CN117294511A - Method for improving damage resistance of infrastructure network and application thereof - Google Patents

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

A method to improve the invulnerability of infrastructure networks and its application

Technical field

The present invention relates to the field of multi-layer network reliability, and in particular to a method for improving the invulnerability of infrastructure networks and its application.

Background technique

In recent years, the rapid development of smart city construction has increased the demand for power networks. Various smart devices, sensors and systems in smart cities have higher requirements for stable and reliable power supply, which requires the power network to be expanded and upgraded to meet the increasing power demand. At the same time, smart city construction also promotes the development of communication networks. Smart devices, sensors and systems require high-speed and reliable communication networks for data transmission and interconnection. Therefore, communication networks need to be expanded and optimized to meet the interconnection needs of large-scale smart devices, including increasing network bandwidth, improving network coverage, and improving network reliability and security. In addition, smart city construction also promotes the integration of power networks and communication networks. Power networks can utilize the infrastructure of communication networks to implement smart grid monitoring and control to improve the efficiency and sustainability of the power system. At the same time, communication networks can also provide smarter services and solutions for smart cities through integration with power networks.

With the rapid development of smart urbanization, the coupling and dependence between power networks and communication networks are gradually strengthening, and the original system boundaries are gradually blurred and broken, which makes the interactions between systems increasingly frequent and complex. Although the mutual coupling and connectivity between complex network systems maximizes the functionality of the network system, at the same time, when the system suffers varying degrees of damage and disturbance, the interdependence will cause faults to cascade and spread, causing Risks spill over and spread throughout the system. Once the connectivity of the entire system is destroyed, immeasurable damage will be caused. Therefore, in the face of these challenges, it is of great significance to improve the invulnerability of the network. For example, in communication networks, this can ensure the reliability and connectivity of communication, while in logistics and supply chain management, it helps ensure the smoothness of logistics transportation and the stability of the supply chain.

In summary, it is necessary to enhance the reliability of the system, reduce risks, improve work efficiency and provide continuous services by improving the invulnerability of the network.

Contents of the invention

In order to solve the deficiencies in the existing technology, this application proposes a method and its application for improving the invulnerability of infrastructure networks. By optimizing the multi-coupled and interdependent infrastructure network, the invulnerability and system reliability are improved. performance and stability purposes.

The technical solutions adopted by the present invention are as follows:

A method to improve the invulnerability of infrastructure networks includes the following steps:

S1. Construct a multi-coupled and interdependent infrastructure network model;

S2. Carry out random attack simulation on the multi-coupled and interdependent infrastructure network model constructed in S1, analyze the infrastructure network model after the attack simulation, and find the optimal cluster size s and the number of external supporting edges M;

S3. Optimize the infrastructure network model based on the optimal cluster size s and the number of external support edges M obtained by S2.

Further, the infrastructure network model is expressed as:

G＝(A,B,V)

Among them, A and B are both undirected and unweighted networks; network A is expressed as (V _A , E _A ), V _A represents the set of all nodes in network A, and E _A represents the set of all connected edges in network A; network B Expressed as (V _B , E _B ), V _B represents the set of all nodes in the network, E _B represents the set of all connected edges in network B; V is the set of nodes in network A and network B; the number of nodes in network A is N _A , the number of nodes of network B is N _B , network B and network A have the same number of nodes, that is, N _A = N _B ;

In a coupled network composed of networks A and B, there are coupling edges between network A and network B, and the coupling edges have dependencies.

Further, the process of S2 is as follows:

S2.1. When the infrastructure network model is attacked, the attacked node and the coupled connected nodes also fail; disconnect all faulty nodes from their neighbor nodes, and remove all faulty nodes from the coupling network and their own network. delete in;

S2.2. Initialize the number of external support edges M and the cluster size s, and filter out functional nodes from the networks A and B where the faulty node is deleted based on M and s;

S2.3. Continuously adjust the cluster size s and the number of external support edges M, and compare the failure rates of the network under different conditions; with the purpose of reducing the failure rate of the network, find the optimal cluster size s and the number of external support edges M.

Further, the process of S2.2 is as follows:

For Network A and Network B where the faulty node has been deleted, first divide the remaining nodes into clusters and obtain the number of nodes in each cluster. If the number of nodes in the divided cluster is lower than the cluster size s, delete the cluster. ;

For the nodes in the remaining clusters, if the number of external supporting edges corresponding to the nodes in the remaining clusters is less than M, the node will be deleted;

The final remaining nodes are functional nodes.

Furthermore, methods for optimizing infrastructure network models in S3 include:

Functional nodes of the infrastructure network model require at least M external supporting edges;

Functional nodes need to be in a local cluster greater than or equal to s.

Furthermore, the proportion of valid nodes with M external supporting edges at the nth step is expressed as follows:

in, They are the proportions of networks A and B that have at least M valid nodes supporting links in the n stage respectively; p is the proportion of remaining nodes in the initial network that was attacked, and 1-p is the proportion of failed nodes in the initial network that was attacked;/> respectively represent the probability that a node in the coupled network has at least M effective support links from the B and A networks in the nth stage; Respectively represent the probability that a node in the coupled network has at least M-1 effective support links from the B and A networks in the nth stage; K _A and K _B are respectively the average support connections from network A to network B in the coupled network. degree, the average degree of the edge supported by network B to network A in the coupled network; P ^A (K _A ) and P ^B (K _B ) are respectively the degree distribution of the edge supported by network A to network B in the coupled network, and the degree distribution of the edge supported by network B to network B in the coupled network. Network A supports degree distribution of connected edges;/> are the proportions of effective nodes in networks A and B respectively.

Furthermore, the proportion of effective nodes in the clusters where the local network is greater than or equal to s at step n is expressed as follows:

in, Respectively, they are the proportion of functional nodes in the local cluster greater than or equal to s at the nth step of failure of networks A and B;/> are the proportions of nodes belonging to components of size s relative to surviving nodes in networks A and B respectively/> proportion; <k _A >, <k _B > are the average degrees of networks A _and B respectively; The generating function, G ₀ '(1) is the average degree of the network.

Further, the proportion of functional nodes at the nth step is expressed as follows:

in, They are the proportion of functional nodes in cluster s or greater and with at least M external supporting edges in networks A and B respectively at the nth step of failure.

An infrastructure network is built using the above method.

Beneficial effects of the present invention:

(1) The present invention improves the invulnerability of the network system by simulating the proportion of functional nodes in the remaining network when a multi-coupled and multi-coupled dependent infrastructure network suffers random attacks under different conditions.

(2) The present invention proposes an accurate analytical expression for the cascading fault process and the proportion of functional nodes in the steady state, and finds that the system will have a sudden phase change behavior after the initial fault, and finds that when the system requires more effective external support edges, more internal connection density is needed to avoid collapse. The present invention also analyzes the established multi-coupled and interdependent infrastructure network model based on statistical physics methods to find out the impact of different cluster sizes and the number of external supporting edges on the system's invulnerability, thereby performing on the infrastructure network model. Optimization, thereby improving the invulnerability of infrastructure networks.

(3) The method proposed by the present invention to improve the invulnerability of infrastructure networks is expected to provide inspiration for the design of more flexible realistic dependence systems. This technology has broad application prospects and can be used to improve the invulnerability and stability of smart city inter-city network systems.

Description of drawings

Figure 1 is a schematic diagram of an infrastructure network invulnerability assessment method provided by an embodiment of the present invention.

Figure 2 is a diagram of the proportion of remaining effective nodes under different M and s under the initial attack.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention and are not intended to limit the present invention.

A method to improve the invulnerability of infrastructure networks includes the following steps:

S1. Construct a multi-coupled and interdependent infrastructure network model, as follows:

First, referring to Figure 1, a multi-coupled and interdependent infrastructure network is constructed based on two networks A and B. The infrastructure network model is expressed as:

G＝(A,B,V)

Among them, A and B are both undirected and unweighted networks; network A is expressed as (V _A , E _A ), V _A represents the set of all nodes in network A, and E _A represents the set of all connected edges in network A; network B Expressed as (V _B , E _B ), V _B represents the set of all nodes in the network, E _B represents the set of all connected edges in network B; V is the set of nodes in network A and network B; the number of nodes in network A is N _A , the number of nodes of network B is N _B , and network B and network A have the same number of nodes, that is, N _A = N _B .

In a coupled network composed of networks A and B, the coupling edge between network A and network B is represented by a set E. A coupling edge is formed by connecting a randomly selected node of network A and a node in network B. , each coupling edge can only connect one node in network A or B, and the coupling edge obeys Poisson distribution; because the coupling edge is dependent, if a node at one end of the coupling edge fails, the node at the other end will also Malfunctions can also occur.

S2. Carry out attack simulation on the multi-coupled and interdependent infrastructure network model constructed in S1, and analyze the infrastructure network model after the attack simulation to find the optimal cluster size s and the number of external support edges M.

The process of attack simulation is as follows:

S2.1. In the infrastructure network model, attack any node in any network and delete the node that fails due to the attack. Combined with Figure 1, assume that the node pointed by the arrow in network A fails and becomes a faulty node. In the coupled network composed of network A and network B, due to the dependency characteristics, network B that is coupled to the faulty node in network A will The corresponding node also fails; in the own network of network A and network B respectively, disconnect all faulty nodes from their neighbor nodes, and delete all faulty nodes from the coupling network and the own network.

S2.2. Filter out functional nodes from networks A and B where the faulty node was deleted in S2.1. details as follows:

For network A that has deleted faulty nodes, count the degree value k _Ai of each remaining node in the coupled network in network A's own network. This degree value is equal to the number of external supporting edges at the remaining nodes;

For network B that has deleted the fault node, count the degree value k _Bi of each remaining node in the coupled network in network B's own network. This degree value is equal to the number of external supporting edges at the remaining nodes;

Divide the remaining nodes into clusters and obtain the number of nodes in each cluster; set the cluster size s in the cluster. If the number of nodes in the divided cluster is lower than the cluster size s, delete the cluster;

For the nodes in the remaining clusters, set the number M of external supporting edges corresponding to the nodes. If the number of external supporting edges corresponding to the nodes in the remaining clusters is less than M, delete the node.

After the above processing, the final remaining nodes are functional nodes.

S2.3. Adjust the cluster size s and the number of external support edges M, and compare the failure rates of the network under different conditions; with the purpose of reducing the failure rate of the network, find the optimal cluster size s and the number of external support edges M.

S3. Optimize the infrastructure network model based on the optimal cluster size s and the number of external support edges M obtained by S2. specifically,

1. The functional nodes of the infrastructure network model require at least M external supporting edges. The proportion of effective nodes with M external supporting edges at step n is expressed as follows:

in, They are the proportions of networks A and B that have at least M valid nodes supporting links in the n stage respectively; p is the proportion of remaining nodes in the initial network that was attacked, and 1-p is the proportion of failed nodes in the initial network that was attacked;/> respectively represent the probability that a node in the coupled network has at least M effective support links from the B and A networks in the nth stage; Respectively represent the probability that a node in the coupled network has at least M-1 effective support links from the B and A networks in the nth stage; K _A and K _B are respectively the pair of network A(B) in the coupled network against network B(A ) supports the average degree of edges; P ^A (K _A ) and P ^B (K _B ) are respectively the degree distribution of the edges supported by network A (B) to network B (A) in the coupled network;/> are the proportions of effective nodes in networks A and B respectively.

2. Functional nodes need to be in the local cluster greater than or equal to s. The proportion of effective nodes in the cluster where the local network is greater than or equal to s at step n is expressed as follows:

in, Respectively, they are the proportion of functional nodes in the local cluster greater than or equal to s at the nth step of failure of networks A and B;/> are the proportions of nodes belonging to components of size s relative to surviving nodes in networks A and B respectively/> proportion; <k _A >, <k _B > are the average degrees of networks A _and B respectively; The generating function, G ₀ '(1) is the average degree of the network.

3. Functional nodes need to be nodes in the local network greater than or equal to cluster s and have at least M external supporting edges; as shown in Figure 2, the proportion of functional nodes in the nth step is expressed as follows:

in, They are the proportion of functional nodes in cluster s or greater and with at least M external supporting edges in networks A and B respectively at the nth step of failure.

As shown in Figure 1(d). By analyzing the entire network failure process, the coupling density within the network, that is, between networks, is increased to reduce the number of network node failures; and the critical points of the network can be determined to help design and optimize the network structure, thereby improving the stability and invulnerability of the network. sex. In addition, identifying critical points can also help predict network failures and take timely measures to avoid network collapse, thereby protecting network reliability and security.

In the implementation of this case, in order to improve the invulnerability of the infrastructure, the selection of cluster s and the number of external support edges M were optimized. These factors are closely related to the failure rate of the network. Specifically, we observe that when the cluster size s and the number of external supporting edges M increase, the failure rate of the network increases significantly, indicating the importance of these two parameters for destructibility. In addition, we also found that when the cluster size s and the number of external supporting edges M remain constant, the increase in the density of connections between networks will lead to a slower failure rate. The successful development and practical application of this technology will provide new and effective methods for the protection and sustainable development of infrastructure networks, thus making an important contribution to the security and sustainability of society. Therefore, the present invention has broad application prospects and will have a significant impact on technological development and social welfare in related fields.

The above embodiments are only used to illustrate the design ideas and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made based on the principles and design ideas disclosed in the present invention are within the protection 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.