CN106488393B - Cluster head election system of clustering wireless sensor network based on evolutionary game mechanism - Google Patents

Cluster head election system of clustering wireless sensor network based on evolutionary game mechanism Download PDF

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CN106488393B
CN106488393B CN201610878800.2A CN201610878800A CN106488393B CN 106488393 B CN106488393 B CN 106488393B CN 201610878800 A CN201610878800 A CN 201610878800A CN 106488393 B CN106488393 B CN 106488393B
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李冬辉
王艺琳
李林
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Tianjin University
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Abstract

The invention relates to a cluster head election model of a clustered wireless sensor network based on an evolutionary game trust mechanism, which comprises three system models, namely a wireless sensor network model, a JDL (Joint Director of laboratories) model and an evolutionary game model. According to the cluster head election model based on the evolutionary game trust mechanism, the dynamic characteristic and the trust timeliness of network communication are fully considered by the model through the improved JDL model and the evolutionary game algorithm, the optimal cluster head is elected while the trust factors such as communication, energy and data are considered, the calculation overhead is optimized, and the energy of the nodes is further saved.

Description

Cluster head election system of clustering wireless sensor network based on evolutionary game mechanism
Technical Field
The invention belongs to the field of wireless sensor networks, relates to mathematical modeling, and particularly relates to a cluster head election model of a clustering wireless sensor network based on an evolutionary game mechanism.
Background
Because the resources such as the computing power, the power supply energy, the communication capability and the like of the sensor nodes in the wireless sensor network are limited, and the wireless sensor network has the characteristics of large network scale, self-organization and the like, the effective utilization of the energy of the network and the enhancement of the safety of the network are very challenges. Due to the vulnerability of the nodes and the variability of the network topological structure, cluster head election is continuously carried out, and when the nodes with low performance and low reliability are cluster heads, the service quality of the network is influenced. The reliability of the cluster head becomes a key for determining whether the network can normally operate, so that designing a cluster head election mechanism with high reliability to reduce or avoid the occurrence of the situation becomes a core problem affecting the reliability of the whole network system.
The wireless sensor network not only has external attack, but also has internal attack with greater harm. The traditional key system security mechanism is mainly used for resisting external attacks, and cannot solve internal attacks generated by malicious nodes, selfish nodes and low-competitiveness nodes, so that how to identify various malicious nodes in a network is particularly important. The trust mechanism is thus introduced into the security issues of clustered wireless sensor networks. Due to the vulnerability of the nodes and the variability of the network topology structure, the cluster head election is in dynamic change, and is also influenced by a plurality of trust factors such as energy, communication, data and the like in the election process, so a cluster head election mechanism with high reliability becomes a core problem influencing the safe operation of the network.
At present, many researchers have conducted intensive research on a cluster head election algorithm considering trust factors in a wireless sensor network. A trust energy balance method for selecting a cluster head in a wireless sensor network, such as Weilim Guo, researches [ J ] network, 2012 and 7(10), proposes a cluster head election model based on energy and trust balance, and compares the cluster head election model based on energy and trust with a cluster head election model based on trust, which singly considers the factors of communication, data and the like. Wangwelon et al. a wireless sensor network cluster head election algorithm [ J ] based on a trust mechanism computer application, 2012,32 (10): 2696-. Marin autumn and the like, a wireless sensor network cluster head selection research [ J ] based on trust and residual energy wireless networks and sensors 2015,25:147- & lt164 & gt proposes a cluster head election algorithm based on trust and residual energy, wherein a cloud evaluation model is introduced into the algorithm, a trust value and residual energy are evaluated in combination with calculation of historical energy consumption to further select cluster head nodes, and the algorithm still has the problem of data omission consistency. The distributed cluster head election optimization algorithm based on the trust mechanism is provided, wherein the algorithm considers two factors of the trust degree of the node and the residual energy of the node, and the problem of ignoring the factors of network communication and data still exists. The method comprises the steps of Zhangxu, Qinzhi, giving consideration to a multi-factor cluster head selection algorithm [ J ]. Chengdu information engineering college statement in a wireless sensor network, 2015,4,30(2): 160-.
Disclosure of Invention
The invention aims to overcome the defects of the research of the malicious program propagation problem in the current clustered wireless sensor network, and provides a cluster head election model of the clustered wireless sensor network based on an evolutionary game mechanism.
The technical scheme adopted by the invention is as follows:
a cluster head election model of a clustering wireless sensor network based on an evolutionary game mechanism is composed of three system models, namely a wireless sensor network model, a JDL (Joint Director of laboratories) model and an evolutionary game model. The wireless sensor network model based on clustering comprises three types of nodes: the sensor node is responsible for sensing acquired data and transmitting the data to the cluster head node for data fusion; the cluster head nodes are generated through competition, are acted by nodes with relatively high trust values, and are responsible for fusing and directly transmitting information data received in the jurisdiction area of the cluster head nodes to the base station; the base station is the strongest node in the network and is responsible for controlling the network and collecting data and managing the trust value of the cluster head node
The JDL model is a database management system including information preprocessing, level 1 processing, i.e., target location/identity estimation, level 2 processing, i.e., situational assessment, level 3 processing, i.e., threat estimation, level 4 processing, i.e., process optimization.
The evolving gaming model has the following three communication behaviors:
1) cooperative behavior: normal node communication behavior.
2) Selfish behavior: and the node refuses the actions of forwarding, relaying and the like for other nodes due to energy limitation.
3) And (3) malicious behaviors: the finger node is attacked by adversaries and falls into a malicious node.
Moreover, the calculation of the cluster head election model of the clustering wireless sensor network based on the evolutionary game trust mechanism comprises the following steps: communication trust degree calculation, energy trust degree calculation, data factor calculation, comprehensive factor calculation and evolutionary game cluster head election calculation.
Moreover, the communication trust calculation is described as:
in the wireless sensor network, if adjacent nodes N in a clusteriAnd NjAnd performing communication, and representing the communication result between the two items of events by using the two items of events. s represents the number of times its communication succeeds; f represents the number of communication failures;
Figure GDA0002129376440000021
represents NiAnd NjDirect communication trust of the communicating. Assuming that nodes successfully communicate with a probability ρ, the Beta trust model is employed herein[34]And carrying out communication trust evaluation.
The mathematical form of the probability density distribution function for the Beta (α) distribution is:
Figure GDA0002129376440000022
wherein, phi is more than or equal to 0 and less than or equal to 1, phi is the probability of occurrence of an event, α is more than 0, β is more than 0, when the prior probability is Beta (α) distribution, the posterior probability distribution is Beta (α + s, β + f), and if the prior distribution of Beta (α) is uniform distribution, the prior distribution can be obtained according to the probability formula
Figure GDA0002129376440000023
Is an unbiased estimate of phi. Then the adjacent node NiAnd NjThe direct communication trust level of (1) is:
Figure GDA0002129376440000024
according to the network dynamic characteristics, the calculation of the direct communication trust is not accurate, so the indirect communication trust is introduced. Computing node NiIn NjTrust onDegree, need to pass through NjNeighbor node N ofmIs converted into a node NjOf the mobile terminal.
Considering that a recommended node may be a malicious node, a confidence coefficient of the recommended node is introduced, which is proportional to the direct confidence probability of its neighboring nodes, namely:
Figure GDA0002129376440000025
wherein k is the number of neighbor nodes.
Node NiIn NjThe indirect communication trust level is as follows:
Figure GDA0002129376440000031
the direct communication trust degree and the indirect communication trust degree are integrated to obtain a node NiAnd NjThe confidence level of communication is as follows:
Figure GDA0002129376440000032
wherein θ is
Figure GDA0002129376440000033
The weight taken up in the communication trust value. Also, θ can be varied by adjusting
Figure GDA0002129376440000034
And
Figure GDA0002129376440000035
the ratio of (a) to (b).
Moreover, the energy confidence calculation is described as:
4. the method for measuring the energy trust degree of the nodes is adopted to divide the energy of the nodes into a plurality of grades, wherein the higher the grade is, the more the energy of the nodes is, namely
energy_rank＝{1,2,3,4,5} (6)
Wherein, 1 represents that the battery energy is consumed; 2, the energy is weak, and only data information can be acquired or data can be received and transmitted; 3, energy is midle, and basic communication can be maintained; 4, strong, enabling relatively sufficient data communication and routing; and 5 indicates that the energy is full.
Definition 1
Figure GDA0002129376440000036
Representing a node NiTo NjThe energy confidence value of (a) is,
Figure GDA0002129376440000037
definition 2, setting sigma as a set energy threshold, and if the energy of a node is lower than sigma, indicating that the energy trust value of the node is level 1.
Definitions 3 hypothetical node NjCurrent energy of is EjInitial energy of E0。
If node energy class
Figure GDA0002129376440000038
The energy trust value of the node is calculated as
Figure GDA0002129376440000039
Residual energy E of noderIf node energy level
Figure GDA00021293764400000310
The remaining energy confidence value of the node is calculated as
Figure GDA00021293764400000311
Node energy trust value
Figure GDA00021293764400000312
Is composed of
Figure GDA00021293764400000313
Moreover, the data factor calculation is described as:
the trust value of the set data is determined by the trust value of the data size and the trust value of the data consistency, and the set node NiAnd NjCommunication is carried out, the acquisition value of data transmission is D, and the threshold value of data transmission is DTIts data trust value
Figure GDA00021293764400000314
Is composed of
Figure GDA0002129376440000041
Node NjData size trust value of
Figure GDA0002129376440000042
Is through node NjThe average of the trust values of the data sent to its neighbor nodes,
Figure GDA0002129376440000043
is composed of
Figure GDA0002129376440000044
Where Q is the set of other recommended nodes, Q ═ Nm|NiNeighbor node of (k), k is node NjThe number of neighbor nodes.
Node NjThe collected data consistency trust value is
Figure GDA0002129376440000045
Wherein, CjIs node NjNumber of times of data collection consistency, ICjIs the number of inconsistent data acquisitions.
Thus, node NjA data trust value of
Figure GDA0002129376440000046
Wherein mu is the weight occupied by the data size trust value, and v is the weight occupied by the data consistency.
Moreover, the calculation of the synthesis factor is described as:
the trust comprehensive factor can be obtained by integrating the calculation of the communication trust degree, the calculation of the energy trust degree and the calculation of the data factor
Figure GDA0002129376440000047
Wherein a, b and c are weighting factors, and a + b + c is 1, and the settlement trust integration factor is selected according to the importance degree of each factor. Setting the minimum trust composite factor critical value W of the systemTComparing the obtained trust composite factor with the minimum trust composite factor if the energy of the node
Figure GDA0002129376440000048
Or trust the composite factor at the threshold WTAnd then, the network is isolated by being judged as a malicious node or a dead node.
Moreover, the calculation of the evolutionary game cluster head election is described as follows:
a primary cluster head node is selected from the wireless sensor network and defined as a primary game G, wherein G is { P, S, U }, and G is a participant set, namely all sensor nodes meeting requirements; s, selecting cooperative or uncooperative strategy combination for the sensor nodes; u is the income the participant gets in a game and is represented by a payment matrix. The following is a concrete analysis of the profit conditions of different strategies for node selection participating in cluster head election, as follows:
the node and the opposite node both select a cooperation strategy:
in this case, all participant nodes participate in the selection of the cluster head node, and the trust gain is cTAnd the node participates in the cluster head to select and forward data to obtain the income ccAnd also consumes self energy cost because of participating in cluster head electionIs ccheIntroducing excitation uT for promoting node cooperationcAnd c is the total profit of the rational nodes participating in cluster head selectionT+ycc-2(x-y)cche(ii) a The total income of the selfish node participating in the cluster head selection is cT+(x-y)cc-2ycche+υTc. The total revenue of participation in cluster head selection is thus cT+xcc-2xcche+υTc；
There is a choice of non-operational policies in the nodes:
if the selfish node does not participate in the cluster head election among the participants of the election cluster head node, the participating node will cause energy loss l, and the own energy consumption cost (x-y) ccheThen the profit of the cluster head node selected to participate is cT-(x-y)cche-l; therefore, the yield of the selfish node not participating in the cluster head node selection is cc(x-y)-ycche. If an excitation is introducedcThe selfish node participates in the cluster head election, the rational node forwards data for normal work due to damage and the like, and the benefit of the selfish node participating in the cluster head election is cT+υTc-yccheL, while the rational node has a profit of ccy-(x-y)cche. In this case, the total benefit of the nodes participating in cluster head selection is cT+υTc-xcche-l; the total node income without participating in cluster head selection is xcc-xcche；
If all participants do not participate in cluster head election:
the cluster head node will not be elected, the network will probably communicate as a planar network, and the benefit can be noted as 0, where each letter or symbol means:
Tcdegree of trust
cTConfidence gain
ccheCost of transmitting self data or forwarding the other node data when participating in cluster head selection
ccRevenue generated by cooperation of nodes of opposite side
loss due to non-cooperation of nodes
x satisfies the number of nodes participating in cluster head election by the threshold, and x belongs to N
y x, y is more than or equal to 0 and less than x, and y belongs to N
Upsilon is a regulatory factor
The specific calculation steps are as follows:
let u (t) be (u)1(t),u2(t)) represents a hybrid strategy for participating in cluster head elections, where u1(t) selecting a collaboration policy s for the participants1Ratio of nodes of u2(t) selecting a do-not-work strategy s for the participant2An example of a node ratio of1+u 21. U is as follows1And (t) is abbreviated as u.
The expected benefit of selecting the cooperative strategy node at the moment t is
P(s1,u)＝u(cT+xcc-2xcche+υTc)+(1-u)[cT+υTc-xcche-l](15)
The expected benefit of selecting the non-operation strategy node at the moment t is
P(s2,u)＝u(xcc-xcche) (16)
The evaluation yields of all participants who can be elected by cluster head are obtained from (15) and (16)
Figure GDA0002129376440000051
Thus, cluster head election evolutionary dynamics replication equation is
Figure GDA0002129376440000052
Let F (u) be 0, the replication equation has a maximum of 3 stable states
Figure GDA0002129376440000053
Figure GDA0002129376440000054
Figure GDA0002129376440000061
Wherein the steady state represented by formula (21) may be the same as the steady state represented by formula (19) or (20). The nature of the evolving stabilization strategy represents a stable state, which is consistent with the stability theorem requirements of differential equations and must be robust to small perturbations. Herein, if u*In a steady state, the condition F' (u) must be satisfied*)＜0。
Theorem 1 if cT+υTc-xcche＞0，cT+υTc-xcche-l＜0，2cT+2υTc-2xcche-l > 0, then
Figure GDA0002129376440000062
And
Figure GDA0002129376440000063
are evolution stable strategies of the wireless sensor network evolution game, and
Figure GDA0002129376440000064
the probability of time (node selection does not participate in the cluster head node election strategy) is less than
Figure GDA0002129376440000065
Time (probability of node selection participating in cluster head election).
The two sides of the formula (18) are proved to be derived
F′(u)＝-3lu2+2[xcche+2l-cT-υTc]u+cT+υTc-xcche-l (22)
Let u be 0 and 1, respectively, to obtain
F′(0)＝cT+υTc-xcche-l＜0 (23)
F′(1)＝xcche-cT-υTc＜0 (24)
From 2cT+2υTc-2xcche-l > 0 to give
cT+υTc-xcche＞-cT-υTc+xcche+l (25)
So that there are
Figure GDA0002129376440000066
As can be seen from the formulae (23) and (24),
Figure GDA0002129376440000067
and
Figure GDA0002129376440000068
the evolution stability strategy of the wireless sensor network evolution game is adopted. As can be seen from equation (26), the probability that the node satisfying the cluster head election condition selects the non-cooperative policy is smaller than the probability that the cooperative policy is selected. Theorem 1 indicates that when a rational node selects a cooperation strategy, c is usedT+xcc-2xcche+υT-xcc+xcche＝cT+υT-xccheIf the value is more than 0, the profit of selecting the cooperative probability by the selfish node is more than the profit of selecting the non-cooperative probability; when rational nodes choose uncooperative strategy, c is usedT+υTc-xccheL is less than 0, and the profit of the selfish node for selecting the probability of the non-cooperative strategy is greater than the profit for selecting the cooperative strategy. Therefore, the temperature of the molten metal is controlled,
Figure GDA0002129376440000069
and
Figure GDA00021293764400000610
the evolution stability strategies of the wireless sensor network evolution game show that cooperation strategies and non-cooperation strategies are possibly selected by nodes meeting the cluster head election conditions.
Theorem 2 if cT+υTc-xcche＞0，cT+υTc-xcche-l＜0，2cT+2υTc-2xccheL < 0, then
Figure GDA00021293764400000611
And
Figure GDA00021293764400000612
are evolution stable strategies of the wireless sensor network evolution game, and
Figure GDA00021293764400000613
the probability of time (node selection does not participate in the cluster head node election strategy) is greater than
Figure GDA00021293764400000614
Time (probability of node selection participating in cluster head election).
Calculation of proof
F′(0)＝cT+υTc-xcche-l＜0 (27)
F′(1)＝xcche-cT-υTc＜0 (28)
Figure GDA00021293764400000615
As can be seen from the formulae (27) and (28),
Figure GDA0002129376440000071
and
Figure GDA0002129376440000072
the evolution stability strategy of the wireless sensor network evolution game is adopted. As can be seen from equation (29), the probability that the node satisfying the cluster head election selects the non-cooperative policy is greater than the probability that the cooperative policy is selected.
Theorem 3 if cT+υTc-ccheIf less than 0, then
Figure GDA0002129376440000073
The evolution stabilization strategy of the wireless sensor network evolution game is disclosed.
The proof being derived by calculation
F′(0)＝cT+υTc-xcche-l＜0 (30)
F′(1)＝xcche-cT-υTc＞0 (31)
As can be seen from the formulas (30) and (31),
Figure GDA0002129376440000074
the evolution stabilization strategy of the wireless sensor network evolution game is disclosed.
Theorem 3 shows that whether a rational node selects a cooperation strategy or an uncooperative strategy, the benefit of selecting the cooperation strategy by the selfish node is always less than the benefit of selecting the uncooperative strategy. The node ratio of the final selection cooperation strategy is stabilized at
Figure GDA0002129376440000075
And (4) selecting the non-operation strategy.
Theorem 4 if cT+υTc-xcche-l > 0, then
Figure GDA0002129376440000076
The evolution stabilization strategy of the wireless sensor network evolution game is disclosed.
Calculation of proof
F′(0)＝cT+υTc-xcche-l＞0 (32)
F′(1)＝xcche-cT-υTc＜-cT-υTc+xcche+l＜0 (33)
As can be seen from the formulae (32) and (33),
Figure GDA0002129376440000077
the evolution stabilization strategy of the wireless sensor network evolution game is disclosed.
Theorem 4 shows that whether a rational node selects a cooperation strategy or an uncooperative strategy, the benefit of selecting the cooperation strategy by the selfish node is always greater than the benefit of selecting the uncooperative strategy. The node ratio of the final selection cooperation strategy is stabilized at
Figure GDA0002129376440000078
At this point, a collaboration policy is selected.
The condition satisfied by theorems 2 and 3 is that the wireless sensor network must be avoided when selecting a cluster head, because the condition indicates that the probability of selecting a non-cooperative strategy by a node is greater than the probability of selecting a cooperative strategy, and finally the wireless sensor network is in an unstable state.
The invention has the advantages and positive effects that:
according to the cluster head election model based on the evolutionary game trust mechanism, the dynamic characteristic and the trust timeliness of network communication are fully considered by the model through the improved JDL model and the evolutionary game algorithm, the optimal cluster head is elected while the trust factors such as communication, energy and data are considered, the calculation overhead is optimized, and the energy of the nodes is further saved.
The model for electing the cluster head based on the evolutionary game trust mechanism provided by the invention considers the communication, energy, data and other factors to calculate the node trust degree, fully considers the network communication and energy dynamics by utilizing the evolutionary game, realizes the purpose of electing the optimal cluster head node, and gives the theorem of achieving an evolutionary stability strategy under different parameter conditions. Finally, the reliability and the safety of the network are enhanced through simulation verification of the model, and the life cycle of the network is prolonged.
Drawings
FIG. 1 is a top level JDL functional model to which the present invention relates;
FIG. 2 is a wireless sensor network cluster head election model based on evolutionary game trust values in accordance with the present invention;
FIG. 3 is a graph of simulated rational node trust composite factor changes to which the present invention relates;
FIG. 4 illustrates a combination of factors for trust in emulating malicious nodes in accordance with the present invention;
FIG. 5 is an evolution curve of the simulation theorem 1 node involved in cluster head selection according to the present invention;
FIG. 6 is an evolution curve of the simulation theorem 2 node participating in the cluster head selection strategy according to the present invention;
FIG. 7 is an evolution curve of the simulation theorem 3 node participating in the cluster head selection strategy according to the present invention;
FIG. 8 is an evolution curve of a simulation theorem 4 node participating in a cluster head node according to the present invention;
FIG. 9 is a cluster head selection evolution curve under different initial values of the simulation excitation mechanism according to the present invention;
FIG. 10 is a cluster head selection evolution curve under the same initial value of the simulation excitation mechanism related to the present invention;
FIG. 11 is a comparison of life cycles of a simulated network in accordance with the present invention.
Detailed Description
The present invention is further illustrated by the following specific examples, which are intended to be illustrative, not limiting and are not intended to limit the scope of the invention.
A cluster head election model of a clustering wireless sensor network based on an evolutionary game mechanism comprises three system models, namely a wireless sensor network model, a JDL (Joint Director of laboratories) model and an evolutionary game model, wherein,
wireless sensor network model
The invention researches a wireless sensor network model based on clustering, and the model comprises three types of nodes: base station, cluster head and sensor node. The sensor node is responsible for sensing and acquiring data and transmitting the data to the cluster head node for data fusion; the cluster head nodes are generated through competition, are acted by nodes with relatively high trust values and are responsible for directly transmitting the information data received in the jurisdiction area to the base station in a fusion manner[16](ii) a The base station is the strongest node in the network and is responsible for controlling the network and collecting data and managing the trust value of the cluster head node. In this context, it is assumed that the base station is absolutely trusted.
In the wireless sensor network, sensor nodes are assumed to be isomorphic, have the same energy, and are randomly distributed and fixed in a certain area, and malicious nodes exist in the network.
JDL (Joint Director of laboratories) model
The JDL model is a model proposed by the information fusion expert group specifically established by the C3 technical committee under the laboratory council of the united states department of defense, as shown in fig. 1. The dashed frame part in the figure is an information fusion part and mainly comprises the functional components of 0-level information preprocessing, 1-level processing, namely target position/identity estimation, 2-level processing, namely situation assessment, 3-level processing, namely threat estimation, 4-level processing, namely process optimization, a database management system and the like. The functional level of the functional model is classified for better explaining the functional composition of the information fusion system, and does not mean the fusion processing sequence of the actual system, and the fusion processing sequence in the actual system must be divided according to the requirements of the actual system.
Evolving game model
In recent years, there have been many scholars studying wireless sensor network problems using the game theory approach. In recent years, the game theory is adopted to solve the research of the security problem of the wireless sensor network. The evolutionary game is a more extensive and effective tool compared with the traditional game theory because the evolutionary game analyzes and researches the behaviors of participants on the basis of the development of psychology and limited proposition. In particular, in the research of node trust cooperation, the evolutionary game method is gradually widely adopted.
The evolutionary game theory has two basic solution concepts, namely an evolutionary stability strategy from a static angle and a replicator dynamic corresponding to a dynamic angle; namely, one is a "mutation mechanism" that generates diversity and one is a "selection mechanism" for a specific species.
In this document, for the evolutionary game model, it is first assumed that a node has the following three communication behaviors on a rational basis:
1) cooperative behavior: normal node communication behavior.
2) Selfish behavior: and the node refuses the actions of forwarding, relaying and the like for other nodes due to energy limitation.
3) And (3) malicious behaviors: the finger node is attacked by adversaries and falls into a malicious node.
The behavior of the sensor nodes participating in the election of the cluster head nodes is regarded as strategy selection of the game, and the process of the election of the cluster head can be regarded as the process of the evolutionary game based on the timeliness of the cluster head nodes. The sensor nodes meeting the threshold values of comprehensive factors such as communication, energy, data and the like can be used as game participants, so that malicious nodes are eliminated, the time for selecting cluster heads is shortened, and the network energy is effectively utilized.
Description of algorithms
Communication trust calculation
In the wireless sensor network, due to the existence of malicious nodes and selfish nodes, actions such as packet loss, data packet tampering and the like can be generated in the communication process so as to achieve the purpose of saving self energy. Monitoring in the communication process is an evaluation basis for judging whether the nodes are malicious nodes and selfish nodes.
If the adjacent node N in the clusteriAnd NjAnd performing communication, and representing the communication result between the two items of events by using the two items of events. s represents the number of times its communication succeeds; f represents the number of communication failures;
Figure GDA0002129376440000091
represents NiAnd NjDirect communication trust of the communicating. Assuming that the nodes successfully communicate with the probability ρ, the Beta trust model is used herein for the evaluation of the communication trust.
The mathematical form of the probability density distribution function for the Beta (α) distribution is:
Figure GDA0002129376440000092
wherein, phi is more than or equal to 0 and less than or equal to 1, phi is the probability of occurrence of an event, α is more than 0, β is more than 0, when the prior probability is Beta (α) distribution, the posterior probability distribution is Beta (α + s, β + f), and if the prior distribution of Beta (α) is uniform distribution, the prior distribution can be obtained according to the probability formula
Figure GDA0002129376440000093
Is an unbiased estimate of phi. Then the adjacent node NiAnd NjThe direct communication trust level of (1) is:
Figure GDA0002129376440000094
according to the network dynamic characteristics, the calculation of the direct communication trust is not accurate, so the indirect communication trust is introduced. Computing node NiIn NjThe confidence level of (C) is required to pass through NjNeighbor node N ofmIs converted into a node NjOf the mobile terminal.
Considering that a recommended node may be a malicious node, a confidence coefficient of the recommended node is introduced, which is proportional to the direct confidence probability of its neighboring nodes, namely:
Figure GDA0002129376440000095
wherein k is the number of neighbor nodes.
Node NiIn NjThe indirect communication trust level is as follows:
Figure GDA0002129376440000096
the direct communication trust degree and the indirect communication trust degree are integrated to obtain a node NiAnd NjThe confidence level of communication is as follows:
Figure GDA0002129376440000101
wherein θ is
Figure GDA0002129376440000102
The weight taken up in the communication trust value. Also, θ can be varied by adjusting
Figure GDA0002129376440000103
And
Figure GDA0002129376440000104
the ratio of (a) to (b).
Energy confidence calculation
The energy of the battery of the sensor node is limited, and the running time of the network is limited, so that the energy problem is critical to the running of the wireless sensor network. In the case of clustered wireless sensor networks, the energy consumption of the nodes must be non-uniform. The literature is adopted herein[24]The method for measuring the energy trust degree of the node divides the energy of the node into a plurality of grades, wherein the higher the grade is, the more the energy of the node is, namely
energy_rank＝{1,2,3,4,5} (6)
Wherein, 1 represents that the battery energy is consumed; 2, the energy is weak, and only data information can be acquired or data can be received and transmitted; 3, energy is midle, and basic communication can be maintained; 4, strong, enabling relatively sufficient data communication and routing; and 5 indicates that the energy is full.
Definition 1
Figure GDA0002129376440000105
Representing a node NiTo NjThe energy confidence value of (a) is,
Figure GDA0002129376440000106
definition 2, setting sigma as a set energy threshold, and if the energy of a node is lower than sigma, indicating that the energy trust value of the node is level 1.
Definitions 3 hypothetical node NjCurrent energy of is EjInitial energy of E0。
If node energy class
Figure GDA0002129376440000107
The energy trust value of the node is calculated as
Figure GDA0002129376440000108
Residual energy E of noderIf node energy level
Figure GDA0002129376440000109
The remaining energy confidence value of the node is calculated as
Figure GDA00021293764400001010
Node energy trust value
Figure GDA00021293764400001011
Is composed of
Figure GDA00021293764400001012
Data factor calculation
After the sensor node collects data, the collected data are transmitted to the cluster head node and finally transmitted to the base station. However, the energy of the sensor nodes is limited, so that the data needs to be fused in the transmission process. In the data fusion process, phenomena such as tampering and packet loss may occur when a malicious node attacks the network, and in order to determine the accuracy of received data, the trust value of the node needs to be evaluated to determine whether the node is trusted. Setting the trust value of data is determined by the data size trust value and the data consistency trust value[15]。
Let node NiAnd NjCommunication is carried out with a threshold value d for data transmissionTIts data trust value
Figure GDA00021293764400001013
Is composed of
Figure GDA0002129376440000111
Node NjData size trust value of
Figure GDA0002129376440000112
Is through node NjThe average of the trust values of the data sent to its neighbor nodes,
Figure GDA0002129376440000113
is composed of
Figure GDA0002129376440000114
Where Q is the set of other recommended nodes, Q ═ Nm|NiNeighbor node of (k), k is node NjThe number of neighbor nodes.
Node NjThe collected data consistency trust value is
Figure GDA0002129376440000115
Wherein, CjIs node NjNumber of times of data collection consistency, ICjIs the number of inconsistent data acquisitions.
Thus, node NjA data trust value of
Figure GDA0002129376440000116
Wherein mu is the weight occupied by the data size trust value, and v is the weight occupied by the data consistency.
Synthesis factor calculation
By calculating trust values of communication, energy, data and the like, comprehensive factors can be obtained through integration
Figure GDA0002129376440000117
Wherein a, b and c are weighting factors, and a + b + c is 1, and the settlement integration factor is selected according to the importance degree of each factor. Setting the minimum comprehensive factor critical value W of the systemTComparing the obtained integration factor with the minimum integration factor if the energy of the node
Figure GDA0002129376440000118
Or the integration factor is at the threshold value WTAnd if the node is judged to be a malicious node or a dead node, the node is isolated out of the networkLinking the collaterals.
Evolutionary game cluster head election computation
According to the description of the cluster head election algorithm of the trust model wireless sensor network based on the evolutionary game, we define as follows:
defining 4, a primary cluster head node in a wireless sensor network is selected and defined as a primary game G, wherein G is (P, S, U), and G is a participant set, namely all sensor nodes meeting requirements; s, selecting cooperative or uncooperative strategy combination for the sensor nodes; u is the income the participant gets in a game and is represented by a payment matrix.
According to the definition, a cluster head election model of the sensor node considering trust factors such as communication, energy and data is mapped to a process of determining a strategy set under the condition that each participant has own utility. The model proposed herein follows the classic JDL functional model as a bus-type structure, fully considering the interaction and penetration between the elements, as shown in fig. 2.
The process of cluster head election may be embodied as an iterative process with feedback of various factors, as shown in fig. 2. In the model, under the condition that the existence of a malicious node and a selfish node is considered, trust factors such as communication, data, energy and the like are fused together, the factors are integrated with information to form a decision by using an evolutionary game method, an optimal cluster head is elected, a final result is fed back to each link to form ordered flow of information, and the cluster head can be updated in real time according to the dynamic characteristics of a network.
When the cluster head nodes are participated in interaction, the cooperation strategy is selected to mean that the nodes are not selfish nodes, and the non-cooperation strategy is selected to mean that the cluster head nodes cannot be selected. For ease of description, a legend such as table 1 is introduced.
TABLE 1 symbol table
Figure GDA0002129376440000121
The following is a concrete analysis of the profit conditions of different strategies for node selection participating in cluster head election, as follows:
1) the node and the other node both select cooperation strategy
In this case, all participant nodes participate in the selection of the cluster head node, and the trust gain is cTAnd the node participates in the cluster head to select and forward data to obtain the income ccAnd the cost of energy consumed by participating in the election of the cluster head is ccheIntroducing excitation uT for promoting node cooperationcAnd c is the total profit of the rational nodes participating in cluster head selectionT+ycc-2(x-y)cche(ii) a The total income of the selfish node participating in the cluster head selection is cT+(x-y)cc-2ycche+υTc. The total revenue of participation in cluster head selection is thus cT+xcc-2xcche+υTc；
2) Selective uncooperative strategy in nodes
If the selfish node does not participate in the cluster head election among the participants of the election cluster head node, the participating node will cause energy loss l, and the own energy consumption cost (x-y) ccheThen the profit of the cluster head node selected to participate is cT-(x-y)cche-l; therefore, the yield of the selfish node not participating in the cluster head node selection is cc(x-y)-ycche. If an excitation is introducedcThe selfish node participates in the cluster head election, the rational node forwards data for normal work due to damage and the like, and the benefit of the selfish node participating in the cluster head election is cT+υTc-yccheL, while the rational node has a profit of ccy-(x-y)cche. In this case, the total benefit of the nodes participating in cluster head selection is cT+υTc-xcche-l; the total node income without participating in cluster head selection is xcc-xcche；
3) If all participants do not participate in cluster head election.
In such a worst case, the cluster head node will not be elected, and the network may communicate as a planar network, where the benefit may be noted as 0.
The paymatrix for the game available is shown in table 2, according to the above description.
TABLE 2 Payment matrix for a game
Figure GDA0002129376440000122
Figure GDA0002129376440000131
Let u (t) be (u)1(t),u2(t)) represents a hybrid strategy for participating in cluster head elections, where u1(t) selecting a collaboration policy s for the participants1Ratio of nodes of u2(t) selecting a do-not-work strategy s for the participant2An example of a node ratio of1+u 21. U is as follows1And (t) is abbreviated as u.
The expected benefit of selecting the cooperative strategy node at the moment t is
P(s1,u)＝u(cT+xcc-2xcche+υTc)+(1-u)[cT+υTc-xcche-l](15)
The expected benefit of selecting the non-operation strategy node at the moment t is
P(s2,u)＝u(xcc-xcche) (16)
The evaluation yields of all participants who can be elected by cluster head are obtained from (15) and (16)
Figure GDA0002129376440000132
Thus, cluster head election evolutionary dynamics replication equation is
Figure GDA0002129376440000133
Let F (u) be 0, the replication equation has a maximum of 3 stable states
Figure GDA0002129376440000134
Figure GDA0002129376440000135
Figure GDA0002129376440000136
Wherein the steady state represented by formula (21) may be the same as the steady state represented by formula (19) or (20). The nature of the evolving stabilization strategy represents a stable state, which is consistent with the stability theorem requirements of differential equations and must be robust to small perturbations. Herein, if u*In a steady state, the condition F' (u) must be satisfied*)＜0。
Theorem 1 if cT+υTc-xcche＞0，cT+υTc-xcche-l＜0，2cT+2υTc-2xcche-l > 0, then
Figure GDA0002129376440000137
And
Figure GDA0002129376440000138
are evolution stable strategies of the wireless sensor network evolution game, and
Figure GDA0002129376440000139
the probability of time (node selection does not participate in the cluster head node election strategy) is less than
Figure GDA00021293764400001310
Time (probability of node selection participating in cluster head election).
The two sides of the formula (18) are proved to be derived
F′(u)＝-3lu2+2[xcche+2l-cT-υTc]u+cT+υTc-xcche-l (22)
Let u be 0 and 1, respectively, to obtain
F′(0)＝cT+υTc-xcche-l＜0 (23)
F′(1)＝xcche-cT-υTc＜0 (24)
From 2cT+2υTc-2xcche-l > 0 to give
cT+υTc-xcche＞-cT-υTc+xcche+l (25)
So that there are
Figure GDA00021293764400001311
As can be seen from the formulae (23) and (24),
Figure GDA0002129376440000141
and
Figure GDA0002129376440000142
the evolution stability strategy of the wireless sensor network evolution game is adopted. As can be seen from equation (26), the probability that the node satisfying the cluster head election condition selects the non-cooperative policy is smaller than the probability that the cooperative policy is selected. Theorem 1 indicates that when a rational node selects a cooperation strategy, c is usedT+xcc-2xcche+υT-xcc+xcche＝cT+υT-xccheIf the value is more than 0, the profit of selecting the cooperative probability by the selfish node is more than the profit of selecting the non-cooperative probability; when rational nodes choose uncooperative strategy, c is usedT+υTc-xccheL is less than 0, and the profit of the selfish node for selecting the probability of the non-cooperative strategy is greater than the profit for selecting the cooperative strategy. Therefore, the temperature of the molten metal is controlled,
Figure GDA0002129376440000143
and
Figure GDA0002129376440000144
the evolution stability strategies of the wireless sensor network evolution game show that cooperation strategies and non-cooperation strategies are possibly selected by nodes meeting the cluster head election conditions.
Theorem 2 if cT+υTc-xcche＞0，cT+υTc-xcche-l＜0，2cT+2υTc-2xccheL < 0, then
Figure GDA0002129376440000145
And
Figure GDA0002129376440000146
are evolution stable strategies of the wireless sensor network evolution game, and
Figure GDA0002129376440000147
the probability of time (node selection does not participate in the cluster head node election strategy) is greater than
Figure GDA0002129376440000148
Time (probability of node selection participating in cluster head election).
Calculation of proof
F′(0)＝cT+υTc-xcche-l＜0 (27)
F′(1)＝xcche-cT-υTc＜0 (28)
Figure GDA0002129376440000149
As can be seen from the formulae (27) and (28),
Figure GDA00021293764400001410
and
Figure GDA00021293764400001411
the evolution stability strategy of the wireless sensor network evolution game is adopted. As can be seen from equation (29), the probability that the node satisfying the cluster head election selects the non-cooperative policy is greater than the probability that the cooperative policy is selected.
Theorem 3 if cT+υTc-ccheIf less than 0, then
Figure GDA00021293764400001412
The evolution stabilization strategy of the wireless sensor network evolution game is disclosed.
The proof being derived by calculation
F′(0)＝cT+υTc-xcche-l＜0 (30)
F′(1)＝xcche-cT-υTc＞0 (31)
As can be seen from the formulas (30) and (31),
Figure GDA00021293764400001413
the evolution stabilization strategy of the wireless sensor network evolution game is disclosed.
Theorem 3 shows that whether a rational node selects a cooperation strategy or an uncooperative strategy, the benefit of selecting the cooperation strategy by the selfish node is always less than the benefit of selecting the uncooperative strategy. The node ratio of the final selection cooperation strategy is stabilized at
Figure GDA00021293764400001414
And (4) selecting the non-operation strategy.
Theorem 4 if cT+υTc-xcche-l > 0, then
Figure GDA00021293764400001415
The evolution stabilization strategy of the wireless sensor network evolution game is disclosed.
Calculation of proof
F′(0)＝cT+υTc-xcche-l＞0 (32)
F′(1)＝xcche-cT-υTc＜-cT-υTc+xcche+l＜0 (33)
As can be seen from the formulae (32) and (33),
Figure GDA00021293764400001416
the evolution stabilization strategy of the wireless sensor network evolution game is disclosed.
Theorem 4 shows that whether a rational node selects a cooperation strategy or an uncooperative strategy, the benefit of selecting the cooperation strategy by the selfish node is always greater than the benefit of selecting the uncooperative strategy. The node ratio of the final selection cooperation strategy is stabilized at
Figure GDA0002129376440000151
At this point, a collaboration policy is selected.
The condition satisfied by theorems 2 and 3 is that the wireless sensor network must be avoided when selecting a cluster head, because the condition indicates that the probability of selecting a non-cooperative strategy by a node is greater than the probability of selecting a cooperative strategy, and finally the wireless sensor network is in an unstable state.
Simulation (Emulation)
MATLAB is adopted as a simulation platform in the experiment, and the network environment is set as follows: 100 nodes are randomly distributed in the range of 100m x 100m, and the base station is positioned in the center of a node distribution area. If 10% of malicious nodes exist in the network, other nodes are normal nodes, the probability of malicious behavior generation of the malicious nodes is 40%, the probability of selfish behavior generation of the common nodes is 5% due to the characteristics of the nodes, and the cluster heads account for 10% of the total number of the surviving nodes.
And selecting rational nodes in the network, wherein the trust combination factor is changed as shown in figure 3. Since the initial value is 0.5, the integrated factor of trust rises rapidly in the early stage. And then, the comprehensive factor is trusted to be in a slow descending trend due to energy consumption, and finally, the electric quantity is exhausted and is stabilized at about 0.7. The trust comprehensive factor of the malicious node changes as shown in fig. 4, the malicious node generates malicious behaviors, the trust comprehensive factor is rapidly reduced and is lower than the threshold value W in the 5 th round or the 5 th roundTThe network judges that it is dead.
As shown in fig. 5, when the initial value of the replication dynamic equation (18) is 0.332, that is, 33.2% of the wireless sensor network nodes select the uncooperative strategy, the nodes participating in the cluster head selection finally select the nodes participating in the cluster head selection in proportion stabilized at the same time through continuous trial and error and simulation through about 40 times of games and continuous adjustment of their own strategies
Figure GDA0002129376440000152
To (3).
As can be seen from theorem two in fig. 6, when the wireless sensor network node with the initial value of the replication dynamic equation (18) of 0.599, i.e., 59.9%, selects the no-cooperation strategy, through about 32 times of games, the no-cooperation strategy is adjustedThe proportion of the nodes which are finally selected to participate in the cluster head selection is stabilized in the own strategy
Figure GDA0002129376440000153
To (3).
As can be seen from theorem 3 in fig. 7, when the initial value of the replication dynamic equation (18) is 0.999, that is, 99.9% of the wireless sensor network nodes select the cooperation strategy, after about 21 times of games, by adjusting the strategy of the wireless sensor network nodes, the proportion of the nodes finally selected to participate in the cluster head selection is stabilized at the value
Figure GDA0002129376440000154
To (3).
As shown in fig. 8, when the initial value of the replication dynamic equation (18) is 0.001, that is, 0.1% of the wireless sensor network node selection cooperation strategy, through about 21 games, the proportion of the nodes finally selected to participate in the cluster head selection is stabilized at
Figure GDA0002129376440000155
To (3).
As shown in fig. 9, when α a is 3, the threshold value of the evolution of the wireless sensor network node cluster head selection is 0.665, and when α a is 4, the threshold value is 0.332, which indicates that when α a is increased from 3 to 4, even if the proportion of the uncooperative strategy for initial selection of the participating nodes is reduced from 66.5% to 33.2%, the proportion will eventually stabilize in the game as the game progresses
Figure GDA0002129376440000156
To (3).
As shown in fig. 10, when the initial values of the replication dynamic equation (18) are all set to 0.700, α a is 4, only 7 games are needed to achieve the result
Figure GDA0002129376440000157
And when α a is equal to 3, the game is played 26 times to reach the system evolution stable point.
The network life cycle of the model presented herein, with 90% node death defined as network death, is shown in fig. 11.
Although the embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that: various substitutions, changes and modifications are possible without departing from the spirit and scope of the invention and the appended claims, and therefore the scope of the invention is not limited to the embodiments disclosed.

Claims (1)

1. A cluster head election system of a clustering wireless sensor network based on an evolutionary game mechanism is characterized in that: the system consists of three system submodels, namely a wireless sensor network model, a JDL (JointDirector of laboratories) model and an evolutionary game model, wherein the wireless sensor network model based on clustering comprises three types of nodes: the sensor node is responsible for sensing acquired data and transmitting the data to the cluster head node for data fusion; the cluster head nodes are generated through competition, are acted by nodes with relatively high trust values, and are responsible for fusing and directly transmitting information data received in the jurisdiction area of the cluster head nodes to the base station; the base station is the strongest node in the network and is responsible for controlling the network, collecting data and managing the trust value of the cluster head node;
the JDL model comprises information preprocessing, level 1 processing, namely target position/identity estimation, level 2 processing, namely situation assessment, level 3 processing, namely threat estimation, level 4 processing, namely process optimization and a database management system;
the evolving gaming model has the following three communication behaviors:
cooperative behavior: communication behavior of normal nodes;
selfish behavior: the node refuses the actions of forwarding, relaying and the like for other nodes due to energy limitation;
and (3) malicious behaviors: the finger nodes are attacked by adversaries and fall into malicious nodes;
the method is characterized in that the sensor node performs cluster head election once and is called a primary game, and the calculation of the cluster head election model of the clustering wireless sensor network based on the evolutionary game trust mechanism comprises the following steps: calculating communication trust, calculating energy trust, calculating data factors, calculating comprehensive factors and calculating an evolutionary game cluster head election;
(1) the communication trust calculation is described as:
in the wireless sensor network, if adjacent nodes N in a clusterjAnd NjCarrying out communication, wherein a communication result between the two is represented by two events, and s represents the number of successful communication; f represents the number of communication failures;
Figure FDA0002311960440000011
represents NiAnd NjDirect communication trust of communication, neighbor node NiAnd NjThe direct communication trust level of (1) is:
Figure FDA0002311960440000012
according to the dynamic characteristics of the network, the calculation of the trust degree of direct communication is not accurate, so the trust degree of indirect communication is introduced, and the node N is calculatediIn NjThe confidence level of (C) is required to pass through NjNeighbor node N ofmIs converted into a node NjThe degree of trust in (2) is,
considering that a recommended node may be a malicious node, a confidence coefficient of the recommended node is introduced, which is proportional to the direct confidence probability of its neighboring nodes, namely:
Figure FDA0002311960440000013
wherein k is the number of neighbor nodes,
node NiIn NjThe indirect communication trust level is as follows:
Figure FDA0002311960440000014
the direct communication trust degree and the indirect communication trust degree are integrated to obtain a node NiAnd NjThe confidence level of communication is as follows:
Figure FDA0002311960440000021
wherein θ is
Figure FDA0002311960440000022
The weight occupied in the communication trust value can be changed by adjusting theta
Figure FDA0002311960440000023
And
Figure FDA0002311960440000024
the ratio of (A) to (B);
(2) the energy confidence calculation is described as:
definition 1
Figure FDA0002311960440000025
Representing a node NiTo NjThe energy confidence value of (a) is,
Figure FDA0002311960440000026
definition 2, setting sigma as a set energy threshold, if the energy of a node is lower than sigma, indicating that the energy trust value of the node is 1 level,
definitions 3 hypothetical node NjCurrent energy of is EjInitial energy of E0，
If node energy class
Figure FDA0002311960440000027
The energy trust value of the node is calculated as
Figure FDA0002311960440000028
Residual energy E of noderIf node energy level
Figure FDA0002311960440000029
Then the remaining energy trust value of the nodeIs counted as
Figure FDA00023119604400000210
Node energy trust value
Figure FDA00023119604400000211
Is composed of
Figure FDA00023119604400000212
(3) The data factor calculation is described as:
the trust value of the set data is determined by the trust value of the data size and the trust value of the data consistency, and the set node NiAnd NjCommunication is carried out, the acquisition value of data transmission is D, and the threshold value of data transmission is DTIts data trust value
Figure FDA00023119604400000213
Is composed of
Figure FDA00023119604400000214
Node NjData size trust value of
Figure FDA00023119604400000215
Is through node NjThe average of the trust values of the data sent to its neighbor nodes,
Figure FDA00023119604400000216
is composed of
Figure FDA00023119604400000217
Where Q is the set of other recommended nodes, Q ═ Nm|NiNeighbor node of (k), k is node NjThe number of the neighbor nodes of (1),
node NjThe collected data consistency trust value is
Figure FDA0002311960440000031
Wherein, CjIs node NjNumber of times of data collection consistency, ICjIs the number of times the data collection is inconsistent,
thus, node NjA data trust value of
Figure FDA0002311960440000032
Wherein mu is the weight occupied by the data size trust value, and v is the weight occupied by the data consistency;
(4) the calculation of the integration factor is described as:
the trust comprehensive factor can be obtained by integrating the calculation of the communication trust degree, the calculation of the energy trust degree and the calculation of the data factor
Figure FDA0002311960440000033
Wherein a, b and c are weighting factors, a + b + c is 1, the trust comprehensive factor is selected according to the importance degree of each factor when the trust comprehensive factor is settled, and the minimum trust comprehensive factor critical value W of the system is setTComparing the obtained trust composite factor with the minimum trust composite factor if the energy of the node
Figure FDA0002311960440000034
Or trust the composite factor at the threshold WTJudging the node as a malicious node or a dead node to isolate the network;
(5) the calculation of the evolutionary game cluster head election is described as follows:
a primary cluster head node is selected from the wireless sensor network and defined as a primary game G, wherein G is { P, S, U }, and G is a participant set, namely all sensor nodes meeting requirements; s, selecting cooperative or uncooperative strategy combination for the sensor nodes; u is the income obtained by the participant in the primary game, represented by a payment matrix, and the income conditions of different strategies selected by the nodes participating in the cluster head election are analyzed as follows:
the node and the opposite node both select a cooperation strategy:
in this case, all participant nodes participate in the selection of the cluster head node, and the trust gain is cTAnd the node participates in the cluster head to select and forward data to obtain the income ccAnd the cost of energy consumed by participating in the election of the cluster head is ccheIntroducing excitation uT for promoting node cooperationcAnd c is the total profit of the rational nodes participating in cluster head selectionT+ycc-2(x-y)cche(ii) a The total income of the selfish node participating in the cluster head selection is cT+(x-y)cc-2ycche+υTcThus the total revenue for participating in cluster head selection is cT+xcc-2xcche+υTc；
There is a choice of non-operational policies in the nodes:
if the selfish node does not participate in the cluster head election among the participants of the election cluster head node, the participating node will cause energy loss l, and the own energy consumption cost (x-y) ccheThen the profit of the cluster head node selected to participate is cT-(x-y)cche-l; therefore, the yield of the selfish node not participating in the cluster head node selection is cc(x-y)-yccheIf an excitation is introduced, utcThe selfish node participates in the cluster head election, the rational node forwards data for normal work due to damage and the like, and the benefit of the selfish node participating in the cluster head election is cT+υTc-yccheL, while the rational node has a profit of ccy-(x-y)ccheIn this case, the total benefit of the nodes participating in cluster head selection is cT+υTc-xcche-l; the total node income without participating in cluster head selection is xcc-xcche；
If all participants do not participate in cluster head election:
the cluster head node will not be elected, the network will probably communicate as a planar network, and the benefit can be noted as 0, where each letter or symbol means:
tc represents the trust degree, cT represents the trust degree income, cche represents the cost generated by transmitting the self data or forwarding the opposite node data when participating in the selection of the cluster head, cc represents the income generated by the cooperation of the opposite node, l represents the loss generated by the non-cooperation of the opposite node, x represents the number of nodes meeting the threshold value and participating in the election of the cluster head, x belongs to N, y represents the number of selfish nodes in x, y is more than or equal to 0 and less than x, y belongs to N, and upsilon is an adjusting factor;
the specific calculation steps are as follows:
let u (t) be (u)1(t)，u2(t)) represents a hybrid strategy for participating in cluster head elections, where u1(t) selecting a collaboration policy s for the participants1Ratio of nodes of u2(t) selecting a do-not-work strategy s for the participant2An example of a node ratio of1+u21, the following u1(t) is abbreviated as u,
the expected benefit of selecting the cooperative strategy node at the moment t is
P(s1，u)＝u(cT+xcc-2xcche+υTc)+(1-u)[cT+υTc-xcche-l]Formula 13
The expected benefit of selecting the non-operation strategy node at the moment t is
P(s2，u)＝u(xcc-xcche) Formula 14
The evaluation yields of all participants in cluster head election can be obtained from the formulas 13 and 14
Figure FDA0002311960440000041
Thus, cluster head election evolutionary dynamics replication equation is
Figure FDA0002311960440000042
Let F (u) be 0, the replication equation has a maximum of 3 stable states
Figure FDA0002311960440000043
Figure FDA0002311960440000051
Figure FDA0002311960440000052
Where the steady state represented by equation 19 may be the same as the steady state represented by equation 17 or equation 18, the nature of the evolving stabilization strategy represents a steady state, which is consistent with the stability condition requirements of differential equations and must be robust to small perturbations, where u is the case*In a steady state, the condition F' (u) must be satisfied*)＜0，
Condition 1 if cT+υTc-xcche＞0，cT+υTc-xcche-l＜0，2cT+2υTc-2xcche-l > 0, then
Figure FDA0002311960440000053
And
Figure FDA0002311960440000054
are evolution stable strategies of the wireless sensor network evolution game, and
Figure FDA0002311960440000055
probability of time being less than
Figure FDA0002311960440000056
Probability of time;
condition 2 if cT+υTc-xcche＜0，cT+υTc-xcche-l＜0，2cT+2υTc-2xccheL < 0, then
Figure FDA0002311960440000057
And
Figure FDA0002311960440000058
are evolution stable strategies of the wireless sensor network evolution game, and
Figure FDA0002311960440000059
probability of time being greater than
Figure FDA00023119604400000510
The probability of time, the probability of the selection of the non-cooperative strategy by the node which meets the selection of the cluster head is greater than the probability of the selection of the cooperative strategy;
condition 3 if cT+υTc-ccheIf less than 0, then
Figure FDA00023119604400000511
The evolution stability strategy of the wireless sensor network evolution game is adopted, whether the rational node selects the cooperation strategy or the non-cooperation strategy, the profit of selecting the cooperation strategy by the selfish node is always smaller than that of selecting the non-cooperation strategy, and the proportion of the nodes of finally selecting the cooperation strategy is stable
Figure FDA00023119604400000512
Selecting a non-operation strategy;
the condition satisfied by the conditions 2 and 3 is a condition that must be avoided when the cluster head of the wireless sensor network elects, because the condition indicates that the probability of selecting the non-cooperation strategy by the node is greater than the probability of selecting the cooperation strategy, and finally the wireless sensor network is in an unstable state.
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