Intelligent calculation method and system for network reliability of logic decision diagram

Abstract

The invention belongs to the technical field of combination of knowledge compilation and network reliability analysis, and particularly relates to an intelligent calculation method and system for network reliability of a logic decision diagram.The method comprises the steps that a network system is modeled into a triple data structure composed of a network topological graph, a terminal node set and an edge available probability set; determining a topological sequence of network nodes and network edges based on the triple data structure; constructing a full binary tree vtree in which leaf nodes are in one-to-one correspondence with network edges according to the topological sequence; the vtree is utilized to compile a network topological graph into a zero suppression statement logic decision diagram, and the zero suppression statement logic decision diagram is used for representing all effective sub-graph sets meeting the terminal node connectivity; and recursively calculating the reliability value of the network system based on the zero suppression statement logic decision diagram.

Description

TECHNICAL FIELD

[0001] The 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 of a logical decision diagram. BACKGROUND

[0002] Network reliability refers to the probability that a network can maintain the connectivity of key nodes under the condition of random failure of its components (such as communication links, power transmission lines or traffic channels), and is an important index for network system design and optimization, and 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 evaluate, analyze and calculate the accurate reliability of high-complexity networks has become a research focus.

[0003] Existing intelligent evaluation, analysis and accurate calculation methods mainly include two categories: enumeration or analytical-based methods, such as subset simulation, minimal cut sets, state enumeration method and factorization theorem, which can obtain theoretical accurate values but have exponentially increasing computational complexity with the network size, and are only suitable for small-scale networks; decision diagram-based methods, such as Binary Decision Diagram (BDD) and Sentential Decision Diagram (SDD). Such methods compile the network into a decision diagram representing all subgraphs satisfying the connectivity condition, and then perform intelligent accurate reliability calculation based on the decision diagram. Among them, the BDD method has faster compilation speed, but the generated decision diagram structure is large, resulting in high subsequent calculation time consumption; the SDD method is more flexible in logical decomposition and can generate more compact structures, but the compilation process is complex and time-consuming. Therefore, when dealing with large-scale networks, existing methods still have difficulty in balancing compilation efficiency and structure compactness. SUMMARY

[0004] To solve the above technical problems, the application provides a network reliability intelligent computing method and system of a logical decision diagram, which solves the problems of high structure compilation cost, decision diagram scale expansion and low calculation efficiency of existing methods in large-scale networks, and realizes compact representation and efficient and accurate intelligent calculation of complex networks.

[0005] To achieve the above purpose, the application provides a network reliability intelligent computing method of a logical decision diagram, which includes a processor and a memory, and the processor performs the following processing:

[0006] Modeling the network system as a triple data structure composed of a network topology graph, a terminal node set and an edge availability probability set;

[0007] Based on the triple data structure, determining the topological order of network nodes and network edges;

[0008] constructing a full binary tree vtree according to the topological order, wherein each leaf node of the vtree corresponds to a network edge;

[0009] compiling the network topology graph into a zero-suppressed Boolean decision diagram using the vtree, wherein the zero-suppressed Boolean decision diagram is used to represent a set of valid subgraphs satisfying the connectivity of terminal nodes;

[0010] calculating the reliability value of the network system recursively based on the zero-suppressed Boolean decision diagram.

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

[0012] processing the network topology graph using a recursive priority search algorithm to generate a node topological order;

[0013] determining the order of edges based on the index values of the two nodes constituting each edge in the node topological order in ascending order of index values.

[0014] Optionally, constructing a full binary tree vtree according to the topological order, wherein each leaf node of the vtree corresponds to a network edge comprises:

[0015] S1, processing each node in ascending order of index values of nodes in the topological order;

[0016] S2, assigning all edges connected to the current node as a leaf node set of the left subtree;

[0017] S3, constructing a balanced binary tree as a left subtree structure based on the leaf node set;

[0018] S4, assigning edges other than the edges connected to the current node as a leaf node set of the right subtree;

[0019] S5, taking the right subtree as a new to-be-processed subtree, and recursively executing steps S2 to S4 until the last node connected to an edge is not empty;

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

[0021] Optionally, compiling the network topology graph into a zero-suppressed Boolean decision diagram using the vtree comprises:

[0022] performing a top-down compilation process from the root node of the vtree;

[0023] applying an implicit partition rule in the compilation process to suppress the generation of zero branches corresponding to no connectivity state;

[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 configured to determine a topological order of network nodes and network edges based on the triple data structure, and construct a full binary tree vtree in which leaf nodes correspond to network edges one by one according to the topological order.

[0038] The sentence logic decision diagram acquisition module is configured to compile a network topology graph into a zero-suppressed sentence logic decision diagram (ZSDD) by using the vtree, wherein the ZSDD is used to represent a set of valid subgraphs that satisfy terminal node connectivity.

[0039] The calculation module is configured to calculate a reliability value of the network system recursively based on the zero-suppressed sentence logic decision diagram.

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

[0041] (1) The present application has reduced compilation overhead and a more compact structure: the zero-suppressed sentence logic decision diagram (ZSDD) is introduced, and invalid branches (i.e., "zero paths" corresponding to no connectivity state) are omitted in the compilation process, which significantly reduces the number of decision diagram nodes and memory occupation. Compared with the existing methods based on BDD or SDD, the ZSDD compilation process is more efficient, the size of the compilation result is smaller, and the calculation complexity can be reduced while maintaining accuracy.

[0042] (2) The present application 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 condition 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 state in real time, prunes branches that have met the terminal connectivity or cannot continue to be connected, significantly reduces the number of compilation branches, and improves the compilation efficiency.

[0043] (3) The present application supports a cache mechanism in the intelligent calculation process to realize efficient and reliable solution: in the recursive reliability intelligent calculation algorithm based on ZSDD, the present application introduces a cache mechanism to store and reuse the calculated intermediate node state, thereby avoiding repeated calculation under different paths and significantly improving the efficiency of reliability intelligent calculation.

[0044] (4) The algorithm structure of the present application is extensible and suitable for multiple types of complex networks: the ZSDD compilation and intelligent calculation framework proposed by the present application has good universality and extensibility, and can be used not only for link reliability analysis of communication networks, but also can be extended to accurate reliability calculation and optimization design of various complex network structures such as power, transportation and industrial control systems.

[0045] (5) The application has superior comprehensive performance, and takes into account the compiling speed and accuracy: under the premise of ensuring the consistency of accurate intelligent calculation results, the application realizes the significant improvement of the compiling speed and the effective compression of the decision graph scale, reduces the storage occupation compared with the traditional BDD method, and reduces the compiling time compared with the SDD method, so that a good balance is achieved among accuracy, efficiency and scalability. BRIEF DESCRIPTION OF DRAWINGS

[0046] The drawings constituting a part of this application are used to provide further understanding of the application, the illustrative embodiments of the application and the description thereof are used to explain the application, and do not constitute improper limitation on the application. In the drawings:

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

[0048] Figure 2 is a schematic diagram of an invalid subgraph caused by not using a heuristic function to construct a vtree according to an embodiment of the application;

[0049] Figure 3 is a zero-suppression statement logical decision graph (ZSDD) compiling algorithm flowchart according to an embodiment of the application;

[0050] Figure 4 is a reliability accurate intelligent calculation algorithm flowchart according to an embodiment of the application. DETAILED DESCRIPTION

[0051] It should be noted that the embodiments in the application and the features in the embodiments can be combined with each other without conflict. The application will be described in detail below with reference to the drawings and in combination with the embodiments.

[0052] It should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a group of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described herein can be executed in an order different from that shown herein.

[0053] The embodiment proposes a network reliability intelligent calculation method of a logical decision graph, as shown in Figure 1 The specific steps are as follows:

[0054] Modeling the network system as a three-tuple data structure composed of a network topology graph, a terminal node set and an edge available probability set;

[0055] Based on the three-tuple data structure, determining the topological order of the network nodes and the network edges;

[0056] According to the topological order, a full binary tree vtree corresponding to the network edges is constructed;

[0057] The network topology graph is compiled into a zero-suppressed sentence logic decision diagram using the vtree, wherein the zero-suppressed sentence logic decision diagram is used to represent a set of all valid subgraphs satisfying the terminal node connectivity;

[0058] Based on the zero-suppressed sentence logic decision diagram, the reliability value of the network system is recursively calculated.

[0059] The embodiment proposes a network reliability intelligent evaluation analysis method based on a zero-suppressed sentence logic decision diagram ZSDD, as shown in Figure 1 The processor performs the following processing:

[0060] The communication system is modeled as a three-tuple data structure composed of a network topology graph, a set of terminal nodes, and a set of edge availability probabilities; wherein the network topology graph nodes correspond to communication base stations, core switches, or control nodes, the topology graph edges correspond to communication links between base stations or switch nodes, the set of terminal nodes corresponds to key base stations or control centers that must remain interconnected, and the edge availability probability represents the probability that the communication link is in a smooth state.

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

[0062] According to the topological order, a full binary tree corresponding to the network edges is constructed;

[0063] The network topology graph is compiled into a zero-suppressed sentence logic decision diagram ZSDD using the full binary tree, wherein the zero-suppressed sentence logic decision diagram ZSDD is used to represent a set of all valid subgraphs satisfying the terminal node connectivity;

[0064] Based on the zero-suppressed sentence logic decision diagram 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 calculation probabilities of each branch in the decision diagram.

[0065] Specifically, I, the network system is modeled as a three-tuple (G, T, P), wherein G=(N, E) is a network topology graph, N is a set of network nodes, and E is a set of network edges; determine the set of terminal nodes that need to be guaranteed to be connected, and the independent availability probability of each edge ; this step abstracts the target system into a probabilistic network model composed of nodes, edges, and a set of terminal nodes for subsequent intelligent reliability calculation.

[0066] II. 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 determined node and edge topology order; wherein the node order is determined by the RFS algorithm, and the order of the edges is determined in ascending order based on the sorting index value of the two nodes constituting the edge in the topology order;

[0067] III. Based on the node and edge order of the network graph obtained in the second step, a heuristic function is used to construct a full binary tree vtree corresponding to the edges of the network graph; the execution rules of the heuristic function are: 1. Process the nodes in ascending order of the topology index; 2. Assign all edges connected to the current node to the left child node set; 3. Build a balanced binary tree as the left child 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] IV. Using the vtree constructed in the third step, a top-down compilation algorithm is executed from the root node to compile the network graph into a zero-suppression statement logic decision graph ZSDD to represent all subgraph sets that meet the connectivity requirement of the terminal node; the compilation algorithm integrates subgraph isomorphism recognition and constraint detection mechanism to complete the pruning operation and avoid exponential growth of the compilation branch. At the same time, according to the zero-suppression rule of ZSDD, the subgraphs that do not meet the connectivity requirement do not need to be represented, which can further reduce the compilation branch and make the compiled decision graph more compact, thereby improving the efficiency of subsequent reliability intelligent calculation.

[0069] V. Traverse the ZSDD obtained in the fourth step, and use a recursive algorithm to start from the root node of the decision graph and recursively calculate the reliability probability of each subnode according to the corresponding vtree node type along the decision graph hierarchy; at the same time, use the cache mechanism to store the calculated node results to avoid repeated calculation, thereby efficiently calculating the accurate reliability of the network graph while ensuring accuracy;

[0070] In multiple sets of experiments, compared with the traditional BDD and SDD method, the network reliability intelligent evaluation analysis and accurate calculation method based on the zero suppression sentence logic decision diagram ZSDD of the application can effectively reduce the compilation result size and improve the intelligent calculation efficiency of network reliability in a network with more than 90 edges. In the embodiments of the application, the data set used for simulation experiment is divided into two types: 1. Real network graph obtained from Topology Zoo, a database collecting global real network topology data; 2. Grid graphs of different sizes (grid4X4,…, grid7X64) constructed by the applicant as simulation network graphs. It is necessary to ensure that the nodes in the set T of connected terminal nodes are randomly set and divided into three cases: two terminal nodes; half of the graph nodes are terminal nodes; all the graph nodes are terminal nodes. The availability probability of the edge is a random value in [0-1]. The simulation experiment will calculate the reliability of the network graph multiple times, and the average calculation time is taken as the experimental result.

[0071] More specifically, the network reliability is the sum of the reliabilities of all subgraphs ensuring the connectivity of the terminal nodes by available edges. The availability probability of the edge is , and the unavailability probability is , assuming that the edge set of the subgraph is The reliability of the network structure is

[0072] ;

[0073] wherein, is the reliability of the network system;

[0074] The reliability of a single subgraph is

[0075] ;

[0076] wherein, e is any edge of the subgraph , and P(e) is the availability probability of the edge e.

[0077] Further, based on the triple data structure, determining the topology order of the network nodes and the network edges comprises:

[0078] processing the network topology graph by using a recursive priority search algorithm to generate a node topology order;

[0079] determining the order of the edges according to the index values of the two nodes constituting each edge in the node topology order in ascending order of the index values.

[0080] Further, according to the topology order, constructing a full binary tree vtree corresponding to the network edges one by one comprises:

[0081] S1, sequentially processing each node in ascending order of index value of the node in the topology order;

[0082] S2, distributing all edges connected to the current node as a leaf node set of the left sub-tree;

[0083] S3, constructing a balanced binary tree as the left sub-tree structure based on the leaf node set;

[0084] S4, distributing edges other than the edges connected to the current node as a leaf node set of the right sub-tree;

[0085] S5, taking the right sub-tree as a new to-be-processed sub-tree, and recursively performing steps S2 to S4 until the last node with non-empty connected edges is processed;

[0086] S6, constructing a balanced binary tree for the edges connected to the last node as a leaf node set of the right sub-tree, and obtaining the full binary tree vtree.

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

[0088] performing a top-down compilation process from the root node of the vtree;

[0089] applying an implicit partition rule in the compilation process to suppress zero branches corresponding to non-connected states;

[0090] detecting and merging equivalent sub-graph structures generated by different compilation branches through a sub-graph isomorphism recognition mechanism, and identifying and removing branches that cannot meet the connectivity requirements of terminal nodes through a constraint condition detection module.

[0091] Specifically, in the embodiments of the present application, Figure 2 invalid sub-graphs that may occur during the compilation process, i.e., cases where the left sub-graph cannot be constructed, are shown. The zero-suppression statement logic decision diagram ZSDD compilation algorithm will divide the network edges corresponding to the leaf nodes of the left and right sub-trees into two sub-graphs and process them in parallel during the execution process. In this process, the connection status of the boundary nodes (i.e., the common nodes of the left and right sub-graphs and the nodes in the left sub-graph that have been connected to the right sub-graph) and the terminal nodes in the left sub-graph determines the connectivity constraints of the left sub-graph, and further determines the topology state and connectivity constraints of the right sub-graph. If the vtree is not constructed properly, it may occur that the connection status of certain boundary nodes and terminal nodes cannot be realized in the left sub-graph, resulting in the generation of invalid branches during the compilation process, thereby increasing the time and space overhead. By constructing the vtree using a heuristic function, the edges connected to the same network node are concentrated in the same sub-tree in the vtree, which can ensure the realizability of the connectivity relationship of the boundary nodes in the structure.

[0092] In the embodiments of the present application, referring to Figure 3 , the zero-suppressed sentence logic decision diagram (ZSDD) compiling algorithm comprises the following steps:

[0093] Firstly, the algorithm takes a network graph G=(N, E), a terminal node set T and a vtree node v as input.

[0094] Next, a top-down compiling algorithm starting from the root node of the vtree will construct the root node of the zero-suppressed sentence logic decision diagram (ZSDD) Z and its corresponding initial graph state: the terminal node set is T, the connection requirement is that all terminal nodes are connected, and the connected state is no connected node.

[0095] Next, according to the type of the vtree node v corresponding to the zero-suppressed sentence logic decision diagram (ZSDD) Z, it is divided into three categories for processing: 1. Shannon node case, that is, the left subtree is a leaf node. At this time, according to the selection of the left subtree corresponding edge , two pairs of elems composed of sub ZSDD prime and sub are obtained; wherein, ZSDD prime is used to represent the value constraint of the variable set corresponding to the left subtree of the vtree, and its essence is to logically describe the feasibility of the left subgraph structure. ZSDD sub is used to represent the right subgraph structure obtained after updating the graph state under the condition specified by prime, which is a sub ZSDD reflecting the feasible combination of the remaining edges under the new connectivity constraint. Therefore, for the Shannon node, prime is a terminal ZSDD representing the value state of the edge , specifically including: (must select the edge), (prohibit selecting the edge), (the edge can be selected or not selected).

[0096] Among them, the prime of the left subgraph is the terminal ZSDD (indicating that the edge needs to be selected), (indicating that the edge cannot be selected), (indicating that the edge can be selected or not selected), and the sub of the right subgraph will be according to the edge Select or not to update the graph state (update the terminal node and node connected in the right subgraph, and the non-terminal node connected with the terminal node will be considered as a terminal node). 2. Decompose the node condition, that is, the left sub-tree is not a leaf node. At this time, the boundary node (the common node of the left and right subgraphs and the node connected with the right subgraph in the left subgraph) is obtained according to the left and right subgraphs, and the connectivity constraint of the left subgraph is determined by enumerating the connection condition of the boundary node and the terminal node in the left subgraph, and the topology state and connectivity constraint of the right subgraph are determined, and the ZSDD Z is constructed, all of which are composed of prime and sub. The graph state of the left and right subgraphs is determined by the connectivity constraint, and the update method is as follows: the terminal node of the left subgraph is updated to the boundary node and the original terminal node, the connectivity constraint is used as the node connection requirement, and the connected node condition remains unchanged; the terminal node of the right subgraph is updated to the boundary node required to be connected with the terminal node and the original terminal node, the node connection requirement inherits the original graph state requirement, and the connected node condition is updated according to the connectivity constraint, that is, if the boundary node requires connection, these boundary nodes are considered as connected. 3. Leaf node condition, according to the current graph state, judge whether the edge corresponding to the leaf node needs to be selected, and construct the corresponding terminal ZSDD.

[0097] Then, for different branches, the ZSDD node constructs the elems of the vtree in the case of shannon / decomposition node, and performs pruning detection of connectivity constraint detection and isomorphic subgraph identification: 1. According to the terminal ZSDD or graph state corresponding to prime, it is judged whether there is a terminal node that cannot be connected with the terminal node in the right subgraph. If so, delete the elem; 2. According to the graph state corresponding to sub, it is judged whether all terminal nodes have been connected. If so, the vtree corresponding to sub is set to the rightmost leaf node of the right sub-tree of v, and sub is constructed as a terminal ZSDD , wherein, is the edge corresponding to the rightmost leaf node; 3. The corresponding hash signature (composed of terminal nodes, connectivity requirements, and connected conditions) is calculated according to the graph state of prime / sub, which is used to detect isomorphic subgraphs. When it is detected that the subgraph structures generated by different branches are the same, the existing nodes are reused instead of being generated again, so as to avoid repeated construction.d. If it is not the above three conditions, pruning is not needed, and the compiling algorithm will construct each prime / sub by re-calling itself. At this time, the graph state in the algorithm input will be updated to the graph state corresponding to prime / sub, and the vtree will be updated to the left sub-tree v l or the right sub-tree v r .

[0098] Finally, a zero-suppression statement logic decision diagram ZSDD representing a subgraph in which all terminal nodes are connected is obtained.

[0099] Further, the implicit partition rule comprises: omitting the zero branch configuration operation corresponding to the invalid connected state, and only retaining the valid subgraph branch capable of realizing the terminal node connection.

[0100] Further, the detection and merging of equivalent subgraph structures generated by different compiling branches through the subgraph isomorphism recognition mechanism comprises:

[0101] calculating the hash signature of each subgraph structure, the hash signature being composed of a terminal node set, a connected requirement and a connected state;

[0102] When it is detected that the hash signatures generated by different compiling branches are the same, the existing subgraph node is reused without recompilation.

[0103] Further, the identification and elimination of branches that cannot meet the terminal node connectivity requirement through the constraint condition detection module comprises:

[0104] In the compiling process, it is judged in real time whether the current subgraph structure has met the terminal node connectivity, and the branch that has met the connectivity is terminated in advance;

[0105] It is judged whether there is a case that the terminal node cannot establish a connection with the terminal node in the remaining subgraph structure, and the branch that cannot complete the connection is eliminated.

[0106] Further, based on the zero suppression statement logic decision diagram ZSDD, the reliability value of the network system is recursively calculated, comprising:

[0107] Starting from the root node of the zero suppression statement logic decision diagram ZSDD, the reliability probability of each subnode is calculated layer by layer according to the node type using the corresponding recursive formula;

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

[0109] Specifically, in the embodiments of the present application, referring to Figure 4 , the accurate intelligent reliability calculation algorithm comprises the following steps:

[0110] First, the zero suppression statement logic decision diagram Z and the available probability set P of the edge obtained from the compiling algorithm stage are taken as inputs.

[0111] Then, the algorithm checks whether the reliability of the input decision diagram has been calculated according to the ZSDD root node ID. If the result is stored in the hash table, the cached value is read without repeated calculation; otherwise, the algorithm judges the current node type and calculates the reliability: 1. Terminal ZSDD, according to the full binary tree node type corresponding to the node, the reliability probability value is calculated and returned, and the calculation result is stored in the form of a hash table. If it is 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] The embodiment realizes efficient and accurate intelligent calculation of network reliability by introducing a zero-suppressed sentence logic decision diagram (ZSDD), a heuristic vtree construction strategy, a compilation algorithm integrating connectivity constraint detection and subgraph isomorphism identification mechanism, and a recursive reliability intelligent calculation algorithm based on cache optimization.

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

[0125] Subsequently, the connectivity constraint detection mechanism and subgraph isomorphism identification are introduced in the ZSDD compilation process, and the merging of repeated subgraphs and the early pruning of invalid branches are realized through connectivity and subgraph state hash detection, which successfully avoids the exponential growth of compilation branches and significantly reduces the space and time consumption.

[0126] In the reliability intelligent calculation phase, the recursive algorithm integrated with the cache mechanism is used to efficiently traverse and reuse the results of ZSDD, which not only significantly reduces the amount of repeated calculation, but also further improves the overall calculation efficiency. Experimental results show that the decision graph obtained by the compilation algorithm in the present application is more compact than the method based on BDD or SDD, and the subsequent reliability intelligent calculation efficiency is significantly improved.

[0127] In addition, ZSDD has the characteristics of polynomial time complexity of Boolean function operations, which provides new calculation support for network reliability optimization. Using the compiled ZSDD, various reliability optimization analysis can be quickly realized without recompilation, such as solving the maximum reliability under given edge consumption constraints, determining the minimum consumption edge set under reliability threshold constraints, or implementing multi-objective optimization based on the relationship between edge weight and reliability change.

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

[0129] In order to further illustrate the practicability of the present application, a certain city road network is exemplified.

[0130] Suppose a certain city road network contains 200 roads (edges), and in the study period (17:00-19:00), the probability of each road being unblocked is denoted as In this example, let (i.e. each road remains passable with 90% probability during the time period). The road network is topologically ordered according to the method of the present application, a full binary tree vtree is established based on the topological order, and the road network is compiled into a zero-suppressed sentence logic decision diagram (ZSDD). After the ZSDD is successfully compiled, recursive probability summation can be directly performed on the ZSDD to obtain an accurate global connectivity probability. It is particularly pointed out that in the example, the passable events of each road are approximated as independent of each other, and the value may be obtained from historical traffic data, sensor statistics or traffic simulation.

[0131] Based on the above calculation results, the passable probability of a single or multiple roads can be further calculated Sensitivity analysis is performed to quantify the contribution of each road to the global connectivity (road importance): the passable probability of a certain road is increased from to , the global connectivity probability is recalculated, and the increment of the connectivity probability is measured to evaluate the marginal contribution of the road. Based on the value of each road, the road set that is preferentially expanded or maintained under a given budget can be determined, so as to achieve optimal allocation of resources.

[0132] The embodiment also proposes a network reliability intelligent computing system of a logic decision diagram, comprising: a triple structure construction module, a full binary tree construction module, a sentence logic decision diagram acquisition module and a calculation module;

[0133] The triple structure construction module is configured to model the network system as a triple data structure composed of a network topology graph, a terminal node set and an edge availability probability set;

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

[0135] The sentence logic decision diagram acquisition module is configured to compile the network topology graph into a zero-suppressed sentence logic decision diagram using the full binary tree, wherein the zero-suppressed sentence logic decision diagram is used to represent a set of valid subgraphs that satisfy terminal node connectivity.

[0136] The calculation module is configured to calculate the reliability value of the network system recursively based on the zero-suppressed sentence logic decision diagram.

[0137] The above merely provides the preferred embodiments of the present application, and the protection scope of the present application is not limited thereto, and any changes or substitutions within the technical scope disclosed by the present application should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection 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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