Event tree analysis method based on binary decision diagram

Abstract

The invention belongs to the field of probabilistic security analysis, and particularly relates to an event tree analysis method based on a binary decision diagram. Comprising the following steps: 1, representing an event tree by using a BDD structure; 2, preprocessing the structure according to a simplification rule of the BDD, deleting redundant nodes and isomorphic subgraphs in the BDD, and merging final nodes to obtain a simplified BDD structure; step 3, optimizing a BDD structure based on a dynamic variable sorting algorithm of adjacent variable exchange; step 4, obtaining a corresponding optimized event tree by utilizing the BDD after the simplification in the step 2 and the dynamic sorting optimization of the variable sequence in the step 3; and 5, performing qualitative analysis and quantitative analysis on the optimized event tree by using a BDD structure. The method has the beneficial effects that a dynamic variable sorting algorithm suitable for simplifying various event trees is provided for the purpose of minimizing the CD sequence of the event tree, the effectiveness of the algorithm is verified through examples, the space and time complexity of the algorithm can be effectively reduced, and the analysis efficiency of the event tree is improved.

Description

Technical Field

[0001] The present invention belongs to the field of probabilistic safety analysis, and in particular relates to an event tree analysis method based on a binary decision diagram. Background Art

[0002] Probabilistic Safety Assessment (PSA) uses probabilistic methods to quantitatively analyze the accident mitigation process in nuclear power plants, identify weaknesses, and improve the safety and economic efficiency of power plants. The first step in applying PSA is to collect reliability data and establish a PSA model for the power plant. Based on the collection and understanding of effective plant information, an event tree and fault tree model is constructed, and the model is qualitatively and quantitatively analyzed.

[0003] Traditional event tree analysis methods follow the chronological order of an accident, starting with a given initiating event and analyzing it step by step to infer possible consequences. When constructing the initial event tree based on temporal logic, structural redundancy is typically not considered. As a result, the resulting event tree structure can be complex, leaving room for optimization in terms of both structure and computation time.

[0004] After obtaining the binary decision diagram (BDD) of the event tree, all possible accident pathways (combinations of functional events leading to CD) resulting from the initiating event are actually obtained. The computational time for analyzing and manipulating the event tree primarily depends on the size (sequences and number of nodes) of the event tree involved. The number of sequences in the event tree directly corresponds to the path along the BDD from the root node to the final node along the graph. The size of the BDD is heavily dependent on the variable order. Therefore, optimizing the variable order and compressing the number of BDD paths can effectively reduce the size of the event tree. Summary of the Invention

[0005] The purpose of the present invention is to provide an event tree analysis method based on binary decision diagrams, which minimizes the event tree CD sequence by simplifying BDD and dynamically sorting and optimizing the variable sequence, thereby reducing the complexity of the event tree and improving the computational efficiency.

[0006] The technical solution of the present invention is as follows: an event tree analysis method based on a binary decision diagram, comprising the following steps:

[0007] Step 1: Use BDD structure to represent the event tree;

[0008] Step 2: Preprocess the structure according to the BDD simplification rules, delete redundant nodes and isomorphic subgraphs in the BDD, and merge the terminal nodes to obtain a simplified BDD structure;

[0009] Step 3: Optimize the BDD structure based on the dynamic variable sorting algorithm with adjacent variable exchange;

[0010] Step 4: Obtain the corresponding optimized event tree using the BDD simplified in step 2 and the dynamically sorted optimized variable order in step 3;

[0011] Step 5: Use the BDD structure to perform qualitative and quantitative analysis on the optimized event tree.

[0012] The step 1 includes: event tree analysis is an accident sequence analysis method from the initiating event to the final state, the event tree header consists of the initiating event and the functional event; the trunk of the event tree represents the initiating event, and the event tree branches represent the success or failure of a safety function of the nuclear power plant. At each branch point, the upward branch represents the successful operation of the safety function, and the downward branch represents the loss of the safety function; the branch endpoint is the result of the combination of the initiating event and subsequent events, representing a state of the power plant, that is, the core is intact OK or the core is damaged CD.

[0013] The simplification rules in step 2 include:

[0014] Rule 1: Remove redundant nodes

[0015] For a node in a BDD, if its 1 branch and 0 branch both point to the same child node, delete the node and connect the branch pointing to the node directly to the corresponding child node;

[0016] Rule 2: Delete isomorphic subgraphs

[0017] For nodes u and v in a BDD, if they have the same Boolean structure, delete node u and connect the branch pointing to node u directly to node v.

[0018] The dynamic variable sorting algorithm based on adjacent variable exchange adopted in step 3 is as follows:

[0019] Under the assumption that the positions of all other variables remain unchanged, find the optimal position of the variable, that is, the position with the least failure path of the corresponding BDD structure. Repeat this process, moving each variable once. For a Boolean function f(x) with n variables, x=(x1, x2, ... x n ),variable x i (i=1,2,...,n) When the positions of other variables remain unchanged, there are n potential positions. The screening algorithm uses enumeration to exchange x in turn. i and x i The adjacent variables, based on the failure path information of the event tree, are variables x i Find the point among these n locations that minimizes the BDD failure path;

[0020] For a Boolean function f(x), x=(x1, x2, ...x n )'s adjacent variable x i , x i+1 When performing Shannon expansion, there is

[0021]

[0022] Swap x i , x i+1 The expansion order of

[0023]

[0024] Exchange the order of adjacent variables in the BDD structure i , x i+1 There are three possible situations:

[0025] 1) Case 1: When x does not exist in the BDD structure i or x i+1 When the node is x, the order of adjacent variables is swapped i , x i+1 It will not affect the BDD structure;

[0026] 2) Case 2: When x exists in the BDD structure i , x i+1 Node, and f 11 , f 10 , f 01 , f 00 If they are different, swap the order of adjacent variables x i , x i+1 Will swap f in the BDD structure 10 (10-branch) and f 01 (01-Branch) location.

[0027] 3) Case 3: When x exists in the BDD structure i ,x i+1 Node, and f 11 ,f 10 ,f 01 ,f 00 When the same function exists in 10 =f 00 ), at this time, the order of adjacent variables x is exchanged i ,x i+1 It can eliminate redundant nodes and simplify the structure of BDD.

[0028] In step 4, since each path from the root node along the BDD graph to the terminal node in the BDD structure represents an event sequence of the event tree, the corresponding event tree is directly obtained using the BDD structure.

[0029] The qualitative analysis in step 5 is to solve the minimum cut set of the event tree. Each minimum cut set represents a failure mode that causes damage to the power plant core after the initiating event occurs. All paths with terminal nodes 1 in the BDD diagram represent the CD sequence of the event tree. The non-terminal nodes located on the 1 branch in the path, that is, the combination of the initiating event and the specific failed power plant safety function, constitute the minimum cut set of the system.

[0030] The quantitative analysis in step 5 uses the BDD structure to calculate the core damage probability CDF after the initiating event in the event tree. If f(x), x=(x1, x2, ... x n ), the variable order is x1 <x2<...<x n , use Shannon expansion theorem to transform f(x) into the following form:

[0031]

[0032] in:

[0033] Indicates safety function x i Failed Boolean function,

[0034] Indicates safety function x i Normally functioning Boolean functions;

[0035] Therefore, the quantitative analysis also follows the above Shannon expansion, and the failure rate of the top event satisfies

[0036]

[0037] Expand F1 and F0 to the nth order and we can get f(x), x=(x1,x2,...,x n ), which is the CDF of the current event tree.

[0038] The beneficial effects of the present invention are as follows: based on the CD sequence information of the event tree, the present invention aims to minimize the CD sequence of the event tree and proposes a dynamic variable sorting algorithm suitable for simplifying various event trees. The effectiveness of the algorithm is verified through examples, and it can effectively reduce the algorithm's space and time complexity, thereby improving the analysis efficiency of the event tree. Testing has also confirmed that the method has high practicality and can optimize the BDD storage structure (the CD sequence of the event tree is reduced by approximately 25%; the number of nodes in the BDD structure is reduced by approximately 15%) while ensuring the accuracy of the calculation engine algorithm, and improve calculation speed (the calculation time of the PSA software analyzing the event tree is reduced by approximately 5%). BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Event tree of breach accident in RRA system;

[0040] Figure 2 BDD structure of the event tree for breach accidents in RRA system;

[0041] Figure 3 This is the rupture diagram of the hot section of the primary circuit of a power plant event tree under the BI1A power operating condition;

[0042] Figure 4 This is the simplified BDD diagram;

[0043] Figure 5 BDD representation optimized for the screening algorithm;

[0044] Figure 6 This is the event tree BI1A diagram after the screening algorithm is optimized;

[0045] Figure 7 Case 1 of exchanging the order of adjacent variables in BDD structure;

[0046] Figure 8 Case 2 of exchanging the order of adjacent variables in BDD structure;

[0047] Figure 9 Case 3 of exchanging the order of adjacent variables in BDD structure. DETAILED DESCRIPTION

[0048] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0049] To address the redundancy problem of event tree structures in current traditional event tree analysis, the present invention provides an event tree analysis method based on binary decision diagrams (BDDs). This method can convert event trees into BDD structures for quantitative analysis and describe the probability of event tree sequences using mathematical formulas and Boolean logic operations. Compared to traditional analysis methods, this method can simplify event trees through operations such as node merging and deleting duplicate variables. Furthermore, by using the CD sequence information of the event tree, with the goal of minimizing the CD sequence of the event tree, a dynamic variable sorting algorithm suitable for simplifying various event trees is provided, further improving the algorithm's operational efficiency.

[0050] An event tree analysis method based on a binary decision diagram comprises the following steps:

[0051] Step 1: Use BDD structure to represent the event tree;

[0052] Event tree analysis is a method for analyzing accident sequences from initiating events to final states. The event tree header consists of initiating events and functional events. The trunk of the event tree represents the initiating event, such as a Level 4 power failure. The branches of the event tree represent the success or failure of a nuclear power plant safety function. At each branch point, an upward branch represents successful operation of the safety function, while a downward branch represents a loss of the safety function. The branch endpoints are the result of the combination of the initiating event and subsequent events, representing a power plant state, such as core integrity (OK) or core damage (CD).

[0053] Take the simplest power plant accident as an example: When a power plant responds to a breach accident in the RRA system, it needs to consider the safety function of core heat removal. If the core heat cannot be removed, core damage (CD) is inevitable. The event tree established by the above analysis is as follows: Figure 1 shown.

[0054] Using an upright tree structure to represent the event tree, we can get the BDD structure of the tree as follows: Figure 2 As shown in the figure, the top event T (initiating event) is called the root node of the BDD; 1 and 0 are terminal nodes, representing the two logical states of core damage CD and core integrity OK, respectively; the non-terminal node X1 is called a basic event, corresponding to the core heat removal safety function of the nuclear power plant. Nodes are connected by downward connections—1 branches (solid lines) and 0 branches (dashed lines). For example, the 1 branch of X1 indicates that if safety function X1 (X1 value is 1) fails, the terminal node 1 (f = 1) is reached; the 0 branch of X1 indicates that if safety function X1 operates normally (X1 value is 0), the terminal node 1 (f = 0) is reached.

[0055] Every path starting from the root node can reach the final node along the BDD graph. Figure 2 There are two paths from the top event to the terminal node of the BDD structure: {T-X1-1}, Corresponding respectively Figure 1 The two sequences in the event tree are: the CD sequence, which indicates that when a breach accident occurs in the initiating event T RRA system, if the X1 safety function - core heat extraction fails, the core will eventually be damaged (CD); the OK sequence, which indicates that when a breach accident occurs in the initiating event T RRA system, if the X1 safety function - core heat extraction succeeds, the core will eventually be intact (OK).

[0056] Expressed as f(X1) Figure 2 The Boolean function of the breach accident in the RRA system is

[0057] f(X1)=TX1

[0058] Where T represents the state of the initiating event T

[0059]

[0060] The value of variable X1 reflects the current status of safety function X1.

[0061]

[0062] The Boolean function f(X1) (top event failure rate) represents the state of the power plant core,

[0063]

[0064] Step 2: Preprocess the structure according to the BDD simplification rules, delete redundant nodes and isomorphic subgraphs in the BDD, and merge the terminal nodes to obtain a simplified BDD structure;

[0065] The simplification rules include:

[0066] Rule 1: Remove redundant nodes

[0067] For a node in a BDD, if its 1 branch and 0 branch both point to the same child node, delete the node and connect the branch pointing to the node directly to the corresponding child node;

[0068] Rule 2: Delete isomorphic subgraphs

[0069] For nodes u and v in a BDD, if they have the same Boolean structure, delete node u and connect the branch pointing to node u directly to node v.

[0070] Step 3: Optimize the BDD structure based on the dynamic variable sorting algorithm with adjacent variable exchange;

[0071] In general, power plants typically need to consider n (≥10) safety functions when responding to an initiating event. Research has shown that the computational time required to analyze and manipulate a BDD depends primarily on the size of the BDDs involved. This BDD size is closely related to the ordering of the basic events (safety functions) in the event tree. Using different ordering methods can result in BDD sizes that differ by dozens of times. This paper applies the following screening algorithm to optimize the variable order, simplify the BDD size, and improve analysis efficiency.

[0072] The general process of the dynamic variable sorting algorithm based on adjacent variable exchange is as follows:

[0073] Assuming that the positions of all other variables remain unchanged, find the optimal position of the variable, that is, the position with the least BDD structure failure path (CD sequence). Repeat this process, moving each variable once. For a Boolean function f(x) with n variables (basic events), x = (x1, x2, ... x n )variable x i(i=1,2,...,n) When the positions of other variables remain unchanged, there are n potential positions. The screening algorithm uses enumeration to exchange x in turn. i and x i The adjacent variables, based on the failure path information of the event tree, are variables x i Find the point among these n locations that minimizes the BDD failure path.

[0074] For a Boolean function f(x), x=(x1, x2, ..., x n )'s adjacent variable x i , x i+1 When performing Shannon expansion, there is

[0075]

[0076] in,

[0077] f 11 Indicates safety function x i , x i+1 Boolean functions that are invalid,

[0078] f 10 Indicates safety function x i Failure, x i+1 Normally running Boolean functions,

[0079] f 01 Indicates safety function x i Success, x i+1 Failed Boolean function,

[0080] f 00 Indicates safety function x i , x i+1 Boolean functions that all work correctly.

[0081] Swap x i , x i+1 The expansion order of the exchanged Boolean function f is i , x i+1 The Shannon expansion of express

[0082]

[0083] Exchange the order of adjacent variables in the BDD structure i , x i+1 There are three possible situations:

[0084] 1) Case 1: If Figure 7 As shown, when x does not exist in the BDD structure i or x i+1 When the node is x, the order of adjacent variables is swappedi , x i+1 Does not affect the BDD structure.

[0085] 2) Case 2: If Figure 8 As shown, when there is x in the BDD structure i , x i+1 Node, and f 11 , f 10 , f 01 , f 00 If they are different, swap the order of adjacent variables x i , x i+1 After that, the f in the BDD structure will be exchanged 10 (10-branch) and f 01 (01-Branch) location.

[0086] 3) Case 3: If Figure 9 As shown, when there is x in the BDD structure i , x i+1 Node, and f 11 , f 10 , f 01 , f 00 When the same function exists in 10 =f 00 ), at this time, the order of adjacent variables x is exchanged i , x i+1 It can eliminate redundant nodes and simplify the structure of BDD.

[0087] Observe the adjacent variable x i , x i+1 After the exchange of the BDD structure, after the variables of two adjacent layers are exchanged, the edges pointing to the structure from the outside will not change, and the functions pointing to the outside of the structure will not change. That is, after the exchange of positions, x i The output edges still point to f1, f2, f3, and f4. Therefore, any exchange of adjacent variables will only affect the position and number of nodes in the exchange layer and will not change the BDD structure of other layers.

[0088] This dynamic variable sorting algorithm based on adjacent variable exchange is referred to as the screening algorithm. The specific steps of the adjacent variable exchange of the screening algorithm are: for variable x i , swap the variable with its adjacent variable in sequence until the variable x i is swapped to the last position, and then the variable x i Swap with the previous adjacent variables in sequence until variable x i Is swapped to the first place. During the algorithm screening process, record the variable x i The failure path information (i.e., the number of CD sequences) of the BDD graph corresponding to each position is completed in the variable x iAfter the optimal sorting screening, move the variable x i , backtrack to the optimal position to restore the optimal sort, that is, the point in all positions that minimizes the BDD failure path.

[0089] The time complexity of the screening algorithm to search for the best position for the selected variable increases linearly with the number of variables n, so it takes O(n) to move each variable once. 2 ) times adjacent variables are exchanged. To control the complexity of the algorithm in the most unfavorable case, the search for variables in a specific direction is terminated when the size of the BDD graph grows to twice its original size.

[0090] Step 4: Obtain the corresponding optimized event tree using the BDD optimized by the simplification in step 2 and the dynamic sorting of the variable order in step 3;

[0091] Since each path in the BDD structure starting from the root node and reaching the end node along the BDD graph represents an event sequence of the event tree, the corresponding event tree can be directly obtained using the BDD structure.

[0092] Step 5: Use the BDD structure to perform qualitative and quantitative analysis on the optimized event tree.

[0093] 1. Qualitative analysis

[0094] Qualitative analysis is to solve the minimum cut set of the event tree, and each minimum cut set represents a failure mode that causes damage to the power plant core after the initiating event occurs.

[0095] All paths with terminal nodes 1 in the BDD graph represent the CD sequence of the event tree, and the non-terminal nodes located at branch 1 in the path (i.e., the combination of the initiating event and the specific failed power plant safety function) constitute the minimum cut set of the system.

[0096] like Figure 2 There are two paths from the top event to the terminal node in the BDD structure: {T-X1-1}, The CD sequence is {T-X1-1}. Since T and X1 are nodes on branch 1, the minimum cut set of the story tree T is {T, X1}, which means that when the initiating event T occurs, the safety function X1 fails, eventually leading to CD.

[0097] 2. Quantitative Analysis

[0098] Use the BDD structure to calculate the core damage probability CDF after the initiating event in the event tree. If f(x), x=(x1, x2, ...x n ), the variable order is x1<x2<...<x n , use Shannon expansion theorem to transform f(x) into the following form:

[0099]

[0100] in:

[0101] Indicates safety function x i Failed Boolean function,

[0102] Indicates safety function x i The Boolean function of normal operation. Therefore, the quantitative analysis also follows the above Shannon expansion, and the failure rate of the top event satisfies

[0103]

[0104] right F 1 and F0 continue to expand to the nth order, we can get f(x), x=(x1,x2,...,x n ), which is the CDF of the current event tree.

[0105] Example 1:

[0106] by Figure 3 Taking the event tree BI1A1 power operating condition as an example, the breach in the primary circuit hot section requires consideration of the following 15 safety functions after the initiating event occurs:

[0107] A02: The shutdown circuit breaker is opened and the control rods are inserted into the core;

[0108] E01: Install a spray pump to take water from the PTR, and after cooling, spray it successfully through the corresponding spray pipeline;

[0109] H01: High-pressure injection pump directly injects through the injection pipeline;

[0110] BIAHE1: The operator used FRC2 procedures to rapidly cool and depressurize the primary circuit within 21 minutes of the accident.

[0111] M03: injection from the injection box;

[0112] H02: High-pressure injection pump recirculates and injects through the injection pipeline;

[0113] BIAHE2: The operator uses ES12 procedure to cool down and depressurize the primary circuit at a cooling rate of 56°C / h.

[0114] M01: injection from the injection box;

[0115] L01: Low-pressure injection pump directly injects through the cold section injection pipeline;

[0116] B01: Direct injection phase, EAS backup RIS, cold segment injection successful;

[0117] L02: Low-pressure injection pump recirculates and injects through the cold section injection pipeline;

[0118] B06: Recirculation stage, RIS takes water and then passes through H4.1, EAS heat exchanger and H4.2;

[0119] B03: During the recirculation phase, EAS backup RIS, cold segment injection successful;

[0120] G01: ASG pump supplies water to SG, which is discharged through the corresponding GCT-A valve;

[0121] E02: Install a spray pump to draw water from the pit, and after cooling, spray it successfully through the corresponding spray pipeline.

[0122] The event tree is analyzed using the method of the present invention.

[0123] Step 1-2: Figure 3 The event tree shown is converted into a binary decision diagram structure. Following the two simplification rules of BDD, the structure is preprocessed to obtain a simplified and ordered BDD structure of the event tree. The initial event tree has 30 accident sequences, of which 20 are core damage (CD) sequences and 9 are sequences that pass through three header events. The BDD diagram of the simplified initial variable sequence is shown in Figure 4 .

[0124] Step 3-4:

[0125] Optimizing the location of mobile nodes using a screening algorithm Figure 4 BDD, get node optimized BDD such as Figure 5 As shown, the optimized event tree obtained by using the BDD is as follows Figure 6 As shown in the figure, the event tree has 23 accident sequences, of which 15 are core damage (CD) sequences and 6 are sequences that pass through 3 header events.

[0126] Step 5: Exploitation Figure 5 (Node-optimized BDD) Qualitative and quantitative analysis were performed on event tree BI1A1.

[0127] Experiments show that using an improved screening algorithm to rearrange the order of variables can effectively compress the failure paths of the BDD structure (the number of CD sequences is reduced from 20 to 15, a reduction of 25%; the number of sequences containing three header events is reduced from 9 to 6, a reduction of 1 / 3), thereby reducing the size of the event tree and improving calculation and analysis efficiency (the calculation time of the event tree analyzed by PSA software is reduced by about 5%). Verification by the power plant PSA model shows that the calculation results of the minimum cut set and CDF of the optimized event tree are completely consistent with those of the original event tree.

[0128] 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. An event tree analysis method based on a binary decision diagram, characterized in that: The steps include: Step 1: Use BDD structure to represent the event tree; Step 2: Preprocess the structure according to the BDD simplification rules, delete redundant nodes and isomorphic subgraphs in the BDD, and merge the terminal nodes to obtain a simplified BDD structure; Step 3: Optimize the BDD structure based on the dynamic variable sorting algorithm with adjacent variable exchange; Step 4: Obtain the corresponding optimized event tree using the BDD simplified in step 2 and the dynamically sorted optimized variable order in step 3; Step 5: Use the BDD structure to perform qualitative and quantitative analysis on the optimized event tree.

2. The event tree analysis method based on a binary decision diagram according to claim 1, characterized in that: The step 1 includes: event tree analysis is an accident sequence analysis method from the initiating event to the final state, the event tree header consists of the initiating event and the functional event; the trunk of the event tree represents the initiating event, and the event tree branches represent the success or failure of a safety function of the nuclear power plant. At each branch point, the upward branch represents the successful operation of the safety function, and the downward branch represents the loss of the safety function; the branch endpoint is the result of the combination of the initiating event and subsequent events, representing a state of the power plant, that is, the core is intact OK or the core is damaged CD.

3. The event tree analysis method based on binary decision diagram according to claim 1, characterized in that: The simplification rules in step 2 include: Rule 1: Remove redundant nodes For a node in a BDD, if its 1 branch and 0 branch both point to the same child node, delete the node and connect the branch pointing to the node directly to the corresponding child node; Rule 2: Delete isomorphic subgraphs For nodes u and v in a BDD, if they have the same Boolean structure, delete node u and connect the branch pointing to node u directly to node v.

4. The event tree analysis method based on a binary decision diagram according to claim 1, characterized in that: The dynamic variable sorting algorithm based on adjacent variable exchange adopted in step 3 is as follows: Assuming that the positions of all other variables remain unchanged, find the optimal position of the variable, that is, the position with the least failure path of the corresponding BDD structure. Repeat this process, moving each variable once. For a Boolean function f(x) with n variables, x=(x1, x2, ...x n ),variable x i (i=1,2,...,n) When the positions of other variables remain unchanged, there are n potential positions. The screening algorithm uses enumeration to exchange x in turn. i and x i The adjacent variables, based on the failure path information of the event tree, are variables x i Find the point among these n locations that minimizes the BDD failure path; For a Boolean function f(x), x=(x1, x2, ...x n )'s adjacent variable x i , x i+1 When performing Shannon expansion, there is Swap x i ,x i+1 The expansion order of the exchanged Boolean function f is i , x i+1 The Shannon expansion of express Exchange the order of adjacent variables in the BDD structure i , x i+1 There are three possible situations: 1) Case 1: When x does not exist in the BDD structure i or x i+1 When the node is x, the order of adjacent variables is swapped i ,x i+1 It will not affect the BDD structure; 2) Case 2: When x exists in the BDD structure i , x i+1 Node, and f 11 , f 10 , f 01 , f 00 If they are different, swap the order of adjacent variables x i , x i+1 Will exchange f 10 (10-branch) and f 01 (01-branch) location; 3) Case 3: When x exists in the BDD structure i , x i+1 Node, and f 11 , f 10 , f 01 , f 00 When the same function exists in 10 =f 00 ), at this time, the order of adjacent variables x is exchanged i , x i+1 It can eliminate redundant nodes and simplify the structure of BDD.

5. The event tree analysis method based on binary decision diagram according to claim 1, characterized in that: In step 4, since each path from the root node along the BDD graph to the terminal node in the BDD structure represents an event sequence of the event tree, the corresponding event tree is directly obtained using the BDD structure.

6. The event tree analysis method based on binary decision diagram according to claim 1, characterized in that: The qualitative analysis in step 5 is to solve the minimum cut set of the event tree. Each minimum cut set represents a failure mode that causes damage to the power plant core after the initiating event occurs. All paths with terminal nodes 1 in the BDD diagram represent the CD sequence of the event tree. The non-terminal nodes located on the 1 branch in the path, that is, the combination of the initiating event and the specific failed power plant safety function, constitute the minimum cut set of the system.

7. The event tree analysis method based on binary decision diagram according to claim 1, characterized in that: The quantitative analysis in step 5 uses the BDD structure to calculate the core damage probability CDF after the initiating event occurs in the event tree. If f(x), x=(x1, x2, ...x n ), the variable order is x1 <x2<...<x n , use Shannon expansion theorem to transform f(x) into the following form: in: Indicates safety function x i Failed Boolean function, Indicates safety function x i Normally functioning Boolean functions; Therefore, the quantitative analysis also follows the above Shannon expansion, and the failure rate of the top event satisfies Expand F1 and F0 to the nth order and we can get f(x), x=(x1,x2,...,x n ), which is the CDF of the current event tree.

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