresponding to a logical combination of N devices (N is a natural number) in the nuclear power plant using a predetermined method, and a plurality of equipment failure events corresponding to each of the plurality of failure combination probabilities. Calculating a configured fault tree, calculating a minimum interrupted set corresponding to the fault tree, and the plurality of minimum interrupted sets corresponding to each of the plurality of failure combination probabilities and the plurality of failure combination probabilities And calculating the probability of each of the device failure events.

Preferably, the plurality of device failure events may be an independent failure, which is a single device failure due to the earthquake event, or a common cause failure, which is a plurality of equipment failures due to the earthquake event.

Preferably, the plurality of failure combination probabilities corresponding to the logical combination may be a plurality of failure combination probabilities corresponding to an AND condition or an OR condition.

Preferably, if the failure combination probability is an OR condition failure combination probability, the step of calculating the plurality of failure combination probabilities includes calculating a plurality of failure combination probabilities of AND conditions corresponding to the logical combination using NVN integration. And calculating the plurality of failure combination probabilities of the OR condition by using the plurality of failure combination probabilities of the AND condition and the principle of inclusion exclusion (IEP).

Preferably, the minimum interruption set may be a minimum interruption set of AND conditions or OR conditions corresponding to each of the plurality of failure combination probabilities.

Preferably, the step of calculating the probability of each of the plurality of device failure events comprises the steps of expressing the plurality of minimum interruption sets as a probability of each of the plurality of device failure events using an REA probability or an MCUB probability, the plurality of It may include generating a plurality of relational expressions based on the probability of failure combination of and the probability of each of the plurality of device failure events, and calculating the probability of each of the device failure events by combining the plurality of relational expressions.

Preferably, further comprising the step of analyzing a device sensitivity corresponding to the logical combination of the N devices by using the probability of each of the device failure events, wherein the device sensitivity is the probability of a system failure of the nuclear power plant It may have an effect on

Preferably, the step of calculating a core damage failure tree consisting of the plurality of equipment failure events, and calculating a core damage frequency based on the probability of each of the core damage failure trees and the plurality of equipment failure events. Can include.

In addition, the apparatus for calculating the probability of equipment failure events for the probabilistic safety evaluation of earthquake events of a nuclear power plant according to an embodiment of the present invention is, by using a predetermined method, N (N is a natural number) of devices in the nuclear power plant. A probability calculation unit that calculates a plurality of failure combination probabilities having partial correlation of an earthquake event corresponding to a logical combination, and a failure tree consisting of a plurality of device failure events corresponding to each of the plurality of failure combination probabilities is calculated, and the failure And a generator for calculating a minimum interruption set corresponding to a tree, and the probability calculation unit comprises a plurality of device failure events based on a plurality of minimum interruption sets corresponding to each of the plurality of failure combination probabilities and the plurality of failure combination probabilities. Each probability is calculated.

Preferably, the device failure event may be an independent failure, which is a single device failure due to the earthquake event, or a common cause failure, which is a plurality of equipment failures due to the earthquake event.

Preferably, the plurality of failure combination probabilities corresponding to the logical combination may be a plurality of failure combination probabilities corresponding to an AND condition or an OR condition.

Preferably, if the failure combination probability is an OR condition failure event, the probability calculation unit calculates the failure combination probability of the AND condition corresponding to the logical combination using NVN integration, and excludes the failure combination probability of the AND condition. Using the principle of (IEP), the probability of failure combination of OR conditions can be calculated.

Preferably, the minimum interruption set may be a minimum interruption set of an AND condition or an OR condition corresponding to an AND condition or an OR condition of the failure combination probability.

Preferably, the generation unit expresses the plurality of minimum interrupted sets as probabilities of each of the plurality of device failure events using REA probability or MCUB probability, and each of the plurality of failure combination probabilities and the plurality of device failure events A plurality of relational expressions may be generated based on the probability of, and the probability of each device failure event may be calculated by combining the plurality of relational expressions.

Preferably, further comprising an analysis unit for analyzing the device sensitivity corresponding to the logical combination of the N devices by using the probability of each of the device failure event, the device sensitivity is a device failure probability of the system failure of the nuclear power plant It may have an effect on

Preferably, a damage frequency calculation unit for calculating a core damage failure tree consisting of the plurality of equipment failure events, and calculating the core damage frequency based on the probability of each of the core damage failure trees and the plurality of equipment failure events. It may contain more.

The present invention calculates the probability of each equipment failure event caused by the earthquake event in a method and apparatus for calculating equipment failure events from the failure combination probability of devices having partial correlation for probabilistic safety evaluation of earthquake events of a nuclear power plant. , It has an effect that can be used for device sensitivity analysis.

1 is a flowchart illustrating a method of calculating the probability of equipment failure events for probabilistic safety evaluation of an earthquake event of a nuclear power plant according to an embodiment of the present invention.
2 is a view showing a fault tree according to an embodiment of the present invention.
3 is a flowchart illustrating a method of calculating a plurality of failure combinations according to an embodiment of the present invention.
FIG. 4 is a flowchart illustrating a method of calculating a probability of each device failure event based on a plurality of failure combination probabilities and a plurality of minimum interruption sets according to an embodiment of the present invention.
5 is a diagram showing an apparatus for calculating the probability of a device failure event for probabilistic safety evaluation of an earthquake event of a nuclear power plant according to an embodiment of the present invention.
6 and 7 are flow charts illustrating a method of calculating the probability of a device failure event for evaluating the probabilistic safety of an earthquake event of a nuclear power plant according to an embodiment of the present invention.

In the present invention, various modifications may be made and various embodiments may be provided, and specific embodiments will be illustrated in the drawings and described in detail in the detailed description. However, this is not intended to limit the present invention to a specific embodiment, it is to be understood to include all changes, equivalents, and substitutes included in the spirit and scope of the present invention. In describing each drawing, similar reference numerals have been used for similar elements.

Terms such as first, second, A, and B may be used to describe various elements, but the elements should not be limited by the terms. These terms are used only for the purpose of distinguishing one component from another component. For example, without departing from the scope of the present invention, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element. The term and/or includes a combination of a plurality of related listed items or any of a plurality of related listed items.

When a component is referred to as being "connected" or "connected" to another component, it is understood that it may be directly connected or connected to the other component, but other components may exist in the middle. Should be. On the other hand, when a component is referred to as being "directly connected" or "directly connected" to another component, it should be understood that there is no other component in the middle.

The terms used in the present application are only used to describe specific embodiments, and are not intended to limit the present invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In the present application, terms such as "comprise" or "have" are intended to designate the presence of features, numbers, steps, actions, components, parts, or combinations thereof described in the specification, but one or more other features. It is to be understood that the presence or addition of elements or numbers, steps, actions, components, parts, or combinations thereof, does not preclude in advance.

Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs. Terms as defined in a commonly used dictionary should be interpreted as having a meaning consistent with the meaning in the context of the related technology, and should not be interpreted as an ideal or excessively formal meaning unless explicitly defined in this application. Does not.

Nuclear power plants contain a complex system consisting of a number of devices, and the failure of one device does not end as a single fault, but has a feature that can affect the failure of other devices.

Many of the above devices may fail due to a cause (internal event) that occurs inside a nuclear power plant, and a malfunction may occur due to an external cause (external event) such as an earthquake event.

Probabilistic safety evaluation is performed on equipment in nuclear power plants to predict the occurrence of equipment failure due to such internal or external events, and to reduce the risk.

1 is a flowchart illustrating a method of calculating the probability of equipment failure events for probabilistic safety evaluation of an earthquake event of a nuclear power plant according to an embodiment of the present invention.

In step S110, the device failure event probability calculation device calculates a plurality of failure combination probabilities corresponding to logical combinations of N (N is a natural number) devices in the nuclear power plant using a predetermined method.

First, the logical combination is a concept corresponding to a combination of devices according to an AND condition or an OR condition, and includes a single device, and may be a concept including a combination formed by an AND condition or an OR combination for a plurality of devices, respectively.

으로 표현될 수 있고, 복수의 기기에 대해서는

으로 표현될 수 있다.For example, if the probability of multiple failure combinations according to the OR condition is 3, the failure combination probability of a single device is

Can be expressed as, for multiple devices

It can be expressed as

In addition, when the number of devices, that is, N is 3, the plurality of failure combination probability can have a total of 7 values as above, and can be expressed as 2 ^N -1 values according to the value of ^N.

In addition, the device failure event probability calculation device may calculate the failure combination probability due to an earthquake event using a predetermined method.

Here, the predetermined method may mean a method of calculating a failure combination probability due to an earthquake event using MVN integration or Reed-McCann integration, but the present invention is not limited thereto.

The NVN integration or Reed-McCann integration is used when the equipment failure event probability calculation device calculates the failure combination probability of failures of equipment having mutual partial dependencies due to an earthquake event.

Partial dependence refers to a case where device failures are simultaneously affected by an event, and in the present invention, it is preferable to regard devices as having partial dependence by an earthquake event.

A specific method of calculating the probability of a plurality of failure combinations corresponding to a logical combination of N devices by the device failure event probability calculation device using NVN integration or Reed-McCann integration is as follows.

First, the symbols and definitions to be used below will be described prior to the description.

X _i = failure event of device i

X _ij = X _i X _j = simultaneous failure event of device i and j, intersection of failure events (AND)

Xi+j = X _i +X _j = failure event of device i or j, sum of failure events (OR)

P _i =P(X _i ) = probability of failure combination of device i

P _j = P(X _j ) = probability of failure combination of device j

P _ij =P(X _ij )=P _ij =P(X _i X _j ) = failure combination probability of device i and j (AND condition)

P _i+j =P(X _i+j )=P(X _i +X _j ) = failure combination probability of device i and j (OR condition)

C _i = Independent device failure event of device i

C _ij = Device failure event that is the common cause of devices i and j

C _ijk = Device failure event that is a common cause of devices i, j and k

Q _i = P(C _i ) = probability of device failure event of device i

Q _ij = P(C _ij ) = Probability of device failure events of devices i and j (AND condition)

Q _ijk = P(C _ijk ) = Probability of device failure events of devices i, j and k (AND condition)

The following describes the covariance and correlation coefficient in order for the device failure event probability calculation device to calculate the failure combination probability of a device.

와

의 값이 같은 방향으로 변화하는지(양의 값) 반대 방향으로 변화하는지(음의 값), 서로 무관한지(0의 값)를 판단하기 위하여,

와

의 결합확률분포(Joint probability distribution)를 이용하여 산출한 산포도(Measures of dispersion)를 공분산(Covariance)이라고 한다.Of two failure events that are random variables

Wow

In order to determine whether the value of is changed in the same direction (positive value) or in the opposite direction (negative value), or not related to each other (value of 0),

Wow

The measure of dispersion calculated using the joint probability distribution of is called covariance.

는 수학식 1과 같이 표현될 수 있다.Covariance

Can be expressed as in Equation 1.

[Equation 1]

는

이고

는

이다.here

Is

ego

Is

to be.

In addition, a covariance matrix is a collection of these and expressed as a matrix.

In the present invention, it is assumed that a symmetric positive definite matrix is as follows.

의 모든 i와 j에서

이면 대칭행렬(Symmetric matrix)이라하고,

의 모든 고윳값(Eigen value)이 양수인 경우

를 양의 정부호 행렬(Positive definite matrix)이라 한다.

In all i and j of

It is called a symmetric matrix,

If all Eigen values of are positive numbers

Is called a positive definite matrix.

와

의 공분산은 확률변수에 따라 그 단위나 크기가 달라 공분산으로 두 자료의 산포도를 비교하기 어려운 경우가 발생한다. 따라서 단위와 무관하게 두 자료를 비교하기 위해 상관계수(Correlation coefficient)를 사용한다. 상관계수는 수학식 2와 같이 표현될 수 있다.Two breakdown events

Wow

The covariance of is different in units or sizes depending on the random variable, so it may be difficult to compare the scatter plots of the two data with covariance. Therefore, a correlation coefficient is used to compare two data regardless of the unit. The correlation coefficient can be expressed as in Equation 2.

[Equation 2]

를 다음과 같이 가정한다\In addition, a correlation coefficient matrix is a combination of these and expressed as a matrix. In the present invention, a symmetric positive definite matrix

Is assumed as

의 모든 i와 j에서

이면 대칭행렬(Symmetric matrix)이라하고,

의 모든 고윳값(Eigen value)이 양수인 경우

를 양의 정부호 행렬(Positive definite matrix)이라한다. Also,

In all i and j of

It is called a symmetric matrix,

If all Eigen values of are positive numbers

Is called a positive definite matrix.

Hereinafter, the failure combination probability is calculated based on the above description.

The device failure event probability calculation device calculates the failure combination probability of a single device.

를 수학식 3과 같이 중앙값(Median)과 두 개의 불확실성(Uncertainty)으로 표현할 수 있다.Ground acceleration capacity of the device to withstand an earthquake event

Can be expressed as a median and two uncertainties as shown in Equation 3.

[Equation 3]

은 지진가속도내력(Median ground acceleration capacity)의 중앙값 이고,

은

의 확률적인 변동성을 반영한 내재적 불확실성(Aleatory uncertainty, randomness uncertainty)이다.here,

Is the median ground acceleration capacity,

silver

It is an inherent uncertainty (randomness uncertainty) that reflects the probabilistic volatility of.

는

의 정보부족을 반영한 불확실성(Epistemic uncertainty, modelling uncertainty)이다. And,

Is

This is the epistemic uncertainty (modeling uncertainty) reflecting the lack of information.

과

는 수학식 4과 같이 로그노말 분포(중앙값 1)를 가정할 수 있다.Two uncertainties

and

May assume a lognormal distribution (median value 1) as shown in Equation 4.

[Equation 4]

Accordingly, the device failure event probability calculation device can calculate the single device failure combination probability P(a) at the earthquake acceleration a as shown in Equation 5.

[Equation 5]

는 표준정규누적분포 함수(Standard normal cumulative distribution function)이고,

는 표준정규누적분포 역함수(Standard normal cumulative distribution function)이다.here,

Is the standard normal cumulative distribution function,

Is the standard normal cumulative distribution function.

Q has a uniform distribution between 0 and 1.

를 0으로 이용하여 고장조합확률을 산출하거나, 복합된

를 이용하여 고장조합확률을 산출할 수 있다.In addition, if necessary, the device for calculating the probability of a device failure event

Is used as 0 to calculate the failure combination probability, or

The probability of failure combination can be calculated using.

[Equation 6]

을 정규분포함수의 적분식으로 표현하면 수학식 7과 같다.In addition,

Equation 7 is expressed as the integral expression of the normal distribution function.

[Equation 7]

In another embodiment, the plurality of failure combination probabilities corresponding to the logical combination may be a plurality of failure combination probabilities corresponding to the AND condition or the OR condition.

Specifically, the device failure event probability calculation device may calculate a failure combination probability of an AND condition or an OR condition by using NVN integration or Reed-McCann integration.

First, a method of calculating a failure combination probability corresponding to a logical combination of a plurality of devices by using the NVN integration by the device failure event probability calculation device is as follows.

The device failure event probability calculation device may calculate the failure combination probability of the AND condition using a multivariate normal distribution as shown in Equation 8 when N devices have partial correlation in an earthquake event.

[Equation 8]

이다.From here

to be.

는

의 행렬식이고,

은

의 역행렬이다.

는 대칭인 양의 정부호 행렬(Symmetric Positive Definite Matrix)이다.Also, also,

Is

Is the determinant of,

silver

Is the inverse matrix of

Is a symmetric positive definite matrix.

In addition, the device failure event probability calculation apparatus may calculate a plurality of failure combination probabilities of an OR condition by using the NVN integration, which will be described later with reference to FIG. 3.

Therefore, when the device failure event probability calculation device includes a plurality of failure combination probabilities of the OR condition described later and N is 2, the failure combination probability of all equipment may be calculated as shown in Equation 9 using the NVN integral.

[Equation 9]

이고,

,

이다.here,

ego,

,

to be.

이다.In addition,

to be.

로 치환하면 수학식 8을 수학식 10과 같이 표현할 수도 있다.Additionally,

If replaced by Equation 8 may be expressed as Equation 10.

[Equation 10]

이고,

,

이다.here,

ego,

,

to be.

In addition, a method of calculating a failure combination probability corresponding to a logical combination of a plurality of devices by using the Reed-McCann integration by the device failure event probability calculation apparatus is as follows.

In an earthquake event, when N devices have partial dependencies, the device failure event probability calculation device can calculate the failure combination probability of the AND condition using Equation 11 and the failure combination probability of the OR condition using Equation 12.

[Equation 11]

[Equation 12]

는 표준정규누적분포 함수이고,

이다.here

Is the standard normal cumulative distribution function,

to be.

In another embodiment, the device failure event may be an independent failure, which is a single device failure due to an earthquake event, or a common cause failure, which is a failure of a plurality of devices due to an earthquake event.

Specifically, a failure may occur alone in any one of the devices in a nuclear power plant due to an earthquake event, and two or more of a plurality of devices in a nuclear power plant may fail simultaneously due to the same earthquake event. have.

로 표현될 수 있고 기기가 복수인 경우

등으로 표현될 수 있는데

은 기기 1의 기기의 단독고장인 독립고장이고,

는 공통된 원인에 의해 발생된 기기 1 및 2의 공통원인고장을 나타낸다.For example, a device failure

Can be expressed as and there are multiple devices

Can be expressed as

Is an independent fault, which is an independent fault of the device of device 1,

Represents a common cause failure of devices 1 and 2 caused by a common cause.

In addition, the device failure event may have a total of 3 values as described above when the number of devices, that is, N is 2, and may be expressed as 2 ^N −1 values according to the value of ^N.

At this time, the number of independent failures is C ₁ and C _2, so there are N, and the common cause failure is C _12, so there are 2 ^N -N-1.

In step S120, the device failure event probability calculation device calculates a failure tree composed of a plurality of equipment failure events corresponding to each of the plurality of failure combination probabilities.

As shown in Fig. 2, the tree of failure is a tree representing a logical combination of equipment failure events.

Specifically, the fault tree may be composed of a basic event that means a device failure event, an AND/OR logical combination of basic events, and a peak event that means a system failure.

In addition, when the device failure event probability calculation device evaluates the reliability of a complex system consisting of a number of devices, the failure tree can be sequentially calculated as follows, and the system failure tree composed of a logical combination of device failure events is calculated. In addition, it can be calculated through the steps of calculating the minimum interrupted set from the fault tree and further expressing the minimum interrupted set as a probability of a device failure event.

In step S130, the device failure event probability calculation device calculates the minimum interruption set corresponding to the failure tree.

The first result obtained while evaluating a faulty tree is the minimum cut set of the faulty tree. The minimum interrupted set expressed in Boolean Equation means the minimum set in which a top event is triggered when all basic events constituting the set occur at the same time.

In other words, the minimum interruption set is a set of sub-events of the peak event in the fault tree, and the minimum interruption set, which is a set for each sub-event can be obtained through the fault tree.

Accordingly, the apparatus for calculating the probability of a device failure event may calculate the minimum interruption set based on a plurality of vertex events.

In another embodiment, the minimum interruption set may be a minimum interruption set of AND conditions or OR conditions corresponding to each of a plurality of failure combination probabilities.

Specifically, the minimum interruption set may consist of logical combinations of AND conditions or OR conditions according to the calculated failure tree, and each minimum interruption set corresponds to each of the calculated probability of failure combinations of the AND condition or OR condition.

For example, when N is 3, the failure combination probability of the AND condition can be calculated as 2 ³ -1 failure combination probability corresponding to the left side of Equation 13, and the minimum interruption set of the AND condition is on the right side of Equation 13. It can be represented by corresponding 2 ³ -1 C ₁ , C ₂ , C ₃ , C ₁₂ , C ₁₃ , C _23, C ₁₂₃ . Similarly, the minimum interrupted set of the OR condition may be represented by 2 ³ -1 C ₁ , C ₂ , C ₃ , C ₁₂ , C ₁₃ , C _23, C _123, etc. corresponding to the right side of Equation 14.

[Equation 13]

[Equation 14]

In step S140, the device failure event probability calculating apparatus calculates the probability of each of the plurality of equipment failure events based on a plurality of minimum interruption sets corresponding to each of the plurality of failure combination probabilities and the plurality of failure combination probabilities.

That is, the device failure event probability calculation apparatus should express the minimum interruption set as the REA probability or the MCUB probability as the probability of each of the device failure events, which will be described later with reference to FIG. 4.

In another embodiment, the device failure event probability calculation device further comprises the step of analyzing a device sensitivity corresponding to a logical combination of N devices by using the probability of each of the device failure events, wherein the device sensitivity indicates that the failure of the device is a nuclear power plant. It may have an effect on the probability of system failure.

등 과 같이 기기민감도 분석을 수행할 수 있다.In the present invention, since the apparatus for calculating the probability of a device failure event as described above can calculate the probability of each of the equipment failure events due to an earthquake event,

Device sensitivity analysis can be performed, such as.

Device sensitivity is the effect of a specific device on the reliability of the facility, and in the field of reliability analysis, it is defined as the effect of a basic event, that is, a device failure, on the probability of a system failure.

In the reliability analysis of facilities such as nuclear power plants, the following four equipment importance are widely used. 1. Birnbaum (BB) device importance, 2. Fussel-Vesely (FV) device importance, 3. Risk Achievement Worth (RAW), 4. Risk Reduction Worth (RRW) The invention is not limited thereto.

3 is a flowchart illustrating a method of calculating a plurality of failure combinations according to an embodiment of the present invention.

In step S310, if the failure combination probability is the OR condition failure combination probability, the device failure event probability calculation device may calculate a plurality of failure combination probability of the AND condition corresponding to the logical combination by using the NVN integration.

The device failure event probability calculation device can directly calculate the failure combination probability of the AND condition by using NVN integration, but if you want to obtain the failure combination probability of the OR condition, the failure combination probability of the AND condition is calculated using Equation 8. It should be calculated first.

In step S320, the device failure event probability calculation apparatus may calculate a plurality of failure combination probabilities of the OR condition using the principle of inclusion and exclusion (IEP) of the plurality of failure combination probabilities of the AND condition.

Here, the inclusion-exclusion principle is a technique for counting the elements of the union of finite sets, and it is the principle of calculating the union by subtracting the intersection of each set from the sum of all the elements of each set.

Accordingly, the device failure event probability calculation apparatus can calculate the failure combination probability of the OR condition, that is, P _IEP , by substituting the value for the failure combination probability of the AND condition into Equation 15 if there is a value.

[Equation 15]

FIG. 4 is a flowchart illustrating a method of calculating a probability of each device failure event based on a plurality of failure combination probabilities and a plurality of minimum interruption sets according to an embodiment of the present invention.

In step S410, in the step of calculating the probability of each of the plurality of device failure events by the device failure event probability calculation device, the plurality of minimum interruption sets can be expressed as the probability of each of the plurality of device failure events using the REA probability or the MCUB probability. have.

That is, P ₁ , P ₂ , P ₃ , P ₁₂ , P ₁₃ , P ₂₃ , and P ₁₂₃ are arranged on the left side as shown in Equation 16, and on the right side are Q ₁ , each probability of a device failure event. It consists of Q ₂ , Q ₃ , Q ₁₂ , Q ₁₃ , Q ₂₃ and Q ₁₂₃ .

In addition, in order for the device failure event probability calculation apparatus to express the right side as the probability of each of the device failure events, each of the minimum interruption sets may be expressed using the REA probability or the MCUB probability.

The MCUB probability is a probability consisting of the equation on the right side of Equation 16, and the REA probability is a probability consisting of the equation on the right side of Equation 17.

In general, since the value calculated by the MCUB probability is smaller than the value calculated by the REA probability, calculating the MCUB probability is advantageous in terms of accuracy, but the present invention is not limited thereto.

In step S420, the apparatus for calculating the probability of a device failure event may generate a plurality of relational expressions based on the plurality of failure combination probabilities and the probability of each of the plurality of device failure events.

For example, the apparatus for calculating the probability of a device failure event expresses each of the device failure events in the AND condition with the left side as a plurality of failure combination probabilities and the right side as the MCUB probability (when N is 3), and Equation 17 is the left side. The right side is expressed as REA probability (when N is 3) for each device failure event under AND condition with multiple failure combination probability.

And Equation 18 is that the device failure event probability calculation device expresses each of the device failure events in the OR condition with the left side as a plurality of failure combination probability and the right side as MCUB probability (when N is 3), and Equation 19 is on the left side. On the right side of the multiple failure combination probability, each device failure event in the OR condition is expressed as the REA probability (when N is 3).

[Equation 16]

[Equation 17]

[Equation 18]

[Equation 19]

In step S430, the device failure event probability calculation apparatus may calculate the probability of each of the device failure events by combining a plurality of relational expressions.

For example, Equation 19 includes a total of 7 relations, and there are a total of 7 unknowns. The apparatus for calculating the probability of a device failure event may calculate the value of each of the seven unknowns, that is, the probability of a device failure, by combining the above seven relations.

In another embodiment, the device failure event probability calculation device calculates a core damage failure tree consisting of a plurality of equipment failure events, and calculates the core damage frequency based on the probability of each of the core damage failure tree and the plurality of equipment failure events. I can.

Specifically, the apparatus for calculating the probability of an equipment failure event may calculate a tree of failures in core damage, which is composed of a logical combination of a plurality of equipment failure events with the core damage as a peak event.

And, after the device failure event probability calculation device calculates a minimum interruption set consisting of a logical combination of a plurality of equipment failure events using the core damage failure tree, the probability of each of the plurality of equipment failure events calculated in step S430 is minimized. By substituting into the set, the frequency of core damage, which is the peak event, can be calculated.

5 is a diagram showing an apparatus for calculating the probability of a device failure event for probabilistic safety evaluation of an earthquake event of a nuclear power plant according to an embodiment of the present invention.

The apparatus for calculating probability of device failure events according to an embodiment of the present invention includes a probability calculation unit 510 and a generation unit 520.

The probability calculation unit 510 calculates the probability of a plurality of failure combinations corresponding to a logical combination of N (N is a natural number) devices in a nuclear power plant using a predetermined method.

The generation unit 520 calculates a failure tree composed of a plurality of device failure events corresponding to each of the plurality of failure combination probabilities, and calculates a minimum interruption set corresponding to the failure tree.

In addition, the probability calculation unit 510 calculates the probability of each of a plurality of device failure events based on a plurality of failure combination probabilities and a plurality of minimum interruption sets corresponding to each of the plurality of failure combination probabilities.

In another embodiment, the device failure event may be an independent failure, which is a single device failure due to an earthquake event, or a common cause failure, which is a plurality of device failures due to an earthquake event.

In another embodiment, a plurality of failure combination probabilities corresponding to a logical combination may be a plurality of failure combination probabilities corresponding to an AND condition or an OR condition.

In another embodiment, if the failure combination probability is an OR condition failure event, the probability calculation unit 510 calculates the failure combination probability of the AND condition corresponding to the logical combination using the NVN integration and calculates the failure combination probability of the AND condition. Using the principle of inclusion and exclusion (IEP), the probability of failure combination of the OR condition can be calculated.

In another embodiment, the minimum interruption set may be a minimum interruption set of an AND condition or an OR condition corresponding to an AND condition or an OR condition of a failure combination probability.

In another embodiment, the generation unit 520 expresses a plurality of minimum interruption sets as a probability of each of a plurality of device failure events using REA probability or MCUB probability, and a plurality of minimum interruptions corresponding to each of the plurality of failure combination probability A plurality of relational expressions may be generated based on the set, and the probability of each device failure event can be calculated by combining the plurality of relational expressions.

In another embodiment, the device further includes an analysis unit (not shown) that analyzes the device sensitivity corresponding to the logical combination of N devices using the probability of each device failure event, and the device sensitivity indicates that the device failure is a system of a nuclear power plant. It may be an effect on the probability of failure.

In another embodiment, the damage frequency calculation unit (not shown) calculates a tree of core damage failures composed of a plurality of device failure events, and calculates the core damage frequency based on the probability of each of the tree of failures and a plurality of device failure events. Can be calculated.

6 and 7 are flow charts illustrating a method of calculating the probability of a device failure event for evaluating the probabilistic safety of an earthquake event of a nuclear power plant according to an embodiment of the present invention.

6 shows a method of calculating each probability of a device failure event under an AND condition using the method and apparatus described so far.

Specifically, the apparatus for calculating the probability of a device failure event calculates failure combination probabilities having partial correlation by arbitrarily selecting the MVN integration or the Reed-McCann integration.

In addition, the device failure event probability calculation device calculates the fault tree of the device failure events consisting of the AND condition, and calculates the minimum interruption set of the AND condition based on the calculated failure tree.

As described above, the device failure event probability calculation device generates a relational expression based on the calculated failure combination probability and minimum disconnection set, and the minimum disconnection set is expressed as the MCUB probability or REA probability of the equipment failure events to respond to the failure combination probability in the relational expression. Make it possible.

Finally, the device failure event probability calculation device combines relational expressions to calculate the probability of each device failure event in the AND condition or the OR condition, and uses the calculated probability of each failure tree to analyze the failure tree.

7 shows a method of calculating each probability of a device failure event under an OR condition.

Specifically, the apparatus for calculating the probability of a device failure event calculates failure combination probabilities having partial correlation by arbitrarily selecting the MVN integration or the Reed-McCann integration.

In addition, when the device failure event probability calculation device uses MVN integration, the failure combination probability consisting of the AND condition is calculated first, and the minimum interruption set of the OR condition is calculated based on the calculated failure combination probability of the AND condition.

When Reed-McCann integration is used, the minimum interrupted set of OR conditions can be calculated immediately.

As described above, the device failure event probability calculation device generates a relational expression based on the calculated failure combination probability and minimum disconnection set, and the minimum disconnection set is expressed as the MCUB probability or REA probability of the equipment failure events to respond to the failure combination probability in the relational expression. Make it possible.

Finally, the device failure event probability calculation device calculates the probability of each device failure event corresponding to the AND condition or the OR condition by combining relational expressions, and uses the calculated probability of each failure tree to analyze the failure tree.

So far, the present invention has been looked at around its preferred embodiments. Those of ordinary skill in the art to which the present invention pertains will be able to understand that the present invention can be implemented in a modified form without departing from the essential characteristics of the present invention. Therefore, the disclosed embodiments should be considered from an illustrative point of view rather than a limiting point of view. The scope of the present invention is shown in the claims rather than the foregoing description, and all differences within the scope equivalent thereto should be construed as being included in the present invention.

500: device failure probability calculation device
510: probability calculation unit
520: generation unit

Claims (14)

In the method for calculating the probability of equipment failure events for the probabilistic stability evaluation of earthquake events of nuclear power plants,
Calculating a plurality of failure combination probabilities corresponding to logical combinations of N devices (N is a natural number) in the nuclear power plant by using a predetermined method;
Calculating a failure tree consisting of a plurality of device failure events corresponding to each of the plurality of failure combination probabilities;
Calculating a minimum interruption set corresponding to the faulty tree; And
Comprising the step of calculating the probability of each of the plurality of device failure events based on the plurality of failure combination probability and a plurality of minimum interruption sets corresponding to each of the plurality of failure combination probability,
The plurality of device failure cases,
A method for calculating the probability of equipment failure events for probabilistic safety evaluation of an earthquake event of a nuclear power plant, characterized in that it is an independent failure that is a single device failure due to the earthquake event, or a common cause failure that is a plurality of equipment failures due to the earthquake event. delete The method of claim 1,
The probability of a plurality of failure combinations corresponding to the logical combination,
A method for calculating the probability of equipment failure events for probabilistic safety evaluation of an earthquake event of a nuclear power plant, characterized in that the probability of a plurality of failure combinations corresponding to the AND condition or the OR condition. The method of claim 3,
If the failure combination probability is the OR condition failure combination probability,
The step of calculating the plurality of failure combination probability,
Calculating a plurality of failure combination probabilities of AND conditions corresponding to the logical combination by using NVN integration; And
For the probabilistic safety evaluation of an earthquake event of a nuclear power plant, comprising the step of calculating a plurality of failure combination probabilities of the OR condition using the plurality of failure combination probabilities of the AND condition and the principle of inclusion and exclusion How to calculate the probability of device failure events. The method of claim 1,
The minimum interruption set,
A method of calculating probability of equipment failure events for probabilistic safety evaluation of an earthquake event of a nuclear power plant, characterized in that it is a minimum disconnection set of AND conditions or OR conditions corresponding to each of the plurality of failure combination probabilities. The method of claim 1,
The step of calculating the probability of each of the plurality of device failure events,
Expressing the plurality of minimum interruption sets as a probability of each of the plurality of device failure events using an REA probability or an MCUB probability;
Generating a plurality of relational expressions based on the plurality of failure combination probability and the probability of each of the plurality of device failure events; And
And calculating the probability of each of the equipment failure events by combining the plurality of relational expressions. A method of calculating the probability of equipment failure events for probabilistic safety evaluation of an earthquake event of a nuclear power plant. The method of claim 1,
Calculating a core damage failure tree consisting of the plurality of equipment failure events; And
Probability of device failure events for probabilistic safety evaluation of an earthquake event of a nuclear power plant, further comprising the step of calculating a core damage frequency based on the core damage failure tree and the probability of each of the plurality of equipment failure events Calculation method. In the device for calculating the probability of equipment failure events for probabilistic safety evaluation of earthquake events of nuclear power plants,
A probability calculation unit for calculating a plurality of failure combination probabilities corresponding to logical combinations of N devices (N is a natural number) in the nuclear power plant by using a predetermined method; And
Comprising a generation unit for calculating a failure tree consisting of a plurality of device failure events corresponding to each of the plurality of failure combination probability, and calculating a minimum interruption set corresponding to the failure tree,
The probability calculation unit calculates the probability of each of the plurality of device failure events based on the plurality of failure combination probabilities and a plurality of minimum interruption sets corresponding to each of the plurality of failure combination probabilities,
The device failure event is,
A device for calculating probability of equipment failure events for probabilistic safety evaluation of an earthquake event of a nuclear power plant, characterized in that it is an independent failure that is a single device failure due to the earthquake event or a common cause failure that is a plurality of equipment failures caused by the earthquake event. delete The method of claim 8,
The probability of a plurality of failure combinations corresponding to the logical combination,
A device for calculating the probability of equipment failure events for probabilistic safety evaluation of an earthquake event of a nuclear power plant, characterized in that the probability of a plurality of failure combinations corresponding to an AND condition or an OR condition. The method of claim 10,
If the failure combination probability is an OR condition failure event,
The probability calculation unit,
A failure combination probability of an AND condition corresponding to the logical combination is calculated using NVN integration, and a failure combination probability of an OR condition is calculated using the principle of inclusion and exclusion (IEP) of the failure combination probability of the AND condition. A device for calculating the probability of equipment failure events for probabilistic safety evaluation of earthquake events of nuclear power plants. The method of claim 8,
The minimum interruption set,
An apparatus for calculating probability of equipment failure events for probabilistic safety evaluation of an earthquake event of a nuclear power plant, characterized in that it is a minimum interruption set of an AND condition or an OR condition corresponding to an AND condition or an OR condition of the failure combination probability. The method of claim 8,
The generation unit,
The plurality of minimum interruption sets is expressed as a probability of each of the plurality of device failure events using REA probability or MCUB probability, and a plurality of relational expressions based on the plurality of failure combination probability and the probability of each of the plurality of device failure events And calculating the probability of each of the equipment failure events by combining the plurality of relational expressions. A device for calculating the probability of equipment failure events for probabilistic safety evaluation of an earthquake event of a nuclear power plant. The method of claim 8,
Further comprising a damage frequency calculation unit for calculating a core damage failure tree consisting of the plurality of equipment failure events, and calculating a core damage frequency based on the core damage failure tree and the probability of each of the plurality of equipment failure events. A device for calculating the probability of equipment failure events for probabilistic safety evaluation of earthquake events of nuclear power plants.

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