CN111132200B - 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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CN111132200B
CN111132200B CN201911417371.9A CN201911417371A CN111132200B CN 111132200 B CN111132200 B CN 111132200B CN 201911417371 A CN201911417371 A CN 201911417371A CN 111132200 B CN111132200 B CN 111132200B
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network topology
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魏连锁
郭媛
韩建
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Qiqihar University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W24/00—Supervisory, monitoring or testing arrangements
    • H04W24/02—Arrangements for optimising operational condition
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B13/00—Transmission systems characterised by the medium used for transmission, not provided for in groups H04B3/00 - H04B11/00
    • H04B13/02—Transmission systems in which the medium consists of the earth or a large mass of water thereon, e.g. earth telegraphy
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W84/00—Network topologies
    • H04W84/18—Self-organising networks, e.g. ad-hoc networks or sensor networks
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses a three-dimensional underwater network topology control method based on a potential game and a rigid subgraph, which comprises the following steps: step one, constructing an underwater wireless sensor network topology; step two, executing a network topology game; step three, removing redundant links; step four, self-adapting and maintaining of the network topology. 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.

Description

Three-dimensional underwater network topology control method based on potential game and rigid subgraph
Technical Field
The invention relates to an underwater sensor network topology control method, in particular to a three-dimensional underwater network topology 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 a topological control algorithm of an 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 and the like map coverage, connectivity, network energy consumption, communication link delay and transmission success rate optimization problems into potential game problems, construct a UWSNs topology control model optimized by multi-target QoS, and design 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, the robustness of the network is enhanced in a mode of always keeping K connection through the network, 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, and the nodes with large energy are dead due to energy consumption.
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 quality C With a sensing radius of R S ；
(2) Node i broadcasts an information packet NCK to the surrounding nodes, wherein,
Figure BDA0002351534680000031
ID i identifying code for i, S i A position coordinate of i, based on the number of pixels in the image sensor>
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 is j A power of j, is->
Figure BDA0002351534680000034
Is the communication power of node i and node j, Δ is the dynamic topology reaction capability, r i,j For the path transmission success rate, U, from node i to node j i A utility function value of the node i in the network;
(4) When the node i receives the ACK of the confirmation information packet of the peripheral node j, the node i adds the node j to the neighbor information table of the node i, and the maximum global network topology view G which can be obtained is established according to the node j max ；
Step two, executing network topology game
(1) Calculating the current power p of the node i i Learning of residual 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 i i The formula of (1) is as follows:
E t (l,r)＝l×E elec +C×H×r×e α(f)×r ×T；
wherein, C =2 π × 0.67 × 10 -9.5 ；
Figure BDA0002351534680000038
f is the transmission frequency; l is the packet size; e elec Energy consumed 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 -i When 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 W i And subgraph matrix G i Wherein:
link weight function lambda ij (t) is:
Figure BDA0002351534680000042
here, χ 1 +χ 2 =1, wherein:
Figure BDA0002351534680000043
for link quality adjustment factor, d (i, j) for node communication distance, E r (t) is the node residual energy;
link weight function lambda ij (t) is a specific weight value of communication of the node i and the neighbor nodes thereof, and a weight link set W i A set of its weight values;
submatrix G i Comprises 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 self i Whether the rigidity matrix is constructed or not is met, if so, the rigidity matrix M and the optimal sub-rigidity matrix M are constructed c Finally, the optimal rigid subgraph matrix is obtainedUpdating the neighbor node set R of each node through the link set D to be deleted when the link set D to be deleted arrives;
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 dying due to energy consumption;
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 the nodes in the UWSNS fail or the energy exhaustion reaches a certain threshold value, the energy consumption of the balanced network nodes needs to be considered, important factors influencing the dynamic topology reaction capability are analyzed, and a network topology restoration and reconstruction algorithm is designed, and the method specifically comprises the following steps:
first, an energy threshold τ is set E And a trigger mechanism, if
Figure BDA0002351534680000052
When it is time to start the network topology repair mechanism, where E 0 (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 τ E Computing node residual energy E r (i) Determining a redundant node;
b. when node residual energy E r (i)＜τ E Adjusting according to the redundant nodes, balancing network energy, completing topology restoration, or returning to a;
c. and 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 manner 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 is the effect of α on the network performance index when β, λ = 1;
fig. 3 is the effect of β on the network performance index when α, λ = 1;
fig. 4 is the effect of λ on the network performance index when α, β = 1;
FIG. 5 is a diagram of network topology adaptive adjustment;
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 changes in the 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 node numbers.
Detailed Description
The technical solutions of the present invention are further described below with reference to the drawings, but the present invention is not limited thereto, and any modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions 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:
1. topology control model of 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 = { V = 1 ,v 2 ,...v N },v 1 ,v 2 ,...v N Is a sensor node;
Figure BDA0002351534680000081
wherein->
Figure BDA0002351534680000082
A link representing an inter-node communication; />
Figure BDA0002351534680000083
Is a power set of nodes, where p min To receive a threshold, is>
Figure BDA0002351534680000084
Is the maximum power, p 1 ,p 2 ,...,p n Power is communicated 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 nodes ij Satisfy d ij ≤r c Then, nodes i and j are called as mutually neighboring nodes, where r c Is the communication radius; if nodes i and j can communicate with each other, then->
Figure BDA0002351534680000085
For the sake of the following studies, 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 perception range is spherical, and the node perception range can be accurately perceived inside the sphere and cannot be perceived 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 v i As a circle center, with R i Sphere of radius, and the sensing range of node i is R S Is a sphere of radius (R) S ≤R i )。
(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: poisson distribution obeying λ (λ is a poisson distribution adjustment factor) as a specific value.
(5) In UWSNs, each sensor node has a unique D i (D i An 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 operating lifetime of the network.
2. Ordinal number 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,. Eta, N }, N is the number of game participants.
2) And (4) a policy set A: a. The i Representing the behavior set of the participant i, if the participant i has k behaviors, then there is A i ＝{a 1 ,a 2 ,...a k In which a is 1 ,a 2 ,...a k In order to be a combination of behaviors,
Figure BDA0002351534680000091
let a be i For a certain behavior of participant i, then a -i ＝(a 1 ,...a i-1 ,a i+1 ,...,a n ) Representing a combination of behaviors of participants other than participant i, typically expressed as a = (a) i ,a -i ) Indicating a particular combination of behaviors.
3) Utility function U (a): u may represent is U = { U = 1 ,u 2 ,...u n }，u 1 ,u 2 ,...u n For profit, U can be used i (a i ,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 ∈ A i Given other participants +>
Figure BDA0002351534680000093
In case of (b), its behavior &>
Figure BDA0002351534680000094
Is the optimal behavior of participant i, having:
Figure BDA0002351534680000095
then
Figure BDA0002351534680000096
Is 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 a function is present>
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 ,a 2 ,...a n ) E is equal to A so that
Figure BDA00023515346800000912
And at least one->
Figure BDA00023515346800000913
So that->
Figure BDA00023515346800000914
If true, then the policy (a) 1 ,a 2 ,...a n ) 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 | | | f i (t)-f j (t) | = d, wherein d is a constant, that is, the motion locus 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.
Definition 5, optimal rigidity graph: 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.
Definition 6,Optimal rigid subgraph: for an arbitrary two topological graphs G (V, E), G ' (V ', E '), if
Figure BDA0002351534680000101
And is provided with
Figure BDA0002351534680000102
Then G ' is called a subgraph of G, and if and only if G ' is the optimal rigid graph, then G ' is called the optimal rigid subgraph of G.
Properties 2: as can be seen from the theory 1 and the definition 5 in the r-dimensional space, the optimal rigid graph is that the constructed topological graph has fewer links, the total weight of the links is minimum, and each vertex is at least connected with r links, i.e. the optimal rigid graph is r-connected and has stronger robustness.
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 connectivity function is thus set 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 the land radio energy consumption model, influence factors are more, so that the node energy consumption model is more defined, and the energy consumption model is introduced. The energy consumption of a node to transmit data can be expressed as:
E t (l,r)＝l×E elec +C×H×r×e α(f)×r ×T (5)；
wherein, C =2 π × 0.67 × 10 -9.5 ；
Figure BDA0002351534680000113
f is the transmission frequency; l is the packet size; e elec Energy 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 node r (l) Comprises the following steps:
E r (l)＝l×E elec (6)。
4) End-to-end delay:
the physical property of analysis water and the influence of network transmission characteristics on transmission delay are comprehensively analyzed, and the end-to-end delay from a receiving node to a sending node is as follows:
Figure BDA0002351534680000121
wherein: k is a radical of s For the number of retransmissions of a packet, l is the packet size, R ij To the transmission rate, D ij (t) is the distance from node i to node j at time t, c is the propagation velocity of the acoustic wave, Δ τ k As the kth of the data packet s Maximum multipath propagation delay difference, p, caused by multipath propagation during secondary retransmission ij For inter-node communication power, κ is the signal threshold magnitude 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 the ratio of the sum of noise powers of received signals which are larger than the interference power. The present invention is defined as:
Figure BDA0002351534680000122
wherein: b is n For the system bandwidth, α (f) is the medium absorption coefficient, r ij In order to be able to transmit the distance,
Figure BDA0002351534680000123
to be the same mu as the node i ik Each group is divided into the same group, m groups, sigma 2 Is the noise variance.
6) Transmission success rate:
the transmission success rate is set as:
Figure BDA0002351534680000131
/>
the number of retransmissions k s The 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
Wherein E 0 (i) And E r (i) Respectively the initial energy and the residual energy of the node i; meanwhile, factors are 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 p i The number of one-hop neighbor nodes in time.
In conclusion, the analysis shows that the connectivity, the coverage, the transmission energy consumption, the end-to-end transmission time delay, the signal-to-interference-and-noise ratio and the signal-to-interference-and-noise ratio of the network,The transmission success rate and the node residual energy are main optimization targets of the UWSNs, and due to the multiplicity of the targets and mutual contradiction between the targets, the performance of the targets can reach the optimal state, which is difficult to realize. 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 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: alpha, beta and lambda are weight adjusting factors respectively and are positive numbers; f i (a i ,a -i ) As a connectivity function, C i (a i ,a -i ) In order to be a function of the coverage,
Figure BDA0002351534680000141
for transmission of energy, S i (a i ,a -i ) For transmission success rate, D i (a i ,a -i ) For transmission delay, E 0 (i) And E r (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 lambda ij (t) is:
Figure BDA0002351534680000142
here, χ 1 +χ 2 =1, wherein:
Figure BDA0002351534680000143
for link quality adjustment factor, d (i, j) is a nodeCommunication distance, E r And (t) is the node residual energy.
(2) Subgraph matrix
For the topological graph G = (V, E), wherein the node i and the neighbor nodes form a subgraph matrix G i Comprises 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) i Number of neighbor nodes in one hop of time) — based on the number of neighbor nodes in one hop of time>
Figure BDA0002351534680000149
A row vector M formed by the corresponding k-th row elements in the rigid matrix M k As follows:
Figure BDA0002351534680000151
a rigid matrix M composed of | e | row vectors in a three-dimensional space |e|×3n As follows:
Figure BDA0002351534680000152
2, introduction: 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) =3n-6.
Property 3: from the above definitions 6, 7 and lemma 2 it follows that: in that r After 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 M c = M (1), and then the rows in the rigid matrix M are added to the matrix M in sequence according to the link weight order c In, if the matrix M is c If the rank is full, adding is continued until the whole W is traversed, and finally obtaining a matrix M c Is an optimal rigidity matrix.
2. 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 the sensor node i to be R on the basis of analyzing the communication distance between the nodes and the link quality C With a sensing radius of R S ；
(2) Node i broadcasts a packet NCK to surrounding nodes, wherein,
Figure BDA0002351534680000153
ID i identification code for i, S i A position coordinate of i, is greater than or equal to>
Figure BDA0002351534680000154
Is of iResidual energy;
(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 is j A power of j +>
Figure BDA0002351534680000162
Is the communication power of the node i and the node j, delta is the dynamic topology reaction capability, r i,j For the path transmission success rate, U, from node i to node j i A 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 G max And 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 and the network robustness in the underwater environment so as to prolong the life cycle and 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) i Learning of residual energy
Figure BDA0002351534680000163
And node selectable power set
Figure BDA0002351534680000164
Wherein +>
Figure BDA0002351534680000165
Respectively the minimum power and the maximum power of node i. Each sectionAnd sequentially selecting power by the point according to the power set, wherein 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 -i When the optimal response policy of node i is ≥ h>
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 is not changed 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 a 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) i And subgraph matrix G i Judging whether the link set constructed by the link set meets the requirement of constructing a rigid matrix or not by definition 4-6 and theorem 2, constructing a rigid matrix M by equations (14) - (16) if the rigid matrix meets the requirement, and constructing an optimal sub-rigid matrix M by property 3 c And 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, the energy consumption imbalance of the nodes can be caused when the network robustness is emphasized too much.
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 expressed by different weight factors of potential game models T = < N, A, U (A) > constructed by the invention), takes balanced energy consumption as a main target, and avoids 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 set E And a trigger mechanism, if
Figure BDA0002351534680000181
If so, starting a network topology repair mechanism; in addition, when there are new in the network topologyWhen a node is added or fails, firstly judging whether the network is connected or not, if so, keeping the network topology unchanged, otherwise, executing a network topology repair mechanism, wherein the specific conditions are as follows:
a. initialization energy threshold τ E Computing node residual energy E r (i) Determining a redundant node;
b. when node residual energy E r (i)＜τ E Adjusting according to the redundant nodes, balancing network energy, completing topology restoration, and otherwise, returning to a;
c. and 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 1PG-OSTCG Algorithm pseudocode description Table
Figure BDA0002351534680000191
3. Performance evaluation of PG-OSTCG algorithm
4 groups of comparison simulation and 1 group of network adaptive adjustment comparison and 1 group of algorithm weight factor selection experiments are designed by utilizing python so as to verify the effectiveness of the PG-OSTCG algorithm. The method specifically comprises the following steps: experiment 1 considers the influence of weight factors alpha, beta and lambda on the network topology performance from three aspects of node transmitting power, node average node degree and neighbor node average residual energy; experiment 2 is a network topology structure diagram of the algorithm constructed by the invention in different underwater environments; experiment 3 is to compare the average node degree and the maximum node degree of four algorithms, namely DEBA, EFPC, 3Dk-RNG and PG-OSTCG, under different node numbers, and analyze the robustness of the PG-OSTCG algorithm; experiment 4 is to compare the average link lengths of the EFPC, 3Dk-RNG and PG-OSTCG algorithms with the average link length of the PG-OSTCG algorithm after running for 100 cycles under different node numbers and to analyze the link quality of the PG-OSTCG algorithm; experiment 5 is the standard deviation of the residual energy of the EFPC, 3Dk-RNG and PG-OSTCG algorithms when the network is reconstructed for 100 times and the standard deviation of the residual energy of the PG-OSTCG algorithms when the alpha values are different, and the effect of the PG-OSTCG algorithms on balancing energy consumption is analyzed; experiment 6 is to compare the network life cycle of EFPC, 3Dk-RNG and PG-OSTCG algorithms with the life cycle of PG-OSTCG algorithms at different alpha values under different nodes, and analyze the effect of PG-OSTCG algorithms on prolonging the network life cycle.
In order to understand the simulation process, performance evaluation indexes of the experimental simulation are given as follows:
(1) Robustness of the network topology: when a certain link of the network is interrupted, the network can select other links to quickly transmit data, namely the connectivity of the network is good, 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 D av Namely:
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 link average length l av Namely:
Figure BDA0002351534680000203
wherein l ij Is the length of the communication link between nodes i and j, and L is the total number of links in the network.
(4) The network life cycle: in the 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 network L Namely:
T L ＝T D -T B (24)；
wherein, T D Time of death of the first node, T B The 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
And randomly placing 80 nodes in a three-dimensional monitoring area (400 multiplied by 400), and adjusting another weight factor to analyze the influence of the weight factor in the algorithm on the network topology performance under the condition that any two weight factor values of alpha, beta and lambda are limited to be 1.
As can be seen from fig. 2: the average transmission power, average node degree and average residual energy of the neighboring nodes decrease with the increase of α, and it can be seen from fig. 3 and 4 that: the average transmitting power, the average node degree and the average residual energy of the neighbor nodes of the node are increased along with the increase of beta, and the change of the three indexes after alpha, beta and lambda is more than or equal to 2 is relatively stable. It can be known from the general theory of network topology structure that when the transmitting power of the nodes in the network is low and the nodes have moderate degree, the topology structure is relatively perfect. In the present invention, α is 1, β is 2, and λ is 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 underwater environments are 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 necessarily 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
Two game theory-based underwater network topology control algorithms DEBA and EFPC and an underwater fault-tolerant topology algorithm 3DK-RNG are selected to be compared 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, which effectively reduce bottleneck nodes, but have too high node degrees and more redundant links, resulting in collision of information transmission between sensor nodes and 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 nodes 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 DEBA, EFPC, 3DK-RNG maximum node degrees are about 13, 15 and 11, respectively, 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 algorithm is analyzed under the condition that the adjustment coefficient alpha is different. Since there are more "bottleneck nodes" and "edge nodes" in the DEBA algorithm, it will not be contrasted with it in the following.
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.
As shown in fig. 13, when the number of the same nodes is small, the average link length decreases with the increasing α, the link quality slightly improves, but the smaller the average link length is, the equalization energy consumption of the PG-OSTCG algorithm increases. It follows that it is feasible to adjust the lifetime of the network by adjusting the size of the weighting factors (i.e. sacrificing or adding a small amount of communication quality), i.e. the network has some adaptive performance.
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 cycle of the EFPC, 3DK-RNG and PG-OSTCG algorithms is 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 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 capability of self-adaptive adjustment and periodic isomorphism, so that the network life cycle of the PG-OSTCG algorithm is better than that of a 3DK-RNG algorithm and an EFPC algorithm.

Claims (3)

1. A three-dimensional underwater network topology control method based on potential game and rigid subgraph is characterized by comprising the following steps:
step one, constructing underwater wireless sensor network topology
(1) Initializing the maximum communication radius of the sensor node i to be R on the basis of analyzing the communication distance between the nodes and the link quality C With a radius of perception of R S ；
(2) Node i broadcasts a packet NCK to surrounding nodes, wherein,
Figure FDA0004017239800000011
ID i identifying code for i, S i A position coordinate of i, is greater than or equal to>
Figure FDA0004017239800000012
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 FDA0004017239800000013
where P is j A power of j +>
Figure FDA0004017239800000014
Is the communication power of node i and node j, Δ is the dynamic topology reaction capability, r i,j For the path transmission success rate, U, from node i to node j i A utility function value of the node i in the network;
(4) When the node i receives the ACK of the confirmation information packet of the peripheral node j, the node i adds the node j to the neighbor information table of the node i, and the maximum global network topology view G which can be obtained is established according to the node j max ；
Step two, executing network topology game
(1) Calculating the current power p of the node i i Learning of residual energy
Figure FDA0004017239800000015
And node selectable power set
Figure FDA0004017239800000016
Wherein +>
Figure FDA0004017239800000017
Respectively calculating the current power p of the node i for the minimum power and the maximum power of the node i i The formula (c) is as follows:
E t (l,r)＝l×E elec +C×H×r×e α(f)×r ×T；
wherein, C =2 π × 0.67 × 10 -9.5 ；
Figure FDA0004017239800000018
f is the transmission frequency; l is the packet size; e elec Energy 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 -i When the optimal response strategy of the node i is
Figure FDA0004017239800000021
(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 comprises the following specific steps of:
(1) Each node i calculates the number k of own neighbors according to the neighbor node set R;
(2) Constructing weight link set W i And subgraph matrix G i The formula is as follows:
link weight function lambda ij (t) is:
Figure FDA0004017239800000022
here, χ 1 +χ 2 =1, wherein:
Figure FDA0004017239800000023
for link quality adjustment factor, d (i, j) for node communication distance, E r (t) is the node residual energy;
link weight function lambda ij (t) is a specific weight value of communication of the node i and the neighbor nodes thereof, and a weight link set W i Is a set of its weight values;
submatrix G i Comprises the following steps:
Figure FDA0004017239800000031
wherein
Figure FDA0004017239800000032
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 self i Whether the rigidity matrix is constructed or not is met, if so, the rigidity matrix M and the optimal sub-rigidity matrix M are constructed c 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;
step four, self-adaptation and maintenance of network topology
(1) Design early warning mechanism real time monitoring underwater environment under water, show underwater adverse circumstances concrete as different grades, simultaneously, the early warning mechanism issues underwater environment grade information to the node in real time to network topology can adjust self in certain time, in order to adapt to upcoming environment, 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 the node in the UWSNS fails or the energy consumption reaches a threshold value, the energy consumption of the balanced network node needs to be considered, important factors influencing the dynamic topology reaction capability 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 set E And a trigger mechanism, if
Figure FDA0004017239800000033
When it is time to start the network topology repair mechanism, where E 0 (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 τ E Computing node residual energy E r (i) Determining a redundant node;
b. when node residual energy E r (i)＜τ E Adjusting according to the redundant nodes, balancing network energy, completing topology restoration, and otherwise, 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.
2. The three-dimensional underwater network topology control method based on potential game and rigid subgraph according to claim 1, characterized in that in the third step, the method for constructing the rigid matrix M is as follows:
in the r-dimensional space, the coordinates of the node i are expressed as
Figure FDA0004017239800000041
Then in three-dimensional space there are: />
Figure FDA0004017239800000042
Randomly deploying n nodes in an r-dimensional space, and thenThe position coordinates of the position coordinates are arranged according to the sequence numbers: />
Figure FDA0004017239800000043
Link set in undirected graph G = (V, E)
Figure FDA0004017239800000044
Wherein each link can be converted into a row vector of a rigid matrix, and then a rigid matrix M is constructed in a three-dimensional space |e|×3n Where | e | is the total number of links in the topology map, the kth link |, is |, and>
Figure FDA0004017239800000045
a row vector M formed by the corresponding k-th row elements in the rigid matrix M k As follows:
Figure FDA0004017239800000046
where k is node i at a transmit power of p i The number of time-hopping neighbor nodes;
a rigid matrix M consisting of | e | row vectors in three-dimensional space |e|×3n As follows:
Figure FDA0004017239800000047
3. the three-dimensional underwater network topology control method based on potential game and rigid subgraph according to claim 1, characterized in that in the third step, an optimal sub-rigid matrix M is constructed c The method comprises the following steps:
in that r In the dimensional space, after the rigid matrixes M of all the links are constructed, constructing a link weight value set W of the rigid matrixes; arranging the weight sets W in ascending order, and initializing a rigid matrix M c = M (1), then add rows in the rigid matrix M to the matrix M in order of link weights c In, if the matrix M is c If the rank is full, adding is continued until the whole W is traversed, and finally obtaining a matrix M c Is an optimal rigidity matrix.
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