CN111800201A - Method for identifying key nodes of Sink node underwater acoustic sensor network - Google Patents

Method for identifying key nodes of Sink node underwater acoustic sensor network Download PDF

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CN111800201A
CN111800201A CN202010584590.2A CN202010584590A CN111800201A CN 111800201 A CN111800201 A CN 111800201A CN 202010584590 A CN202010584590 A CN 202010584590A CN 111800201 A CN111800201 A CN 111800201A
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CN111800201B (en
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申晓红
员一帆
王海燕
孙霖
马石磊
李宁
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Xi'an Hanzhi Ruientropy Technology Co ltd
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Northwestern Polytechnical University
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    • H04B13/02—Transmission systems in which the medium consists of the earth or a large mass of water thereon, e.g. earth telegraphy
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Abstract

The invention provides a method for identifying key nodes of a Sink node underwater acoustic sensor network, which is characterized in that 7 characteristics of the use degree, hop distance, degree, betweenness, compactness, feature vector centrality and vulnerability of the Sink node underwater acoustic sensor network are collected and multi-dimensional characteristics are fused to finally obtain an importance evaluation value of each node, so that very effective prerequisite information is provided for network topology control and safety protection. The invention carries out multidimensional, effective and accurate evaluation on the importance of each node in the network, can greatly improve the delivery rate and the throughput of the network and reduce the network delay. Meanwhile, under the hostile environment, by strengthening the defense on own key nodes, the potential threats are eliminated in time, and the own network security is enhanced.

Description

Method for identifying key nodes of Sink node underwater acoustic sensor network
Technical Field
The invention relates to the technical field of underwater acoustic sensor networks, in particular to a Sink node underwater acoustic sensor network key node identification method which can provide necessary information for the topological control and safety protection of an underwater acoustic sensor network.
Background
Abundant resources are stored in oceans, and the realization of ocean observation, resource exploration and development is one of the most concerned problems of various ocean countries at present. In recent years, the underwater acoustic sensor network has made great progress due to the expansion of the field of application of marine information, and has been applied to marine military, research on marine environment and weather, development of marine resources, and the like.
The underwater acoustic sensor network mostly adopts a Sink node topological structure due to the service requirement. There are two types of nodes in the network architecture: one is a buoy node deployed on the water surface, which is also called a Sink node; the other is a common sensor node deployed in the underwater space of a designated area. The Sink node is provided with a wireless modem and a hydroacoustic modem, and the wireless modem and the hydroacoustic modem are used for communication among the Sink node, the Sink node and the monitoring center. The latter uses the communication between Sink node and ordinary sensor node. The common sensor node is only provided with a underwater sound modem, and the node can communicate with the neighbor node by using the device. Since all the Sink nodes are equipped with wireless modems, any Sink node which successfully receives the data packet can quickly forward the data packet to other Sink nodes or a monitoring center through wireless communication. The structure can ensure that the underwater acquisition node can quickly send data to the overwater node and send the data to a network manager through a satellite.
In practical application of the underwater acoustic sensor network, each node is located at a position with different network topologies and has unequal resources, so that each node plays different roles in the network. Therefore, there are some key nodes, and once these nodes fail, they will cause network segmentation, communication interruption, data packet loss, etc., which greatly affect the connectivity of the network, and further cause the network communication to fail to operate normally. Meanwhile, as the key node is in a key position in the network, once malicious behaviors occur in the key node, the network performance is sharply reduced. Therefore, efficient discovery of critical nodes can provide the necessary information for network topology control and security protection.
Because the key nodes have important influence on the network, the research on key node identification at home and abroad obtains a plurality of achievements, and some key node identification algorithms are proposed and summarized as follows: single index identification algorithms, composite index identification algorithms, identification algorithms based on destructive equivalence to critical ideas, and the like.
However, through analysis of the existing key node algorithm, the existing algorithm is only limited to the calculation of the topology, and the influence of various factors (the traffic size, the communication environment and the like) when the node actually runs in the network is not considered. The existing key node identification algorithm is researched for a land network, and a key node identification technology for an underwater network is not available. Therefore, it is meaningful to provide a key node identification algorithm for the underwater acoustic sensor network.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method for identifying key nodes of a Sink node underwater acoustic sensor network. In order to quickly find key nodes in a network in the working process of an underwater acoustic sensor network, provide necessary information for further network topology control and safety protection, and provide a method for identifying the key nodes of a Sink node underwater acoustic sensor network aiming at the problems that the underwater network has the requirement on the importance of the nodes in the topology and safety protection, the importance of the nodes is difficult to evaluate and the like. According to the invention, by collecting 7 characteristics of the service degree, hop distance, degree, betweenness, compactness, feature vector centrality and vulnerability of the Sink node underwater acoustic sensor network and carrying out multi-dimensional feature fusion, the importance evaluation value of each node is finally obtained, thereby providing very effective prerequisite information for network topology control and safety protection.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
the first step is as follows: the Sink node is used as a destination node and collects each communication path in the network working process;
in the network working process, when each node forwards a data packet, the node number and the position information of the node are added into the data packet, and finally, a destination node receives a data packet communication path except data and the position information of each node;
the second step is that: generating a network topological graph;
according to the communication path obtained in the first step, whether a path exists between any two points in the network is known; if the path is connected, connecting the two nodes, otherwise, not connecting, and simultaneously calculating the length of each path according to the node position information to finally obtain a network topological graph;
the third step: calculating the degree, betweenness, compactness, feature vector centrality, vulnerability and use degree feature values of each node;
according to the topological graph obtained in the second step, the degree D (a), the betweenness B (a), the compactness C (i), the feature vector centrality E (a), the vulnerability V (i) and the use degree U (a) of each node are respectively calculated by expressions (1) - (6);
(1) the expression for the degree D (a) is:
Figure BDA0002554187780000021
in the formula
Figure BDA0002554187780000031
Wherein a, i is a node vaAnd node viV represents the set of all nodes in the network;
(2) the expression of the betweenness B (a) is:
Figure BDA0002554187780000032
wherein P (i, j) is node viAnd vjThe shortest path number between P (i, a, j) is node viAnd vjBetween via node vaThe shortest path number of (2);
(3) the expression for the compactness C (i) is:
Figure BDA0002554187780000033
in the formula dijRepresenting a node viAnd vjThe length of the shortest path between;
(4) the expression of the feature vector centrality e (a) is:
Figure BDA0002554187780000034
where λ is a constant satisfying the equation Mx ═ λ x, and M is the adjacency matrix { x ] of the topological undirected graph1,x2,...,xi,...,xnIs a feature vector;
(5) the expression for vulnerability V (i) is:
Figure BDA0002554187780000035
in the formula (I), the compound is shown in the specification,
Figure BDA0002554187780000036
is the global efficiency of the network, FiIs to remove node viAnd the network global efficiency behind all edges;
(6) the degree of use u (a) is expressed as:
Figure BDA0002554187780000037
in the formula (I), the compound is shown in the specification,
Figure BDA0002554187780000038
indicating node v in the t-last communicationaAs the number of times the communication node is used;
the fourth step: counting the hop count of each node of the network and calculating the hop distance characteristic value;
the hop count of each node is added into the data packet, and finally the hop count is sent to the Sink destination node along with the data packet; the destination node counts the hop count of each node of the network, and then calculates the hop distance H (a) corresponding to each node, wherein the expression of the hop distance H (a) is as follows:
H(a)＝h(a)-h(s) (7)
wherein h(s) represents the hop count of the Sink node, and h (a) represents the hop count of the a node;
the fifth step: data preprocessing normalization;
forming a vector [ a ] by each eigenvalue of all nodes calculated in the third step and the fourth stepi1,…,ain]]Wherein a isi1A value representing an ith characteristic of the first node; the 7 eigenvalues of all nodes in the network are respectively degree, betweenness, compactness, eigenvector centrality, vulnerability, use degree and hop distance, and the 7 eigenvalues finally form a decision matrix A ═ aij)7×nNormalizing the decision matrix A to obtain a normalized decision matrix B ═ (B)ij)7×nWherein:
Figure BDA0002554187780000041
and a sixth step: constructing a weighting specification matrix;
the normalized decision matrix B obtained from the fifth step is (B)ij)m×nConstructing a weighting norm matrix C ═ (C)ij)7×nThe expression of the weighting specification matrix is:
cij＝wj·bij,i＝1,2,,m；j＝1,2,…,n (9)
wherein w ═ w1,w2,...wn]TGiving a weight vector of each characteristic value for a decision maker;
the seventh step: determining a positive ideal solution and a negative ideal solution, and solving the distance from each node to the positive ideal scheme and the negative ideal scheme;
the positive ideal solution expression is:
Figure BDA0002554187780000042
the negative ideal solution expression is:
Figure BDA0002554187780000043
the distance from the positive ideal solution is expressed as:
Figure BDA0002554187780000044
the distance to the negative ideal solution is expressed as:
Figure BDA0002554187780000051
eighth step: calculating the comprehensive evaluation index f of each nodei *I.e. importance, and is arranged from large to small; the expression of the comprehensive evaluation index is as follows:
Figure BDA0002554187780000052
finally, the importance evaluation value f of each node in the network is obtainedi *Selecting an importance evaluation value fi *The first 10% of nodes are used as key nodes, and next-step network topology control and safety protection are performed on the key nodes, so that the efficiency of the network topology control and safety protection is improved.
The method has the beneficial effects that the method for identifying the key nodes of the Sink node underwater acoustic sensor network can be used for carrying out multidimensional, effective and accurate evaluation on the importance of each node in the network in a complex underwater environment. In the topology control of the underwater acoustic sensor network, the delivery rate and the throughput of the network can be greatly improved and the network delay is reduced by controlling the identified key nodes. Meanwhile, in an enemy environment, by strengthening defense on key nodes of the own party, if replacement nodes and safety monitoring are added in due time, potential threats are eliminated in time, and the network safety of the own party is enhanced. Therefore, the invention has great significance for the research of the network topology of the underwater acoustic sensor network, promotes the application and development of the network space safety in the underwater sensor network, and provides a technical basis for the development of the air-sea integrated network in China.
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FIG. 1 is a general process block diagram of the present invention.
FIG. 2 is a network simulation scenario of the present invention
FIG. 3 network topology graph generated during simulation of the present invention
Fig. 4 is a simulation result of the importance evaluation value of each node according to the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
Taking an EALR layered opportunistic routing protocol widely used in the underwater acoustic sensor network as an example, the following embodiments of corresponding key node identification are given:
a Sink node underwater acoustic sensor network node scene based on an earr hierarchical opportunistic routing protocol is shown in fig. 2, and information transmission is performed between nodes by using acoustic signals. And the node No. 1 is a Sink node and is distributed on the water surface. The 2-21 nodes are all ordinary nodes and are distributed at positions of different depths underwater according to task requirements, and the ordinary nodes send data to the Sink node according to self service requirements.
As shown in fig. 1, the steps of the technical solution adopted by the present invention to solve the technical problem are as follows:
the first step is as follows: the Sink node is used as a destination node and collects each communication path in the network working process;
in the network working process, when each node forwards a data packet, the number and the position information of the node are added into the data packet, and finally, a destination node receives a data packet communication path except data and the position information of each node, for example, the data packet communication path is forwarded from the node No. 10 to the node No. 1 through the nodes No. 7, 5 and 3, namely the communication path of 10-7-5-3-1;
the second step is that: generating a network topological graph;
according to the communication path obtained in the first step, whether a path exists between any two points in the network is known; if the path is connected, connecting the two nodes, otherwise, not connecting, and simultaneously calculating the length of each path according to the node position information to finally obtain a network topological graph;
the third step: calculating the degree, betweenness, compactness, feature vector centrality, vulnerability and use degree feature values of each node;
according to the topological graph obtained in the second step, the degree D (a), the betweenness B (a), the compactness C (i), the feature vector centrality E (a), the vulnerability V (i) and the use degree U (a) of each node are respectively calculated by expressions (1) - (6);
(1) the expression for the degree D (a) is:
Figure BDA0002554187780000061
in the formula
Figure BDA0002554187780000062
Wherein a, i is a node vaAnd node viV represents the set of all nodes in the network;
(2) the expression of the betweenness B (a) is:
Figure BDA0002554187780000063
wherein P (i, j) is node viAnd vjThe shortest path number between P (i, a, j) is node viAnd vjBetween via node vaThe shortest path number of (2);
(3) the expression for the compactness C (i) is:
Figure BDA0002554187780000064
in the formula dijRepresenting a node viAnd vjThe length of the shortest path between;
(4) the expression of the feature vector centrality e (a) is:
Figure BDA0002554187780000071
where λ is a constant satisfying the equation Mx ═ λ x, and M is the adjacency matrix of the topological undirected graph, { x1,x2,...,xi,...,xnIs a feature vector;
(5) the expression for vulnerability V (i) is:
Figure BDA0002554187780000072
in the formula (I), the compound is shown in the specification,
Figure BDA0002554187780000073
is the global efficiency of the network, FiIs to remove node viAnd the network global efficiency behind all edges;
(6) the degree of use u (a) is expressed as:
Figure BDA0002554187780000074
in the formula (I), the compound is shown in the specification,
Figure BDA0002554187780000075
indicating node v in the t-last communicationaAs the number of times the communication node is used;
the fourth step: counting the hop count of each node of the network and calculating the hop distance characteristic value;
the hop count of each node is added into the data packet, and finally the hop count is sent to the Sink destination node along with the data packet; the destination node counts the hop count of each node of the network, and then calculates the hop distance H (a) corresponding to each node, wherein the expression of the hop distance H (a) is as follows:
H(a)＝h(a)-h(s) (7)
wherein h(s) represents the hop count of the Sink node, and h (a) represents the hop count of the a node;
the fifth step: data preprocessing normalization;
all sections calculated in the third and fourth stepsEach eigenvalue of a point constitutes a vector ai1,…,ain]Wherein a isi1A value representing an ith characteristic of the first node; the 7 eigenvalues of all nodes in the network are respectively degree, betweenness, compactness, eigenvector centrality, vulnerability, use degree and hop distance, and the 7 eigenvalues finally form a decision matrix A ═ aij)7×nNormalizing the decision matrix A to obtain a normalized decision matrix B ═ (B)ij)7×nWherein:
Figure BDA0002554187780000076
and a sixth step: constructing a weighting specification matrix;
the normalized decision matrix B obtained from the fifth step is (B)ij)m×nConstructing a weighting norm matrix C ═ (C)ij)7×nThe expression of the weighting specification matrix is:
cij＝wj·bij,i＝1,2,…,m；j＝1,2,…,n (9)
wherein w ═ w1,w2,...wn]TGiving a weight vector of each characteristic value for a decision maker;
the seventh step: determining a positive ideal solution and a negative ideal solution, and solving the distance from each node to the positive ideal scheme and the negative ideal scheme;
the positive ideal solution expression is:
Figure BDA0002554187780000081
the negative ideal solution expression is:
Figure BDA0002554187780000082
the distance from the positive ideal solution is expressed as:
Figure BDA0002554187780000083
the distance to the negative ideal solution is expressed as:
Figure BDA0002554187780000084
eighth step: calculating the comprehensive evaluation index f of each nodei *I.e. importance, and is arranged from large to small; the expression of the comprehensive evaluation index is as follows:
Figure BDA0002554187780000085
finally, the importance evaluation value f of each node in the network is obtainedi *Selecting an importance evaluation value fi *The first 10% of nodes are used as key nodes, and next-step network topology control and safety protection are performed on the key nodes, so that the efficiency of the network topology control and safety protection is improved.
The specific implementation steps are as follows:
the first step is as follows: no. 1 node as destination node for collecting each communication path in network working process
In the network working process, when the underwater common nodes 2-21 transmit the data packet, the node number and the position information (x _ position, y _ position) of the node are added into the data packet. Finally, node 1, upon receiving the packet, stores each communication path (e.g., 3-16-1) within the packet. And meanwhile, the position information of the nodes 2 to 21 is updated.
The second step is that: generating a network topology map
And the node 1 analyzes whether a path exists between any two points in the network according to the communication path saved in the first step. If 3-16-1, a path exists between node No. 3 and node No. 16, and a path exists between node No. 16 and node No. 1. If the path is passed, the two nodes are connected, otherwise, the two nodes are not connected. And meanwhile, the length of each path is calculated according to the node position information, and finally the whole network topological graph is obtained. As shown in fig. 3.
The third step: 5 characteristics of the topological hierarchy and the use degree characteristics are calculated.
Node 1 calculates the degree D (a), the betweenness B (a), the compactness C (i), the feature vector centrality E (a) and the vulnerability V (i) of nodes 2-21 according to the network topology of FIG. 3 by the above formulas (1), (2), (3), (4) and (5). Meanwhile, the utilization degree U (a) of the No. 2-21 node in the communication of nearly 100 times is calculated by the formula (6) according to the communication path. The calculation results are shown in table 4.
In the simulation process of the invention, 7 characteristic values of each node are calculated as shown in a graph 4:
TABLE 4 node eigenvalues
Figure BDA0002554187780000091
The fourth step: and collecting the use degree characteristics of the nodes in the network.
In the network operation process, the node 1 updates the hop count of the node 2-21 at regular time according to the node hop count information carried in the hierarchical control packet. And (4) according to the formula (7), subtracting the node hop count of No. 1 from the node hop count to calculate the hop distance H (a) of the No. 2-21 nodes. The calculation results are shown in table 4.
The fifth step: and preprocessing the characteristic raw data.
The degree D (a), the number B (a), the compactness C (i), the feature vector centrality E (a), the fragility V (i), the jump distance H (a) and the usage U (a) obtained by the calculation are processed into a normalized decision matrix by a formula (8).
And a sixth step: constructing a weighted norm matrix
Considering that the above 7 features represent different aspects of node importance, each criterion is compared pairwise and assigned a relative importance. The degree of use reflects the fact that the node was actually used in the network for the last period of time. The hop distance also represents the distance between the node at the current moment and the destination node No. 1. Betweenness and vulnerability reflect the indirect control ability of one node over other nodes throughout the network. The compactness reflects the position of the node in the topology, either near the center or at the edges. The feature vector centrality reflects the influence of neighbors.
Therefore, by the above comprehensive consideration, a weight vector is finally given:
w＝[0.16,0.13,0.09,0.03,0.13,0.19,0.27]
w represents the proportion of degree D (a), medium B (a), compactness C (i), feature vector centrality E (a), fragility V (i), jump distance H (a) and use degree U (a) in the evaluation process of importance degree. The normalized decision matrix B obtained from the fifth step is (B)ij)m×nThe weighting norm matrix C is constructed by the formula (9) ═ Cij)m×n。
The seventh step: determining a positive ideal solution and a negative ideal solution and solving the distance from each node to the positive ideal scheme and the negative ideal scheme
And (4) calculating a positive ideal solution and a negative ideal solution according to the result of the sixth step and the formulas (10) and (11). The distance of each node from the positive ideal solution and the negative ideal solution is then calculated according to equations (12) (13).
The positive ideal solution is a virtual optimal solution that does not exist in the decision set, and each attribute value of the solution is the optimal value of the attribute in the decision matrix. While a negative ideal solution is a virtual worst case solution, each attribute value of which is the worst value for that attribute in the decision matrix. The distances from the nodes 2-21 to the positive ideal solution and the negative ideal solution are calculated and compared. Nodes closer to the positive ideal solution and further from the negative ideal solution are the most important nodes, and vice versa are the least important nodes in the network.
Eighth step: calculating the comprehensive evaluation index f of each node according to the formula (14)i *I.e., importance, and is arranged from large to small. And selecting the first 20% of nodes as key nodes, and performing next-step network topology control and safety protection aiming at the key nodes, so that the efficiency of the network topology control and safety protection is improved.
And aiming at the process, the performance of the OPNET is simulated by adopting the OPNET. As shown in fig. 2, the network size is set to 2km × 5km, one Sink node is randomly deployed on the upper layer of the network, and other common sensor nodes are deployed on the lower layer of the network and are responsible for acquiring data. The number of the sensor nodes is 21, and the sensor nodes are randomly distributed in the network domain. The maximum communication distance of all nodes is 1km, the maximum transmitting power is 1W, the receiving power is 0W, and the energy consumption in idle is 0W. And the common sensor node randomly sends acquired data to the Sink node according to the service requirement. BPSK modulation is used in the physical layer, CDMA is used in the MAC layer, and the transmission rate of the acoustic modem is 5000bps, and the simulation result is shown in fig. 4.
In the simulation result of fig. 4, the x direction is the node number, and the y direction is the importance of the node identified by the key node identification method. From simulation results, it can be seen that 2, 3, 14, 15, and 16 of all the nodes are nodes closest to the Sink node, and meanwhile, the nodes with more output transmission pass through, and the importance is higher. And the nodes 7, 8 and 9 are used as the nodes at the bottom layer of the network, so that the opportunity of participating in communication is not much, and the importance degree is lower. In conclusion, the key node identification algorithm can accurately identify the importance of the node in the network.

Claims (1)

1. A method for identifying key nodes of a Sink node underwater acoustic sensor network is characterized by comprising the following steps:
the first step is as follows: the Sink node is used as a destination node and collects each communication path in the network working process;
in the network working process, when each node forwards a data packet, the node number and the position information of the node are added into the data packet, and finally, a destination node receives a data packet communication path except data and the position information of each node;
the second step is that: generating a network topological graph;
according to the communication path obtained in the first step, whether a path exists between any two points in the network is known; if the path is connected, connecting the two nodes, otherwise, not connecting, and simultaneously calculating the length of each path according to the node position information to finally obtain a network topological graph;
the third step: calculating the degree, betweenness, compactness, feature vector centrality, vulnerability and use degree feature values of each node;
according to the topological graph obtained in the second step, the degree D (a), the betweenness B (a), the compactness C (i), the feature vector centrality E (a), the vulnerability V (i) and the use degree U (a) of each node are respectively calculated by expressions (1) - (6);
(1) the expression for the degree D (a) is:
Figure FDA0002554187770000011
in the formula
Figure FDA0002554187770000012
Wherein a, i is a node vaAnd node viV represents the set of all nodes in the network;
(2) the expression of the betweenness B (a) is:
Figure FDA0002554187770000013
wherein P (i, j) is node viAnd vjThe shortest path number between P (i, a, j) is node viAnd vjBetween via node vaThe shortest path number of (2);
(3) the expression for the compactness C (i) is:
Figure FDA0002554187770000014
in the formula dijRepresenting a node viAnd vjThe length of the shortest path between;
(4) the expression of the feature vector centrality e (a) is:
Figure FDA0002554187770000021
where λ is a constant satisfying the equation Mx ═ λ x, and M is the adjacency matrix of the topological undirected graph, { x1,x2,...,xi,...,xnIs a feature vector;
(5) the expression for vulnerability V (i) is:
Figure FDA0002554187770000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002554187770000023
is the global efficiency of the network, FiIs to remove node viAnd the network global efficiency behind all edges;
(6) the degree of use u (a) is expressed as:
Figure FDA0002554187770000024
in the formula (I), the compound is shown in the specification,
Figure FDA0002554187770000025
indicating node v in the t-last communicationaAs the number of times the communication node is used;
the fourth step: counting the hop count of each node of the network and calculating the hop distance characteristic value;
the hop count of each node is added into the data packet, and finally the hop count is sent to the Sink destination node along with the data packet; the destination node counts the hop count of each node of the network, and then calculates the hop distance H (a) corresponding to each node, wherein the expression of the hop distance H (a) is as follows:
H(a)＝h(a)-h(s) (7)
wherein h(s) represents the hop count of the Sink node, and h (a) represents the hop count of the a node;
the fifth step: data preprocessing normalization;
forming a vector [ a ] by each eigenvalue of all nodes calculated in the third step and the fourth stepi1,…,ain]Wherein a isi1A value representing an ith characteristic of the first node; the 7 eigenvalues of all nodes in the network are respectively degree, betweenness, compactness, eigenvector centrality, vulnerability, use degree and hop distance, and the 7 eigenvalues finally form a decision matrix A ═ aij)7×nNormalizing the decision matrix A to obtain a normalized decision matrix B ═ (B)ij)7×nWherein:
Figure FDA0002554187770000026
and a sixth step: constructing a weighting specification matrix;
the normalized decision matrix B obtained from the fifth step is (B)ij)m×nConstructing a weighting norm matrix C ═ (C)ij)7×nThe expression of the weighting specification matrix is:
cij＝wj·bij,i＝1,2,…,m；j＝1,2,…,n (9)
wherein w ═ w1,w2,...wn]TGiving a weight vector of each characteristic value for a decision maker;
the seventh step: determining a positive ideal solution and a negative ideal solution, and solving the distance from each node to the positive ideal scheme and the negative ideal scheme;
the positive ideal solution expression is:
Figure FDA0002554187770000031
the negative ideal solution expression is:
Figure FDA0002554187770000032
the distance from the positive ideal solution is expressed as:
Figure FDA0002554187770000033
the distance to the negative ideal solution is expressed as:
Figure FDA0002554187770000034
eighth step: calculating the comprehensive evaluation index f of each nodei *I.e. importance, and is arranged from large to small; expression of the overall evaluation index asThe following:
Figure FDA0002554187770000036
finally, the importance evaluation value f of each node in the network is obtainedi *Selecting an importance evaluation value fi *The first 10% of nodes are used as key nodes, and next-step network topology control and safety protection are performed on the key nodes, so that the efficiency of the network topology control and the safety protection is improved.
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