A network connectivity reliability algorithm considering epistemic uncertainty

Abstract

The invention belongs to the technical field of network reliability, and specifically discloses a network connectivity reliability algorithm considering cognitive uncertainty, comprising: establishing a network topology diagram according to each node in the network and the links connecting the nodes; adding variables for considering whether the nodes and links are normal to the network topology diagram to obtain an extended uncertainty diagram; constructing a connectivity state pattern for the variables through a connectivity function, and establishing a network connectivity reliability model considering the reliability of the connectivity state pattern; equivalently converting the reliability of the connectivity state pattern into the most reliable connectivity path; finding the most reliable connectivity path between two nodes; calculating the connectivity reliability of the most reliable connectivity path, and completing the solution of the network connectivity reliability model; having the following advantages: considering cognitive uncertainty by describing the states of nodes and edges in the network as Boolean uncertain distribution, and quantitatively calculating the connectivity reliability of the network by establishing an extended uncertainty diagram.

Description

Technical Field

[0001] The present invention relates to the technical field of network reliability, and in particular to a network connectivity reliability algorithm taking cognitive uncertainty into consideration. Background Art

[0002] Network systems, such as supply chain networks, communication networks, and transportation networks, play a vital role in people's daily lives. With the progress of society and scientific development, the structure of these networks is becoming more and more complex and the scale is becoming larger and larger, which makes it inevitable that failures will occur in the network. Network connectivity reliability is a basic indicator of network reliability, which focuses on the possibility of a connectivity path between specified nodes in the network.

[0003] Traditional network connectivity reliability algorithms are usually based on probability theory. These evaluation methods assume that the distribution of node failure times in the network is known or accurately measured. However, for many real-world networks, such as satellite networks and wireless sensor networks, due to the complex network structure and time or financial constraints, there is a lack of sufficient observation data, which results in cognitive uncertainty in the network failure data. Therefore, traditional network reliability algorithms based on probability theory have their own limitations in solving the above problems.

[0004] The theorems involved in this patent include the following:

[0005] Uncertain measure: Let Γ be a non-empty set, is a σ-algebra on Γ, then The elements in Λ are called events. is called an uncertainty space. Uncertain measure From to [0,1] that satisfies the following 4 axioms:

[0006] Axiom 1 (Normativity) For the entire set Γ, we have

[0007] Axiom 2 (Duality) For any event Λ, we have

[0008] Axiom 3 (Subadditivity) For a countable sequence of events Λ1, Λ2, Λ3, ..., we have

[0009] Axiom 4 for a series of uncertain spaces The product σ-algebra is For any Choose Λ at random g , product uncertainty measure on product σ-algebra satisfy

[0010] Uncertain variables: Let ξ be a variable from the uncertain space A function of the set of real numbers R is called an uncertain variable if, for any Borel set B, the set {ξ∈B}={γ∈Γ|ξ(γ)∈β} is an event.

[0011] If an uncertain variable takes the value 0 or 1, then the uncertain variable is called a Boolean uncertain variable. For example, the following ξ is a Boolean uncertain variable,

[0012]

[0013] where is a real number between 0 and 1.

[0014] Uncertain distribution: The uncertainty distribution Φ of an uncertain variable is defined as Where x is any real number.

[0015] Theorem 1 Assume ξ1, ξ2, …, ξ n are independent Boolean uncertain variables. For i = 1, 2, ..., we have

[0016]

[0017] If f is a monotonically increasing Boolean function, then for a Boolean uncertain variable ξ=f(ξ1,ξ2,…,ξ n )have

[0018]

[0019] Among them B i is a subset of the set {0,1}, i = 1, 2,…,.

[0020] Therefore, a network connectivity reliability algorithm with cognitive uncertainty is proposed to solve the above problems. Summary of the invention

[0021] The present invention aims to provide a network connectivity reliability algorithm that takes into account cognitive uncertainty, so as to solve or improve the networks in the real world, such as satellite networks, wireless sensor networks, etc., which lack sufficient observation data due to the complex network structure and time or financial constraints, and thus the fault data in the network mainly has cognitive uncertainty problems.

[0022] In view of this, a first aspect of the present invention is to provide a network connectivity reliability algorithm taking into account epistemic uncertainty.

[0023] The first aspect of the present invention provides a network connectivity reliability algorithm that takes into account cognitive uncertainty, comprising the following steps: S1, establishing a network topology graph based on each node in the network and the links connecting the nodes; S2, adding variables that consider whether the nodes and links are normal to the network topology graph to obtain an extended uncertainty graph; S3, constructing a connectivity state pattern of the extended uncertainty graph for the variables through a connectivity function, and establishing a network connectivity reliability model that takes into account the reliability of the connectivity state pattern; S4, converting the reliability of the connectivity state pattern into the most reliable connectivity path; S5, finding the most reliable connectivity path between two nodes in the extended uncertainty graph; S6, calculating the connectivity reliability of the most reliable connectivity path, and completing the solution of the network connectivity reliability model; wherein, the connectivity state pattern indicates whether any two nodes in the extended uncertainty graph are connected.

[0024] The present invention provides a network connectivity reliability algorithm that takes into account cognitive uncertainty, which establishes a network topology diagram based on the nodes in the network and the connection relationships between them, including a node set and a link set representing the connection between the nodes;

[0025] Based on the fault data of each node and link in the network, the Boolean uncertainty distribution of whether each node and edge is normal is obtained according to the uncertain statistical method, and the extended uncertainty graph is established based on the network topology;

[0026] For a two-state network, there are only two states between nodes in the network: connected and disconnected. The connected state mode is used to describe whether the nodes are connected.

[0027] According to the network connectivity reliability model, to calculate the connectivity reliability of the network, we first need to calculate the connectivity state pattern. The connectivity reliability between nodes in the extended uncertainty graph is equal to the connectivity reliability of the most reliable connectivity path. Therefore, calculating the connectivity state pattern is transformed into finding the most reliable connectivity path.

[0028] For the most reliably connected path, a path is connected if and only if all links and nodes on the path exist;

[0029] Epistemic uncertainty is considered by describing the states of nodes and edges in the network, normal or faulty, as Boolean uncertainty distributions, and the connectivity reliability of the network is quantitatively calculated by building an extended uncertainty graph.

[0030] In addition, the technical solution provided according to the embodiment of the present invention also has the following additional technical features:

[0031] In any of the above technical solutions, the connectivity state mode is specifically the following formula: sn =f sn (c1, c2, ..., c m+n), where c sn is the connected state mode, f sn is the connectivity function, c1, c2, …, c m+n To extend the uncertain graph, we consider Boolean uncertain variables of whether nodes and links are normal.

[0032] In this technical solution, the connected state mode c is used sn To describe the node v s With node v t Whether it is connected. sn = 1, node v s With node v t are connected, when c sn = 0, node v s With node v t There is no connection between them. In the extended uncertain graph G(V, E, C), the connected state pattern c sn Expressed as the above formula, f sn is a monotonically increasing Boolean function.

[0033] In any of the above technical solutions, the connectivity reliability model is specifically the following formula: Among them, R sn，G represents the slave node v in the extended uncertain graph s To node v t The connectivity reliability, v s and v t is any point in the network.

[0034] In any of the above technical solutions, a node v is selected in the extended uncertain graph. s and node v t , the equivalent conversion in S4 is specifically the following formula: in, Represents the path P * From node v s To node v t connectivity reliability.

[0035] In this technical solution, p * To expand the uncertain graph G from node v s To node v t A path from node v in the extended uncertainty graph G s To node v t The path p has Then call P * To expand the uncertain graph G from node v s To node v t The most reliable connectivity path. and Rsn，p Respectively represent the path P * and the connectivity reliability of path p;

[0036] In the extended uncertain graph G, P * Represents the node v in the extended uncertain graph G s With node v t The most reliable connection path between them is:

[0037]

[0038] Where R sn，G In the extended uncertain graph G, from node v s To node v t The reliability of connectivity, Represents the path P * From node v s To node v t Connectivity reliability;

[0039] Specifically, assume that G(V,E,C) is an extended uncertain graph, where V = {v1, v2, ..., v n}, E = {e1, e2, ..., e m}, C={c1,c2,…,c m+n}. The connectivity reliability in the extended uncertain graph G is:

[0040]

[0041] Among them, B i is a subset of the set {0, 1}, i = 1, 2, ..., m + n.

[0042] In the extended uncertain graph G there exists therefore, Proof required

[0043] Because f sn is a monotonically increasing function. When f sn (B1,B2,…,{0},…,B m+n )=1

[0044] When it is established, the following equation is also established

[0045] f sn (B1,B2,…,{1,0},…,B m+n )=1

[0046] There is a set Takes the value {1} or {0, 1}, so that

[0047]

[0048] Taking into account When is {0, 1}, Therefore, the above writing

[0049]

[0050] where j and J are Medium elements and scale.

[0051] Then the subgraph S consisting of a total number of edges and nodes J contains a line from node v s To node v t Path, remove the edges or nodes that do not belong to the path in subgraph S, and get a new subgraph S1, which contains a total of J-1 edges and nodes. At this time, S1 contains a path and satisfies

[0052]

[0053] where j′ is the index of the edge or vertex being removed.

[0054] So we get

[0055]

[0056] Repeat the above process until there are no other edges and nodes in the subgraph except the edges and nodes in the path. Get a path p that satisfies

[0057] R sn，G =R sn，P

[0058] Because p * is the most reliable connection path, so there is

[0059]

[0060] In summary, we get

[0061]

[0062] therefore

[0063] In any of the above technical solutions, the extended uncertainty graph is G(V, E, C); wherein V = {v1, v2, ..., v n} is a node set, E = {e1, e2, ..., e m} is a link set, C = {c1, c2, ..., c m+n} is a set of variables that consider whether nodes and links are normal.

[0064] In this technical solution, Wherein, i=1, 2, ..., m+n; represents the normal uncertainty measure of node or edge i, that is, the confidence reliability of node or edge i;

[0065] Based on the extended uncertain graph, the adjacency matrix of the extended uncertain graph is expressed as:

[0066]

[0067] Where 0≤α ij ≤1, i, j = 1, 2, ..., n. When i = j, α ij Represents node v i There is an uncertainty measure, when i≠j, α ij Represents node v i With node v j There is an uncertain measure of the existence of a link between them.

[0068] In any of the above technical solutions, the step S5 is specifically as follows: S501, respectively setting the node set S of the most reliable connection path, the other node set U and the link set L of the most reliable connection path; wherein S includes the node v s , U contains V except v s The node v i ; S502, with v s As the starting point; S503, for all i ∈U link e s，i , choose so that α s，i ∧α i，i The link with the largest value e s，i and node v i , and put them into L and S respectively; S504, let node v s = v of S503 i , and delete node v of S503 from U i , return to node v from S502 to S503 i For node v t ; Among them, α s，i For node v s With node v i There is an uncertainty measure between the links, α i，i For node v i There is uncertainty in the measure.

[0069] In this technical solution, at the pre-desired v s and v t Find the most reliable connection path between them, and according to step S502, find a node and v in S502 s The most reliable connection path and v i, and in S503 the currently found v i Starting point v s Until S503 finds v i The expected v t .

[0070] In any of the above technical solutions, the connectivity reliability is calculated using the following formula: Among them, ev i For path p * Uplink or node, c i For path p * The status mode of the node or link, is an uncertain measure.

[0071] In this technical solution, for the most reliable connection path p * , if and only if path p * When all links and nodes on the path exist, the path p * Is connected.

[0072] Compared with the prior art, the present invention has the following beneficial effects:

[0073] Epistemic uncertainty is considered by describing the states of nodes and edges in the network, normal or faulty, as Boolean uncertainty distributions, and the connectivity reliability of the network is quantitatively calculated by building an extended uncertainty graph.

[0074] Additional aspects and advantages of embodiments according to the present invention will become apparent in the following description or may be learned through practice of embodiments according to the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] The drawings are only for the purpose of illustrating particular embodiments and are not to be construed as limiting the invention.

[0076] Figure 1 It is the algorithm flow chart of the present invention;

[0077] Figure 2 It is a schematic diagram of the backbone network of the present invention. DETAILED DESCRIPTION

[0078] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments are combined with each other in the absence of conflict.

[0079] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0080] See also Figure 1 , a first aspect of the present invention provides a network connectivity reliability algorithm considering cognitive uncertainty, comprising the following steps:.

[0081] S1: Establish network topology G(V, E);

[0082] According to the connection relationship between each node in the network, a network topology G(V, E) is established, where V = {v1, v3, ..., v n} is a node set, E = {e1, e2, ..., e m} is a link set.

[0083] S2: Establish an extended uncertain graph G(V, E, C);

[0084] Based on the fault data of each node and link in the network, the Boolean uncertainty distribution of whether each node and link is normal is obtained according to the uncertain statistical method. On the basis of the network topology G(V, E), an extended uncertain graph G(V, E, C) is established, where V = {v1, v3, ..., v n} is a node set, E = {e1, e2, ..., e m} is a link set, C = {c1, c2, ..., c m+n} is a set of Boolean uncertain variables describing whether nodes and links are normal, where:

[0085]

[0086] Here, i=1, 2,…, m+n. It represents the uncertainty measure of whether the node or link i is normal, that is, the certainty reliability of the node or link i.

[0087] Based on the extended uncertain graph, the adjacency matrix of the extended uncertain graph is expressed as:

[0088]

[0089] Where 0≤α ij ≤1, i, j = 1, 2, ..., n. When i = j, α ij Represents node v i The uncertainty measure exists, when i≠j, it means that the node v i With node v j There is an uncertainty measure α between the links ij .

[0090] S3: Establish a network connectivity reliability model;

[0091] For a two-state network, the node v in the network sWith node v t There are only two states: connected and disconnected. Use the connected state mode c sn To describe the node v s With node v t Whether it is connected. sn = 1, node v s With node v t are connected, when c sn = 0, node v s With node v t There is no connection between them. In the extended uncertain graph G(V, E, C), the connected state pattern c sn Expressed as

[0092] c sn =f sn (c1, c2, ..., c m+n )

[0093] Among them, c1, c2, …, c m+n A Boolean uncertain variable indicating whether the nodes and links in the extended uncertain graph G are normal, f sn is a connectivity function that characterizes the state patterns c1, c2, …, c of nodes and links in the extended uncertain graph G. m+n For node v s With node v t Connectivity status mode c sn Obviously, f sn is a monotonically increasing Boolean function.

[0094] Therefore, the connectivity reliability model of the network is:

[0095]

[0096] S4: Calculate the connectivity state mode;

[0097] According to the network connectivity reliability model, to calculate the network connectivity reliability, we first need to calculate the connectivity state mode c sn . Expand the node v in the uncertain graph G s With node v t The connectivity reliability between is equal to the connectivity reliability of the most reliable connectivity path. Therefore, the connectivity state mode c is calculated. sn Translated into finding the most reliable connectivity path.

[0098] The most reliable connection path: p * To expand the uncertain graph G from node v s To node v t A path from node v in the extended uncertainty graph G s To node vt The path p has Then call p * To expand the uncertain graph G from node v s To node v t The most reliable connectivity path. and R sn，p Respectively represent the path P * and the connectivity reliability of path p.

[0099] In the extended uncertain graph G, P * Represents the node v in the extended uncertain graph G s With node v t The most reliable connection path between

[0100]

[0101] Where R sn，G In the extended uncertain graph G, from node v s To node v t The reliability of connectivity, Represents the path P * From node v s To node v t connectivity reliability.

[0102] Specifically, assume that G(V,E,C) is an extended uncertain graph, where V = {v1, v2, ..., v n}, E = {e1, e2, ..., e m}, C={c1,c2,…,c m+n}. The connectivity reliability in the extended uncertain graph G is:

[0103]

[0104] Among them, B i is a subset of the set {0, 1}, i = 1, 2, ..., m + n.

[0105] In the extended uncertain graph G there exists therefore, We just need to prove

[0106] Because f sn is a monotonically increasing function. When f sn (B1,B2,…,{0},…,B m+n )=1, the following equation also holds true

[0107] f sn (B1,B2,…,{1,0},…,B m+n )=1

[0108] There is a set Takes the value {1} or {0, 1}, so that

[0109]

[0110] Taking into account When is {0, 1}, Therefore, the above writing

[0111]

[0112] where j and J are Medium elements and scale.

[0113] Then the subgraph S consisting of a total number of edges and nodes J contains a line from node v s To node v t Path, remove the edges or nodes that do not belong to the path in subgraph S, and get a new subgraph S1, which contains a total of J-1 edges and nodes. At this time, S1 contains a path and satisfies

[0114]

[0115] where j′ is the index of the edge or vertex being removed.

[0116] So we get

[0117]

[0118] Repeat the above process until there are no other edges and nodes in the subgraph except the edges and nodes in the path. Get a path p that satisfies

[0119] R sn，G =R sn，P

[0120] Because P * is the most reliable connection path, so there is

[0121]

[0122] In summary, we get

[0123]

[0124] therefore

[0125] S5: Find the most reliable connection path.

[0126] In the extended uncertain graph G(V, E, C), find the node v s With node v tThe most reliable connection path between. Further, the specific process of step S5 is:

[0127] S5-1: Take three sets S, U and L. Let S contain only nodes, that is, S = {v s}, U contains all the parts of V except v s Other nodes outside, that is, U=VS,

[0128] S5-2: Starting point v s , for all v i ∈U link e s，i , choose so that α s，i ∧α i，i The link and vertex with the largest value. For example, v i′ and e s，i′ Update the sets S, U and L so that S = S∪{v i′},U=U-{v i′}, L = L∪{e s，i′};

[0129] S5-3: Take i′ as the new starting point and repeat the above steps until the node v t Included in the set S. The final set S is the node set of the most reliable connection path, and the set L is the link set of the most reliable connection path.

[0130] S6: Calculate the connectivity reliability of the most reliable connectivity path

[0131] For the most reliable connected path P * , if and only if path P * When all links and nodes on the path exist, the path P * Therefore, path p * The connectivity reliability is calculated by the following formula:

[0132]

[0133] Among them, ev i Represents the path P * Uplink or node, c i Represents the path P * The status mode of the node or link.

[0134] Example 1

[0135] like Figure 2As shown, the application process of the present invention is described by taking the NSFNET network as an example. NSFNET is a scientific research backbone network, consisting of 14 nodes and 21 links. In the network, each node represents a computing center, and each link represents a communication line between nodes. The nodes and links in the NSFNET network have only two states: failure and normal operation, and the failures on the nodes and links are independent of each other. The following is a calculation process of the connectivity reliability between several specified nodes in the network.

[0136] Firstly, the network topology G(V, E) is constructed according to the connection relationship between each node in NSFNET. The topology G(V, E) contains 14 nodes and 21 links.

[0137] Then, based on the uncertain statistical method, the Boolean uncertainty distribution of each node and link in the network is obtained according to the fault data or expert experience. The node information and link information of the NSFNET network are shown in Table 1 and Table 2 respectively.

[0138] Table 1 Node information

[0139]

[0140]

[0141] Table 2 Link information

[0142]

[0143] Based on the network topology G(V, E) and the information in Tables 1 and 2, an extended uncertain graph G(V, E, C) is established. The adjacency matrix of the extended uncertain graph is:

[0144]

[0145] Based on the extended uncertain graph, first find the node v s With node v t The most reliable connection path between them is then calculated, and then the corresponding connection reliability is calculated. Table 3 gives the most reliable connection paths and connection reliability between several sets of node pairs.

[0146] Table 3 Network connectivity reliability

[0147]

[0148]

[0149] In the description of the present invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside" and "outside" etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0150] The embodiments described above are only descriptions of the preferred modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A network connectivity reliability algorithm considering epistemic uncertainty, characterized in that: The steps include: S1, establish a network topology map based on each node in the network and the links connecting the nodes; S2, add variables that consider whether nodes and links are normal to the network topology graph to obtain an extended uncertainty graph; S3, constructing a connectivity state pattern of the extended uncertainty graph for the variables through a connectivity function, and establishing a network connectivity reliability model that takes into account the reliability of the connectivity state pattern; S4, converting the reliability of the connectivity state mode into the most reliable connectivity path; S5, in the extended uncertain graph, find the most reliable connected path between two nodes; S6, calculating the connectivity reliability of the most reliable connectivity path, and completing the solution of the network connectivity reliability model; Wherein, the connectivity state mode indicates whether any two nodes in the extended uncertainty graph are connected; The connectivity state mode is specifically the following formula: c sn =f sn (c1,c2,…,c m+n ); Among them, c sn is the connected state mode, f sn is the connectivity function, c1, c2, …, c m+n To expand the uncertainty graph, consider the Boolean uncertain variables of whether nodes and links are normal; The connectivity reliability model is specifically the following formula: Among them, R sn，G represents the slave node v in the extended uncertain graph s To node v t The connectivity reliability, v s and v t is any point in the network; Select a node v in the extended uncertain graph s and node v t , the equivalent conversion in S4 is specifically the following formula: in, Represents the path P * From node v s To node v t Connectivity reliability; The extended uncertainty graph is G(V, E, C); Where V = {v1, v2, ..., v n } is a node set, E = {e1, e2, ..., e m } is a link set, C = {c1, c2, ..., c m+n } is a set of variables that consider whether nodes and links are normal.

2. A network connectivity reliability algorithm considering cognitive uncertainty according to claim 1, characterized in that: The step of S5 is specifically as follows: S501, respectively set the node set S of the most reliable connection path, the other node set U and the link set L of the most reliable connection path; wherein S includes the node v s , U contains all the parts of V except v s The external node v i ; S502, with v s as a starting point; S503, for all v i ∈U link e s，i , choose so that α s，i ∧α i,i The link with the largest value e s，i and node v i , and put in L and S respectively; S504, let node v s = v of S503 i , and delete node v of S503 from U i , return to node v from S502 to S503 i For node v t ; Among them, α s，i For node v s With node v i There is an uncertainty measure between the links, α i，i For node v i There is uncertainty in the measure.

3. The network connectivity reliability algorithm considering cognitive uncertainty according to claim 1, characterized in that: The connectivity reliability is calculated using the following formula: Among them, ev i For path P * Uplink or node, c i For path P * The status mode of the node or link, is an uncertain measure.

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