CN107944705B - Full-end reliability calculation method for dividing communication communities based on modularity - Google Patents
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Abstract
The invention discloses a modularity-based whole-end reliability calculation method for dividing a communication community, which comprises modularity-based power communication network community division and minimum path set-based whole-end reliability calculation. The complexity of the internal topological structure of the communication community divided by the modularity is far lower than that of the whole power communication and is mutually independent, parallel calculation is introduced for the analysis of the internal full-end reliability, the finally obtained communication community connection topological structure is simpler, and the analysis time consumption of the full-end reliability is less.
Description
Technical Field
The invention relates to the technical field of a full-end reliability calculation method, in particular to a full-end reliability calculation method for dividing a communication community based on modularity.
Background
With the gradual increase of the scale and the increasingly complex structure of the power communication network, the information amount of various services carried on the power communication network also increases rapidly, and the risks faced by the power communication network also increase or decrease. The dependence of the power grid on the communication network makes the reliability research of the communication network to be quite important. The full-end reliability refers to the probability of keeping connection among all nodes in the whole network, and is a popular reliability evaluation method nowadays. However, the conventional full-end reliability evaluation usually utilizes a probability analysis method to derive the system condition from the full-end reliability calculation of a local simple network, and the calculation method has accurate results but is only suitable for small-scale networks. However, the power communication network in China has been gradually developed into a large-scale complex system, and the traditional full-end reliability calculation method cannot accurately evaluate the full-end reliability of the power communication network in province level and above large range. The invention provides a comprehensive end reliability calculation method based on a complex network theory, which is used for evaluating the comprehensive end reliability of a wide area power communication network.
Connectivity-based network reliability analysis is a classic problem in network reliability research. How to accurately compute the full-end reliability is an NP-hard problem. At present, the full-end reliability calculation is mainly focused on 3 methods, namely the full-end reliability calculation based on minimum cut, the full-end reliability calculation based on a minimum path set and the full-end reliability replacement by utilizing the approximate values of the upper and lower bounds of the full-end reliability. The methods are mainly suitable for networks with few nodes and simple network topology structures, and for complex networks, the computing methods have the defects of low computing speed and high algorithm cost. The invention provides a comprehensive end reliability calculation method suitable for a complex power communication network based on a complex network theory. The characteristic that the clustering coefficient of the power communication network is large is utilized to cluster the nodes closely connected with the power communication network, the network topology structure is simplified, and then the whole-end reliability of the simplified complex network is calculated, so that the whole-end reliability of the complex network is described.
In order to understand the development status of the reliability calculation method and technology for the complex network in the existing power communication network, the existing papers and patents are searched, compared and analyzed, and the following technical information with high relevance to the invention is screened out:
the technical scheme 1: the invention discloses a full voltage grade reliability assessment method with patent publication number CN103927691A, and relates to a full voltage grade reliability assessment method in a power system, which analyzes power grid topology, divides a power grid into a power generation system, a power transmission system, a transformer substation main wiring and a power distribution system, carries out reliability assessment on full load conditions of the power generation system and the power transmission system, establishes a transformer substation main wiring equivalent model by taking reliability indexes of the power generation system and the power transmission system as equivalent power parameters of the power distribution system, adds the equivalent model to the power distribution system, determines the reliability indexes of the power distribution system by adopting a minimum cut set method, and finally determines the reliability indexes of the full voltage grade.
The technical scheme 2 is as follows: the invention discloses a power distribution system reliability algorithm with the patent publication number of CN104636993A, which comprises the following steps: the method comprises the following steps that firstly, assuming that all transformer substations are completely stopped, the probability that each load point is independently powered by a distributed power supply is obtained through calculation; secondly, searching a normal minimum path set, marking the minimum path set as a conventional minimum path set and a standby minimum path set in order to distinguish the transformer substation from the distributed power supply, and adding an attribute of effective probability to the standby minimum path set; thirdly, generating minimum cut sets by using a conventional minimum path set, and calculating the reliability parameters of each minimum cut set; fourthly, correcting the reliability parameters of the minimal cut set according to the standby minimal path set; fifthly, calculating a load point reliability index; and sixthly, calculating the reliability index of the system.
The technical scheme 1 can realize the reliability evaluation of the full voltage level and improve the reliability evaluation level of the power system. The minimal cut-set approach employed is not suitable for large complex networks.
The technical scheme 2 adopts a minimum path set and minimum cut set improvement algorithm, comprehensively considers the situations of scheduled maintenance and switch switching time, and greatly saves the calculation time on the premise of ensuring the reliability calculation requirement of the power distribution system. However, in a large complex network, the minimum path set algorithm is not applicable, and the calculation speed is slow and the cost is high.
In summary, the existing invention patents do not take the reliability of the whole end of the power communication network into account, and for a large network, it is an NP-hard problem to accurately calculate the reliability of the whole end, so these methods are not suitable for a large complex network.
Disclosure of Invention
In view of the above situation, in order to overcome the defects of the prior art, the present invention provides a method for calculating the reliability of all terminals of a communication community based on modularity, which comprises the steps of firstly, analyzing the topological structure of an electric power communication network, and dividing the whole electric power communication network into a plurality of communication communities with smaller scales by using a community division algorithm based on modularity; and then, calculating the whole-end reliability of the inside of the community and the whole-end reliability between the communities to obtain the whole-end reliability of the whole network. Finally, the performance analysis of the algorithm is given by comparing the accurate whole-end reliability value with the whole-end reliability obtained by randomly dividing the community simplified network.
The technical scheme for solving the problem is that the method for calculating the reliability of the whole end based on the modularity degree divided communication community comprises the power communication network community division based on the modularity degree and the reliability calculation of the whole end based on the minimum path set, the power communication network community division based on the modularity degree comprises the following steps,
s1, in the network G, the degree of any node i is recorded as ki＝∑jAijWherein A represents the adjacency matrix of diagram G; c represents a community containing node i, then the degree of node i can be divided into two parts:
wherein the content of the first and second substances,
indicating the number of connecting edges of i with nodes outside the community C,
representing the number of edges between i and other nodes within C;
if C satisfies the condition:
then the sub-graph C is called a strong community;
if C satisfies the condition:
then the subgraph C is called as a weak community;
s2, dividing the communication community, wherein modularity is a method for measuring the structural strength of the network community, and in the method, the modularity is used for measuring the mutual communication robustness of the communication nodes in the communication community, and the robustness represents the communication probability among the communication nodes;
the modularity Q is defined as follows:
wherein the content of the first and second substances,
ti＝∑jPij
Pijrepresenting the probability of normal operation of the optical fibers between the communication nodes i, j, M representing the sum of the probabilities of normal operation of all the optical fibers in the network, tiThe sum of the probabilities of all optical fibers connected with the communication node i working normally is represented, and the modularity formula represents the connection in the networkSubtracting an expected value of the ratio of the two nodes which are arbitrarily connected under the same community structure from the ratio of the edges of the nodes in the community structure;
s3, clustering closely-connected communication sites in the power communication network to form a communication community by using a Fast Unfolding algorithm, and the method comprises the following three stages:
it is assumed that there are N nodes in the network,
a, in an initial state, distributing a community number i to each node i, wherein the network has N communities;
b, considering that the adjacent node j of each node i is added into the corresponding community of i, calculating the modularity Q under the action, and accepting the change if the added modularity variable quantity delta Q is positive;
and c, when the iteration times are less than the total iteration times, repeating the step b.
Due to the adoption of the technical scheme, compared with the prior art, the invention has the following advantages;
compared with the method for analyzing the reliability of the whole terminal by randomly dividing the communication community, the method has the advantages that the general trend of the method for analyzing the reliability of the whole terminal based on the modularity division communication community is consistent with the accurate value of the reliability of the whole terminal, the error is gradually reduced along with the gradual complexity of the communication topological structure, and finally, the error is kept within 6%, which is obviously better than that of the random method.
And 2, dividing a communication community based on modularity to analyze the reliability of the whole end, theoretically merging a plurality of minimum path sets which have small influence on the reliability of the whole end, reserving trunk paths which have large influence on the path sets, merging the branches which have small influence into a node after analyzing the reliability of the branches, and reducing the collection space of the minimum path sets by using the weight of the node to replace the connection probability value of the branches. Since the integration space of the minimum path set is reduced, the obtained full-end reliability is always smaller than the accurate full-end reliability, and thus the method can be used as the lower limit value of the full-end reliability.
In time complexity, the method obviously reduces the complexity of network topology through a community division mode, greatly reduces the state space of the network through space decomposition, and relieves the problem of 'state space explosion' to a certain extent, thereby reducing the time spent by the algorithm on searching the minimum path set. The complexity of the internal topological structure of the communication community divided by the modularity is far lower than that of the whole power communication and is mutually independent, parallel calculation is introduced for the analysis of the internal full-end reliability, the finally obtained communication community connection topological structure is simpler, and the analysis time consumption of the full-end reliability is less. With the increasing complexity of the power communication network topology, the advantage of the method in time complexity is more obvious.
Drawings
FIG. 1 is a network community structure division diagram of a method for dividing a communication community based on modularity and calculating reliability of all terminals.
Fig. 2 is a topological structure diagram of 5 simple graphs with 6 nodes according to the method for calculating the reliability of the whole terminal based on modularity division of communication communities.
Fig. 3 is a node division diagram obtained by node combination of relationships of close connections in a simple network by using a modularity-based community division algorithm according to the modularity-based communication community full-end reliability calculation method of the present invention.
FIG. 4 is a reliability graph calculated by three modes of the full-end reliability calculation method for dividing communication communities based on modularity.
Detailed Description
The foregoing and other technical matters, features and effects of the present invention will be apparent from the following detailed description of the embodiments, which is to be read in connection with the accompanying drawings of fig. 1 to 4. The structural contents mentioned in the following embodiments are all referred to the attached drawings of the specification.
In one embodiment, the method for calculating the reliability of the whole end based on modularity to divide the communication communities comprises the power communication network community division based on modularity and the reliability calculation of the whole end based on a minimum path set,
s1, there is no generally accepted formalization definition for the concept of communities, but essentially, all community definitions have such a consensus: the connection between nodes in the communities is relatively close, the connection between nodes in different communities is relatively sparse, and the formalized community definition proposed by Raddichi is adopted. The definition is as follows:
in the network G, the degree of any node i is recorded as ki＝∑jAijWhere A represents the adjacency matrix of diagram G. C represents a community containing node i, then the degree of node i can be divided into two parts:
wherein the content of the first and second substances,
indicating the number of connecting edges of i with nodes outside the community C,
representing the number of edges between i and other nodes within C;
if C satisfies the condition:
then the sub-graph C is called a strong community;
if C satisfies the condition:
then the subgraph C is called as a weak community;
s2, dividing the communication community, wherein modularity is a method for measuring the structural strength of the network community, and in the method, the modularity is used for measuring the mutual communication robustness of the communication nodes in the communication community, and the robustness represents the communication probability among the communication nodes; the size of the communication community is mainly determined by the division of the communication communities, the larger the value of the communication community is, the better the community division effect is proved, the higher the communication robustness of each node in each communication community is, otherwise, the poor community division effect is proved, and the lower the communication robustness of each node in each communication community is.
The modularity Q is defined as follows:
wherein the content of the first and second substances,
ti＝∑jPij
Pijrepresenting the probability of normal operation of the optical fibers between the communication nodes i, j, M representing the sum of the probabilities of normal operation of all the optical fibers in the network, tiThe method comprises the steps that the sum of the probabilities of normal work of all optical fibers connected with a communication node i is represented, a modularity formula represents the proportion of edges connecting internal nodes of a community structure in a network, and the expected value of the proportion of the two nodes which are arbitrarily connected under the same community structure is subtracted; in order to find a communication community in the power communication network, the invention uses Fast Unfolding algorithm which is a community division algorithm based on modularity, makes full use of the self-similarity of a complex power grid and naturally incorporates the concept of a hierarchical structure, and the community is established in the construction process.
S3, clustering closely-connected communication sites in the power communication network to form a communication community by using a Fast Unfolding algorithm, and the method comprises the following three stages:
it is assumed that there are N nodes in the network,
a, in an initial state, distributing a community number i to each node i, wherein the network has N communities;
b, considering that the adjacent node j of each node i is added into the corresponding community of i, calculating the modularity Q under the action, and accepting the change if the added modularity variable quantity delta Q is positive;
and c, when the iteration times are less than the total iteration times, repeating the step b.
Converting a complex power grid into a communication community set C by using Fast Unfolding algorithm, wherein CiThe weight of (b) represents the overall reliability of the communication community i. Connectivity S between "communitiesijIndicates the robustness of the connection between "Community" i and "Community" j, Sij∈[0,1]，SijThe larger the size, the higher the accessibility of communication between "community" i and "community" j, SijSmaller means lower reachability between "community" i and "community" j, Sij0 indicates that "community" i and "community" j are not reachable.
Degree of connectivity SijAnd "Community" Ci，CjThe probability of optical fiber connection between the communication nodes in (1) is related. Is defined as:
wherein, PmnAnd the probability of normal operation of the optical fiber between the grid node m and the node n is represented.
In a second embodiment, on the basis of the first embodiment, the overall-end reliability calculation based on the minimum path set specifically includes the following steps;
a, based on the characteristics of the small-world network of the power communication network, decomposing the whole complex network into a plurality of networks with smaller scale and mutual independence by using a 'community' structure of the complex network, solving the internal whole-end reliability of the networks, nodularizing the small-scale networks, wherein the node weight is the value of the whole-end reliability of the small-scale networks, then solving the whole-end reliability among the small-scale networks, and finally obtaining the whole-end reliability representing the whole-end reliability of the whole network.
When the whole-end reliability inside the community and the whole-end reliability between the communities are analyzed, the whole-end reliability of the network can be solved by utilizing the traditional minimum path set because the network scale is greatly reduced.
Solving the network full-end reliability by using the minimum path set is a main method for calculating the full-end reliability in the prior art. A path set is a set of edges that ensure that all nodes in the network are connected, and if a path set is no longer a path set except any edge, the path set is called a minimum path set. Thus, a minimum set of ways is a spanning tree.
And if all the edges and nodes in the minimum path set work normally, the system works normally. In the case of full-end reliability, it means that at least one minimum way set is working properly. The full-end reliability r (g) may be determined by the minimum route set, i.e.:
R(G)＝Pr(A1∪A2∪...∪An)×Pr(B1∩B2∩...∩Bm) (7)
wherein A isjAn event indicating that all edges in way set j are working properly, j is 1,2, …, n. B isiIndicating an event that node i is working properly.
In the calculation method of R (G), each node is independent, and the probability theory shows that:
Pr(B1∩B2∩...∩Bm)＝Pr(B1)×Pr(B2)×...×Pr(Bm) (8)
due to event A in equation (7)iAnd AjIs not an independent event, so for Pr (A)1∪A2∪...∪An) The solution is more complex, and the invention uses the non-intersection algorithm to carry out simplified calculation on the formula.
For the probability basic formula Pr (A)1∪A2∪...∪An) In an undirected graph G ═ (V, E), where V represents the set of vertices in the graph, E represents the set of all edges in the graph, aiRepresenting the edge E in the minimum path set i as EiAll events of normal operation, EiRepresenting the set of all edges in the minimum way set i,
represents the edge E (E-E)i) All events working normally; the probability basic formula shows that:
wherein:
Pr(Ai)＝∏Pr(e) e∈Ei (10)；
formula (10) represents the probability that all edges e in the minimum path set i work normally;
b, according to the formula:
formula Pr (A)1∪A2∪···∪An) Further converting into:
the number of operations can be further reduced according to the following boolean algebraic expression:
c, the Sum of Disjoint algorithm is to find the Sum of Disjoint Products (SDP) according to the formula (12), and to simplify the operation process by using the formula (13). Writing the disjoint sum algorithm into a function SDP (P, Edge, N), wherein P is a structural body for storing a set of minimum path sets, N represents the number of the minimum path sets, and effective probability of edges is stored in Edge; the return value is reliability R;
the function SDP (P, Edge, N) has the following steps:
1. if only one minimum path set is input (N is 1), calculating the reliability R of the path set; otherwise, executing step 2;
2. solving the probability R of the first minimum path set;
3. for the 2 nd to Nth minimum path sets, circularly executing the steps 4 to 7;
4. respectively subtracting the first i-1 minimum path sets from the ith path set to obtain num sets;
5. removing redundant sets according to equation (13);
6. recursive invocation of SDP function for probability R of union of num sets1；
7. Solving the probability R of the ith minimum path set2Return reliability R ═ R + R2*(1-R1)。
When the method is used, because the calculation of the whole-end reliability of the complex network is an NP problem, 5 simple graphs with the number of nodes of 6 are used for carrying out performance analysis on the algorithm, the topological structure of the simple graphs is shown in FIG. 2, the topological structures of the 5 graphs are gradually complex, the method is used for analyzing the whole-end reliability of the network, and the performance of the method is analyzed by comparing the whole-end reliability with the accurate whole-end reliability value and the whole-end reliability obtained by randomly dividing the community simplified network;
node combination is carried out on the relationship of tight connection in the simple network by using a community division algorithm based on modularity, and node division as shown in FIG. 3 can be obtained;
as can be seen from the data in fig. 4, as the topology of the network becomes more complex, the robustness of the network is improved, so the reliability of the whole network is gradually increased. Therefore, according to the calculation of the reliability of the whole terminal, the network operation risk can be effectively monitored, and the network risk can be effectively controlled. Compared with the method for analyzing the reliability of the whole end by randomly dividing the communication community, the method for analyzing the reliability of the whole end by dividing the communication community based on the modularity keeps the same general trend with the accurate value of the reliability of the whole end, and the error is gradually reduced along with the gradual complexity of the communication topological structure, and finally the error is kept within 6 percent, which is obviously better than that of the random method.
Dividing a communication community based on modularity to analyze the reliability of the whole end, theoretically merging a plurality of minimum path sets which have small influence on the reliability of the whole end, reserving trunk paths which have large influence on the path sets, merging the branches which have small influence into a node after analyzing the reliability, and replacing the connection probability value of the branches by the weight of the node to reduce the collection space of the minimum path sets. Because the integration space of the minimum path set is reduced, the solved full-end reliability is always smaller than the accurate full-end reliability, and the method can be used as the lower limit value of the full-end reliability.
In time complexity, the algorithm obviously reduces the complexity of network topology by means of community division, greatly reduces the state space of the network by spatial decomposition, and relieves the problem of 'state space explosion' to a certain extent, thereby reducing the time spent by the algorithm on searching the minimum path set. The complexity of the internal topological structure of the communication community divided by the modularity is far lower than that of the whole power communication and is mutually independent, parallel calculation is introduced for the analysis of the internal full-end reliability, the finally obtained communication community connection topological structure is simpler, and the analysis time consumption of the full-end reliability is less. With the gradual complexity of the topological structure of the power communication network, the advantage of the algorithm of the invention on the time complexity is more obvious.
While the invention has been described in further detail with reference to specific embodiments thereof, it is not intended that the invention be limited to the specific embodiments thereof; for those skilled in the art to which the present invention pertains and related technologies, the extension, operation method and data replacement should fall within the protection scope of the present invention based on the technical solution of the present invention.
Claims (1)
1. A method for calculating the reliability of all ends of communication communities divided based on modularity comprises the power communication network community division based on modularity and the reliability calculation of all ends based on a minimum path set, and is characterized in that the power communication network community division based on modularity comprises the following steps,
s1, in the network G, the degree of any node i is recorded as ki＝∑jAijWherein A represents the adjacency matrix of diagram G; c represents a community containing node i, then the degree of node i can be divided into two parts:
wherein the content of the first and second substances,
indicating the number of connecting edges of i with nodes outside the community C,
representing the number of edges between i and other nodes within C;
if C satisfies the condition:
then the sub-graph C is called a strong community;
if C satisfies the condition:
then the subgraph C is called as a weak community;
s2, dividing the communication community, wherein modularity is needed to define, and is a method for measuring the structural strength of the network community, in the text, the modularity is used for measuring the mutual communication robustness of the communication nodes in the communication community, and the robustness represents the communication probability among the communication nodes;
the modularity Q is defined as follows:
wherein the content of the first and second substances,
Pijrepresenting the probability of normal operation of the optical fibers between the communication nodes i, j, M representing the sum of the probabilities of normal operation of all the optical fibers in the network, tiThe method comprises the steps of representing the sum of the probabilities of normal operation of all optical fibers connected with a communication node i, and representing the proportion of edges connecting internal nodes of a community structure in a network by a modularity formula, and subtracting the probability of connecting the two nodes arbitrarily under the same community structureA desired value of the ratio;
s3, clustering closely-connected communication sites in the power communication network to form a communication community by using a Fast Unfolding algorithm, and the method comprises the following three stages:
it is assumed that there are N nodes in the network,
a, in an initial state, distributing a community number i to each node i, wherein the network has N communities;
b, considering that the adjacent node j of each node i is added into the corresponding community of i, calculating the modularity Q under the action, and accepting the change if the added modularity variable quantity delta Q is positive;
c, when the iteration times are less than the total iteration times, repeating the step b;
on the basis of the modularity-based power communication network community division, performing full-end reliability calculation based on a minimum path set, dividing the whole power communication network into a plurality of communication communities with smaller scales by using a modularity-based power communication network community division algorithm, decomposing the whole complex network into a plurality of networks with smaller scales and mutually independent networks by using a community structure of the complex network based on the characteristics of the small-world network of the power communication network, solving the internal full-end reliability of the networks with smaller scales and mutually independent networks, nodularizing the small-scale networks, wherein a node weight is a value of the full-end reliability of the small-scale network, then solving the full-end reliability among the small-scale networks, the finally obtained full-end reliability represents the full-end reliability of the whole network, solving the full-end reliability of the network by using the minimum path set, wherein the path set is a set of edges which ensure the communication of all nodes in the network, if one path set is removed, any edge of the path set is not a path set any more, the path set is called a minimum path set, under the condition of full-end reliability, at least one minimum path set works normally, and the full-end reliability is determined by the minimum path set;
the overall end reliability calculation based on the minimum path set comprises the following specific steps;
a, for the probability basic formula Pr (A)1∪A2∪...∪An) In an undirected graph G ═ (V, E), where V represents the set of vertices in the graphAnd E represents a set of all edges in the graph, AiRepresenting the edge E in the minimum path set i as EiAll events of normal operation, EiRepresenting the set of all edges in the minimum way set i,
represents the edge E (E-E)i) All events working normally; the probability basic formula shows that:
wherein:
Pr(Ai)＝∏Pr(e)e∈Ei(10)；
formula (10) represents the probability that all edges e in the minimum path set i work normally;
b, according to the formula:
formula Pr (A)1∪A2∪…∪An) Further converting into:
the number of operations can be further reduced according to the following boolean algebraic expression:
c, solving the sum of the disjointed products according to a formula (12), simplifying the operation process by using a formula (13), and writing the disjointed products into a function SDP (P, Edge, N), wherein P is a structure for storing the set of the minimum path sets, N represents the number of the minimum path sets, and the effective probability of the edges is stored in the Edge; the return value is reliability R;
the function SDP (P, Edge, N) has the following steps:
1. if only one minimum path set N is input to be 1, calculating the reliability R of the path set; otherwise, executing step 2;
2. solving the probability R of the first minimum path set;
3. for the 2 nd to Nth minimum path sets, circularly executing the steps 4 to 7;
4. respectively subtracting the first i-1 minimum path sets from the ith path set to obtain num sets;
5. removing redundant sets according to equation (13);
6. recursive invocation of SDP function for probability R of union of num sets1；
7. Solving the probability R of the ith minimum path set2Return reliability R ═ R + R2*(1-R1)。
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