A network reliability intelligent computing method and system of a logic decision diagram

Abstract

The present application belongs to the technical field of knowledge compilation and network reliability analysis, and particularly relates to a network reliability intelligent computing method and system for a logical decision graph, comprising: modeling a network system as a triple data structure composed of a network topology graph, a terminal node set and an edge availability probability set; determining a topology order of network nodes and network edges based on the triple data structure; constructing a full binary tree vtree with leaf nodes corresponding to network edges one by one according to the topology order; and compiling the network topology graph into a zero-suppression statement logical decision graph using the vtree, wherein the zero-suppression statement logical decision graph is used to represent a set of valid subgraphs that satisfy terminal node connectivity; and recursively calculating a reliability value of the network system based on the zero-suppression statement logical decision graph.

Description

Technical Field

[0001] This invention belongs to the technical field of knowledge compilation and network reliability analysis, and particularly relates to a network reliability intelligent calculation method and system for logical decision graphs. Background Technology

[0002] Network reliability refers to the probability that a network can maintain the connectivity of critical nodes even when its components (such as communication links, power transmission lines, or transportation corridors) fail randomly. It is an important indicator for network system design and optimization, as well as for measuring the stability and security of complex systems. With the increasing scale and complexity of communication networks, smart grids, and urban transportation systems, how to efficiently and intelligently assess, analyze, and calculate the accurate reliability of highly complex networks has become a research focus.

[0003] Existing intelligent evaluation analysis and accurate calculation methods mainly fall into two categories: enumeration- or analytical methods, such as subset simulation, minimal cut sets, state enumeration, and factorization theorem, which can obtain theoretically accurate values, but their computational complexity increases exponentially with network size, making them only suitable for small-scale networks; and decision graph-based methods, such as Binary Decision Diagram (BDD) and Sentential Decision Diagram (SDD). These methods compile the network into a decision graph representing all subgraphs satisfying connectivity conditions, and then perform accurate and reliable intelligent calculations based on this decision graph. Among these, the BDD method has a faster compilation speed, but the generated decision graph structure is large, leading to high computational time consumption in subsequent calculations; the SDD method is more flexible in logical decomposition and can generate a more compact structure, but the compilation process is complex and time-consuming. Therefore, when dealing with large-scale networks, existing methods still struggle to balance compilation efficiency and structural compactness. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a network reliability intelligent computing method and system for logical decision graphs. This method solves the problems of high structure compilation costs, decision graph scaling, and low computational efficiency in existing methods for large-scale networks, and achieves compact representation and efficient, accurate intelligent computing for complex networks.

[0005] To achieve the above objectives, the present invention provides a network reliability intelligent computing method for logical decision graphs, comprising a processor and a memory, wherein the processor performs the following processing:

[0006] The network system is modeled as a triplet data structure consisting of a network topology graph, a set of terminal nodes, and a set of edge availability probabilities.

[0007] Based on the triplet data structure, the topological order of network nodes and network edges is determined;

[0008] Based on the topological order, construct a full binary tree vtree with leaf nodes and network edges in one-to-one correspondence.

[0009] Using the vtree, the network topology graph is compiled into a zero-suppression statement logic decision graph, wherein the zero-suppression statement logic decision graph is used to represent the set of all valid subgraphs that satisfy the connectivity of terminal nodes;

[0010] Based on the zero-suppression statement logic decision graph, the reliability value of the network system is recursively calculated.

[0011] Optionally, determining the topological order of network nodes and network edges based on the triplet data structure includes:

[0012] The network topology graph is processed using a recursive-first search algorithm to generate the node topology order.

[0013] The order of the edges is determined based on the index values ​​of the two nodes that make up each edge in the node topology order, according to the ascending index value rule.

[0014] Optionally, constructing a full binary tree (vtree) with leaf nodes corresponding one-to-one with network edges according to the topological order includes:

[0015] S1. Process each node in ascending order of its index value in the topological order;

[0016] S2. Assign all edges connected to the current node as the set of leaf nodes of the left subtree;

[0017] S3. Construct a balanced binary tree as the left subtree structure based on the set of leaf nodes;

[0018] S4. Assign all edges except those connected to the current node to the set of leaf nodes of the right subtree;

[0019] S5. Treat the right subtree as a new subtree to be processed, and recursively execute steps S2 to S4 until the last node with a non-empty connection edge is processed.

[0020] S6. Construct a balanced binary tree by directly using the edges connected to the last node as the set of leaf nodes of the right subtree, and obtain the full binary tree vtree.

[0021] Optionally, using the vtree, compiling the network topology graph into a zero-suppression statement logic decision graph includes:

[0022] The compilation process is performed from the root node of the vtree in a top-down manner.

[0023] Implicit partitioning rules are applied during compilation to suppress the generation of zero branches corresponding to disconnected states;

[0024] The subgraph isomorphism detection mechanism detects and merges equivalent subgraph structures generated by different compilation branches, and the constraint detection module identifies and removes branches that cannot meet the connectivity requirements of terminal nodes.

[0025] Optionally, the implicit partitioning rules include: omitting the zero-branch construction operation corresponding to invalid connected states, and only retaining the valid subgraph branches that can achieve terminal node connectivity.

[0026] Optionally, detecting and merging equivalent subgraph structures generated by different compilation branches through a subgraph isomorphism recognition mechanism includes:

[0027] Calculate the hash signature of each subgraph structure, wherein the hash signature consists of the set of terminal nodes, connectivity requirements, and connectivity status;

[0028] When the hash signatures generated by different compilation branches are found to be the same, the existing subgraph node is reused instead of being recompiled.

[0029] Optionally, the constraint detection module can identify and remove branches that fail to meet the connectivity requirements of the terminal nodes, including:

[0030] During compilation, it is determined in real time whether the current subgraph structure has satisfied the terminal node connectivity, and the compilation and expansion of branches that have satisfied connectivity are terminated in advance;

[0031] Determine if there are any terminal nodes that cannot establish connections with terminal nodes in the remaining subgraph structure, and remove branches that cannot complete the connection.

[0032] Optionally, based on the zero-suppression statement logic decision graph, the reliability value of the network system is recursively calculated as follows:

[0033] Starting from the root node of the zero-suppression statement logic decision graph, the reliability probability of each child node is calculated layer by layer according to the node type using the corresponding recursive formula.

[0034] The reliability probabilities of each child node are weighted and summed to obtain the accurate reliability value of the network system.

[0035] This invention also proposes a network reliability intelligent computing system for logical decision graphs, comprising: a triplet structure construction module, a full binary tree construction module, a statement logical decision graph acquisition module, and a calculation module;

[0036] The triplet structure construction module is used to model the network system as a triplet data structure consisting of a network topology graph, a set of terminal nodes, and a set of edge availability probabilities.

[0037] The full binary tree construction module is used to determine the topological order of network nodes and network edges based on the triplet data structure; and to construct a full binary tree vtree with leaf nodes and network edges corresponding one-to-one according to the topological order.

[0038] The statement logic decision graph acquisition module is used to compile the network topology graph into a zero-suppression statement logic decision graph using the vtree, wherein the zero-suppression statement logic decision graph is used to represent the set of all valid subgraphs that satisfy the connectivity of terminal nodes;

[0039] The calculation module is used to recursively calculate the reliability value of the network system based on the zero-suppression statement logic decision graph.

[0040] Compared with the prior art, the present invention has the following advantages and technical effects:

[0041] (1) This invention reduces compilation overhead and makes the structure more compact: It introduces the Zero Suppression Statement Decision Graph (ZSDD), which omits invalid branches (i.e., "zero paths" corresponding to disconnected states) during compilation, significantly reducing the number of decision graph nodes and memory usage. Compared with existing methods based on BDD or SDD, the ZSDD compilation process is more efficient, the compilation result is smaller, and it can reduce computational complexity while maintaining accuracy.

[0042] (2) This invention integrates subgraph isomorphism recognition and constraint detection to avoid repeated compilation and invalid expansion: In the top-down compilation algorithm, a subgraph isomorphism recognition mechanism and a constraint detection module are integrated: the former is used to detect equivalent subgraphs generated under different edge selection combinations, thereby avoiding repeated compilation; the latter judges the network connectivity status in real time and prunes branches that have satisfied terminal connectivity or cannot continue to be connected, significantly reducing the number of compilation branches and improving compilation efficiency.

[0043] (3) The intelligent computing process of this invention supports a caching mechanism to achieve efficient and reliable solution: In the recursive reliability intelligent computing algorithm based on ZSDD, this invention introduces a caching mechanism to store and reuse the calculated intermediate node states, avoid repeated calculations under different paths, and thus significantly improve the efficiency of reliability intelligent computing.

[0044] (4) The algorithm structure of this invention is scalable and applicable to various types of complex networks: The ZSDD compilation and intelligent computing framework proposed in this invention has good versatility and scalability. It can be used for link reliability analysis of communication networks and can also be extended to the accurate reliability calculation and optimization design of various complex network structures such as power, transportation and industrial control systems.

[0045] (5) The present invention has excellent overall performance, taking into account both compilation speed and accuracy: While ensuring the consistency of accurate intelligent calculation results, the present invention achieves a significant improvement in compilation speed and effective compression of decision graph size. Compared with the traditional BDD method, it reduces storage occupation, and compared with the SDD method, it reduces compilation time, thus achieving a good balance between accuracy, efficiency and scalability. Attached Figure Description

[0046] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0047] Figure 1 This is a flowchart of a network reliability intelligent calculation method based on a logical decision graph according to an embodiment of the present invention;

[0048] Figure 2 This is a schematic diagram illustrating the invalid subgraph resulting from constructing a vtree without using heuristic functions, according to an embodiment of the present invention.

[0049] Figure 3 This is a flowchart of the Zero Suppression Statement Logic Decision Graph (ZSDD) compilation algorithm according to an embodiment of the present invention.

[0050] Figure 4 This is a flowchart of the reliability-accurate intelligent calculation algorithm according to an embodiment of the present invention. Detailed Implementation

[0051] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0052] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0053] This embodiment proposes an intelligent calculation method for network reliability using logical decision graphs, such as... Figure 1 As shown, it specifically includes a processor and a memory, the processor performing the following processes:

[0054] The network system is modeled as a triplet data structure consisting of a network topology graph, a set of terminal nodes, and a set of edge availability probabilities.

[0055] Based on the triplet data structure, the topological order of network nodes and network edges is determined;

[0056] Based on the topological order, construct a full binary tree vtree with leaf nodes and network edges in one-to-one correspondence.

[0057] Using the vtree, the network topology graph is compiled into a zero-suppression statement logic decision graph, wherein the zero-suppression statement logic decision graph is used to represent the set of all valid subgraphs that satisfy the connectivity of terminal nodes;

[0058] Based on the zero-suppression statement logic decision graph, the reliability value of the network system is recursively calculated.

[0059] This embodiment proposes a network reliability intelligent assessment and analysis method based on Zero Suppression Statement Logic Decision Graph (ZSDD), such as... Figure 1 As shown, it specifically includes a processor and a memory, the processor performing the following processes:

[0060] The communication system is modeled as a triplet data structure consisting of a network topology graph, a set of terminal nodes, and a set of edge availability probabilities. The nodes in the network topology graph correspond to communication base stations, core switches, or control nodes. The edges of the topology graph correspond to the communication links between base stations or switching nodes. The set of terminal nodes corresponds to the key base stations or control centers that must be kept interconnected. The edge availability probability represents the probability that the communication link is in a smooth state.

[0061] Based on the triplet data structure, the topological order of network nodes and network edges is determined;

[0062] Based on the topological order, construct a full binary tree in which leaf nodes correspond one-to-one with network edges;

[0063] Using the full binary tree, the network topology graph is compiled into a zero-suppression statement logic decision graph (ZSDD), wherein the ZSDD is used to represent the set of all valid subgraphs that satisfy the connectivity of terminal nodes.

[0064] Based on the Zero Suppression Statement Logic Decision Graph (ZSDD), the reliability value of the communication system, i.e., the overall probability of maintaining connectivity between key base stations, is obtained by recursively summing the probabilities of each branch in the decision graph.

[0065] Specifically, firstly, the network system is modeled as a triple (G,T,P), where G=(N,E) is the network topology graph, N is the set of network nodes, and E is the set of network edges; then, the set of terminal nodes whose connectivity needs to be guaranteed is determined. and each side Independent availability probability This step abstracts the target system into a probabilistic network model consisting of a set of nodes, edges, and terminal nodes, which is used for subsequent intelligent reliability calculations.

[0066] 2. Take the network topology graph G obtained in the first step as the input of the heuristic algorithm RFS, and output the network graph with the topological order of nodes and edges determined; wherein, the node order is determined by the RFS algorithm, and the edge order is determined according to the sorting index value of the two nodes constituting the edge in the topological order, according to the ascending order rule.

[0067] 3. Based on the node and edge order of the network graph obtained in step 2, a full binary tree vtree with leaf nodes and network graph edges is constructed using a heuristic function. The execution rules of the heuristic function are as follows: 1. Process nodes in ascending order according to their topological index; 2. Assign all edges connected to the current node to the leaf node set of the left subtree; 3. Construct a balanced binary tree as the left subtree structure based on the leaf node set; 4. Recursively execute the above process until all edges are mapped to the leaf nodes of the tree.

[0068] Fourth, using the vtree constructed in step three, starting from the root node, a top-down compilation algorithm is executed to progressively compile the network graph into a Zero-Suppression Statement Logic Graph (ZSDD), representing the set of all subgraphs that satisfy the terminal node connectivity requirement. The compilation algorithm integrates subgraph isomorphism recognition and constraint detection mechanisms to perform pruning operations and avoid exponential growth of compilation branches. Simultaneously, according to the zero-suppression rule of ZSDD, it is unnecessary to represent subgraphs that do not meet the connectivity requirement, further reducing compilation branches and making the compiled decision graph more compact, thus improving the efficiency of subsequent reliable intelligent computation.

[0069] Fifth, traverse the ZSDD obtained in step four, and use a recursive algorithm to calculate the reliability probability of each child node along the decision graph hierarchy, starting from the root node and based on the corresponding vtree node type. At the same time, use a caching mechanism to store the calculated node results to avoid repeated calculations, thereby efficiently calculating the accurate reliability of the network graph while ensuring accuracy.

[0070] In multiple experiments, compared with traditional BDD and SDD-based methods, the network reliability intelligent assessment and accurate calculation method based on Zero Suppression Statement Logic Decision Graph (ZSDD) of this invention effectively reduces the size of the compilation result and improves the intelligent calculation efficiency of network reliability in networks with more than 90 edges. In the embodiments of this application, the datasets used for simulation experiments are divided into two types: 1. Real network graphs obtained from the TopologyZoo database, which collects real global network topology data; 2. Self-constructed grid graphs of different sizes (grid4X4, ..., grid7X64) as simulated network graphs. It is necessary to ensure that the nodes in the connected terminal node set T are randomly set, and there are three cases: two terminal nodes; half of the graph nodes are terminal nodes; and all graph nodes are terminal nodes. The edge availability probability is set to a random value within [0-1]. The simulation experiment will calculate the reliability of the network graph multiple times, and the average calculation time will be used as the experimental result.

[0071] More specifically, network reliability is the sum of the reliability of all subgraphs that ensure end nodes are connected by available edges. The probability of availability is The probability of it being unavailable is Assume the set of edges of the subgraph is Reliability of network structure:

[0072] ;

[0073] in, For the reliability of the network system;

[0074] Single subgraph Reliability:

[0075] ;

[0076] Where e is a subgraph For any edge, P(e) is the probability that edge e is available.

[0077] Furthermore, based on the triplet data structure, determining the topological order of network nodes and network edges includes:

[0078] The network topology graph is processed using a recursive-first search algorithm to generate the node topology order.

[0079] The order of the edges is determined based on the index values ​​of the two nodes that make up each edge in the node topology order, according to the ascending index value rule.

[0080] Furthermore, according to the aforementioned topological order, constructing a full binary tree (vtree) with leaf nodes corresponding one-to-one with network edges includes:

[0081] S1. Process each node in ascending order of its index value in the topological order;

[0082] S2. Assign all edges connected to the current node as the set of leaf nodes of the left subtree;

[0083] S3. Construct a balanced binary tree as the left subtree structure based on the set of leaf nodes;

[0084] S4. Assign all edges except those connected to the current node to the set of leaf nodes of the right subtree;

[0085] S5. Treat the right subtree as a new subtree to be processed, and recursively execute steps S2 to S4 until the last node with a non-empty connection edge is processed.

[0086] S6. Construct a balanced binary tree by directly using the edges connected to the last node as the set of leaf nodes of the right subtree, and obtain the full binary tree vtree.

[0087] Furthermore, using the vtree, compiling the network topology graph into a zero-suppression statement logic decision graph includes:

[0088] The compilation process is performed from the root node of the vtree in a top-down manner.

[0089] Implicit partitioning rules are applied during compilation to suppress the generation of zero branches corresponding to disconnected states;

[0090] The subgraph isomorphism detection mechanism detects and merges equivalent subgraph structures generated by different compilation branches, and the constraint detection module identifies and removes branches that cannot meet the connectivity requirements of terminal nodes.

[0091] Specifically, in the embodiments of this application, Figure 2 This demonstrates the possibility of invalid subgraphs during compilation, specifically cases where the left subgraph cannot be constructed. The Zero Suppression Statement Decision Graph (ZSDD) compilation algorithm, during execution, divides the network edges corresponding to the leaf nodes of the left and right subgraphs into two subgraphs for parallel processing, based on the vtree structure. During this process, the connections between boundary nodes (i.e., common nodes of the left and right subgraphs and nodes in the left subgraph already connected to the right subgraph) and terminal nodes in the left subgraph determine the connectivity constraints of the left subgraph, and further determine the topological state and connectivity constraints of the right subgraph. If the vtree is improperly constructed, some connection states between boundary nodes and terminal nodes may not be realized in the left subgraph, leading to invalid branches during compilation and increasing time and space overhead. Constructing the vtree using heuristic functions ensures that edges connected to the same network node are concentrated in the same subtree, structurally guaranteeing the feasibility of boundary node connectivity relationships.

[0092] In the embodiments of this application, see Figure 3 The Zero Suppression Statement Logic Decision Graph (ZSDD) compilation algorithm includes the following steps:

[0093] First, the algorithm takes the network graph G=(N,E), the set of terminal nodes T, and the nodes v of the full binary tree vtree as input.

[0094] Next, the top-down compilation algorithm starting from the root node of the vtree will construct the root node of the Zero Suppression Statement Decision Graph (ZSDD) Z and its corresponding initial graph state: the set of terminal nodes is T, the connection requirement is that all terminal nodes are connected, and the connected state is no connected nodes.

[0095] Next, based on the type of the vtree node v corresponding to Z in the Zero Suppression Statement Decision Graph (ZSDD), we will process them into three categories: 1. Shannon node case, i.e., the left subtree is a leaf node. In this case, we will process the nodes according to the edge corresponding to the left subtree of v. Whether or not the ZSDD is selected, two pairs of elems are obtained, each consisting of a ZSDD prime and a ZSDD sub. The ZSDD prime represents the value constraints of the variable set corresponding to the left subtree of the current vtree, essentially providing a logical characterization of the feasibility of the left subgraph structure. The ZSDD sub represents the right subgraph structure obtained after updating the graph state under the value specified by prime, reflecting the feasible combinations of the remaining edges under the new connectivity constraints. Therefore, for Shannon nodes, prime represents the edge... The terminal ZSDD with the value state includes: (This edge must be selected) (This side is not selected) (This edge is optional).

[0096] Here, the prime representing the left subgraph is the terminal ZSDD obtained based on the graph state. (Indicates that the edge needs to be selected) (Indicates that the edge cannot be selected) (Indicates that the edge can be selected or not), indicating that the subgraph of the right subgraph will be selected based on the edge. 1. Selecting whether to update the graph state (updating the connection status of terminal nodes and nodes in the right subgraph; non-terminal nodes connected to terminal nodes will be considered terminal nodes). 2. Decompose the node situation, i.e., the left subtree is not a leaf node. At this time, obtain the boundary nodes (common nodes of the left and right subgraphs and nodes in the left subgraph that are connected to the right subgraph) according to the left and right subgraphs corresponding to the left and right subgraphs, and determine the connectivity constraints of the left subgraph and the topological state and connectivity constraints of the right subgraph by enumerating the connection status of the boundary nodes and the terminal nodes in the left subgraph, and construct all elems composed of prime and sub in ZSDD Z; where the graph state of the left and right subgraphs is determined by the connectivity constraints, and the update method is as follows: the terminal nodes of the left subgraph are updated to boundary nodes and the original terminal nodes, and the connectivity constraints are used as node connection requirements, and the status of already connected nodes remains unchanged; the terminal nodes of the right subgraph are updated to the boundary nodes that are required to be connected to the terminal nodes and the original terminal nodes, and the node connection requirements inherit the original graph state requirements, and the status of already connected nodes is updated according to the connectivity constraints, i.e., if the boundary nodes are required to be connected, these boundary nodes are considered to be connected. 3. Leaf node status: Based on the current graph status, determine whether the edge corresponding to the leaf node needs to be selected, and construct the corresponding terminal ZSDD.

[0097] Then, for different branches, the elems constructed by ZSDD nodes when the vtree is a Shannon / decomposition node undergo pruning detection, including connectivity constraint detection and isomorphic subgraph identification: 1. Determine whether any terminal node cannot be connected to terminal nodes in the right subgraph based on the terminal ZSDD or graph state corresponding to the prime. If so, delete the elem; 2. Determine whether all terminal nodes are connected based on the graph state corresponding to the sub. If so, set the vtree corresponding to the sub to the rightmost leaf node of the right subtree of v, and construct the sub as a terminal ZSDD. ,in, 1. The edge corresponding to the rightmost leaf node; 2. Calculate the corresponding hash signature (composed of terminal node, connectivity requirement, and connected state) based on the graph state of prime / sub, which is used to detect isomorphic subgraphs. When the subgraph structure generated by different branches is detected to be the same, the existing node is reused instead of being regenerated, thus avoiding repeated construction. 3. If it is not one of the above three cases, no pruning is required, and the compilation algorithm will reconstruct each prime / sub by calling itself again. At this time, the graph state in the algorithm input will be updated to the graph state corresponding to prime / sub, and vtree will be updated to the left subtree v l Or the right subtree v r .

[0098] Ultimately, a zero-suppression statement logic decision graph (ZSDD) was obtained, representing a subgraph that connects all terminal nodes.

[0099] Furthermore, the implicit partitioning rule includes: omitting the zero-branch construction operation corresponding to the invalid connected state, and only retaining the valid subgraph branches that can achieve terminal node connectivity.

[0100] Furthermore, the subgraph isomorphism detection mechanism detects and merges equivalent subgraph structures generated by different compilation branches, including:

[0101] Calculate the hash signature of each subgraph structure, wherein the hash signature consists of the set of terminal nodes, connectivity requirements, and connectivity status;

[0102] When the hash signatures generated by different compilation branches are found to be the same, the existing subgraph node is reused instead of being recompiled.

[0103] Furthermore, the constraint detection module identifies and removes branches that fail to meet the connectivity requirements of the terminal nodes, including:

[0104] During compilation, it is determined in real time whether the current subgraph structure has satisfied the terminal node connectivity, and the compilation and expansion of branches that have satisfied connectivity are terminated in advance;

[0105] Determine if there are any terminal nodes that cannot establish connections with terminal nodes in the remaining subgraph structure, and remove branches that cannot complete the connection.

[0106] Furthermore, based on the Zero Suppression Statement Decision Graph (ZSDD), the reliability value of the recursively calculated network system includes:

[0107] Starting from the root node of the Zero Suppression Statement Logic Decision Graph (ZSDD), the reliability probability of each child node is calculated layer by layer according to the node type using the corresponding recursive formula.

[0108] The reliability probabilities of each child node are weighted and summed to obtain the accurate reliability value of the network system.

[0109] Specifically, in the embodiments of this application, see... Figure 4 The reliability-accurate intelligent calculation algorithm includes the following steps:

[0110] First, the zero-suppression statement logic decision graph Z and the set of available edge probabilities P obtained from the compilation algorithm stage are used as input.

[0111] Next, the algorithm checks whether the reliability of the input decision graph has already been calculated based on the ZSDD root node ID. If the result is stored in the hash table, the cached value is read, and no recalculation is needed; otherwise, the algorithm determines the current node type and calculates the reliability: 1. The terminal ZSDD calculates and returns the reliability probability value based on the full binary tree node type corresponding to the node, and stores the calculation result in a hash table. If it corresponds to a leaf node, the reliability probability value is:

[0112] ;

[0113] in, express A reliability probability value that can be selected or not. The corresponding edge of the left subtree; express The probability value that must be selected, i.e. The probability of availability; express The probability of not being selectable, i.e., the probability of being unavailable.

[0114] If it corresponds to an internal node, then the reliability probability is:

[0115]

[0116]

[0117]

[0118] in, This represents the set of edges corresponding to the leaf nodes of the internal nodes of a full binary tree. Indicates except Whether or not it is selected, the reliability probability value is that the other edges cannot be selected; Indicates except The probability value that the remaining edges cannot be selected must be chosen; This represents the probability that all edges are unselectable.

[0119] 2. Decompose ZSDD, then recursively calculate the reliability of the prime and sub nodes, with the node reliability probability value being:

[0120]

[0121] in, This represents all elems of a ZSDD node, consisting of a ZSDD prime and a sub. and Representing sub-ZSDD and The reliability probability.

[0122] Finally, the result returned from the ZSDD root node is the accurate reliability value R(Z) of the entire network.

[0123] This embodiment achieves efficient compilation and accurate solution of the reliability of complex networks with an arbitrary number of terminal nodes by introducing Zero Suppression Statement Decision Graph (ZSDD), heuristic vtree construction strategy, compilation algorithm integrating connectivity constraint detection and subgraph isomorphism recognition mechanism, and recursive reliability intelligent calculation algorithm based on cache optimization.

[0124] First, based on the network topology and terminal node characteristics, the RFS algorithm is used to determine the order of nodes and edges in the network graph, and a full binary tree (vtree) is constructed through heuristic rules. This effectively reduces the generation of redundant nodes in the ZSDD compilation process, alleviates compilation overhead, and ensures that the generated zero-suppression statement logic decision graph (ZSDD) structure is more compact.

[0125] Subsequently, a connectivity constraint detection mechanism and subgraph isomorphism recognition were introduced during the ZSDD compilation process. By using connectivity and subgraph state hash detection, duplicate subgraphs were merged and invalid branches were pruned in advance, which successfully avoided the exponential growth of compilation branches and significantly reduced space and time consumption.

[0126] In the reliability intelligent computation stage, a recursive algorithm with an integrated caching mechanism is used to efficiently traverse ZSDD and reuse results, which not only significantly reduces redundant computations but also further improves overall computational efficiency. Experimental results show that the decision graph obtained by the compilation algorithm in this invention is more compact than that based on BDD or SDD, and the efficiency of subsequent reliability intelligent computation is significantly improved.

[0127] Furthermore, ZSDD possesses Boolean function operations with polynomial time complexity, providing new computational support for network reliability optimization. Using pre-compiled ZSDD, various reliability optimization analyses can be quickly implemented without recompilation, such as: solving for maximum reliability under given edge consumption constraints; determining the minimum consumption edge set under reliability threshold constraints; or achieving multi-objective optimization based on the relationship between edge weights and reliability changes.

[0128] Therefore, this invention not only achieves efficient and accurate intelligent calculation of network reliability, but also provides a unified structured intelligent computing framework for the reliability design and resource allocation optimization of complex systems, and has good versatility, scalability and engineering application value.

[0129] To further illustrate the feasibility of the present invention, an exemplary description of a city road network is provided below.

[0130] Assuming a city's road network comprises 200 roads (edges), during the study period (17:00-19:00), under the assumption of independent and identically distributed traffic flow, the probability of smooth traffic flow for each road is denoted as... In this example, let (That is, each road remains passable with a 90% probability during this time period). The road network is constructed with a topological order according to the method of this invention. Based on this topological order, a full binary tree (vtree) corresponding one-to-one with each road is built, and the road network is compiled into a Zero-Suppression Statement Logic Decision Graph (ZSDD). After successful compilation of the ZSDD, recursive probability summation can be directly performed on the ZSDD to obtain the accurate global connectivity probability. Specifically, in the example, the passability events of each road are approximated as independent, and their values... It can be obtained from historical traffic data, sensor statistics, or traffic simulation.

[0131] Based on the above calculation results, the probability of smooth traffic flow on one or more roads can be further assessed. Perform sensitivity analysis to quantify the contribution of each road to overall connectivity (road importance): This involves adjusting the probability of a road being unobstructed from... Upgraded to Recalculate the global connectivity probability and measure the increment of the connectivity probability. To assess the marginal contribution of the road. Based on each road's... Value sorting can determine the set of roads to be prioritized for expansion or maintenance under a given budget, thereby achieving optimal resource allocation.

[0132] This embodiment also proposes a network reliability intelligent computing system for logical decision graphs, including: a triplet structure construction module, a full binary tree construction module, a statement logical decision graph acquisition module, and a calculation module;

[0133] The triplet structure construction module is used to model the network system as a triplet data structure consisting of a network topology graph, a set of terminal nodes, and a set of edge availability probabilities.

[0134] The full binary tree construction module is used to determine the topological order of network nodes and network edges based on the triplet data structure; and to construct a full binary tree in which leaf nodes and network edges correspond one-to-one according to the topological order, wherein the full binary tree is a full binary tree in which leaf nodes and graph edges correspond one-to-one; wherein the full binary tree is a full binary tree in which leaf nodes and graph edges correspond one-to-one.

[0135] The statement logic decision graph acquisition module is used to compile the network topology graph into a zero-suppression statement logic decision graph using the full binary tree, wherein the zero-suppression statement logic decision graph is used to represent the set of all valid subgraphs that satisfy the connectivity of terminal nodes;

[0136] The calculation module is used to recursively calculate the reliability value of the network system based on the zero-suppression statement logic decision graph.

[0137] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A network reliability intelligent calculation method for logical decision graphs, characterized in that, Includes a processor and memory, the processor performing the following processes: The network system is modeled as a triplet data structure consisting of a network topology graph, a set of terminal nodes, and a set of edge availability probabilities. Based on the triplet data structure, the topological order of network nodes and network edges is determined; Based on the topological order, construct a full binary tree vtree with leaf nodes and network edges in one-to-one correspondence. Using the vtree, the network topology graph is compiled into a zero-suppression statement logic decision graph, wherein the zero-suppression statement logic decision graph is used to represent the set of all valid subgraphs that satisfy the connectivity of terminal nodes; Based on the zero-suppression statement logic decision graph, the reliability value of the network system is recursively calculated.

2. The intelligent calculation method for network reliability of logical decision graphs according to claim 1, characterized in that, Based on the triplet data structure, determining the topological order of network nodes and network edges includes: The network topology graph is processed using a recursive-first search algorithm to generate the node topology order. The order of the edges is determined based on the index values ​​of the two nodes that make up each edge in the node topology order, according to the ascending index value rule.

3. The intelligent calculation method for network reliability of logical decision graphs according to claim 2, characterized in that, Constructing a full binary tree (vtree) with leaf nodes and network edges corresponding one-to-one according to the topological order includes: S1. Process each node in ascending order of its index value in the topological order; S2. Assign all edges connected to the current node as the set of leaf nodes of the left subtree; S3. Construct a balanced binary tree as the left subtree structure based on the set of leaf nodes; S4. Assign all edges except those connected to the current node to the set of leaf nodes of the right subtree; S5. Treat the right subtree as a new subtree to be processed, and recursively execute steps S2 to S4 until the last node with a non-empty connection edge is processed. S6. Construct a balanced binary tree by directly using the edges connected to the last node as the set of leaf nodes of the right subtree, and obtain the full binary tree vtree.

4. The intelligent calculation method for network reliability of logical decision graphs according to claim 3, characterized in that, Using the vtree, compiling the network topology graph into a zero-suppression statement logic decision graph includes: The compilation process is performed from the root node of the vtree in a top-down manner. Implicit partitioning rules are applied during compilation to suppress the generation of zero branches corresponding to disconnected states; The subgraph isomorphism detection mechanism detects and merges equivalent subgraph structures generated by different compilation branches, and the constraint detection module identifies and removes branches that cannot meet the connectivity requirements of terminal nodes.

5. The intelligent calculation method for network reliability of logical decision graphs according to claim 4, characterized in that, The implicit partitioning rules include: omitting the zero-branch construction operation corresponding to invalid connected states, and only retaining the valid subgraph branches that can achieve terminal node connectivity.

6. The intelligent calculation method for network reliability of logical decision graphs according to claim 4, characterized in that, The subgraph isomorphism detection mechanism is used to detect and merge equivalent subgraph structures generated by different compilation branches, including: Calculate the hash signature of each subgraph structure, wherein the hash signature consists of the set of terminal nodes, connectivity requirements, and connectivity status; When the hash signatures generated by different compilation branches are found to be the same, the existing subgraph node is reused instead of being recompiled.

7. The intelligent calculation method for network reliability of logical decision graphs according to claim 4, characterized in that, The constraint detection module identifies and removes branches that fail to meet the connectivity requirements of the terminal nodes, including: During compilation, it is determined in real time whether the current subgraph structure has satisfied the terminal node connectivity, and the compilation and expansion of branches that have satisfied connectivity are terminated in advance; Determine if there are any terminal nodes that cannot establish connections with terminal nodes in the remaining subgraph structure, and remove branches that cannot complete the connection.

8. The intelligent calculation method for network reliability of logical decision graphs according to claim 1, characterized in that, Based on the zero-suppression statement logic decision graph, the reliability value of the recursive calculation network system includes: Starting from the root node of the zero-suppression statement logic decision graph, the reliability probability of each child node is calculated layer by layer according to the node type using the corresponding recursive formula. The reliability probabilities of each child node are weighted and summed to obtain the accurate reliability value of the network system.

9. A network reliability intelligent computing system for logical decision graphs, used to implement the computing method as described in any one of claims 1-8, characterized in that, include: The module includes a triplet structure construction module, a full binary tree construction module, a statement logic decision graph acquisition module, and a calculation module. The triplet structure construction module is used to model the network system as a triplet data structure consisting of a network topology graph, a set of terminal nodes, and a set of edge availability probabilities. The full binary tree construction module is used to determine the topological order of network nodes and network edges based on the triplet data structure; and to construct a full binary tree vtree with leaf nodes and network edges corresponding one-to-one according to the topological order. The statement logic decision graph acquisition module is used to compile the network topology graph into a zero-suppression statement logic decision graph using the vtree, wherein the zero-suppression statement logic decision graph is used to represent the set of all valid subgraphs that satisfy the connectivity of terminal nodes; The calculation module is used to recursively calculate the reliability value of the network system based on the zero-suppression statement logic decision graph.

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