CN111132200A - Three-dimensional underwater network topology control method based on potential game and rigid subgraph - Google Patents

Three-dimensional underwater network topology control method based on potential game and rigid subgraph Download PDF

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CN111132200A
CN111132200A CN201911417371.9A CN201911417371A CN111132200A CN 111132200 A CN111132200 A CN 111132200A CN 201911417371 A CN201911417371 A CN 201911417371A CN 111132200 A CN111132200 A CN 111132200A
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魏连锁
郭媛
韩建
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Qiqihar University
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Abstract

本发明公开了一种基于势博弈与刚性子图的三维水下网络拓扑控制方法，所述方法包括如下步骤：步骤一、水下无线传感器网络拓扑的构建；步骤二、网络拓扑博弈的执行；步骤三、冗余链路的剔除；步骤四、网络拓扑的自适应与维护。该方法充分考虑水下因素，设计包括网络的连通性、覆盖性、能量消耗、传输延迟以及数据传输成功率、信干噪比等多个优化目标的UWSNs拓扑控制方法，并利用最优刚性子图原理剔除网络拓扑中的冗余链路，降低节点的负载；同时，通过调节网络中权重因子使网络能够对抗不同的水下环境，具有较强的自适应性。

Figure 201911417371

The invention discloses a three-dimensional underwater network topology control method based on potential game and rigid subgraph. The method comprises the following steps: step 1, construction of underwater wireless sensor network topology; step 2, execution of network topology game; Step 3, elimination of redundant links; Step 4, self-adaptation and maintenance of network topology. The method fully considers underwater factors, and designs a topology control method for UWSNs with multiple optimization objectives including network connectivity, coverage, energy consumption, transmission delay, data transmission success rate, signal-to-interference-noise ratio, etc. The graph principle eliminates redundant links in the network topology and reduces the load of nodes; at the same time, by adjusting the weight factor in the network, the network can fight against different underwater environments and has strong adaptability.

Figure 201911417371

Description

Three-dimensional underwater network topology control method based on potential game and rigid subgraph
Technical Field
The invention relates to a topological control method of an underwater sensor network, in particular to a three-dimensional underwater network topological control method based on a potential game and a rigid subgraph.
Background
An Underwater Wireless Sensor Network (UWSNs) is a physical network comprising sound, a magnetic field, an electrostatic field and the like, is widely applied to the aspects of marine data acquisition, pollution prediction, ocean exploration, ocean monitoring and the like, and can play an important advantage in future naval operations. Network topology control is one of the key technologies in the research field of UWSNs. The transmission of underwater acoustic signals is greatly influenced by an underwater complex environment, so that the problems of frequent change of network topology, poor energy efficiency and the like of the UWSNs caused by uncertain factors such as high error rate, long propagation delay, intermittent interruption of links, node mobility and the like exist. Therefore, the influence of factors such as energy consumption balance and energy efficiency on high-performance UWSNs is comprehensively considered, the optimized network topology control algorithm is further researched, the sensor node communication efficiency of the UWSNs can be improved, the life cycle of the whole network can be prolonged, the method is the basis of key technologies such as underwater sensor node positioning, clock synchronization and Mac protocol, and meanwhile, a theoretical support is laid for the application research of the UWSNs.
At present, scholars at home and abroad obtain some achievements on the topological control algorithm of the underwater wireless sensor network. Yang et al propose an energy control algorithm EFPC of an underwater wireless sensor network, the algorithm introduces a game theory to avoid the selfishness of nodes, balance the network energy consumption and have Nash equilibrium, and avoid interfering underwater creatures by limiting the power level. The algorithm realizes good network topology control, improves the performance of the network, balances node energy consumption by adopting a game theory, but has complex underwater environment and does not consider some important factors influencing network energy consumption. Liu L et al maps the coverage, connectivity, network energy consumption, communication link delay and transmission success rate optimization problems into potential game problems, constructs a multi-objective QoS optimized UWSNs topology control model, and designs a corresponding distributed node regulation algorithm, but the robustness of the network cannot be guaranteed. Therefore, Liu L and the like use a complex network to construct a scale-free MUWSNs topology, then node states are analyzed, nodes are classified according to coverage probability and communication probability among the nodes, and node energy consumption is reduced through sleep and awake states, so that the topology has higher coverage, less energy consumption and robustness of a network structure. WangY and the like design an underwater three-dimensional fault-tolerant topology, and the robustness of the network is enhanced by keeping the K connection of the network all the time, but the algorithm does not consider the problems of node degree, link redundancy, propagation delay and the like of nodes in a network topology structure, so that the nodes with much energy are exhausted and die.
Disclosure of Invention
The invention provides a three-dimensional underwater network topology control method based on a potential game and a rigid subgraph, aiming at the problems of unbalanced energy consumption of an underwater sensor network, more redundant network topology links, short life cycle, poor self-adaption and the like. The method takes underwater factors into full consideration, designs a UWSNs topology control method comprising a plurality of optimization targets such as network connectivity, coverage, energy consumption, transmission delay, data transmission success rate, signal-to-interference-and-noise ratio and the like, and eliminates redundant links in the network topology by utilizing an optimal rigid subgraph principle to reduce the load of nodes; meanwhile, the network can resist different underwater environments by adjusting the weight factors in the network, and has strong self-adaptability.
The purpose of the invention is realized by the following technical scheme:
a three-dimensional underwater network topology control method based on potential game and rigid subgraph comprises the following steps:
step one, constructing underwater wireless sensor network topology
(1) Initializing the maximum communication radius of a sensor node i to be R on the basis of analyzing the communication distance between nodes and the link qualityCWith a radius of perception of RS；
(2) Node i broadcasts a packet NCK to surrounding nodes, wherein,
Figure BDA0002351534680000031
IDiidentifying code for i, SiIs the position coordinates of i and is,
Figure BDA0002351534680000032
a residual energy of i;
(3) when the sensor node j receives the information packet NCK of the node i, the node j sends an information packet ACK to the node i, wherein,
Figure BDA0002351534680000033
where P isjIs a power of j and is,
Figure BDA0002351534680000034
is the communication power of the node i and the node j, Delta is the dynamic topology reaction capability, ri,jFor the path transmission success rate, U, from node i to node jiA utility function value of the node i in the network;
(4) when the node i receives the acknowledgement information packet ACK of the surrounding node j, the node i adds the node j to a neighbor information table of the node i so as to establish the maximum learnable global network topology view Gmax；
Step two, executing network topology game
(1) Calculating the current power p of the node iiLearning the remaining energy
Figure BDA0002351534680000035
And node selectable power set
Figure BDA0002351534680000036
Wherein
Figure BDA0002351534680000037
Respectively calculating the current power p of the node i for the minimum power and the maximum power of the node iiThe formula of (1) is as follows:
Et(l,r)＝l×Eelec+C×H×r×eα(f)×r×T；
wherein, C is 2 pi multiplied by 0.67 multiplied by 10-9.5；
Figure BDA0002351534680000038
f is the transmission frequency; l is the packet size; eelecEnergy expended to receive a unit of data; t is the transmission time of data; h is the average water depth of the node; r is the communication distance between nodes;
(2) each node sequentially selects power according to the power set, only one node adjusts the power in each round, and the power of other nodes is unchanged;
(3) given the power p of the other participants-iWhen the optimal response strategy of the node i is
Figure BDA0002351534680000041
(4) In the game execution process, if the node selects power communication lower than the current power, observing whether the obtained income is increased, and if the income is increased, indicating that the lower power is more suitable to be used as the communication power of the node; otherwise, the node keeps the current power unchanged;
(5) when the power of each node i is more optimal to the power of other nodes, namely the power of all the nodes reaches an optimal state, and the power of any node does not change in the node power set P, so that the network gain is increased, the network at the moment reaches a balanced state, namely Nash balance, and at the moment, a neighbor node set R of the nodes is constructed by the information table of each final node, so that a network topological graph is generated;
step three, elimination of redundant link
Introducing an optimal rigid graph principle, and removing redundant links in a network, wherein the method specifically comprises the following steps:
(1) each node i calculates the number k of neighbors according to the neighbor node set R;
(2) constructing weight link set WiAnd subgraph matrix GiWherein:
link weight function lambdaij(t) is:
Figure BDA0002351534680000042
here, χ1+χ 21, wherein:
Figure BDA0002351534680000043
for link quality adjustment factor, d (i, j) for node communication distance, Er(t) is the node residual energy;
link weight function lambdaij(t) is a specific weight value of communication of the node i and the neighbor nodes, and a weight link set WiA set of its weight values;
submatrix GiComprises the following steps:
Figure BDA0002351534680000044
wherein
Figure BDA0002351534680000051
A communication link between a node i and a node j is defined, and E is a set of all links in the network;
(3) judging the weight link set W constructed by the selfiWhether the rigid matrix is constructed is satisfied, if so, the rigid matrix M and the optimal sub-rigid matrix M are constructedcFinally, obtaining a link set D to be deleted from the optimal rigid subgraph matrix, and updating the neighbor node set R of each node through the link set D to be deleted;
step four, self-adaptation and maintenance of network topology
(1) The design is early warning mechanism real time monitoring underwater environment under water, and the adverse circumstances concrete representation under water is different grades, and simultaneously, early warning mechanism issues underwater environment grade information to the node in real time to network topology can adjust self in a certain time, in order to adapt to upcoming environment, and the concrete description is as follows:
a. when the environment is stable: the network topology takes the residual energy of the nodes as a main consideration factor and takes balanced energy consumption as a main target, so that the nodes are prevented from being dead due to energy exhaustion;
b. when the environment is severe: the network topology takes robustness as a main factor, and network paralysis caused by impact of ocean current or large organisms on nodes is avoided;
(2) when a node in the UWSNS fails or energy is exhausted to reach a certain threshold, the energy consumption of balanced network nodes needs to be considered, important factors influencing dynamic topology reaction capacity are analyzed, and a network topology repair and reconstruction algorithm is designed, and the method specifically comprises the following steps:
first, an energy threshold τ is setEAnd a trigger mechanism, if
Figure BDA0002351534680000052
Then a network topology repair mechanism is started, wherein E0(i) Is the initial energy of node i; in addition, when a new node is added or fails in the network topology, it is first determined whether the network is connected, if so, the network topology is not changed, otherwise, a network topology repair mechanism is executed, and the specific situation is described as follows:
a. initialization energy threshold τEComputing node residual energy Er(i) Determining a redundant node;
b. when node residual energy Er(i)＜τEAdjusting according to the redundant nodes, balancing network energy, completing topology restoration, or returning to a;
c. and (c) when the node is added and the node fails, the network connectivity and the network coverage rate are not influenced, returning to the step (a), otherwise, executing a topology repair algorithm.
Compared with the prior art, the invention has the following advantages:
1. in the aspect of network evaluation indexes, factors such as connectivity, coverage, transmission energy consumption, transmission end-to-end time delay, signal-to-interference-and-noise ratio, transmission success rate, node residual energy and the like of an underwater network are comprehensively considered, and the factors are converted into a multi-target game solving process, so that the underwater network evaluation index is more consistent with the underwater environment.
2. In the aspect of network robustness, the invention provides a method for eliminating redundant links in a network by utilizing an optimal rigid subgraph model and constructing weight links containing factors such as node load, residual energy and the like, so that the node load is reduced, the life cycle of the network is prolonged, and the network has stronger robustness.
3. In the aspect of topology self-adaptation, the network topology model constructed by the invention can generate different network topology structures in a way of adjusting the weight factor, the network topology structures can work in different underwater environments, and the network topology has stronger self-adaptation.
4. Simulation experiments show that compared with the existing network topology model, the network topology model constructed by the method is more suitable for the underwater environment, the redundant links in the network are fewer, the node load is lower, the network robustness is stronger, the network balance is stronger, the network life cycle is longer, and the topology has stronger self-adaptive performance.
Drawings
FIG. 1 is a rigid map model, (a) a rigid map, (b) a deformable map;
fig. 2 shows the effect of α on network performance indicators when β, λ 1;
fig. 3 is a graph of the impact of β on network performance metrics when α, λ 1;
fig. 4 is the effect of λ on the network performance indicator when α is 1;
FIG. 5 is a network topology adaptation;
FIG. 6 is a DEBA algorithm network topology;
FIG. 7 is an EFPC algorithm network topology;
FIG. 8 is a 3DR-RNG algorithm network topology;
FIG. 9 is a PG-OSTCG algorithm network topology;
FIG. 10 is a graph of node average contrast;
FIG. 11 is a graph of maximum node degree contrast;
FIG. 12 is a comparison graph of average link lengths for different numbers of nodes;
FIG. 13 is a graph comparing the average link length for variations in adjustment factor α;
FIG. 14 is a comparison graph of standard deviation of node residual energy;
fig. 15 is a comparison graph of network life cycles for different numbers of nodes.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.
The invention provides a three-dimensional underwater network topology control method based on a potential game and a rigid subgraph. And then introducing a link weight function of node load and node residual energy, and removing redundant links in the network by using an optimal rigid subgraph principle. And finally, grading the underwater environment, and enabling the network to have stronger self-adaptability by adjusting the weight factor in the model. The method specifically comprises the following steps:
topology control model of one-potential game and optimal rigid subgraph
1. Network model and associated assumptions
In three-dimensional space, the wireless sensor network can be mapped into an undirected graph G (V, E, P), where V ═ V1,v2,...vN},v1,v2,...vNIs a sensor node;
Figure BDA0002351534680000081
wherein
Figure BDA0002351534680000082
A link representing an inter-node communication;
Figure BDA0002351534680000083
is a power set of nodes, where pminIn order to receive the threshold value(s),
Figure BDA0002351534680000084
is the maximum power, p1,p2,...,pnCommunicating power for the node. In an underwater network, for any two nodes i, j belongs to V, and if the Euclidean distance d between the two nodesijSatisfy dij≤rcThen, nodes i and j are said to be mutually neighboring nodes, where rcIs the communication radius; if nodes i and j can communicate with each other, then
Figure BDA0002351534680000085
For convenience of the following study, the UWSNs were constrained as follows:
(1) the underwater sensor node can adjust suspension at any depth according to the self pressure sensor; the node sensing range is spherical, and the sensing can be accurately conducted in the sphere, but cannot be conducted outside the sphere.
(2) The working mode among the sensor nodes is a semi-duplex mode, and the communication range of the node i refers to a node viAs a circle center, with RiSphere of radius, and the sensing range of node i is RSIs a sphere of radius (R)S≤Ri)。
(3) N nodes are randomly deployed in the underwater three-dimensional network, and each node is rational selfish.
(4) The initial energy of each node is heterogeneous, and the value range is as follows: obeying a poisson distribution where λ (λ is the poisson distribution adjustment factor) is a specific value.
(5) In UWSNs, each sensor node has a unique Di(DiAn identification code for node i).
(6) When all nodes in the network select the maximum communication radius, the connectivity and the coverage of the network can be ensured.
(7) The lifetime of the node at death is also the operational lifetime of the network.
2. Ordinal potential game model
The potential game is one of the strategy games, and in the strategy game T ═ N, a, u (a) >, 3 elements are mainly included: participants, policy sets, utility functions. The specific description is as follows:
1) participant N: n ═ 1,2,.., N is the number of game participants.
2) And (4) a policy set A: a. theiRepresenting the behavior set of the participant i, if the participant i has k behaviors, then there is Ai＝{a1,a2,...akIn which a is1,a2,...akIn order to be a combination of behaviors,
Figure BDA0002351534680000091
let aiFor a certain behavior of participant i, then a-i＝(a1,...ai-1,ai+1,...,an) Representing combinations of behaviour of participants other than participant i, typically denoted by a ═ a (a)i,a-i) Representing a particular combination of behaviors.
3) Utility function u (a): u may be expressed as U ═ U1,u2,...un}，u1,u2,...unFor profit, U is availablei(ai,a-i) A → R indicates that participant i is in the policy combination (a)i,a-i) The utility of (1).
Definition 1, nash equilibrium: given a game model T with n players<N,A,U(A)>If for
Figure BDA0002351534680000092
And ai ∈ AiGiven other participants
Figure BDA0002351534680000093
In the case of (2), its behavior
Figure BDA0002351534680000094
Is the optimal behavior of participant i, having:
Figure BDA0002351534680000095
then
Figure BDA0002351534680000096
Is the game model T ═<N,A,U(A)>A nash equalization.
Defining 2, ordinal potential game and ordinal potential function: in a game model T ═<N,A,U(A)>In, for
Figure BDA0002351534680000097
There are two different strategies
Figure BDA0002351534680000098
If there is a function
Figure BDA0002351534680000099
Such that:
Figure BDA00023515346800000910
the game model is called an ordinal potential game model, wherein
Figure BDA00023515346800000911
Sgn (-) is a sign function for the ordinal potential function of the game model.
Definition 3, pareto optimal: if there is not one policy set (a)1,a2,...an) E is equal to A so that
Figure BDA00023515346800000912
And at least one exists
Figure BDA00023515346800000913
So that
Figure BDA00023515346800000914
If true, then the policy (a)1,a2,...an) e.A is a pareto optimum.
3. Rigid graph model
The rigid graph is an undirected graph. In the graph G (V, E), for any two vertices (i, j) ∈ E, the motion trajectory f (t) of the node satisfies | | fi(t)-fjAnd (t) | | d, wherein d is a constant, namely the motion trail of the vertex in the undirected graph is constant, the undirected graph is called as a rigid graph, and the undirected graph is called as a deformable graph in the opposite direction. The rigid graph can be combined with a network topology in an underwater three-dimensional environment, the vertex of the rigid graph is represented as a node of the network topology, and the edge of the rigid graph is represented by the communication link between the nodes, so that the network topology is a rigid topology. As shown in (a) and (b) of fig. 1, they are represented as a rigid topology and a variable topology composed of 5 nodes in a three-dimensional environment, respectively.
Properties 1: as defined by the rigid graph, the rigid graph is an undeformable graph, namely, the topological graph constructed by the rigid graph has stronger stability.
Definition 4, minimum rigidity graph: if any deletion of an edge in a graph results in rigidity of the graph while maintaining the rigidity of the graph, the graph is referred to as a minimum rigidity graph.
Introduction 1: if the total number of links in the graph constructed by the n nodes is n (n-1)/2 at most, the graph having the number of links of n × r-r × (r +1)/2 in the rigidity graph of the r-dimensional space is the minimum rigidity graph.
Define 5, optimal stiffness map: if a topological graph is the least rigid graph and the weighted sum of the links in the graph is the smallest under the condition of the same vertex, the graph is called as the optimal rigid graph.
Define 6, optimal rigid subgraph: for an arbitrary two topological graphs G (V, E), G ' (V ', E '), if
Figure BDA0002351534680000101
And is
Figure BDA0002351534680000102
Then G ' is said to be a subgraph of G, and if and only if G ' is the optimal rigid graph, G ' is said to be the optimal rigid subgraph of G.
Properties 2: as can be seen from the theorem 1 and the definition 5 in the r-dimensional space, the optimal rigid graph has the advantages that the total number of links in the constructed topological graph is small, the total weight of the links is minimum, each vertex is at least connected with r links, namely the optimal rigid graph is r-connected, and the robustness is high.
4. Utility function
Because the underwater environment is complex, the benefit of the node is difficult to quantify, and in order to truly reflect the network condition, the invention considers a benefit function U from the following aspects:
1) network connectivity:
the network communication is a necessary condition for the normal operation of the network, and the invention can ensure that the network can still keep a communication state after a plurality of game iterations under the condition that the node reduces the self transmitting power by adding the connectivity function. The set-up communication function is therefore as follows:
Figure BDA0002351534680000111
2) network coverage:
let the network coverage function be:
Figure BDA0002351534680000112
3) network energy consumption:
the underwater acoustic communication energy consumption model is different from a land radio energy consumption model, and the influence factors are more, so that the definition of the node energy consumption model is more, and the energy consumption model is introduced in the invention. The energy consumption of a node to send data can be expressed as:
Et(l,r)＝l×Eelec+C×H×r×eα(f)×r×T (5)；
wherein, C is 2 pi multiplied by 0.67 multiplied by 10-9.5；
Figure BDA0002351534680000113
f is the transmission frequency; l is the packet size; eelecEnergy expended to receive a unit of data; t is the transmission time of data; h is the average water depth of the node; and r is the communication distance between nodes.
Energy consumption E of receiving data packet with length of l by noder(l) Comprises the following steps:
Er(l)＝l×Eelec(6)。
4) end-to-end delay:
comprehensively analyzing the physical properties of water and the influence of network transmission characteristics on transmission delay, wherein the end-to-end delay from a receiving node to a sending node is as follows:
Figure BDA0002351534680000121
wherein: k is a radical ofsFor the number of data packet retransmissions, l is the data packet size, RijTo the transmission rate, Dij(t) is the distance from node i to node j at time t, c is the propagation velocity of the acoustic wave, Δ τkAs the kth of the data packetsMaximum multipath propagation delay difference, p, caused by multipath propagation during secondary retransmissionijFor inter-node communication power, κ is the signal threshold size that the receiver can handle.
5) Signal to interference plus noise ratio SINR:
in an underwater wireless network, the signal-to-interference-and-noise ratio is an important index for evaluating signal quality, and is defined as a ratio of the sum of noise powers of received signals which are much smaller than the interference power. The present invention is defined as:
Figure BDA0002351534680000122
wherein: b isnFor system bandwidth, α (f) is the medium absorption coefficient, rijIn order to be able to transmit the distance,
Figure BDA0002351534680000123
to be the same as mu of node iikEach group is divided into the same group, m groups, sigma2Is the noise variance.
6) Transmission success rate:
the transmission success rate is set as:
Figure BDA0002351534680000131
the number of retransmissions ksThe relationship with the transmission success rate is:
Figure BDA0002351534680000136
7) node residual energy:
the node residual energy is a main consideration factor for the topology control of the underwater network, and can reflect the life cycle of the network and the energy consumption balance problem of the network. In order to achieve energy consumption balance in the network, nodes with large residual energy need to be purposefully adjusted to participate in the forwarding task. Therefore, the invention adds factors to the utility function
Figure BDA0002351534680000132
WhereinE0(i) And Er(i) Respectively the initial energy and the residual energy of the node i; meanwhile, factor is considered to be added in order to improve average residual energy of neighbor nodes
Figure BDA0002351534680000133
Where k is node i at a transmit power of piThe number of one-hop neighbor nodes in time.
In summary, connectivity, coverage, transmission energy consumption, end-to-end transmission delay, signal-to-interference-and-noise ratio, transmission success rate, and node residual energy of the network are main optimization targets of the UWSNs, and due to the multiplicity of the targets and the contradiction between the targets, it is difficult to achieve the optimal performance of the targets. Therefore, the distributed multi-objective optimization is converted into game solving, and the dynamic solving of the distributed multi-objective optimization problem is realized by utilizing the repeated game process. Therefore, the invention satisfies the various properties of the utility function and simultaneously
Figure BDA0002351534680000134
Game model T ═<N,A,U(A)>The utility function of (2) is defined as:
Figure BDA0002351534680000135
wherein α, λ are weight adjustment factors, both positive numbers, Fi(ai,a-i) As a connectivity function, Ci(ai,a-i) In order to be a function of the coverage,
Figure BDA0002351534680000141
for transmission of energy, Si(ai,a-i) For transmission success rate, Di(ai,a-i) For transmission delay, E0(i) And Er(i) Respectively, the initial energy and the remaining energy of the node i.
5. Optimal rigid subgraph matrix construction
(1) Link weight function construction
Let the link weight function lambdaij(t) is:
Figure BDA0002351534680000142
here, χ1+χ 21, wherein:
Figure BDA0002351534680000143
for link quality adjustment factor, d (i, j) for node communication distance, ErAnd (t) is the node residual energy.
(2) Subgraph matrix
For the topological graph G ═ V, E, the node i and its neighbor nodes form a subgraph matrix GiComprises the following steps:
Figure BDA0002351534680000144
(3) rigid matrix
In the r-dimensional space, the coordinates of the node i are generally expressed as
Figure BDA0002351534680000145
Then in three-dimensional space there are:
Figure BDA0002351534680000146
randomly deploying n nodes in an r-dimensional space, and arranging the nodes according to sequence numbers to obtain position coordinates:
Figure BDA0002351534680000147
link set in undirected graph G ═ V, E
Figure BDA0002351534680000148
Where each link can be converted into a row vector of a rigid matrix. A rigid matrix M is constructed in three-dimensional space|e|×3n(where | e | is the total number of links in the topology), the k-th link in the graph (k is the node i at a transmission power of p)iNumber of one-hop neighbor nodes in time)
Figure BDA0002351534680000149
A row vector M formed by the corresponding k-th row elements in the rigid matrix MkAs follows:
Figure BDA0002351534680000151
a rigid matrix M consisting of | e | row vectors in three-dimensional space|e|×3nAs follows:
Figure BDA0002351534680000152
2, leading: if an undirected graph with n vertices in r-dimensional space builds a matrix M, then the graph is the least rigid graph and only if the rank of its rigid matrix is satisfied:
rank(M)＝n×r-r(r+1)/2 (17)。
therefore, as can be seen from equation (16), the rank of the minimum stiffness map including n vertices in the three-dimensional space is rank (m) 3 n-6.
Properties 3: from the above definitions 6, 7 and lemma 2 it follows that: in thatrAfter the rigid matrix M of all links in the dimensional space is constructed, a link weight set W of the rigid matrix is constructed by equation (12). Arranging the weight set W according to an ascending order, and initializing a rigid matrix McThen, the rows in the rigid matrix M are added to the matrix M in sequence according to the link weight ordercIn, if the matrix M iscIf the rank is full, adding is continued until the whole W is traversed, and finally obtaining a matrix McIs an optimal rigidity matrix.
Two, PG-OSTCG (potential game and rigid subgraph underwater sensor network topology control algorithm) topology control algorithm
1. Network topology construction
(1) Initializing the maximum communication radius of a sensor node i to be R on the basis of analyzing the communication distance between nodes and the link qualityCWith a radius of perception of RS；
(2) Node i broadcasts to surrounding nodes a packet NCK, whichIn (1),
Figure BDA0002351534680000153
IDiidentifying code for i, SiIs the position coordinates of i and is,
Figure BDA0002351534680000154
a residual energy of i;
(3) when the sensor node j receives the information packet NCK of the node i, the node j sends an information packet ACK to the node i, wherein,
Figure BDA0002351534680000161
where P isjIs a power of j and is,
Figure BDA0002351534680000162
is the communication power of the node i and the node j, Delta is the dynamic topology reaction capability, ri,jFor the path transmission success rate, U, from node i to node jiA utility function value of the node i in the network;
(4) when the node i receives the acknowledgement information packet ACK of the surrounding node j, the node i adds the node j to a neighbor information table of the node i so as to establish the maximum learnable global network topology view GmaxAnd strategy selection is provided for the subsequent topological game stage.
2. Network topology game execution phase
The main task of the topological game stage is to dynamically adjust the network topology according to the network energy consumption in the underwater environment and the network robustness so as to prolong the life cycle and the survivability of the underwater network. The method adopts a network topology adjusting stage mode that the node transmitting power is adjusted, and the node transmitting power is set to correspond to the transmitting power of the nodes in different underwater environments as the optimal transmitting power, so that the network topology structure conforming to the underwater environments is obtained. After the topology is built, the node i calculates the current power p by the formula (5)iLearning the remaining energy
Figure BDA0002351534680000163
And node selectable power set
Figure BDA0002351534680000164
Wherein
Figure BDA0002351534680000165
Respectively the minimum power and the maximum power of node i. And each node sequentially selects power according to the power set, only one node adjusts the power in each round, and the power of other nodes is unchanged. To ensure convergence to nash equilibrium, the present invention employs a better-reflecting strategy update scheme that must converge to nash equilibrium in finite number potential gambling. Thus, for the present invention, if the power p of the other participants is given-iWhen the optimal response strategy of the node i is
Figure BDA0002351534680000166
In the game execution process, if the node selects power communication lower than the current power, observing whether the obtained income is increased, and if the income is increased, indicating that the lower power is more suitable to be used as the communication power of the node; otherwise, the node keeps the current power unchanged. When the power of each node i is better than the power of other nodes, that is, the power of all nodes reaches the optimal state, and the power of any node does not change in the node power set P, so that the network gain is increased, the network at this time reaches a balanced state, that is, nash balance. At this time, a neighbor node set R of the nodes is constructed by the information table of each final node, and a network topological graph is generated.
3. Redundant link culling stage
After the last stage, although the network reaches the Nash equilibrium solution, the network model excessively emphasizes the energy consumption equilibrium and the network survivability, so that part of nodes in the network have the problems of link redundancy, large link weight and the like. Therefore, the invention introduces the principle of optimal rigid graph, and redundant links in the network are eliminated by the method. Each node i calculates the number k of its neighbors according to the neighbor node set R, and a weight link set W is constructed by the formulas (12) and (13)iAnd subgraph matrix GiJudging whether the self constructed link set meets the requirement of just constructing the link set by definition 4-6 and lemma 2A property matrix, if satisfied, constructing a rigid matrix M by the equations (14) - (16), and constructing an optimal sub-rigid matrix M by the property 3cAnd finally, obtaining a link set D to be deleted from the optimal rigid subgraph matrix, and updating the neighbor node set R of each node through the link set D to be deleted.
4. Network topology adaptation and maintenance phase
The underwater wireless sensor node has the problems of node damage, movement and the like caused by the fact that the node is easily corroded by seawater, ocean currents, large organisms and the like due to the fact that the working environment of the underwater wireless sensor node is severe. Therefore, the underwater network topological structure has certain robustness, and the influence of node failure on the normal operation of the network is reduced. Meanwhile, because the energy of the sensor nodes is limited, when the network robustness is emphasized excessively, the problems of unbalanced energy consumption of the nodes and the like can occur.
Considering the above problems comprehensively, the underwater network topology constructed by the invention has the characteristics of self-adaption, network periodic maintenance and the like so as to adapt to different underwater environments, and the specific description is as follows:
(1) an underwater early warning mechanism is designed to monitor underwater environment in real time, and underwater severe environment is embodied into different grades. Meanwhile, the early warning mechanism issues underwater environment grade information to the nodes in real time, so that the network topology can adjust itself within a certain time to adapt to the upcoming environment. The specific description is as follows:
a. when the environment is stable: the network topology takes the residual energy of the nodes as a main consideration factor (comprehensively shows that the potential game model T ═ N, A, U (A)) constructed by the method has different weight factors, and takes balanced energy consumption as a main target to avoid the death of the nodes due to the energy consumption.
b. When the environment is severe: the network topology takes robustness as a main factor, and network paralysis caused by collision of ocean currents or large organisms on nodes is avoided.
(2) When the nodes in the UWSNS fail or the energy is exhausted to reach a certain threshold, the whole network life cycle is influenced. Therefore, the energy consumption of the network nodes needs to be balanced, important factors influencing the dynamic topology reaction capability need to be analyzed, and a network topology repair and reconstruction algorithm needs to be designed.
First, an energy threshold τ is setEAnd a trigger mechanism, if
Figure BDA0002351534680000181
If so, starting a network topology repair mechanism; in addition, when a new node is added or fails in the network topology, it is first determined whether the network is connected, if so, the network topology is not changed, otherwise, a network topology repair mechanism is executed, and the specific situation is described as follows:
a. initialization energy threshold τEComputing node residual energy Er(i) Determining a redundant node;
b. when node residual energy Er(i)＜τEAdjusting according to the redundant nodes, balancing network energy, completing topology restoration, or returning to a;
c. and (c) when the node is added and the node fails, the network connectivity and the network coverage rate are not influenced, returning to the step (a), otherwise, executing a topology repair algorithm.
5. PG-OSTCG algorithm
The PG-OSTCG algorithm pseudo code is shown in table 1:
TABLE 1 PG-OSTCG Algorithm pseudocode description Table
Figure BDA0002351534680000191
Performance evaluation of PG-OSTCG algorithm
The method comprises the following steps that 4 groups of comparison simulation and 1 group of network self-adaptive adjustment comparison are designed by utilizing python, and 1 group of algorithm weight factor selection experiments are designed so as to verify the effectiveness of a PG-OSTCG algorithm, specifically, experiment 1 considers the influence of weight factors α and lambda on network topology performance from three aspects of node transmission power, node average node degree and neighbor node average residual energy, experiment 2 is a network topology structure diagram of the algorithm constructed in the invention in different underwater environments, experiment 3 compares the average node degree and the maximum node degree of four algorithms including DEBA, EFPC, 3Dk-RNG and PG-OSTCG under different node numbers, analyzes the robustness of the PG-OSTCG algorithm, experiment 4 analyzes the average link length of the PG-OSTCG algorithm after 100 cycles when the average link length of the DEPC, 3Dk-RNG algorithm and PG-OSTCG algorithm under different node numbers and under different α values, analyzes the average link length of the PG-OSTCG algorithm after 100 cycles when the average link length of the EFPC, 3Dk-RNG algorithm and the PG algorithm under different node average node length and the energy consumption of the PG algorithm under different α values, analyzes the energy consumption difference of the reconstructed network life cycle of the PG-OSTCPG algorithm under different node length, and energy consumption standard, and life cycle of the energy consumption of the power consumption of the PG algorithm, and the life cycle of the power of the PG-OSTCPG algorithm, and power of the rest of the power of the PG-OSTCPG algorithm, and power consumption of the life cycle of the same power under different nodes.
In order to understand the simulation process, performance evaluation indexes of experimental simulation are given as follows:
(1) robustness of the network topology: when a link of the network is interrupted, the network can select other links to quickly transmit data, namely the connectivity of the network is heat preserving, and the robustness of the network is stronger.
(2) Node average degree: in an underwater sensor network, the ratio of the sum of degrees of each sensor node to the total number of network nodes is called the node mean degree DavNamely:
Figure BDA0002351534680000201
in the formula (I), the compound is shown in the specification,
Figure BDA0002351534680000202
and N is the total number of the network nodes.
(3) Average length of communication link: in UWSNs, the ratio of the sum of the length of each communication link between nodes to the total number of network links is called the average link length lavNamely:
Figure BDA0002351534680000203
wherein lijIs the length of the communication link between nodes i and j, L isTotal number of links of the network.
(4) The network life cycle: in an underwater sensor network, the difference between the time when the dead node appears in the first node and the time when the network starts to work is called the life cycle T of the networkLNamely:
TL＝TD-TB(24)；
wherein, TDTime of death of the first node, TBThe moment when the network starts to operate.
1. Setting of simulation experiment environment parameters
Table 2 simulation environment parameter settings
Figure BDA0002351534680000211
2. Analysis of influence of weighting factors on network topology
80 nodes are randomly placed in a three-dimensional monitoring area (400 multiplied by 400), and under the condition that any two weight factor values in the defined α and lambda are 1, another weight factor is adjusted to analyze the influence of the weight factor in the algorithm on the network topology performance.
It can be seen from fig. 2 that the average transmission power, the average node degree of the node and the average residual energy of the neighboring nodes decrease with the increase of α, and from fig. 3 and 4, the average transmission power, the average node degree of the node and the average residual energy of the neighboring nodes increase with the increase of β, and the changes of the three indexes are relatively stable after α and λ ≧ 2.
3. Network topology adaptive analysis
Under the experimental simulation environment, network topological graphs of different levels are obtained by changing and adjusting the link weight factors. Because the underwater environment is complex and changeable, the environments of the network at different moments are different, and meanwhile, the network has a contradiction between robustness and network energy consumption, namely, the load of a node is inevitably increased (namely, the life cycle of the network is reduced) while the network robustness is increased. Therefore, the network should have different topologies at different times to extend the life cycle and survivability of the network as much as possible. As shown in fig. 5, the present invention will adjust the network topology adaptively for different underwater environments.
The specific description is as follows:
when the collision of ocean currents and large organisms occurs, the network issues an early warning mechanism, the network at the moment mainly aims at building robustness to enhance the survivability of the network, and although the load of the nodes at the moment is large, the survivability of the network is strong.
When the underwater environment is relatively stable, the network topology at the moment can reduce the robustness of the network, so that the load of the nodes is reduced, and the life cycle of the network is prolonged.
4. PG-OSTCG robustness analysis
Selecting two underwater network topology control algorithms DEBA and EFPC based on game theory and an underwater fault-tolerant topology algorithm 3DK-RNG to compare with the PG-OSTCG algorithm provided by the invention. Firstly, comparing network topological structures generated by 4 algorithms; 80 nodes are randomly generated in a three-dimensional monitoring area (400 multiplied by 400), and in the same simulation environment, when the number of sensor nodes is changed from 70 to 150, the maximum node degree and the node average degree of DEBA, EFPC, 3DK-RNG and PG-OSTCG provided by the invention are compared, so that the network topology robustness of the PG-OSTCG algorithm is verified.
Fig. 6 shows that the DEBA algorithm adopts a game theory to balance node energy consumption method to construct a network topology structure, and it can be seen from fig. 6 that: the method has the problems that more bottleneck nodes with less residual energy exist, so that the full coverage of the network and the connectivity of the network cannot be completely guaranteed. Fig. 7 and 8 respectively show a network topology node EFPC constructed by pure policy game through power control, and a fault-tolerant topology control (i.e., capable of bearing a certain degree of node/link failure) 3DK-RNG in an underwater environment, wherein the two algorithms effectively reduce bottleneck nodes, but have too high node degrees and more redundant links, which cause information transmission between sensor nodes to generate conflict and cause unnecessary energy consumption.
Fig. 9 shows that the PG-OSTCG algorithm optimizes a network topology structure by combining potential game and optimal rigid subgraph model, not only considering node load energy consumption, but also balancing network energy consumption, and uses nodes with much residual energy as data relay forwarding nodes, so that premature death of key nodes and edge nodes due to too fast energy consumption is alleviated, and redundant links in the network are reduced, thereby effectively prolonging the life cycle of the network.
FIGS. 10 and 11 show graphs comparing the average degree and the maximum degree of the DEBA, EFPC, 3DK-RNG and the nodes of the PG-OSTCG algorithm proposed by the invention. The overall display shows that the maximum degree and the average degree of the nodes are increased along with the increase of the number of the nodes, and the average node degree of the nodes reaches a relatively stable state when the number of the nodes reaches a certain amount, but as can be seen from fig. 11: the maximum node degree of the DEBA and EFPC algorithms is relatively high because both algorithms are based on balancing node energy consumption and power, resulting in a large deviation of the average node degree of the node from the maximum node degree.
Specifically, the maximum node degree of the PG-OSTCG algorithm is lower than that of DEBA, EFPC and 3DK-RNG, the maximum node degree of the PG-OSTCG is about 9, and the node average degree is about 5; the maximum node degrees of DEBA, EFPC and 3DK-RNG are respectively about 13, 15 and 11, and the node average degrees are about 2.5, 6.5 and 7. In an underwater wireless sensor network, if the node degree of a node is too high, serious interference and collision are generated between transmission signals, so that data packets need to be transmitted for multiple times, more energy waste is caused, and a longer link exists between nodes due to too low node degree. The optimal node degree of the nodes in the underwater network is approximate to 6, and the PG-OSTCG has small difference with the node average degree, and the average node degree of the nodes is 5, so that the network topology structure generated by the PG-OSTCG has good robustness.
5. PG-OSTCG link quality analysis
In the experimental simulation environment, the average link lengths of the EFPC, 3DK-RNG and PG-OSTCG algorithms are contrastively analyzed by changing the number of nodes, and the link quality of the PG-OSTCG algorithms is analyzed under different conditions of the regulating coefficient α.
Fig. 12 shows the change of the average link length of the 3DK-RNG, EFPC and PG-OSTCG algorithm proposed by the present invention with the network topology where the number of nodes increases from 70 to 150. The average link length of a topological structure formed by the 3DK-RNG is longest, namely when the nodes are equal, the network topological link generated by the 3DK-RNG algorithm has poor quality and high energy consumption; in addition, the average link length of the EFPC algorithm is smaller than that of the 3DK-RNG algorithm but larger than that of the PG-OSTCG algorithm, which shows that the link communication quality of the network topology generated by the PG-OSTCG algorithm is better than that of the 3DK-RNG algorithm and the EFPC algorithm.
It can be seen from fig. 13 that, when the number of the same nodes is small, the average length of the link is reduced and the link quality is slightly improved with the increase of α, but the smaller the average length of the link is, the equalization energy consumption of the PG-OSTCG algorithm is increased.
6. PG-OSTCG equilibrium energy consumption analysis
Energy consumption among the nodes needs to be balanced, and not only the residual energy among the nodes but also the load conditions of the nodes are considered. And (3) carrying out comparative analysis on the balanced energy consumption of the 3DK-RNG, EFPC and PG-OSTCG algorithms in the network operation process under the same experimental simulation environment.
Fig. 15 shows that the 3DK-RNG, EFPC and PG-OSTCG algorithms compare the node residual energy standard deviation of the 3 algorithms as the network runs. Because the 3DK-RNG algorithm does not consider the load energy consumption of the nodes, the rising speed of the residual energy standard deviation of the algorithm is high, the energy consumption of part of the nodes is high, and the unbalanced degree of the energy consumption is high; the EFPC algorithm balances the node energy consumption through a node playing strategy, the node residual energy standard deviation growth speed is relatively slow, the network energy consumption balancing capability is relatively good, but the sensor node residual energy standard deviation is larger than the PG-OSTCG algorithm because the energy consumption condition of the sensor node is not considered. The PG-OSTCG algorithm considers the residual energy of the nodes by using a game theory to balance energy consumption, simultaneously eliminates redundant links in the network by using a rigid graph theory and adopting a link weight function with node load and residual energy, and periodically reconstructs the network to further avoid the overweight of the node load, so that the residual energy standard deviation of the PG-OSTCG algorithm is small in change along with the time operation.
7. PG-OSTCG effect analysis for prolonging network life cycle
The PG-OSTCG algorithm is verified to prolong the network life cycle, which is the main target of energy consumption balance. Therefore, under the same experimental simulation environment, the network life cycles of the EFPC, 3DK-RNG and PG-OSTCG algorithms are compared under different node numbers.
Fig. 15 shows a comparison of the network life cycles of the 3DK-RNG, EFPC and PG-OSTCG algorithms at different node numbers for these 3 algorithms. As can be seen from the figure, the PG-OSTCG algorithm is better than the 3DK-RNG algorithm and the EFPC algorithm as the number of nodes increases gradually, because the 3DK-RNG and the EFPC algorithm only focus on the robustness of the network topology but not on the load and the residual energy of the nodes. Although the EFPC algorithm reduces the energy consumption of the nodes through the game theory but does not balance the energy consumption of the network, the PG-OSTCG algorithm constructed by the invention comprehensively considers the load of the nodes, the residual energy of the nodes and the problem of redundant links in the network, and meanwhile, the network has the capabilities of self-adaptive regulation and periodic isomorphism, so the network life cycle of the PG-OSTCG algorithm is better than that of the 3DK-RNG and EFPC algorithms.

Claims (5)

1.一种基于势博弈与刚性子图的三维水下网络拓扑控制方法，其特征在于所述方法包括如下步骤：1. a three-dimensional underwater network topology control method based on potential game and rigid subgraph, is characterized in that described method comprises the steps: 步骤一、水下无线传感器网络拓扑的构建Step 1. Construction of underwater wireless sensor network topology (1)在分析节点间通信距离和链路质量的基础上，初始化传感器节点i的最大通信半径为RC，感知半径为RS；(1) On the basis of analyzing the communication distance and link quality between nodes, initialize the maximum communication radius of sensor node i as R C , and the sensing radius as R S ; (2)节点i向周围节点广播信息包NCK，其中，
Figure FDA0002351534670000011
IDi为i标识码，Si为i的位置坐标，
Figure FDA0002351534670000012
为i的剩余能量；(2) Node i broadcasts a packet NCK to surrounding nodes, where,
Figure FDA0002351534670000011
ID i is the identification code of i, S i is the position coordinate of i,
Figure FDA0002351534670000012
is the remaining energy of i; (3)当传感器节点j接收到节点i信息包NCK后，节点j向节点i发送信息包ACK，其中，
Figure FDA0002351534670000013
这里Pj为j的功率，
Figure FDA0002351534670000014
为节点i与节点j的通信功率，Δ为动态拓扑反应能力，ri,j为节点i到节点j的路径传输成功率，Ui为节点i在网络中的效用函数值；(3) After the sensor node j receives the node i information packet NCK, the node j sends the information packet ACK to the node i, wherein,
Figure FDA0002351534670000013
Here P j is the power of j,
Figure FDA0002351534670000014
is the communication power between node i and node j, Δ is the dynamic topology response capability, ri ,j is the transmission success rate of the path from node i to node j, U i is the utility function value of node i in the network; (4)当节点i收到周围节点j的确认信息包ACK后，则节点i将节点j添加至节点i邻居信息表中，以此建立可获知的最大全局网络拓扑视图Gmax；(4) after node i receives the acknowledgment packet ACK of surrounding node j, then node i adds node j to the node i neighbor information table, thereby establishing the largest known global network topology view G max ; 步骤二、网络拓扑博弈的执行Step 2. Execution of the network topology game (1)计算节点i当前功率pi，获知剩余能量
Figure FDA0002351534670000015
及节点可选功率集
Figure FDA0002351534670000016
其中
Figure FDA0002351534670000017
分别为节点i的最小功率和最大功率；(1) Calculate the current power p i of node i, and know the remaining energy
Figure FDA0002351534670000015
and node selectable power sets
Figure FDA0002351534670000016
in
Figure FDA0002351534670000017
are the minimum power and maximum power of node i, respectively; (2)每个节点根据功率集依次选择功率，每一轮只有一个节点调节功率，其他节点功率不变；(2) Each node selects the power in turn according to the power set, only one node adjusts the power in each round, and the power of other nodes remains unchanged; (3)若给定其他参与者的功率p-i时，节点i的最优响应策略为
Figure FDA0002351534670000018
(3) If the power p- i of other participants is given, the optimal response strategy of node i is:
Figure FDA0002351534670000018
 (4)博弈执行过程中，若节点选择比当前功率低的功率通信时，观察所获得的收益是否变大，若变大，则说明较低的功率更适合作为该节点的通信功率；否则，节点保持当前功率不变；(4) During the execution of the game, if the node selects a power communication lower than the current power, observe whether the obtained income becomes larger. If it becomes larger, it means that the lower power is more suitable as the communication power of the node; otherwise, The node keeps the current power unchanged; (5)当每个节点i功率对于其他节点的功率更优，即所有节点的功率达到最优状态，且节点功率集P不存在改变任意节点的功率使网络收益变大，则此时的网络达到一种均衡状态，即纳什均衡，此时，由最终各节点的信息表构建节点的邻居节点集合R，生成网络拓扑图；(5) When the power of each node i is better than the power of other nodes, that is, the power of all nodes reaches the optimal state, and the node power set P does not exist to change the power of any node to increase the network revenue, then the network at this time A state of equilibrium is reached, that is, Nash equilibrium. At this time, the neighbor node set R of the node is constructed from the final information table of each node, and the network topology map is generated; 步骤三、冗余链路的剔除Step 3. Elimination of redundant links 引入最优刚性图原理，剔除网络中的冗余链路，具体步骤如下：The principle of optimal rigid graph is introduced to eliminate redundant links in the network. The specific steps are as follows: (1)每个节点i根据邻居节点集合R，计算自己的邻居个数k；(1) Each node i calculates its own neighbor number k according to the neighbor node set R; (2)构建权值链路集Wi和子图矩阵Gi；(2 ) construct weight link set Wi and subgraph matrix G i ; (3)判断自身所构建的权值链路集Wi是否满足构建刚性矩阵，若满足则构建刚性矩阵M和最优子刚性矩阵Mc，最终由最优刚性子图矩阵得到待删除链路集合D，通过待删除链路集合D更新各节点的邻居节点集合R；(3) Judging whether the weight link set W i constructed by itself satisfies the construction of rigid matrix, if so, construct rigid matrix M and optimal sub-rigid matrix M c , and finally obtain the link to be deleted from the optimal rigid sub-graph matrix Set D, update the neighbor node set R of each node through the link set D to be deleted; 步骤四、网络拓扑的自适应与维护Step 4. Network topology adaptation and maintenance (1)设计水下预警机制实时监控水下环境，将水下恶劣环境具体表现为不同的等级，同时，预警机制实时向节点发布水下环境等级信息，以便网络拓扑能够在一定时间内调节自身，以适应即将到来的环境，具体描述如下：(1) Design an underwater early warning mechanism to monitor the underwater environment in real time, and express the harsh underwater environment into different levels. At the same time, the early warning mechanism releases information on the underwater environment level to nodes in real time, so that the network topology can adjust itself within a certain period of time. , to accommodate the upcoming environment, as described below: a、当环境较为稳定时：网络拓扑以节点的剩余能量为主要考虑因素，以均衡能耗为主要目标，避免节点耗尽能量而死亡；a. When the environment is relatively stable: the network topology takes the remaining energy of the node as the main consideration, and the main goal is to balance the energy consumption, so as to avoid the death of the node due to exhaustion of energy; b、当环境较为恶劣时：网络拓扑以鲁棒性为主要因素，避免节点因洋流或大型生物撞击而造成网络瘫痪；b. When the environment is relatively harsh: the network topology is mainly based on robustness to avoid network paralysis caused by the impact of ocean currents or large organisms; (2)当UWSNS中节点出现失效或能量耗尽达到一定阀值时，需要考虑均衡网络节点的能量消耗，分析影响动态拓扑反应能力重要因子，设计网络拓扑修复与重构算法，具体步骤如下：(2) When the node in UWSNS fails or the energy exhaustion reaches a certain threshold, it is necessary to consider the energy consumption of the balanced network nodes, analyze the important factors affecting the dynamic topology response capability, and design the network topology repair and reconstruction algorithm. The specific steps are as follows: 首先设定能量阈值τE和触发机制，若
Figure FDA0002351534670000031
时，则启动网络拓扑修复机制，其中E0(i)为节点i的初始能量；另外，当网络拓扑中有新的节点加入或者失效时，先判断网络是否是连通的，若连通，则网络拓扑不变，否则执行网络拓扑修复机制，具体情况描述如下：First set the energy threshold τ E and trigger mechanism, if
Figure FDA0002351534670000031
When , start the network topology repair mechanism, where E 0 (i) is the initial energy of node i; in addition, when a new node joins or fails in the network topology, first determine whether the network is connected, if connected, the network The topology remains unchanged, otherwise the network topology repair mechanism is implemented. The specific situation is described as follows: a、初始化能量阈值τE，计算节点剩余能量Er(i)，确定冗余节点；a. Initialize the energy threshold τ E , calculate the remaining energy E r (i) of the node, and determine the redundant node; b、当节点剩余能量Er(i)＜τE，依据冗余节点进行调整，均衡网络能量，完成拓扑修复，否则返回a；b. When the node residual energy E r (i)<τ E , adjust according to redundant nodes, balance the network energy, and complete the topology repair, otherwise return to a; c、当节点加入、节点失效时，对网络连通性和网络覆盖率无影响，则返回a，否则执行拓扑修复算法。c. When the node joins and the node fails, it has no effect on the network connectivity and network coverage, and returns to a, otherwise, the topology repair algorithm is executed. 2.根据权利要求1所述的基于势博弈与刚性子图的三维水下网络拓扑控制方法，其特征在于所述步骤二中，计算节点i当前功率pi的公式如下：2. the three-dimensional underwater network topology control method based on potential game and rigid subgraph according to claim 1, is characterized in that in described step 2, the formula of calculating node i current power p i is as follows: Et(l,r)＝l×Eelec+C×H×r×eα(f)×r×T；E t (l,r)=l×E elec +C×H×r×e α(f)×r ×T; 其中，C＝2π×0.67×10-9.5；
Figure FDA0002351534670000032
f为发射频率；l为数据包大小；Eelec为接收单位数据消耗的能量；T为数据的传输时间；H为节点平均水深；r为节点间通信距离。Wherein, C=2π×0.67×10 −9.5 ;
Figure FDA0002351534670000032
f is the transmission frequency; l is the size of the data packet; E elec is the energy consumed by receiving unit data; T is the data transmission time; H is the average water depth of the nodes; r is the communication distance between nodes. 3.根据权利要求1所述的基于势博弈与刚性子图的三维水下网络拓扑控制方法，其特征在于所述步骤三中，构建权值链路集Wi和子图矩阵Gi的公式如下：3. the three-dimensional underwater network topology control method based on potential game and rigid subgraph according to claim 1, is characterized in that in described step 3 , the formula of constructing weight link set Wi and subgraph matrix G i is as follows : 链路权重函数λij(t)为：The link weight function λ ij (t) is:
Figure FDA0002351534670000041
Figure FDA0002351534670000041
 这里，χ1+χ2＝1，其中：
Figure FDA0002351534670000042
为链路质量调节因子，d(i,j)为节点通信距离，Er(t)为节点剩余能量；Here, χ 1 +χ 2 =1, where:
Figure FDA0002351534670000042
is the link quality adjustment factor, d(i,j) is the communication distance of the node, E r (t) is the remaining energy of the node; 链路权重函数λij(t)为节点i的与其邻居节点的通信的权重具体值，权值链路集Wi为其权重值的集合；The link weight function λ ij (t) is the specific value of the weight of the communication between node i and its neighbor nodes, and the weight link set W i is the set of weight values; 子图矩阵Gi为：The subgraph matrix G i is:
Figure FDA0002351534670000043
Figure FDA0002351534670000043
 其中
Figure FDA0002351534670000044
为节点i与节点j的通信链路，E为网络中所有链路的集合。in
Figure FDA0002351534670000044
is the communication link between node i and node j, and E is the set of all links in the network. 4.根据权利要求1所述的基于势博弈与刚性子图的三维水下网络拓扑控制方法，其特征在于所述步骤三中，构建刚性矩阵M的方法如下：4. the three-dimensional underwater network topology control method based on potential game and rigid subgraph according to claim 1, is characterized in that in described step 3, the method for constructing rigid matrix M is as follows: 在r维空间中，将节点i的坐标表示为
Figure FDA0002351534670000045
则在三维空间中有：
Figure FDA0002351534670000046
将n个节点随机部署在r维空间中，将其按照序号排列其位置坐标为：In r-dimensional space, the coordinates of node i are expressed as
Figure FDA0002351534670000045
Then in three-dimensional space there are:
Figure FDA0002351534670000046
Deploy n nodes randomly in the r-dimensional space, and arrange them according to the serial number and their position coordinates are:
Figure FDA0002351534670000047
Figure FDA0002351534670000047
 在无向图G＝(V,E)中的链路集
Figure FDA0002351534670000048
其中每条链路都可以转换为刚性矩阵的行向量，则在三维空间中构建刚性矩阵M|e|×3n时，其中|e|为拓扑图中的链路总数，第k条链路
Figure FDA00023515346700000410
在刚性矩阵M中对应的第k行元素构成的行向量mk如下所示：A link set in an undirected graph G=(V,E)
Figure FDA0002351534670000048
Each link can be converted into a row vector of a rigid matrix, then when a rigid matrix M |e|×3n is constructed in three-dimensional space, where |e| is the total number of links in the topology map, and the kth link
Figure FDA00023515346700000410
The row vector m k formed by the corresponding k-th row elements in the rigid matrix M is as follows:
Figure FDA0002351534670000049
Figure FDA0002351534670000049
 其中k为节点i在发射功率为pi时的一跳邻居节点个数；where k is the number of one-hop neighbor nodes of node i when the transmit power is p i ; 则由|e|个行向量在三维空间中构成的刚性矩阵M|e|×3n如下所示：Then the rigid matrix M |e|×3n composed of |e| row vectors in three-dimensional space is as follows:
Figure FDA0002351534670000051
Figure FDA0002351534670000051
 5.根据权利要求1所述的基于势博弈与刚性子图的三维水下网络拓扑控制方法，其特征在于所述步骤三中，构建最优子刚性矩阵Mc的方法如下：5. the three-dimensional underwater network topology control method based on potential game and rigid subgraph according to claim 1, is characterized in that in described step 3, the method for constructing optimal sub rigidity matrix M c is as follows: 在r维空间中，所有链路的刚性矩阵M构建完成之后，构建刚性矩阵的链路权值集W；将权重集W按照升序排列，初始化刚性矩阵Mc＝M(1)，然后按照链路权值顺序依次将刚性矩阵M中的行添加到矩阵Mc中，如果矩阵Mc为满秩，则继续添加直至遍历完整个W，则最终得到的矩阵Mc为最优刚性矩阵。In the r -dimensional space, after the rigid matrix M of all links is constructed, construct the link weight set W of the rigid matrix; arrange the weight set W in ascending order, initialize the rigid matrix M c =M(1), and then follow the chain The road weights sequentially add the rows in the rigid matrix M to the matrix M c . If the matrix M c is full rank, continue to add until the entire W is traversed, and the final matrix M c is the optimal rigid matrix.
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