CN117294511A - Method for improving damage resistance of infrastructure network and application thereof - Google Patents
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Abstract
The invention discloses a method for improving the survivability of an infrastructure network and application thereof, wherein an infrastructure network model of multiple coupling dependent correlations is constructed; random attack simulation is carried out on the constructed infrastructure network model with multiple coupling dependent correlations, the infrastructure network model after the attack simulation is analyzed, and the optimal cluster size s and the number M of external supporting edges are found; and optimizing the infrastructure network model based on the optimal cluster size s and the number M of external supporting edges. The invention analyzes the established infrastructure network model of the multi-coupling dependent association based on a statistical physical method to find out the influence of different cluster sizes s and the number M of external supporting edges on the system destruction resistance. Analysis of infrastructure network survivability may provide a hint for designing a more resilient reality dependent system. And can be used for improving the survivability and stability of infrastructure network systems such as a power system, a traffic system, a communication network and the like, and has wide application prospect.
Description
Technical Field
The invention relates to the field of multi-layer network reliability, in particular to a method for improving the survivability of an infrastructure network and application thereof.
Background
In recent years, the rapid development of smart city construction has increased the demand for power networks. Various intelligent devices, sensors and systems in smart cities have higher requirements for stable and reliable power supply, which requires power networks to be extended and upgraded to meet the ever-increasing power demands. Meanwhile, the development of communication networks is also promoted by the construction of smart cities. Smart devices, sensors and systems require high-speed and reliable communication networks for data transmission and interconnection. Therefore, the communication network needs to be expanded and optimized to meet the interconnection requirements of large-scale intelligent devices, including increasing network bandwidth, improving network coverage, and improving reliability and security of the network. In addition, smart city construction has also facilitated the convergence of power and communication networks. The power network may utilize the infrastructure of the communication network to enable monitoring and control of the smart grid to improve the efficiency and sustainability of the power system. Meanwhile, the communication network can also provide more intelligent services and solutions for the smart city through integration with the power network.
With the rapid development of the smart city process, the coupling and the dependency relationship between the power network and the communication network are gradually strengthened, and the original system boundary is gradually blurred and broken, so that the interaction between the systems is gradually frequent, complex and changeable. While the mutual coupling communication among complex network systems enables the functionality of the network systems to be exerted to a greater extent, the interdependence relationship enables the faults to generate cascade sub-link diffusion when the systems are damaged and disturbed to different degrees, so that risks overflow and spread to the whole system. Once the connectivity of the entire system is broken, immeasurable damage will be caused. Thus, in the face of these challenges, improving the survivability of the network is of great importance. This may ensure reliability and connectivity of communications, as in communication networks, while it helps to ensure smoothness of logistics transportation and stability of supply chains in logistics and supply chain management.
In summary, there is a need to enhance the reliability of the system, reduce risks, increase the working efficiency and provide continued service by increasing the survivability of the network.
Disclosure of Invention
In order to solve the defects in the prior art, the application provides a method for improving the survivability of an infrastructure network and application thereof, and aims of improving the survivability, the reliability, the stability and the like of the system by optimizing the infrastructure network with multiple coupling dependent correlations.
The technical scheme adopted by the invention is as follows:
a method of improving the survivability of an infrastructure network, comprising the steps of:
s1, constructing an infrastructure network model of multiple coupling dependent correlations;
s2, carrying out random attack simulation on the infrastructure network model with multiple coupling dependency correlations constructed in the S1, analyzing the infrastructure network model after attack simulation, and searching the optimal cluster size S and the number M of external supporting edges;
and S3, optimizing the infrastructure network model based on the optimal cluster size S and the number M of the external supporting edges obtained in the step S2.
Further, the infrastructure network model is expressed as:
G＝(A,B,V)
wherein, A and B are both undirected and unauthorized networks; network a is denoted as (V A ,E A )，V A Representing a set of all nodes in network A, E A Representing a set of all edges in network a; network B is denoted as (V B ,E B )，V B Representing a set of all nodes in the network, E B Representing a set of all edges in network B; v is a set of nodes of network a and network B; the node number of the network A is N A The node number of the network B is N B Network B has the same number of nodes as network a, i.e., N A ＝N B ；
In the coupling network composed of the networks A and B, a coupling connection edge exists between the network A and the network B, and the coupling connection edge has dependence.
Further, the process of S2 is as follows:
s2.1, when the infrastructure network model is attacked, the attacked node and the coupled node also fail; disconnecting the edges of all the fault nodes and the neighbor nodes thereof, and deleting all the fault nodes from the coupling network and the self network;
s2.2, initializing the number M of external support edges and the cluster size S, and screening out functional nodes from the networks A and B deleted fault nodes based on the M and the S respectively;
s2.3, continuously adjusting the cluster size S and the number M of external supporting edges, and comparing the failure rates of different networks; and aiming at reducing the failure rate of the network, searching the optimal cluster size s and the number M of external supporting edges.
Further, the process of S2.2 is as follows:
for the network A and the network B of the deleted fault node, firstly carrying out cluster division on the rest nodes, and obtaining the number of nodes in each cluster, if the number of the nodes in the divided cluster is lower than the cluster size s, deleting the cluster;
for the nodes in the rest clusters, if the number of the external supporting edges corresponding to the nodes in the rest clusters is smaller than M, deleting the nodes;
the final remaining nodes are functional nodes.
Further, the method for optimizing the infrastructure network model in S3 includes:
the functional nodes of the infrastructure network model require at least M external support edges;
the functional nodes need to be in local s clusters or more.
Further, the proportion of the active nodes having M external support edges at the nth step is expressed as follows:
wherein,the ratio of the nodes of the network A, B having at least M effective support links in the n phase; p is the ratio of the residual nodes of the initial network under attack, and 1-p is the initial networkThe proportion of nodes which are attacked and fail by the network; />Respectively representing the probability that a node in the coupled network has at least M valid support links from the B and a networks in the nth phase;respectively representing the probability that a node in the coupled network has at least M-1 valid support links from the B and a networks in the nth phase; k (K) A 、K B The average degree of the connecting edges supported by the network A and the network B in the coupling network and the average degree of the connecting edges supported by the network B and the network A in the coupling network are respectively; p (P) A (K A )、P B (K B ) The degree distribution of the connecting edge supported by the network A to the network B in the coupling network is respectively that of the connecting edge supported by the network B to the network A; />The effective node ratios in the network A, B, respectively.
Further, the proportion of the active nodes in the cluster with the local network being s or more in the nth step is expressed as follows:
wherein,the ratio of the functional nodes in the local s cluster is greater than or equal to that of the network A, B in the invalid nth step; />The ratio of nodes belonging to a component of size s relative to surviving nodes in network A, B, respectively +.>Is a ratio of (3);<k A >、<k B >average degree of network A, B, respectively; x represents the probability of the edge connection state; h (x) is a generating function of the overrun distribution; g 0 (x) G is a generating function of the network 0 ' the term (1) is the average degree of the network.
Further, the functional node ratio at the nth step is expressed as follows:
wherein,the network A, B has a proportion of nodes in the cluster s that are functional nodes at the nth step of failure and have at least M external support edges, respectively.
An infrastructure network is built by adopting the method.
The invention has the beneficial effects that:
(1) The invention improves the survivability of the network system by simulating the proportion of the functional nodes in the residual network when the infrastructure network with the multi-coupling dependent association under different conditions suffers random attack.
(2) The invention provides an accurate analysis expression of the proportion of the functional nodes in the cascade fault process and the stable state, and discovers that the system can have sudden phase change behavior after initial fault, and discovers that when the system needs more effective external supporting edges, more internal connection density is needed to avoid breakdown. The invention also analyzes the established infrastructure network model with multiple coupling dependent correlations based on a statistical physical method to find out the influence of different cluster sizes and the number of external supporting edges on the system destruction resistance, thereby optimizing the infrastructure network model and further improving the infrastructure network destruction resistance.
(3) The method for improving the network destruction resistance of the infrastructure is expected to provide a hint for designing a more elastic reality dependent system. The technology has wide application prospect, and can be used for improving the survivability and stability of the network system between smart cities.
Drawings
Fig. 1 is a schematic diagram of a method for evaluating the survivability of an infrastructure network according to an embodiment of the present invention.
Fig. 2 is a graph of the remaining valid node proportions of different M and s under an initial attack.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
A method of improving the survivability of an infrastructure network, comprising the steps of:
s1, constructing an infrastructure network model of multiple coupling dependent correlations, which is specifically as follows:
referring first to fig. 1, an infrastructure network of multiple coupling dependent associations is built based on two networks a and B, the infrastructure network model being represented as:
G＝(A,B,V)
wherein, A and B are both undirected and unauthorized networks; network a is denoted as (V A ,E A )，V A Representing a set of all nodes in network A, E A Representing a set of all edges in network a; network B is denoted as (V B ,E B )，V B Representing a set of all nodes in the network, E B Representing a set of all edges in network B; v is a set of nodes of network a and network B; the node number of the network A is N A The node number of the network B is N B Network B has the same number of nodes as network a, i.e., N A ＝N B 。
In the coupling network composed of the networks A and B, the coupling connection edge between the networks A and B is represented by a set E, one coupling connection edge is formed by connecting a randomly selected node of one network A with a node in the network B, each coupling connection edge can only be connected with one node in the network A or B, and the coupling connection edge obeys Poisson distribution; because the coupling edge has dependence, if one end node of the coupling edge fails, the other end node also fails.
S2, performing attack simulation on the infrastructure network model with the multiple coupling dependent correlations constructed in the S1, analyzing the infrastructure network model after the attack simulation, and searching the optimal cluster size S and the number M of external supporting edges.
The process of attack simulation is as follows:
s2.1, in the infrastructure network model, any node in any network is attacked, and the node which is attacked and has faults is deleted. With reference to fig. 1, it is assumed that a node pointed by an arrow in a network a fails to become a failed node, and in a coupling network formed by the network a and a network B, due to the dependency characteristic, a corresponding node in the network B coupled to the failed node in the network a also fails; and disconnecting the edges of all the fault nodes and the neighbor nodes in the own networks of the network A and the network B respectively, and deleting all the fault nodes from the coupling network and the own network.
S2.2, screening out functional nodes from networks A and B of deleting the fault node from the S2.1. The method comprises the following steps:
for the network A with the fault nodes deleted, counting the degree value k of each remaining node in the network A in the coupling network Ai The degree value is equal to the number of external support edges at the remaining nodes;
for the network B with the fault node deleted, counting the degree value k of each remaining node in the network B in the network itself in the coupling network Bi The degree value is equal to the number of external support edges at the remaining nodes;
carrying out cluster division on the rest nodes, and obtaining the number of nodes in each cluster; setting a cluster size s in a cluster, and deleting the cluster if the number of nodes in the divided cluster is lower than the cluster size s;
and setting the number M of the external supporting edges corresponding to the nodes for the nodes in the rest clusters, and deleting the nodes if the number M of the external supporting edges corresponding to the nodes in the rest clusters is smaller than M.
After the processing, the final remaining nodes are functional nodes.
S2.3, adjusting the cluster size S and the number M of external supporting edges, and comparing failure rates of different networks; and aiming at reducing the failure rate of the network, searching the optimal cluster size s and the number M of external supporting edges.
And S3, optimizing the infrastructure network model based on the optimal cluster size S and the number M of the external supporting edges obtained in the step S2. In particular, the method comprises the steps of,
1. the functional node of the infrastructure network model needs at least M external support edges, and the proportion of the effective node having M external support edges at the nth step is expressed as follows:
wherein,the ratio of the nodes of the network A, B having at least M effective support links in the n phase; p is the ratio of the rest nodes of the initial network under attack, and 1-p is the ratio of the invalid nodes of the initial network under attack; />Respectively representing the probability that a node in the coupled network has at least M valid support links from the B and a networks in the nth phase;respectively representing the probability that a node in the coupled network has at least M-1 valid support links from the B and a networks in the nth phase; k (K) A 、K B The average degree of the connecting edges of the network A (B) and the network B (A) in the coupling network is respectively supported; p (P) A (K A )、P B (K B ) The degree distribution of the connecting edge is supported by the network A (B) to the network B (A) in the coupling network respectively; />The effective node ratios in the network A, B, respectively.
2, the proportion of the functional nodes in the local clusters with the size of s or more in the nth step and the clusters with the size of s or more in the local network is expressed as follows:
wherein,the ratio of the functional nodes in the local s cluster is greater than or equal to that of the network A, B in the invalid nth step; />The ratio of nodes belonging to a component of size s relative to surviving nodes in network A, B, respectively +.>Is a ratio of (3);<k A >、<k B >average degree of network A, B, respectively; x represents the probability of the edge connection state; h (x) is a generating function of the overrun distribution; g 0 (x) G is a generating function of the network 0 ' the term (1) is the average degree of the network.
3. The functional node needs to be a node which is in the local network and is more than or equal to the cluster s and has at least M external supporting edges; as shown in fig. 2, the functional node ratio at the nth step is represented as follows:
wherein,the network A, B has a proportion of nodes in the cluster s that are functional nodes at the nth step of failure and have at least M external support edges, respectively.
As shown in fig. 1 (d). The whole network fault process is analyzed, so that the coupling density inside the network, namely between networks, is increased, and the number of network node faults is reduced; and the critical points of the network can be determined to help design and optimize the network structure, thereby improving the stability and survivability of the network. In addition, the identification of critical points can also help to predict the failure condition of the network, and measures are taken in time to avoid the breakdown of the network, so that the reliability and the safety of the network are protected.
In the present embodiment, in order to improve the survivability of the infrastructure, the selection of the cluster s and the number M of external supporting edges is optimized, and these factors are closely related to the failure rate of the network. In particular, we observe that as the cluster size s and the number of external support edges M increases, the failure rate of the network increases significantly, indicating the importance of these two parameters to destructiveness. Furthermore, we have found that when the cluster size s and the number of external support edges M remain constant, the increase in the inter-network connection density results in a slow failure rate. Successful development and practical application of this technology will provide a new and effective way for the protection and sustainable development of infrastructure networks, thus making an important contribution to the security and sustainability of society. Therefore, the invention has wide application prospect and can bring obvious influence to the technical development and social welfare of the related fields.
The above embodiments are merely for illustrating the design concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement the same, the scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications according to the principles and design ideas of the present invention are within the scope of the present invention.
Claims (10)
1. A method of improving the survivability of an infrastructure network, comprising the steps of:
s1, constructing an infrastructure network model of multiple coupling dependent correlations;
s2, carrying out random attack simulation on the infrastructure network model with multiple coupling dependency correlations constructed in the S1, analyzing the infrastructure network model after attack simulation, and searching the optimal cluster size S and the number M of external supporting edges;
and S3, optimizing the infrastructure network model based on the optimal cluster size S and the number M of the external supporting edges obtained in the step S2.
2. A method of improving the survivability of an infrastructure network as claimed in claim 1, wherein the infrastructure network model is expressed as:
G＝(A,B,V)
wherein, A and B are both undirected and unauthorized networks; network a is denoted as (V A ,E A )，V A Representing a set of all nodes in network A, E A Representing a set of all edges in network a; network B is denoted as (V B ,E B )，V B Representing a set of all nodes in the network, E B Representing a set of all edges in network B; v is a set of nodes of network a and network B; the node number of the network A is N A The node number of the network B is N B Network B has the same number of nodes as network a, i.e., N A ＝N B ；
In the coupling network composed of the networks A and B, a coupling connection edge exists between the network A and the network B, and the coupling connection edge has dependence.
3. A method of improving the survivability of an infrastructure network as claimed in claim 2, wherein the process of S2 is as follows:
s2.1, when the infrastructure network model is attacked, the attacked node and the coupled node also fail; disconnecting the edges of all the fault nodes and the neighbor nodes thereof, and deleting all the fault nodes from the coupling network and the self network;
s2.2, initializing the number M of external support edges and the cluster size S, and screening out functional nodes from the networks A and B deleted fault nodes based on the M and the S respectively;
s2.3, continuously adjusting the cluster size S and the number M of external supporting edges, and comparing the failure rates of the networks under different M and S; and aiming at reducing the failure rate of the network, searching the optimal cluster size s and the number M of external supporting edges.
4. A method of improving the survivability of an infrastructure network according to claim 3, wherein the process of S2.2 is as follows:
for the network A and the network B of the deleted fault node, firstly carrying out cluster division on the rest nodes, and obtaining the number of nodes in each cluster, if the number of the nodes in the divided cluster is lower than the number s of the nodes, deleting the cluster;
for the nodes in the rest clusters, if the number of the external supporting edges corresponding to the nodes in the rest clusters is smaller than M, deleting the nodes;
the final remaining nodes are functional nodes.
5. The method of claim 4, wherein the optimizing the infrastructure network model in S3 comprises:
the functional nodes of the infrastructure network model require at least M external support edges;
the functional nodes need to be in local s clusters or more.
6. A method of improving the survivability of an infrastructure network as defined in claim 5, wherein the proportion of M external support edges owned by the active node at step n is as follows:
wherein,the ratio of the nodes of the network A, B having at least M effective support links in the n phase; p is the ratio of the rest nodes of the initial network under attack, and 1-p is the ratio of the invalid nodes of the initial network under attack; />Respectively representing the probability that a node in the coupled network has at least M valid support links from the B and a networks in the nth phase;respectively representing the probability that a node in the coupled network has at least M-1 valid support links from the B and a networks in the nth phase; k (K) A 、K B The average degree of the connecting edges supported by the network A and the network B in the coupling network and the average degree of the connecting edges supported by the network B and the network A in the coupling network are respectively; p (P) A (K A )、P B (K B ) The degree distribution of the connecting edge supported by the network A to the network B in the coupling network is respectively that of the connecting edge supported by the network B to the network A; />The effective node ratios in the network A, B, respectively.
7. A method of improving the survivability of an infrastructure network as claimed in claim 5, wherein the proportion of active nodes in the local network at s or more in step n is represented as follows:
wherein,the ratio of the functional nodes in the local s cluster is greater than or equal to that of the network A, B in the invalid nth step; />The ratio of nodes belonging to a component of size s relative to surviving nodes in network A, B, respectively +.>Is a ratio of (3);<k A >、<k B >average degree of network A, B, respectively; x represents the probability of the edge connection state; h (x) is a generating function of the overrun distribution; g 0 (x) G is a generating function of the network 0 ' the term (1) is the average degree of the network.
8. A method of improving the survivability of an infrastructure network as claimed in claim 5, wherein the ratio of the functional nodes at step n is represented as follows:
wherein,the network A, B has a proportion of nodes in the cluster s that are functional nodes at the nth step of failure and have at least M external support edges, respectively.
9. An infrastructure network constructed using a method of improving the survivability of an infrastructure network as claimed in claim 1.
10. Use of an infrastructure network according to claim 9, wherein the infrastructure network is applied to a coupling system of a power system and a communication system.
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