Non-monotonic correlation fault tree analysis method based on ternary decision diagram

Abstract

The invention belongs to the field of probabilistic safety analysis, and particularly relates to a non-monotonic correlation fault tree analysis method based on a ternary decision diagram. Comprising the following steps: step 1, starting from a determined top event, establishing a fault tree model of a system; 2, converting the fault tree model into a ternary decision diagram structure; 3, performing qualitative analysis on the ternary decision diagram structure; and 4, carrying out quantitative analysis on the ternary decision diagram structure. The non-monotonic associated fault tree analysis method based on the ternary decision diagram has the beneficial effects that the method is proved to have relatively high practicability in a test process, can be suitable for a non-monotonic associated fault tree and a monotonic fault tree at the same time, has relatively high universality, and can be applied to a non-monotonic associated fault tree and a monotonic fault tree. And specific analysis of the fault tree model of each nuclear power plant has pertinence and specificity.

Description

Technical Field

[0001] The present invention belongs to the field of probabilistic safety analysis, and in particular relates to a non-monotonic correlation fault tree analysis method based on a ternary decision diagram. Background Art

[0002] Fault Tree Analysis (FTA) is a key method for system reliability and safety assessment. It is a graphical deductive technique for identifying system faults and their interrelationships. It was first developed and applied by Bell Labs in the United States in 1961 when analyzing the Minuteman missile launch control system. It has since been widely used in aerospace, chemical engineering, electric power, automotive, software, and other industries related to system safety and reliability engineering. In 1974, the U.S. Atomic Energy Commission successfully introduced FTA into the probabilistic safety assessment of nuclear power plants in its WASH-1400 report. Since then, FTA has been widely used in nuclear power plant reliability and safety research.

[0003] Traditional fault tree analysis methods, based on cut sets, are highly complex and prone to combinatorial explosion when analyzing complex systems, making them difficult to implement on computers. Furthermore, for large-scale fault trees, traditional fault tree analysis methods require approximation and deletion calculations, which can lead to errors in the quantitative calculation results. To address these shortcomings of traditional analysis methods, binary decision diagram algorithms have been introduced into the field of reliability engineering.

[0004] The Binary Decision Diagram (BDD) algorithm for fault trees is a quantitative analysis method that converts fault trees into BDD structures. It uses mathematical formulas and Boolean logic operations to describe and calculate system reliability and failure probability. While the BDD algorithm offers significant advantages over traditional fault tree analysis methods, solving some large, complex fault trees with BDD still requires a significant amount of memory. To improve the computational efficiency of the BDD algorithm, Jung introduced the Zero-suppressed Binary Decision Diagram (ZBDD) algorithm for fault tree analysis in 2004. Compared to the BDD algorithm, the ZBDD algorithm uses less memory and is therefore suitable for analyzing large, complex fault trees.

[0005] Although BDD and ZBDD algorithms can quickly perform qualitative and quantitative analysis on fault trees with monotonically related faults, they are not suitable for fault trees with non-monotonic related faults containing non-logical faults. Summary of the Invention

[0006] The purpose of the present invention is to provide a non-monotonic correlation fault tree analysis method based on a ternary decision diagram, which can effectively solve the problem that a complete cut set cannot be obtained from the top event structure function of a non-monotonic correlation fault tree. The method can quickly identify all cut sets in a non-monotonic correlation fault tree, has a more efficient computational efficiency in processing non-logic, and summarizes the qualitative and quantitative analysis methods of fault trees based on the ternary decision diagram structure.

[0007] The technical solution of the present invention is as follows: a non-monotonic correlation fault tree analysis method based on a ternary decision diagram, comprising the following steps:

[0008] Step 1: Starting from the determined top event, establish the fault tree model of the system;

[0009] Step 2: Convert the fault tree model into a ternary decision diagram structure;

[0010] Step 3: Qualitative analysis of the ternary decision diagram structure;

[0011] Step 4: Quantitatively analyze the structure of the ternary decision diagram.

[0012] In step 1, the variable x is introduced into the fault tree. i , where i = (1, 2, ..., n) represents each device component in the power plant system, and the variable value reflects the current status of the device.

[0013]

[0014] Then the structure function of the fault tree is represented by f

[0015]

[0016] Where x=(x1,...,x n ).

[0017] The step 2 includes the following:

[0018] 1) TDD conversion of fault tree model:

[0019] Obtain the structure function f(x) of the fault tree from step 1, i = (1, 2, ..., n), and use the ifre formula to construct the TDD

[0020]

[0021] in:

[0022] Represents device x i The Boolean function that failed,

[0023] Represents device x i Normally running Boolean function; the ifre expansion of f can be further represented by TDD structure.

[0024] In the logical operation of TDD, each basic event is regarded as an ifre expression. For any basic event X, X =<X,1,0,0> Similarly,

[0025] Logical operation of TDD: Let x and y be two basic events, and the expansion order is x<y, is any Boolean operation, then G(x)=<x,G1,G0,G2> and H(y)=<y,H1,H0,H2> The TDD logic operation rules are as follows:

[0026]

[0027] 2) ZTDD conversion of fault tree:

[0028] The structural function of the fault tree f(x), i = (1, 2, ..., n), also uses the ifre formula to construct ZTDD

[0029]

[0030] Logical operation of ZTDD: Let x and y be two basic events, and the expansion order is x<y, is any Boolean operation, then G(x)=<x,G1,G0,G2> and H(y)=<y,H1,H0,H2> The ZTDD logic operation rules are as follows:

[0031] G(x)·H(y)=<x,G1·H,G0H,G2·H>

[0032] G(x)+H(y)=<x,G1,G0,G2+H>

[0033] G(x)·H(x)=<x,G1·H1+G1·H2+G2·H1,G0·H0+G0·H2+G2·H0,G2·H2>

[0034] G(x)+H(x)=<x,G1+H1,G0+H0,G2+H2>

[0035] ZTDD can directly calculate the inverse function of a Boolean expression. According to Morgan's theorem, if

[0036]

[0037] but

[0038] In step 3, the possible failure modes of the system are found through qualitative analysis of the ternary decision diagram algorithm, that is, the minimum cut set of the fault tree is solved. In the fault tree, the set of basic events that lead to the top event is called a cut set. When any basic event in the cut set is removed and no top event occurs, such a cut set is called a minimum cut set. After the ternary decision diagram TDD / ZTDD of the fault tree is obtained, the minimum cut set of the fault tree can be obtained by directly traversing the ternary decision diagram.

[0039] In step 3, each path starting from the root node can reach the terminal nodes 1 and 0 along the ternary decision diagram. The terminal nodes 1 and 0 represent the two logical states of system unavailability and normal operation of the system, respectively. The non-terminal nodes correspond to the basic events of the fault tree. If the basic event occurs, that is, the equipment fails, then the path proceeds along the solid line of branch 1. If the basic event does not occur, that is, the equipment operates normally, then the path proceeds along the dotted line of branch 0. If the system state is unrelated to the current equipment state, then the path proceeds along the C-dashed line of branch C. All non-terminal nodes on the path from the root node along the TDD / ZTDD diagram to the terminal node 1, located on branches 1 and 0, excluding branch C, constitute the system's cut set / minimum cut set.

[0040] The step 4 includes the following:

[0041] 1) Using TDD structure to calculate the failure rate of the top event of the fault tree

[0042] TDD is a variant of BDD. The two structures are equivalent in Boolean logic and can be converted into each other:

[0043]

[0044] After converting the TDD structure into the BDD structure, calculate the failure rate of the top event of the fault tree

[0045]

[0046]

[0047] Continue to expand G and H to the nth order, and we can get f(x), x=(x1, x2, ..., x n ) Top event failure rate, that is, the unavailability of the system.

[0048] 2) Use the ZTDD structure to calculate the failure rate of the top event of the fault tree,

[0049] The ZTDD quantitative analysis follows the ifre formula in step 2, and its top event failure rate can be recursively calculated from the bottom of the ternary decision diagram structure.

[0050]

[0051] The beneficial effects of the present invention are as follows: the non-monotonic correlation fault tree analysis method based on the ternary decision diagram described in the present invention has been proven to be highly practical during the test process, and can be applied to non-monotonic correlation fault trees as well as monotonic fault trees, with high universality. The specific analysis of the fault tree model of each nuclear power plant is targeted and specific, and is expected to be used in the subsequent autonomous development of probabilistic safety analysis (PSA) software. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Express the fault tree structure function f using TDD structure;

[0053] Figure 2 for TDD representation;

[0054] Figure 3 for ZTDD representation. DETAILED DESCRIPTION

[0055] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0056] The present invention provides a non-monotonic correlation fault tree analysis method based on a ternary decision diagram, which effectively solves the problem that a complete cut set cannot be obtained from the top event structure function of the non-monotonic correlation fault tree. Compared with the binary decision diagram, the ternary decision diagram is more efficient in processing non-logic. The fault tree is transformed using a ternary decision diagram (TDD) and a zero-suppressed ternary decision diagram (ZTDD) algorithm. An additional calculation is performed at the third variable of the ternary decision diagram to ensure that all cut sets unrelated to the current node can be accurately identified by the ternary decision diagram. After the ternary decision diagram of the fault tree is obtained, all failure modes and failure paths of the system have actually been obtained. The minimum cut set can be obtained by traversing the ternary decision diagram. At the same time, the top event failure rate can be recursively calculated from the bottom of the ternary decision diagram structure from bottom to top.

[0057] A non-monotonic correlation fault tree analysis method based on a ternary decision diagram includes the following steps:

[0058] Step 1: Based on the actual situation of the system, starting from the determined top event, following the basic rules and methods of the fault tree and the actual situation of the power plant system, establish the fault tree model of the system.

[0059] Introducing variable x into the fault tree i, where i = (1, 2, ..., n) represents each device component in the power plant system, and the variable value reflects the current status of the device.

[0060]

[0061] Then the structure function of the fault tree is represented by f

[0062]

[0063] Where x=(x1,...,x n ).

[0064] Step 2: Convert the fault tree model into a ternary decision diagram structure

[0065] 1) TDD conversion of fault tree model:

[0066] Obtain the structure function f(x) of the fault tree from step 1, i = (1, 2, ..., n), and use the ifre formula to construct the TDD

[0067]

[0068] in:

[0069] N=GH,

[0070] Represents device x i The Boolean function that failed,

[0071] Represents device x i Normally running Boolean functions.

[0072] The ifre expansion form of f can be further represented by TDD structure, such as Figure 1 shown.

[0073] In the figure, x is the root node of TDD, G, H, and N are the 1-branch, 0-branch, and C-branch of x, respectively. In the figure, x has three connecting lines pointing downward. If device x fails (x is 1), then G (f = G) is considered; if device x operates normally (x is 0), then H (f = H) is considered; if the situation is unrelated to device x, then N (f = N) is considered.

[0074] In the logical operation of TDD, each basic event is regarded as an ifre expression, so for any basic event X, X =<X,1,0,0> Similarly,

[0075] Logical operation of TDD: Let x and y be two basic events, and the expansion order is x<y, For any Boolean operation, according to formula (1), let G1, G0, G2 be the 1 / 0 / C-branch of G(x) based on ifre expansion of x, and H1, H0, H2 be the 1 / 0 / C-branch of H(y) based on ifre expansion of y, then the TDD logic operation rules of G(x) = <x, G1, G0, G2> and H(y) = <y, H1, H0, H2> are as follows:

[0076]

[0077] 2) ZTDD conversion of fault tree:

[0078] The structural function of the fault tree f(x), i = (1, 2, ..., n), also uses the ifre formula to construct ZTDD

[0079]

[0080] Logical operation of ZTDD: Let x and y be two basic events, and the expansion order is x<y, For any Boolean operation, according to formula (2), let G1, G0, G2 be the 1 / 0 / C-branch of G(x) based on ifre expansion x, and H1, H0, H2 be the 1 / 0 / C-branch of H(y) based on ifre expansion y, then the ZTDD logic operation rules of G(x) = <x, G1, G0, G2> and H(y) = - <y, H1, H0, H2> are as follows:

[0081] G(x)·H(y)=<x,G1·H,G0·H,G2·H>

[0082] G(x)+H(y)=<x,G1,G0,G2+H>

[0083] G(x)·H(x)=<x,G1·H1+G1·H2+G2·H1,G0·H0+G0·H2+G2·H0,G2·H2>

[0084] G(x)+H(x)=<x,G1+H1,G0+H0,G2+H2>

[0085] ZTDD can directly calculate the inverse function of a Boolean expression. According to Morgan's theorem, if

[0086]

[0087] but

[0088] Step 3: Qualitative analysis of the ternary decision diagram structure

[0089] The goal of qualitative analysis using the ternary decision diagram algorithm is to identify possible failure modes in a system, that is, to find the minimum cut set of the fault tree. In a fault tree, the set of basic events that lead to the top event (system failure) is called a cut set. When removing any basic event from the cut set no longer leads to the top event, the cut set is called a minimum cut set.

[0090] When the fault tree is a monotonically associated fault tree, the operation of a certain device will not lead to an increase in system unavailability. Therefore, analysts only need to consider which device failures in the minimum cut set will lead to adverse consequences such as system failure or core damage. The cut set is all positive variables x i The collection of (device x i Failure leads to system unavailability). However, for non-monotonic correlation fault trees, some normally operating devices may also cause adverse consequences such as system failure. Therefore, the cut set of non-monotonic correlation fault trees is usually all positive and negative variables. The collection of (device x i Failure does not cause the system to be unavailable, but the device x i Failed and device x j Normal operation will cause the system to be unavailable). Compared with the binary decision diagram algorithm, the ternary decision diagram is more efficient in processing non-logical More efficient in terms of performance.

[0091] After obtaining the ternary decision diagram (TDD / ZTDD) of the fault tree, all the failure modes (basic event combinations that affect the top event state) and failure paths of the system have actually been obtained. The minimum cut set of the fault tree can be obtained by directly traversing the ternary decision diagram.

[0092] Every path from the root node can reach terminal nodes 1 and 0 along the ternary decision diagram. Terminal nodes 1 and 0 represent the two logical states of system unavailability and normal operation, respectively. Non-terminal nodes correspond to basic events (i.e., system equipment) in the fault tree. If the basic event occurs, i.e., the equipment fails, the path proceeds along branch 1 (solid line). If the basic event does not occur, i.e., the equipment operates normally, the path proceeds along branch 0 (dashed line). If the system state is unrelated to the current equipment state, the path proceeds along branch C (dashed line). All non-terminal nodes (equipment) located on branches 1 and 0 (excluding branch C) along the path from the root node to terminal node 1 along the TDD / ZTDD diagram constitute the system's cut set / minimum cut set.

[0093] Step 4: Quantitative analysis of the ternary decision diagram structure

[0094] 1) Using TDD structure to calculate the failure rate of the top event of the fault tree

[0095] Since TDD is a variant of BDD, the two constructs are Boolean equivalent and can be converted to each other:

[0096]

[0097] Therefore, after converting the TDD structure into the BDD structure, the failure rate of the top event of the fault tree can be calculated.

[0098]

[0099] Continue to expand G and H to the nth order, and we can get f(x), x=(x1, x2, ..., x n ) Top event failure rate, that is, the unavailability of the system.

[0100] 2) Use the ZTDD structure to calculate the failure rate of the top event of the fault tree.

[0101] The ZTDD quantitative analysis follows the ifre formula in step 2, and its top event failure rate can be recursively calculated from the bottom of the ternary decision diagram structure.

[0102]

[0103] The present invention will be further described below in conjunction with the embodiments:

[0104] Example 1 (TDD algorithm):

[0105] Step 1: Create a fault tree based on the specific situation of the nuclear power plant system T1. The system contains three devices A, B, and C. The structure function of the fault tree is as follows:

[0106]

[0107] Step 2: Convert the fault tree into a ternary decision diagram structure and convert T1 into TDD

[0108]

[0109] The TDD structure of T1 is as follows Figure 2 shown

[0110] Step 3: Qualitative analysis of the TDD structure

[0111] Traversal Figure 2 In the TDD structure, all non-terminal nodes on the 1 and 0 branches (excluding the C branch) on the path to the terminal node 1 constitute the cut set of the system. Therefore, the cut set of T1 is

[0112]

[0113] It means when the following three situations occur:

[0114] 1) Device A fails and device C is running, 2) Device A is running and device B fails, 3) Device B fails and device C is running, resulting in system T1 being unavailable.

[0115] Step 4: Quantitative analysis of TDD structure

[0116] Unavailability of system T1:

[0117]

[0118] Example 2 (ZTDD algorithm):

[0119] Step 1: Establish a fault tree based on the specific situation of a system T2 in a nuclear power plant. The system contains three devices A, B, and C. The structure function of the fault tree is as follows:

[0120]

[0121] Step 2: Convert the fault tree into a ternary decision diagram structure and convert T1 into ZTDD

[0122]

[0123] The ZTDD structure of T2 is as follows Figure 3 shown

[0124] Step 3: Qualitative analysis of the ZTDD structure

[0125] Traversal Figure 3 In the ZTDD structure, all non-terminal nodes on the 1 and 0 branches (excluding the C branch) on the path to the terminal node 1 constitute the minimum cut set of the system. Therefore, the minimum cut set of T2 is

[0126]

[0127] It means when the following two situations occur:

[0128] 1) Device A is running, 2) Devices B and C are running at the same time, causing system T2 to be unavailable.

[0129] Step 4: Quantitative analysis of the ZTDD structure

[0130] Unavailability of system T2:

[0131]

[0132] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Any equivalent changes or modifications made in accordance with the spirit of the present invention are intended to be covered by the scope of protection of the present invention.

Claims

1. A non-monotonic correlation fault tree analysis method based on a ternary decision diagram, characterized in that: The steps include: Step 1: Starting from the determined top event, establish the fault tree model of the system; Step 2: Convert the fault tree model into a ternary decision diagram structure; Step 3: Qualitative analysis of the ternary decision diagram structure; Step 4: Quantitatively analyze the structure of the ternary decision diagram.

2. The non-monotonic correlation fault tree analysis method based on a ternary decision diagram according to claim 1, characterized in that: In step 1, the variable x is introduced into the fault tree. i , where i = (1, 2, ..., n) represents each device component in the power plant system, and the variable value reflects the current status of the device. Then the structure function of the fault tree is represented by f Where x=(x1,...,x n ).

3. The non-monotonic correlation fault tree analysis method based on a ternary decision diagram according to claim 1, characterized in that: The step 2 includes the following: 1) TDD conversion of fault tree model: Obtain the structure function f(x) of the fault tree from step 1, i = (1, 2, ..., n), and use the ifre formula to construct the TDD in. Represents device x i The Boolean function that failed, Represents device x i Normally functioning Boolean functions; The ifre expansion form of f can be further represented by the TDD structure; In the logical operation of TDD, each basic event is regarded as an ifre expression. For any basic event X, X = <x, 1, 0, 0>. Similarly, Logical operation of TDD: Let x and y be two basic events, and the expansion order is x < y. For any Boolean operation, the TDD logical operation rules of G(x) = <x, G1, G0, G2> and H(y) = <y, H1, H0, H2> are as follows: 2) ZTDD conversion of fault tree: The structural function of the fault tree f(x), i = (1, 2, ..., n), also uses the ifre formula to construct ZTDD Logical operations of ZTDD: Let x and y be two basic events, and the expansion order is x < y. For any Boolean operation, the ZTDD logical operation rules for G(x) = <x, G1, G0, G2> and H(y) = <y, H1, H0, H2> are as follows: G(x)·H(y)= <x,G1·H,G0·H,G2·H> G(x)+H(y)= <x,G1,G0,G2+H> G(x)·H(x)= <x,G1·H1+G1·H2+G2·H1,G0·H0+G0·H2+G2·H0,G2·H2> G(x)+H(x)= <x,G1+H1,G0+H0,G2+H2> ZTDD can directly calculate the inverse function of a Boolean expression. According to Morgan's theorem, if but 4. The non-monotonic correlation fault tree analysis method based on a ternary decision diagram according to claim 1, characterized in that: In step 3, the possible failure modes of the system are found through qualitative analysis of the ternary decision diagram algorithm, that is, the minimum cut set of the fault tree is solved. In the fault tree, the set of basic events that lead to the top event is called a cut set. When any basic event in the cut set is removed and no top event occurs, such a cut set is called a minimum cut set. After the ternary decision diagram TDD / ZTDD of the fault tree is obtained, the minimum cut set of the fault tree can be obtained by directly traversing the ternary decision diagram.

5. The non-monotonic correlation fault tree analysis method based on a ternary decision diagram according to claim 4, characterized in that: In step 3, each path starting from the root node can reach the terminal nodes 1 and 0 along the ternary decision diagram. The terminal nodes 1 and 0 represent the two logical states of system unavailability and normal operation of the system, respectively. The non-terminal nodes correspond to the basic events of the fault tree. If the basic event occurs, that is, the equipment fails, then the path proceeds along the solid line of branch 1. If the basic event does not occur, that is, the equipment operates normally, then the path proceeds along the dotted line of branch 0. If the system state is unrelated to the current equipment state, then the path proceeds along the C-dashed line of branch C. All non-terminal nodes on the path from the root node along the TDD / ZTDD diagram to the terminal node 1, located on branches 1 and 0, excluding branch C, constitute the system's cut set / minimum cut set.

6. The non-monotonic correlation fault tree analysis method based on a ternary decision diagram according to claim 1, characterized in that: The step 4 includes the following: 1) Using TDD structure to calculate the failure rate of the top event of the fault tree TDD is a variant of BDD. The two structures are equivalent in Boolean logic and can be converted into each other: After converting the TDD structure into the BDD structure, calculate the failure rate of the top event of the fault tree Continue to expand G and H to the nth order, and we can get f(x), x=(x1,x2,...,x n ) Top event failure rate, that is, the unavailability of the system.

7. The non-monotonic correlation fault tree analysis method based on a ternary decision diagram according to claim 6, characterized in that: The step 4 includes the following: 2) Use the ZTDD structure to calculate the failure rate of the top event of the fault tree, The ZTDD quantitative analysis follows the ifre formula in step 2, and its top event failure rate can be recursively calculated from the bottom of the ternary decision diagram structure.

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