CN115499324A - Elastic representation construction and evaluation method for field-oriented Internet of things - Google Patents
Elastic representation construction and evaluation method for field-oriented Internet of things Download PDFInfo
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Abstract
The invention discloses a field-oriented Internet of things elastic characterization construction and evaluation method, which introduces quantifiable elastic characterization indexes from three aspects of network connectivity, robustness and redundancy according to the characteristics of field-oriented Internet of things network node heterogeneity and multiple communication mode fusion. According to the characteristic that the data flow direction in the network is bidirectional, a field area network directed network topological graph is constructed in graph theory. By utilizing the analysis theory of network topology in a complex network, on the basis of comprehensively considering the reliability of a communication link and the node capacity, closed expressions of field domain internet of things connectivity, robustness and redundancy are respectively obtained, and the representation of network elasticity is obtained according to the three performances. From the perspective of network topology, the elastic performance characteristics and evaluation of the field network are comprehensively and systematically researched, and the analysis result is more in line with the network characteristics; based on field domain internet of things elasticity assessment and analysis, power supply reliability and power quality are guaranteed.
Description
Technical Field
The invention belongs to the technical field of communication networks, and particularly relates to a field-oriented Internet of things elasticity characterization construction and evaluation method.
Background
The field Internet of things (field network for short) is the last mile network of the smart grid and is a key network for connecting the low-voltage side of a power distribution network to users. In recent years, with the rapid development of social economy, users have made higher demands for stable and reliable power supply. With the rapid development of the smart grid and the gradual evolution of the smart grid into a large-scale complex network, the types and the number of the load-bearing services are increased in a number level, and the load-bearing services are more susceptible to the potential threats of random faults and external malicious attacks. Therefore, the field internet of things needs to be elastically evaluated and analyzed to ensure power supply reliability and power quality.
The field area network has the characteristics of complex network structure, various equipment types, multiple and wide operation points and the like, provides network connection for a large number of local terminal equipment, and combines various communication modes, so that the comprehensive perception and interconnection of information in the field area network are realized, the efficient information transmission and the reliable communication quality are ensured, and the field area network is a heterogeneous complex network with multi-mode perception fusion. In the field of system science, in order to systematically study theories of complex systems so as to better control real complex systems, complex network science has developed, complex networks can be regarded as a plurality of individuals in the complex systems and interactions among the individuals are abstracted into nodes and a graph formed by connecting the nodes, and the complex network theory focuses on summarizing general properties of general networks from phenomena of a plurality of real networks and guiding research of more real networks by using the general properties. According to the traditional simulation-based elasticity evaluation method for the power distribution system, due to the fact that network topology has the characteristics of a large number of scene optimization models, time is consumed, existing research on network elasticity is mainly conducted on the basis of homogeneous networks, research on the elasticity of the power distribution network is mainly focused on the medium-high voltage side, and at present, research on the elasticity of a communication network of a power distribution network low-voltage side heterogeneous field area network is not conducted.
Disclosure of Invention
The invention aims to solve the technical problems of elastic performance analysis of field Internet of things and complex elastic evaluation and efficiency of a power distribution system.
In order to solve the technical problems, the invention adopts the following technical scheme:
a field-oriented Internet of things elasticity characterization construction and evaluation method is used for constructing a target field Internet of things network elasticity characterization by executing the following steps aiming at the target field Internet of things, and further evaluating a target field network based on the target field Internet of things network elasticity characterization:
step A: aiming at each routing node and each sensor node in the target field Internet of things, constructing a directed topological graph of a target field network;
and B, step B: connection between sensor nodes and routing nodes in directed topological graph based on target field area network, and connectivity representation C of target field area network is constructed R ；
And C: a directed topological graph based on a target field area network is combined with each connected subgraph of the target field area network to construct a robustness representation Rb of the target field area network R ；
Step D: redundancy characterization F of target field area network is constructed based on connection among all routing nodes in directed topological graph of target field area network R ；
And E, step E: and constructing a network elasticity representation of the target field area network based on the connectivity representation, robustness representation and redundancy representation of the target field area network.
As a preferred technical solution of the present invention, a directed topology graph of the target field area network is G (V, E), where V represents a total node set including each routing node and each sensor node; v = V M UV W ，
V M Representing all routing nodes, V, in the target field Internet of things M ＝{v m |m＝1，2，…，N 1 }；V W All sensor nodes, V, in the Internet of things representing the target field W ＝{v w |w＝1，2，…，N 2 }; e represents a chain edge set in the target field Internet of things, and E = { E = { (E) ij |v i ，v j ∈V}，e ij Representing a source node v i To the destination node v j The link of (2).
As a preferred technical solution of the present invention, in the step B, the following step is specifically executed to construct a connectivity characterization C of the target field area network R ：
Step B1: based on the connection between the sensor nodes and the routing nodes in the directed topological graph of the target field area network, a connection matrix of the target field area network is obtained, and the connection matrix is as follows:
in the formula, A K Representing sensor nodes v in a target field area network w And routing node v m The reachable matrix is reached through K times of relay,
and step B2: constructing a connectivity representation C of the target field area network based on the connection matrix of the target field area network R ：
In the formula (I), the compound is shown in the specification,
as a preferred technical solution of the present invention, in the step C, the following steps are specifically executed to construct the robustness characterization Rb of the target field area network R ：
Step C1: and obtaining each connected subgraph of the target field network based on the directed topological graph G (V, E) of the target field network
And C2: each connected subgraph based on target field area network
Obtaining maximum connected subgraph of target field area network
The maximum connected subgraph satisfies the following conditions:
wherein the content of the first and second substances,
P g，k is node v g And v k The set of links between the first and second nodes,
and C3: based on the maximum connected subgraph of the target field area network, the robustness characterization Rb of the target field area network is constructed through the following formula R ：
In the formula, G SCC A set of connected subgraphs representing a target field network,
each represents a connected subgraph in the target field network connected subgraph set,
representing a set of nodes in the maximum connected subgraph,
representing the set of chain edges in the maximal connected subgraph.
As a preferred technical solution of the present invention, in the step D, a redundancy characterization F of the target field area network is constructed through the steps D1 to D2 R ：
Step D1: and (3) respectively executing the steps D1.1 to D1.2 aiming at each routing node in the target field area network, and obtaining the average reliable path number respectively corresponding to each routing node:
step D1.1: directed topology graph based on target field area networkObtaining the routing node v m To routing node v s All paths M of ms ，v s ∈V M 、v m ≠v s And executing the following steps D1.1.1 to D1.1.2 respectively aiming at each path to obtain the path reliability corresponding to each path:
step D1.1.1: acquiring a node set l contained in the path node ，l node ＝{v 1 ，v 2 ，…，v n }；
Step D1.1.2: based on the node set contained in the path, the reliability Q of the path is obtained through the following formula l ；
In the formula: n is the number of nodes included in the path l,
is the reliability of the kth node among the nodes comprised by path l,
is the reliability of the path/kth hop link, q p The reliability of PLC transmission is shown, P represents probability, and the value is [0,1]]， SINR st Indicating the signal to interference plus noise ratio, SINR, of the receiving node 0 Representing a signal to interference plus noise ratio threshold;
step D1.2: based on the path reliability corresponding to each path, obtaining the average reliable path number of the routing node through the following formula;
step D2: in a target-based field area networkThe average reliable path number corresponding to each routing node is constructed by the following formula to represent the redundancy of the target field area network F R ：
In the formula (I), the compound is shown in the specification,
Cap m representing a routing node v m Capacity of (d), w m Representing a routing node v m The capacity of (a) is a proportion of the total capacity.
As a preferred technical solution of the present invention, the network elasticity characterization of the target domain network in step E is as follows:
R＝αC R +βRb R +γF R
in the formula, α, γ are preset weighting factors of connectivity, robustness and redundancy in network elasticity, respectively, and α + β + γ =1.
As a preferred technical solution of the present invention, in the step E, based on connectivity characterization, robustness characterization, and redundancy characterization of the target field area network, a network elasticity characterization of the target field area network is obtained through the following steps:
step E1: obtaining the global connectivity characterization of the target field area network based on the connectivity characterization of the target field area network
As shown in the following equation:
in the formula (I), the compound is shown in the specification,
representing the connectivity representation of the network after the target field area network removes the i nodes;
step E2:obtaining global robustness representation of the target field area network based on robustness representation of the target field area network
As shown in the following equation:
in the formula (I), the compound is shown in the specification,
representing the robustness representation of the network after the i nodes of the target field area network are removed;
step E3: obtaining the global redundancy characterization of the target field area network based on the redundancy characterization of the target field area network
The following formula shows:
in the formula (I), the compound is shown in the specification,
representing the redundancy representation of the network after the i nodes of the target field area network are removed;
step E4: constructing a network elastic representation of the target field area network based on the global connectivity representation, the global robustness representation and the global redundancy representation of the target field area network, wherein the following formula is shown:
in the formula, α, β, γ are preset weighting factors of connectivity, robustness and redundancy in network elasticity, respectively, and α + β + γ =1.
The invention has the beneficial effects that: the invention provides a field Internet of things oriented elastic characterization construction and evaluation method, which is characterized in that field Internet of things network node heterogeneity, multiple communication modes are fused and a large-scale complex network is provided, the field Internet of things elastic performance characterization is analyzed from the aspect of topology based on a complex network theory, the field Internet of things elastic performance characterization and evaluation are comprehensively and systematically researched from the aspect of network topology based on graph theory and a complex network theory basis, and the analysis result is more in line with the network characteristics; based on field domain internet of things elasticity assessment and analysis, power supply reliability and power quality are guaranteed.
Drawings
Fig. 1 is a schematic diagram of a field internet of things network architecture;
FIG. 2 is a directed topology diagram of a domain Internet of things;
FIG. 3 is a comparison diagram of FAN resilient characterization under node random failure and malicious attack in the first embodiment;
FIG. 4 is a comparison diagram of FAN elastic characterization after sequentially removing one node in the first embodiment;
FIG. 5 is a random network topology diagram of ER and a non-scale network topology diagram of BA in the second embodiment;
fig. 6 is a graph comparing the resiliency of ER random networks and BA scale-less networks under random failures and malicious attacks.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are presented to enable one of ordinary skill in the art to more fully understand the present invention and are not intended to limit the invention in any way.
The invention takes the field internet of things network structure shown in fig. 1 as an example. In such a scenario, most of the underlying sensor nodes cannot be directly connected to the controller, but transmit data to the controller through a multi-hop transmission manner via a Mesh network formed by routing nodes of the field area network. In order to realize the comprehensive sensing and interconnection of information and guarantee the efficient information transmission and reliable communication quality, the field area network is difficult to realize by only one communication mode, so that the field area network is a multi-mode sensing fusion network combining a plurality of communication modes, namely high-speed power line carrier, field area power line carrier, micropower wireless and low-power wireless. Due to the characteristics of large scale, complexity and heterogeneous integration of the field area network, the complexity of the traditional elastic analysis method is greatly improved, so that graph theory modeling is introduced, the analysis is carried out from the topological angle based on the complex network theory, and equipment abstract nodes and communication links in the network are abstracted to form edges, so that the directed network topological graph shown as the graph II is obtained.
Based on the field internet of things network architecture shown in fig. 1 and the directed network topology diagram shown in fig. 2, the invention provides a method for characterizing and evaluating the field internet of things elasticity performance based on a complex network theory. The method solves the problem of elasticity performance analysis in the target field Internet of things, and comprehensively and systematically researches field net elasticity performance characterization and evaluation.
Example 1
The embodiment provides a field-domain-oriented Internet of things elasticity characterization construction and evaluation method, which is characterized by comprising the following steps of constructing a network elasticity characterization, namely a network total elasticity characterization, of a target field-domain Internet of things aiming at the target field-domain Internet of things, and evaluating a target field network based on the network elasticity characterization of the target field-domain Internet of things.
Determining that the elasticity performance of the field area network provided by the invention is analyzed and evaluated by a method based on a complex network theory from the aspect of topology analysis, and determining that the node types in an analysis scene are a center node, a routing node and a sensor node, wherein the communication capacities of the three nodes are from high to low in sequence; the communication modes in the field area network comprise field area power line carrier communication, micro-power wireless communication and low-power wireless communication; the field Internet of things network can adapt to dynamic environment change, bear faults and quickly recover response, the elastic performance of the field network is determined to be analyzed from three aspects of connectivity, robustness and redundancy, and a closed expression of quantitative representation of the three performances of the connectivity, the robustness and the redundancy is deduced on the basis of comprehensively considering the reliability of a communication link and the node capacity through a complex network theory analysis method.
Step A: and constructing a directed topological graph of the target field area network aiming at each routing node and each sensor node in the target field area Internet of things. The field Internet of things network topological graph with the characteristics of network node isomerism and integration of multiple communication modes is constructed by introducing a graph theory, the directed topological graph of the target field network is G (V, E), wherein V represents a total node set comprising each routing node and each sensor node; v = V M ∪V W ，
V M Representing all routing nodes, V, in the target field Internet of things M ＝{v m |m＝1,2,…,N 1 }；V W All sensor nodes, V, in the Internet of things representing the target field W ＝{v w |w＝1,2,…,N 2 }; e represents a chain edge set in the target field Internet of things, and E = { E = { (E) ij |v i ,v j ∈V}，e ij Representing a source node v i To the destination node v j The link of (2).
In wireless transmission, it is defined that a receiving node is considered to be connected if the signal to interference plus noise ratio of the two nodes is greater than a threshold SINR 0. Using a lognormal shadow path loss model, wherein the model is suitable for a sensor network in a complex environment, and the path loss is expressed as:
where d is the communication distance between two nodes, d 0 Is a close reference distance (preferably 1 m), so that PL (d) when the wireless signal frequency is 2.4GHz 0 ＝1)＝40dB，L s Is a path loss exponent, X δ Is a random variable with a gaussian distribution with a mean of 0 and a variance of δ caused by shadowing effects. The path loss is reduced to the expression related to the distance d:
wherein K L Is constant, defined as:
the small-scale multipath fading considered herein is Rayleigh fading, assuming P i Is a node v i Of the terminal v j Received power is
Wherein h is ij Representing a node v i To terminal v j The channel gain in between, obeys an exponential distribution with a parameter of 1. The noise is mean 0 and variance σ 2 White additive gaussian noise. The interference suffered by the target terminal is the accumulated interference I of all other nodes except the communication node n The calculation is as follows:
node v j Received (a)
Then
The connection of two nodes of a field power line carrier transmission in a network can be represented as
Wherein d is ij Is node v i And v j A distance between, D 0 Is the maximum distance of PCL transmission.
And B: connection between sensor nodes and routing nodes in directed topological graph based on target field area network, and connectivity characterization C of target field area network is constructed R . The connectivity is defined as the ratio of the sensor nodes which can be connected to the routing nodes to the total sensor nodes, and is calculated by using an adjacency matrix in a complex network, so that the connectivity ensures that a controller of the field Internet of things can acquire all equipment data and can perform scheduling.
In the step B, the following steps are specifically executed to construct a connectivity characterization C of the target field area network R ：
The conventional adjacency matrix is
A P Is an adjacency matrix of a field power line carrier transmission network, A W Is an adjacency matrix of the wireless transport network.
As defined by the adjacency matrix A, A is the sensor node v m And routing node v m Can reach the matrix if the sensor node v m And routing node v m A path of length L =2 exists between the two nodes, then
By analogy, A is known K For the network, K hops can reach the matrix if A K Element (1) of
Is a non-zero element, then represents the sensor node v w And routing node v m May be interconnected by up to K relays. Defining a connected matrix C, wherein the element C mw Indicates whether the sensor node can be connected to the routing node, if c mw =1, then it represents the sensor node v w Capable of connecting to at least one routing node v m ，
Further, a connectivity representation C of the target field area network is constructed through the following processes R 。
Step B1: based on the connection between the sensor nodes and the routing nodes in the directed topological graph of the target field area network, a connection matrix of the target field area network is obtained, and the connection matrix is as follows:
in the formula, A K Representing sensor nodes v in a target field area network w And routing node v m The reachable matrix is reached through K times of relay,
and step B2: constructing a connectivity representation C of the target field area network based on the connection matrix of the target field area network R ：
In the formula (I), the compound is shown in the specification,
and C: a directed topological graph based on a target field area network is combined with each connected subgraph of the target field area network to construct a robustness representation Rb of the target field area network R (ii) a The relative size of the maximum connected subgraph is defined to measure the robustness, and the robustness represents the network performance which is still better under the condition that the nodes are failed due to random failure and malicious attack.
In the step C, the following steps are specifically executed to construct the robustness representation Rb of the target field area network R ：
Step C1: and obtaining each connected subgraph of the target field network based on the directed topological graph G (V, E) of the target field network
And C2: each connected subgraph based on target field area network
Obtaining maximum connected subgraph of target field area network
The maximum connected subgraph satisfies the following conditions:
wherein, the first and the second end of the pipe are connected with each other,
P g，k is node v g And v k The set of links between the first and second nodes,
and C3: based on the maximum connected subgraph of the target field area network, the robustness characterization Rb of the target field area network is constructed through the following formula R ：
In the formula, G SCC A set of connected subgraphs representing the target field area network,
each represents a connected subgraph in the target field network connected subgraph set,
representing a set of nodes in the maximum connected subgraph,
representing the set of chain edges in the maximum connected subgraph.
Step D: constructing redundancy characterization F of the target field area network based on the connection between each routing node in the directed topological graph of the target field area network R (ii) a The average reliable path number between the routing node pairs in the network topology is derived, the redundancy indicates that redundant resources exist in the network, once partial links or nodes are in failure, other resources are still available, and timely and reliable delivery of data is guaranteed.
In the step D, a redundancy characterization F of the target field area network is constructed through the steps D1 to D2 R ：
Step D1: and (3) respectively executing the steps D1.1 to D1.2 aiming at each routing node in the target field area network, and obtaining the average reliable path number respectively corresponding to each routing node:
step D1.1: obtaining the routing node v based on the directed topological graph of the target field area network m To routing node v s All paths M of ms ，v s ∈V M 、v m ≠v s And executing the following steps D1.1.1 to D1.1.2 respectively aiming at each path to obtain the path reliability corresponding to each path:
step D1.1.1: acquiring a node set l contained in the path node ，l node ＝{v 1 ，v 2 ，…，v n }; including routing node v m And routing node v s ；
Step D1.1.2: based on the node set contained in the path, the reliability Q of the path is obtained through the following formula l (ii) a The reliability of a single path l is related to the reliability of all nodes and all links between the nodes contained in the path;
wherein the content of the first and second substances,
in the formula: n is the number of nodes included in the path l,
is the reliability of the kth node among the nodes comprised by path l,
is the reliability of the k-th hop link of path l, q p The reliability of PLC transmission is shown, P represents probability, and the value is [0,1]]， SINR st Representing the signal to interference plus noise ratio, SINR, of the receiving node 0 Representing a signal to interference plus noise ratio threshold;
step D1.2: based on the path reliability corresponding to each path, obtaining the average reliable path number of the routing node through the following formula;
step D2: based on the average reliable path number corresponding to each routing node in the target field area network, the redundancy characterization F of the target field area network is constructed through the following formula R ：
In the formula, the difference of node capacity caused by the node residual capacity is taken into consideration as the weight of the node,
Cap m is a routing node v m Capacity of (d), w m Representing a routing node v m The capacity of (a) is a proportion of the total capacity.
Step E: and constructing a network elasticity representation of the target field area network based on the connectivity representation, robustness representation and redundancy representation of the target field area network to obtain a total elasticity representation closed expression of the network.
The network elasticity characterization of the target field area network in the step E is as follows:
R＝αC R +βRb R +γF R
in the formula, α, β, γ are preset weighting factors of connectivity, robustness and redundancy in network elasticity, respectively, and α + β + γ =1. And aiming at the total elasticity characterization of the network corresponding to each state of the network, the elasticity of the target field Internet of things in each state can be evaluated.
This example uses MATLAB to perform a simulation experiment to evaluate the elasticity of FAN, where 40 paths are provided in a space of 500mAnd 1-10 sensor nodes are randomly distributed around each routing node by the routing node. Based on the existing research on the channel characteristics of the industrial wireless sensor network, the path loss attenuation factor n is set to be 1.33, based on the existing research on the wireless communication of the smart grid, the frequency of a wireless signal is set to be 2.4GHz 0 Set to-12 dB, noise σ 2 at-105dBm, the maximum communication distance D of the PLC 0 To 100m, the reliability q of the plc link p And =1. The constructed small FAN topology is also shown in fig. 2.
To evaluate the resilience of the FAN, node random failures and malicious attacks were simulated separately herein. The random failure of a node is not specific to a specific node, and each node has equal probability of failure. The method adopts the random removal of nodes in the network and all edges connected by the nodes so as to simulate the node failure caused by various random events. A certain number of nodes were removed at random each time, and the results were averaged over 10 experiments to avoid chance. Malicious attacks target the rapid loss of network service, and will preferentially attack the more important nodes in the network. The degree of the node is used for measuring the importance degree of the node, and the higher the degree of the node is, the more important the node is in the network. In order to simulate the influence of malicious attacks on the network, the degrees of the nodes in the network are sequenced, and the node with the highest degree and all edges connected with the node are removed in each round of attack.
The pair of FAN elastic characterizations under node random failure and malicious attack is shown in FIG. 3, which shows the change of each elastic characterization of FAN when the node random failure and malicious attack cause the number of failed nodes to increase from 0 to 100%, and the abscissa represents the percentage of removed nodes, wherein the values of α, β and γ are respectively 0.3,0.3,0.4. Fig. 3 (a) shows a change situation of connectivity, in two modes causing node failure, the difference between the two modes is not large, and as the number of removed nodes increases, the connectivity of FAN under random failure is obviously higher than that of malicious attack. Fig. 3 (b) is a robustness change curve, and two curves of 0 to 20% of the removed nodes almost coincide with each other because the LCC is not greatly affected by the small number of the removed nodes at the beginning and there are still a large number of connected edges in the network. Starting from 30% of the removed nodes, the robustness under the malicious attack is reduced sharply, and because the malicious attack preferentially removes nodes with a large number of degrees, namely a large number of connected edges are removed at the same time, and random failure is to select nodes randomly, the number of the remaining edges in the network is larger than that of the malicious attack. Fig. 3 (c) is a comparison of redundancy, where the removal node has the greatest effect on redundancy, and both curves decrease exponentially, but the redundancy under random failure is slightly higher than that of a malicious attack. Fig. 3 (d) shows a comparison of the total resilience of the FAN, and the two curves descend faster than they are in terms of connectivity and robustness, and slower than redundancy, it can be seen that the FAN is more resilient against random failures than malicious attacks. The comparison of FAN elastic representations after one node is removed in sequence is shown in FIG. 4, the abscissa represents the number of the removed node, the abscissa is 0 and represents the initial value of each elastic representation of the network, and besides robustness, other elastic representations have obvious changes. It can be seen that the total resilience of FAN is reduced the most by removing node number 38, which indicates that removing the node has the greatest impact on the resilience of the network, and the node is the weakest point of resilience in the network.
Example 2
A field-oriented Internet of things elasticity characterization construction and evaluation method is used for constructing a target field Internet of things network elasticity characterization by executing the following steps aiming at the target field Internet of things, and further evaluating a target field network based on the target field Internet of things network elasticity characterization:
the embodiment provides a field-domain-oriented Internet of things elasticity characterization construction and evaluation method, which is characterized by comprising the following steps of constructing a network elasticity characterization, namely a network total elasticity characterization, of a target field-domain Internet of things aiming at the target field-domain Internet of things, and evaluating a target field network based on the network elasticity characterization of the target field-domain Internet of things.
Determining that the elasticity performance of the field area network provided by the invention is analyzed and evaluated by a method based on a complex network theory from the aspect of topology analysis, and determining that the node types in an analysis scene are a center node, a routing node and a sensor node, wherein the communication capacities of the three nodes are from high to low in sequence; the communication modes in the field area network comprise field area power line carrier communication, micro-power wireless communication and low-power wireless communication; the elastic performance of the field area network is analyzed from three aspects of connectivity, robustness and redundancy.
Step A: and constructing a directed topological graph of the target field network aiming at each routing node and each sensor node in the target field Internet of things. Constructing a field domain Internet of things network topological graph with the characteristics of network node isomerism and integration of multiple communication modes by introducing a graph theory, wherein the directed topological graph of the target field domain network is G (V, E), and V represents a total node set comprising each routing node and each sensor node; v = V M ∪V W ，
V M All routing nodes in the target domain internet of things are represented,
V M ＝{v m |m＝1,2,…,N 1 }；V W all sensor nodes, V, in the Internet of things representing the target field W ＝{v w |w＝1,2,…,N 2 }; e represents a chain edge set in the target field Internet of things, and E = { E = { (E) ij |v i ,v j ∈V}，e ij Representing a source node v i To the destination node v j The link of (2).
The connection of two nodes in the network wireless transmission can be expressed as
Wherein
SINR 0 Is the signal-to-interference-and-noise ratio threshold of wireless transmission, and the interference suffered by the target terminal is the accumulated interference of all other nodes except the communication node
The small-scale multipath fading considered herein is Rayleigh fading, assuming P i Is a node v i Of the terminal v j Received power is
Wherein h is ij Representing the channel gain, obeys an exponential distribution with a parameter of 1. The noise is mean 0 and variance σ 2 White additive gaussian noise. The connection of two nodes of a field power line carrier transmission in a network can be represented as
Wherein d is ij Is node v i And v j A distance between, D 0 Is the maximum distance of PCL transmission.
And B: connection between sensor nodes and routing nodes in directed topological graph based on target field area network, and connectivity representation C of target field area network is constructed R . The connectivity is defined as the ratio of the sensor nodes which can be connected to the routing nodes to the total sensor nodes, and is calculated by using an adjacency matrix in a complex network, so that the connectivity ensures that a controller of the field Internet of things can acquire all equipment data and can perform one of the key requirements of scheduling.
In the step B, the following steps are specifically executed to construct a connectivity representation C of the target field area network R ：
The conventional adjacency matrix is
A P Is an adjacency matrix of a field power line carrier transmission network, A W Is an adjacency matrix of the wireless transport network.
As defined by the adjacency matrix A, A is the sensor node v w And routing node v m Can reach the matrix if the sensor node v w And routing node v m A path of length L =2 exists between the two nodes, then
By analogy, A is known K For the network, K hops can reach the matrix if A K Element (1) of
Is a non-zero element, then represents the sensor node v w And routing node v m May be interconnected by up to K relays. Defining a connected matrix C, wherein the element C mw Indicates whether the sensor node can be connected to the routing node, if c mw =1, then it represents the sensor node v w Capable of connecting to at least one routing node v m ，
Further, a connectivity representation C of the target field area network is constructed through the following processes R 。
Step B1: based on the connection between the sensor nodes and the routing nodes in the directed topological graph of the target field area network, a connection matrix of the target field area network is obtained, and the connection matrix is as follows:
in the formula, A K Representing sensor nodes v in a target field area network w And routing node v m The reachable matrix is reached through K times of relay,
and step B2: constructing a connectivity characterization C of the target field area network based on the connection matrix of the target field area network R ：
In the formula (I), the compound is shown in the specification,
and C: a directed topological graph based on a target field area network is combined with each connected subgraph of the target field area network to construct a robustness representation Rb of the target field area network R (ii) a Defining the relative size of the maximum connected subgraph to measure robustnessThe robustness represents the network performance which is still better under the condition that the node failure is caused by random failure and malicious attack.
In the step C, the following steps are specifically executed to construct the robustness characterization Rb of the target field area network R ：
Step C1: and obtaining each connected subgraph of the target field network based on the directed topological graph G (V, E) of the target field network
And step C2: each connected subgraph based on target field area network
Obtaining maximum connected subgraph of target field area network
The maximum connected subgraph satisfies the following conditions:
wherein the content of the first and second substances,
P g，k is node v g And v k The set of links between the first and second nodes,
and C3: based on the maximum connected subgraph of the target field area network, the robustness characterization Rb of the target field area network is constructed through the following formula R ：
In the formula, G SCC A set of connected subgraphs representing a target field network,
each represents a connected subgraph in the target field network connected subgraph set,
representing a set of nodes in the maximum connected subgraph,
representing the set of chain edges in the maximum connected subgraph.
Step D: redundancy characterization F of target field area network is constructed based on connection among all routing nodes in directed topological graph of target field area network R (ii) a The average reliable path number between the routing node pairs in the network topology is deduced, the redundancy indicates that redundant resources exist in the network, once partial links or nodes have faults, other resources are still available, and timely and reliable delivery of data is guaranteed.
In the step D, a redundancy characterization F of the target field area network is constructed through the steps D1 to D2 R ：
Step D1: and (3) respectively executing the steps D1.1 to D1.2 aiming at each routing node in the target field area network, and obtaining the average reliable path number respectively corresponding to each routing node:
step D1.1: obtaining the routing node v based on the directed topological graph of the target field area network m To routing node v s All paths M of mn ，v s ∈V M 、v m ≠v s And executing the following steps D1.1.1 to D1.1.2 respectively aiming at each path to obtain the path reliability corresponding to each path:
step D1.1.1: acquiring a node set l contained in the path node ，l node ＝{v 1 ，v 2 ，…，v n }; including routing node v i And routing node v j ；
Step D1.1.2: based on the node set contained in the path, the reliability Q of the path is obtained through the following formula l (ii) a Single roadThe reliability of the path l is related to the reliability of all nodes contained in the path and all links among the nodes;
wherein the content of the first and second substances,
in the formula: n is the number of nodes included in the path l,
is the reliability of the kth node among the nodes comprised by the path l,
is the reliability of the path/kth hop link, q p The reliability of PLC transmission is shown, P represents probability, and the value is [0,1]]， SINR st Indicating the signal to interference plus noise ratio, SINR, of the receiving node 0 Representing a signal to interference plus noise ratio threshold;
step D1.2: based on the path reliability corresponding to each path, obtaining the average reliable path number of the routing node through the following formula;
step D2: based on the average reliable path number corresponding to each routing node in the target field area network, the redundancy characterization F of the target field area network is constructed through the following formula R ：
In the formula, the difference of node capacity caused by the node residual capacity is taken into consideration as the weight of the node,
Cap m is a routing node v m Capacity of (d), w m Representing a routing node v m The capacity of (a) is a proportion of the total capacity.
Step E: and constructing a network elasticity representation of the target field area network based on the connectivity representation, robustness representation and redundancy representation of the target field area network to obtain a global elasticity representation closed expression of the network.
In the step E, based on the connectivity characterization, robustness characterization and redundancy characterization of the target field area network, the network elasticity characterization, namely the global elasticity characterization, of the target field area network is obtained through the following steps:
step E1: obtaining the global connectivity characterization of the target field area network based on the connectivity characterization of the target field area network
Namely, the relational expression between the global connectivity and the connectivity of the network in a certain state, as shown in the following formula:
in the formula (I), the compound is shown in the specification,
representing the connectivity representation of the network after the target field area network removes the i nodes; in the embodiment, if the network nodes are randomly removed, the same nodes may not be the same, the nodes removed by the malicious attack are removed according to the importance of the nodes in an order, and the nodes removed by i =2 are removed one more according to the order on the basis of i =1.
And E2: obtaining global robustness characterization of the target field area network based on the robustness characterization of the target field area network
Namely the relational expression between the global robustness and the robustness of the network in a certain state, as shown in the following formula:
in the formula (I), the compound is shown in the specification,
representing the robustness representation of the network after the i nodes of the target field area network are removed;
step E3: obtaining the global redundancy characterization of the target field area network based on the redundancy characterization of the target field area network
Namely, the relational expression between the global redundancy and the redundancy in a certain state of the network, as shown in the following formula:
in the formula (I), the compound is shown in the specification,
representing the redundancy representation of the network after the i nodes of the target field area network are removed;
step E4: constructing a network elastic characterization of the target field area network based on the global connectivity characterization, the global robustness characterization and the global redundancy characterization of the target field area network, namely the global elastic characterization, wherein the network elastic characterization is shown in the following formula:
in the formula, α, β, γ are preset weighting factors of connectivity, robustness and redundancy in network elasticity, respectively, and α + β + γ =1. The weighting factor is the same as the overall elastic characterization factor. Based on the global elastic characterization of the network, the overall performance state of the network can be evaluated, and performance evaluation comparison can be carried out among a plurality of networks.
In this embodiment, in order to verify the universality of the algorithm of this document, the algorithm is generalized to a general network, and this document uses a classical network model in a complex network: experiments were performed with a BA scale-free network and an ER random network. The method simulates network random failure and malicious attack respectively, observes the change of network topology performance, and evaluates the change of network elasticity reflected under the defined elasticity representation. And finally, global elastic characteristics of the FAN, BA scale-free network and ER random network are respectively compared.
For a generic homogeneous network, there is only one type of node. Thus, when evaluated using the elasticity model, N = N 1 ＝N 2 . Connectivity is defined as the ratio of the number of non-isolated nodes in the network to the total number of nodes, redundancy is defined as the number of reliable paths between pairs of nodes in the network, robustness is defined as the ratio of the number of nodes contained in the LCC to the total number of nodes, and the total elasticity of the network is a weighted sum of 3 elasticity indicators.
The simulation was performed using MATLAB, first establishing random network and scale-free network models, with the network scale set to N =50. The construction mode of the ER random network is as follows: given N nodes and the probability of edge connection p ∈ [0,1], each node pair is connected with a probability p. The connection probability p =0.06 of the ER random network is set, the constructed ER random network topology is shown in fig. 5, the ER random network topology is on the left, the BA scale-free network topology is on the right, the node size and the color represent the degree of the node, and the larger the radius and the darker the color indicates that the degree is larger, so that the distribution of the degree of the node of the ER random network topology is relatively uniform.
Two important characteristics of BA scaleless networks that distinguish them from stochastic network models are:
1) Growth characteristics: i.e., the network size is constantly expanding.
2) Connection preference characteristics: i.e. new nodes tend to connect with nodes of higher degree.
The steps for constructing the BA scale-free network are as follows: first from one with m 0 Connected network of individual nodesThe network starts, each time a new node is introduced to connect to m (m)<m 0 ) An existing node, a new node and an existing node v i Probability of connection Pr i And node v i Degree k of i Satisfy the relationship between
The above expression embodies the connection preference characteristic, and the newly added node is connected to the node v with larger degree i Probability of (Pr) i The larger. A BA scaleless network topology (N =50, m = 3) constructed according to the steps is shown in fig. 6, and due to the growth and connection preference characteristics of the BA scaleless network, a small number of nodes with a large degree exist in the network, and a large number of nodes with a small degree exist.
The degree distribution of the nodes in the ER random network is uniform, and the importance degree of the nodes is similar. The degree distribution of the BA scale-free network has heterogeneity, that is, a small number of nodes in the network have a large degree, and such nodes are often important hubs in the network, but the degree of most of nodes is small, and the influence on the network performance is small. Because the number of the hubs is small, the probability of randomly removing nodes with high degrees is small, and malicious attacks preferentially remove the nodes with high degrees, the elasticity of the system is rapidly reduced, so that theoretically, the elasticity of the ER random network under the malicious attacks is higher than that of the BA scale-free network, and the elasticity of the ER random network under the random failure is lower than that of the BA scale-free network.
The resilience pairs for both ER random networks and BA scaleless networks under both attacks are shown in fig. 6, with the abscissa being the percentage of nodes removed and the ordinate being the total resilience of the network. It can be seen that both networks fall more resilient to malicious attacks than random failures, indicating that they are less resilient to malicious attacks. Because the degree distribution of the ER random network is uniform, the difference between the elasticity change of malicious attack and random failure is not large, and the BA scale-free network has better tolerance to the random failure due to the extreme heterogeneity of the degree distribution, but the elasticity is sharply reduced by the malicious attack, which is consistent with the theory, and the elasticity model has universality. Global resiliency comparison with table 1, it can be seen that the global resiliency of the FAN is the highest no matter under random failure or malicious attack, which indicates that the resiliency performance of the FAN under attack is better than that of the other two networks.
TABLE 1 Global elastic contrast
The invention designs a field Internet of things oriented elastic characterization construction and evaluation method, which is characterized in that field network node heterogeneity, multiple communication modes are fused and a large-scale complex network is provided, the field Internet of things elastic performance characterization is analyzed from the aspect of topology based on a complex network theory, the field network elastic performance characterization and evaluation are comprehensively and systematically researched from the aspect of network topology based on graph theory and a complex network theory basis, and the analysis result is more in line with the network characteristics; based on field domain internet of things elasticity assessment and analysis, power supply reliability and power quality are guaranteed.
Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments described in the foregoing detailed description, or equivalent changes may be made in some of the features of the embodiments described above. All equivalent structures made by using the contents of the specification and the attached drawings of the invention can be directly or indirectly applied to other related technical fields, and are also within the protection scope of the patent of the invention.
Claims (7)
1. A field-oriented Internet of things elastic characterization construction and evaluation method is characterized by comprising the following steps: aiming at the target field Internet of things, the following steps are executed, the network elasticity characterization of the target field Internet of things is constructed, and then the target field network is evaluated based on the network elasticity characterization of the target field Internet of things:
step A: aiming at each routing node and each sensor node in the target field Internet of things, constructing a directed topological graph of a target field network;
and B: connection between sensor nodes and routing nodes in directed topological graph based on target field area network, and connectivity representation C of target field area network is constructed R ；
And C: a directed topological graph based on a target field area network is combined with each connected subgraph of the target field area network to construct a robustness representation Rb of the target field area network R ；
Step D: redundancy characterization F of target field area network is constructed based on connection among all routing nodes in directed topological graph of target field area network R ；
Step E: and constructing a network elasticity representation of the target field area network based on the connectivity representation, robustness representation and redundancy representation of the target field area network.
2. The elastic characterization construction and evaluation method for the field-oriented internet of things according to claim 1, characterized in that: the directed topological graph of the target field area network is G (V, E), wherein V represents a total node set comprising each routing node and each sensor node; v = V M ∪V W ，
V M Representing all routing nodes, V, in the target field Internet of things M ＝{v m |m＝1,2,…,N 1 }；V W All sensor nodes, V, in the Internet of things representing the target field W ＝{v w |w＝1,2,…,N 2 }; e represents a chain edge set in the target field Internet of things, and E = { E = { (E) ij |v i ,v j ∈V}，e ij Representing a source node v i To the destination node v j The link of (2).
3. The field-oriented internet of things elasticity characterization construction and evaluation method according to claim 2, characterized in that: in the step B, the following steps are specifically executed to construct a connectivity representation C of the target field area network R ：
Step B1: based on the connection between the sensor nodes and the routing nodes in the directed topological graph of the target field area network, a connection matrix of the target field area network is obtained, and the connection matrix is as follows:
in the formula, A K Representing sensor nodes v in a target field area network w And routing node v m The reachable matrix is reached through K times of relay,
and step B2: constructing a connectivity representation C of the target field area network based on the connection matrix of the target field area network R ：
In the formula (I), the compound is shown in the specification,
4. the elastic characterization construction and evaluation method for the field-oriented internet of things according to claim 2, characterized in that: in the step C, the following steps are specifically executed to construct the robustness representation Rb of the target field area network R ：
Step C1: and obtaining each connected subgraph of the target field network based on the directed topological graph G (V, E) of the target field network
And step C2: each connected subgraph based on target field area network
Obtaining maximum connected subgraph of target field area network
The maximum connectivity subgraph satisfies the following conditions:
wherein the content of the first and second substances,
P g，k is node v g And v k The set of links between the first and second nodes,
step C3: based on the maximum connected subgraph of the target field area network, the robustness characterization Rb of the target field area network is constructed through the following formula R ：
In the formula, G SCC A set of connected subgraphs representing a target field network,
each represents a connected subgraph in the target field network connected subgraph set,
representing a set of nodes in the maximum connected subgraph,
representing the set of chain edges in the maximum connected subgraph.
5. The elastic characterization construction and evaluation method for the field-oriented internet of things according to claim 2, characterized in that: in the step D, a redundancy characterization F of the target field area network is constructed through the steps D1 to D2 R ：
Step D1: and (3) respectively executing the steps D1.1 to D1.2 aiming at each routing node in the target field area network, and obtaining the average reliable path number respectively corresponding to each routing node:
step D1.1: obtaining the routing node v based on the directed topological graph of the target field area network m To routing node v s All paths M of ms ，v s ∈V M 、v m ≠v s And executing the following steps D1.1.1 to D1.1.2 aiming at each path respectively to obtain the path reliability corresponding to each path:
step D1.1.1: acquiring a node set l contained in the path node ，l node ＝{v 1 ,v 2 ,...,v n }；
Step D1.1.2: based on the node set contained in the path, the reliability Q of the path is obtained through the following formula l ；
Wherein the content of the first and second substances,
in the formula: n is the number of nodes included in the path l,
is the reliability of the kth node among the nodes comprised by path l,
is the reliability of the path/kth hop link, q p The reliability of PLC transmission is represented, P represents probability, and the value is [0,1]]，SINR st Indicating the signal to interference plus noise ratio, SINR, of the receiving node 0 Representing a signal to interference plus noise ratio threshold;
step D1.2: based on the path reliability corresponding to each path, obtaining the average reliable path number of the routing node through the following formula;
step D2: based on the average reliable path number corresponding to each routing node in the target field area network, the redundancy characterization F of the target field area network is constructed through the following formula R ：
In the formula (I), the compound is shown in the specification,
Cap m representing routing nodes v m Capacity of (d), w m Representing a routing node v m The capacity of (a) is a proportion of the total capacity.
6. The field-oriented internet of things elasticity characterization construction and evaluation method according to claim 1, characterized in that: the network elasticity characterization of the target field area network in the step E is as follows:
R＝αC R +βRb R +γF R
in the formula, α, β, γ are preset weighting factors of connectivity, robustness and redundancy in network elasticity, respectively, and α + β + γ =1.
7. The elastic characterization construction and evaluation method for the field-oriented internet of things according to claim 1, characterized in that: and E, based on the connectivity characterization, robustness characterization and redundancy characterization of the target field area network, obtaining the network elasticity characterization of the target field area network through the following steps:
step E1: obtaining the global connectivity characterization of the target field area network based on the connectivity characterization of the target field area network
As shown in the following equation:
in the formula (I), the compound is shown in the specification,
representing the connectivity representation of the network after the target field area network removes the i nodes;
and E2: obtaining global robustness representation of the target field area network based on robustness representation of the target field area network
As shown in the following equation:
in the formula (I), the compound is shown in the specification,
representing the robustness representation of the network after the i nodes of the target field area network are removed;
step E3: obtaining the global redundancy characterization of the target field area network based on the redundancy characterization of the target field area network
As shown in the following equation:
in the formula (I), the compound is shown in the specification,
representing the redundancy representation of the network after the i nodes of the target field area network are removed;
and E4: constructing a network elastic representation of the target field area network based on the global connectivity representation, the global robustness representation and the global redundancy representation of the target field area network, wherein the following formula is shown:
in the formula, α, β, γ are preset weighting factors of connectivity, robustness and redundancy in network elasticity, respectively, and α + β + γ =1.
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