Underwater wireless sensor network propagation model construction method based on cellular automaton

Abstract

The invention belongs to the technical field of wireless sensor networks, and particularly relates to an underwater wireless sensor network propagation model construction method based on a cellular automaton, which comprises the following steps of: establishing an underwater wireless sensor network model, acquiring the position of a node at each moment, continuously updating the state and the position of the node by adopting a new cellular space and an updating rule, and constructing an underwater wireless sensor network propagation model. And constructing an underwater wireless sensor network propagation model based on the cellular automaton based on the new updating mechanism. According to the method, the spatial distribution change of malicious program propagation in the underwater wireless sensor network and the global change trend of infected nodes are described, and the problem that in the prior art, a malicious program propagation model based on a cellular automaton model lacks underwater wireless sensor network malicious program propagation description is solved.

Description

Technical Field

[0001] This application belongs to the technical field of wireless sensor networks, and particularly relates to a method for constructing a propagation model of an underwater wireless sensor network based on cellular automata. Background Art

[0002] Nowadays, underwater wireless sensor networks (UWSN) are increasingly widely applied in various aspects such as life, economy, and military. Due to the limited resources of sensor nodes in underwater wireless sensor networks and their frequent deployment in harsh environments, underwater wireless sensor networks are easily invaded by malicious programs. These malicious programs may steal network information and even damage the entire underwater wireless sensor network. Therefore, the security situation of underwater wireless sensor networks is becoming increasingly severe. Existing technologies use the CA model to construct a malicious program propagation model. Through the malicious program propagation models they constructed, it is found that the characteristics of the underwater environment and node mobility have a greater impact on the propagation of malicious programs. However, in the above malicious program propagation models based on the CA model, they did not consider the influence of the underwater environment and node mobility ability in UWSN, resulting in a large deviation in the analysis results. Summary of the Invention

[0003] Based on the above problems, this application proposes a method for constructing a propagation model of an underwater wireless sensor network based on cellular automata, and its technical solution is as follows:

[0004] A method for constructing a propagation model of an underwater wireless sensor network based on cellular automata includes the following steps: S1. Abstract the space where the underwater wireless sensor network is located into a gridless two-dimensional space, establish a cellular automata model of the underwater wireless sensor network, and classify all nodes into two categories: sensor nodes and autonomous underwater vehicles;

[0005] S2. Use a movement model to generate the position of each autonomous underwater vehicle after movement and obtain the real-time position of each autonomous underwater vehicle;

[0006] S3. Redesign the cellular space and transition rules according to the characteristics of the underwater wireless sensor network, and continuously update the states of underwater nodes and autonomous underwater vehicles according to the redesigned transition rules;

[0007] Cellular space: Set an overall space as the cellular space of the cellular automata;

[0008] Transition rule: Use the method of judging the existence of nodes within the communication radius with the node as the center as the cellular neighbor; S4. Based on the mutual influence of the two types of nodes, construct a propagation model of the underwater wireless sensor network based on cellular automata.

[0009] Preferably, in step S1, a cellular automaton model of the underwater wireless sensor network is established, which is mainly characterized in that the definition of the space, state and transition rules of the underwater wireless sensor network is more in line with the characteristics of the underwater wireless sensor network. Specifically, the space where the underwater wireless sensor network is located is abstracted into a two-dimensional space of L×L without cells. The above space can also be set as an irregular two-dimensional graph, but for the convenience of subsequent calculations, the space is set as a square space convenient for calculation. N underwater sensor nodes and M autonomous underwater vehicles are evenly distributed in the two-dimensional space. All sensor nodes and autonomous underwater vehicles can communicate with each other, but there are slight differences in communication performance. Moreover, the sensor nodes are relatively fixed, while the autonomous underwater vehicles have strong mobility. Generally speaking, the communication range of a node is fixed. If a node leaves the communication range during the movement process, it will cause the interruption of communication.

[0010] Preferably, the specific steps of step S2 are as follows:

[0011] S21. Use the random walk model as the movement model of the autonomous underwater vehicle to simulate the underwater environment affected by various environmental factors;

[0012] S22. Randomly generate the initial positions of the autonomous underwater vehicles, make them evenly distributed in the environment, and set the external influencing factors;

[0013] S23. Iteratively update the positions of the autonomous underwater vehicles at fixed time intervals, and add the influences of external influencing factors such as water flow velocity, energy consumption and obstacle distribution to the position update formula;

[0014] S24. Read the current coordinates of the autonomous underwater vehicle and obtain the position of the autonomous underwater vehicle in real time.

[0015] Preferably, in step S3, a redesigned cellular space and transition rules are adopted to realize the iterative update of the cellular automaton model, which specifically includes the following steps:

[0016] S31. Set the size range and boundary conditions of the cellular space of the underwater wireless sensor network, and assign initial states and initial positions to all nodes. In addition, the two types of nodes, namely sensor nodes and autonomous underwater vehicles, are distinguished in their characteristic attributes;

[0017] S32. Set the specific requirements for the conversion between different states of the cells. When meeting certain spatial and neighbor requirements, the cells can be converted from one state to another state, and make them able to perform conversions according to the conversion rules; S33. Determine the method for judging the cell neighbors, that is, taking the cell as the center, calculate the number of different types of cells within the communication radius;

[0018] S34. Traverse all cells, generate the new state value of this cell according to the conversion rules using the number of states counted in step S33, and then replace the values of all old states with the new state values;

[0019] S35. Detect the number of time steps. If the fixed number of time steps is reached, stop the iteration; otherwise, continue the iteration. Preferably, in step S4, the specific definitions of different types of cells in the cellular automaton model are as follows: when node_state = 0, the underwater sensor node N U is in the susceptible state S; when node_state = 1, the underwater sensor node N U is in the exposed state E; when node_state = 2, the underwater sensor node N U is in the infected state I; when auv_state = 0, the autonomous underwater vehicle N A is in the susceptible state S; when auv_state = 1, the autonomous underwater vehicle N A is in the exposed state E; when auv_state = 2, the autonomous underwater vehicle N A is in the infected state I.

[0020] Preferably, the cellular automaton model in step S4 is specifically:

[0021] A = {L, S, T, N, V, f};

[0022] Assume that a cell i has k neighbors, then the set of neighborhood nodes of cell i at time t is represented as V t,i = {S t,1 , S t,2 , …, S t,k}; f represents the redesigned conversion rule of the cell. The state of cell i at time t is determined based on its neighborhood state at time t - 1, which is expressed as:

[0023] S t,i = f(V t-1,i );

[0024] N represents the new neighborhood function. The number of neighborhood nodes of cell i at time t is based on whether the distance between it and other cell j is less than the communication radius r of the cell, which is expressed as:

[0025]

[0026] Among them, A represents the cellular automaton system; L represents the divided cell space; S represents the finite set of cell states; T represents the time set; V represents the set of neighborhood cells of the cell.

[0027] Preferably, the underwater wireless sensor network propagation model based on cellular automata is specifically as follows:

[0028]

[0029] S U (t), E U (t), I U (t) represent the number of underwater sensor nodes in the susceptible state S, exposed state E, and infected state I at time t, respectively. S A (t), E A (t), I A (t) represent the number of autonomous underwater vehicles in the susceptible state S, exposed state E, and infected state I at time t, respectively.

[0030] Preferably, the iterative process of underwater sensor nodes is as follows:

[0031] P(S i (t + ΔT + 1) = 1)

[0032] = 1 - P(S i (t + ΔT + 1) = 0) - P(S i (t + ΔT + 1) = 2)

[0033] = 1 - P(S i (t + ΔT + 1) = 0|S i (t) = 0)P(S i (t) = 0)

[0034] - P(S i (t + ΔT + 1) = 2|S i (t) = 1)P(S i (t) = 1)

[0035] - P(S i (t + ΔT + 1) = 2|S i (t) = 2)P(S i (t) = 2)

[0036] The state of a specific node i at time t can be obtained through the total probability:

[0037]

[0038] According to the time dependence and local spatial dependence between node i and its neighboring nodes, the subsequent iterative process is as follows:

[0039]

[0040] Among them, the vector is the state vector of the neighbors of the underwater node i at time t, and the vector represents the state parameter of, that is, s j (t) = 0, 1 or 2; β ji = p1p2 is the probability that the infected node j with state parameter 1 or 2 infects its already infected neighbor i, where p1 represents the probability of successfully infecting a healthy node when an infected node communicates with an uninfected node, and p2 represents the probability of a healthy node being infected during the spread of malicious programs.

[0041] Preferably, the iterative expression of state I is derived based on the dependence of the local space and the state of node i at time t + 1. The specific process can be expressed as:

[0042]

[0043] where γ ji represents the probability that the infected node j with state I successfully infects other communicating healthy node i, and this healthy node i has been infected but has not received an attack command. Finally, the conversion rule can be expressed as:

[0044]

[0045] where the state transition function represents whether the healthy node i will convert to state E after time t + T; then represents whether the state of the underwater node i changes after receiving an attack command from a communicable node in state E; f random (x) represents the recovery function, which reflects that the probability of the state of node i changing after receiving an attack command is δ i , and random is a decimal randomly generated between 0 and 1.

[0046] Compared with the prior art, the beneficial effects of this application are as follows:

[0047] The present invention constructs a propagation model of an underwater wireless sensor network based on a cellular automaton by establishing an underwater wireless sensor network model, using a cell-free space as a new cellular space, and setting state transition rules for underwater sensor nodes and autonomous underwater vehicles and malicious program propagation conversion rules in the cellular automaton model. By setting a new cellular space and conversion rules, the influence of the underwater environment on underwater sensor nodes and autonomous underwater vehicles is simulated, and the problem in the prior art that the malicious program propagation model based on the CA model lacks the simulation of UWSN is solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is the flowchart of this application;

[0049] Figure 2 Schematic diagram of the state transition of underwater sensor nodes and autonomous underwater vehicles;

[0050] Figure 3 This is a simulation effect diagram. The circular nodes represent sensor nodes and the triangular nodes represent autonomous underwater vehicles. DETAILED DESCRIPTION

[0051] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific implementation described herein is only used to explain the present invention and is not intended to limit the present invention.

[0052] like Figure 1 FIG. 1 is a flow chart of a method for designing a propagation model of an underwater wireless sensor network based on cellular automata according to the present invention. A method for designing a propagation model of an underwater wireless sensor network based on cellular automata comprises the following steps:

[0053] S1, abstract the underwater wireless sensor network into a two-dimensional space and establish an underwater wireless sensor network model;

[0054] S2, using the mobile model to generate the position of each autonomous underwater vehicle after the node moves, and obtaining the real-time position of each autonomous underwater vehicle;

[0055] S3, using the redesigned cellular space and update rules, and continuously updating the status and position of underwater nodes and autonomous underwater vehicles according to the above rules;

[0056] S4. Based on the new cellular space and working state transformation rules and the malicious program propagation transformation rules in the cellular automaton model, a cellular automaton-based underwater wireless sensor network propagation model is constructed.

[0057] In step S1, the present invention abstracts the deployment space of the underwater wireless sensor network into a two-dimensional space of size L×L, in which N underwater sensor nodes and M autonomous underwater vehicles are deployed. These underwater sensor nodes and autonomous underwater vehicles are evenly distributed in the space area, and the two types of nodes can communicate with each other. In this space area, the density of underwater sensor nodes and autonomous underwater vehicles is ρ1=N / L respectively. 2 and ρ2=M / L 2 All underwater sensors and AUV nodes can communicate with each other, but there are slight differences in communication performance. In addition, underwater sensor nodes are relatively fixed, while AUVs have strong mobility.

[0058] Cellular Space

[0059] Suppose N sensor nodes and M autonomous underwater vehicles are evenly distributed in the simulation area of L km × L km at the initial moment, and the device density λ in this area is λ = (M + N) / L 2 . After moving underwater, the position coordinates (x it , y it ) at time t represent a cell c i , where i = 1, 2,..., N, t = 1, 2,..., n, N is the total number of underwater nodes, and n represents the simulation time. That is to say, the cell c i can be occupied by the underwater node i. The entire cell space is composed of a two-dimensional plane consisting of M + N cell units, and its communication relationship is represented by the connection lines between nodes. For the two-dimensional cellular automaton model, the cell space C can be expressed as C = {(x it , y it ), 1 < x it < L, 1 < y it < L}, and each node moves within the simulation area according to the movement model at the very beginning.

[0060] In the underwater wireless sensor network, the underwater node i directly exchanges data and other information with its neighbor nodes through underwater communication technology. In this study, the actual number of neighbor nodes of node i is considered to be k = |N i |, and the number of k depends on the actual number of nodes within the communication range at time t, where N i represents the neighbor of node i, which can be expressed as According to the characteristics of underwater wireless sensor nodes, it can be known that the above definitions are all in line with the actual topology of the underwater wireless sensor network.

[0061] In step S2, all nodes are divided into two categories. The underwater sensor nodes are basically fixed, while the autonomous underwater vehicles use the movement model to generate the position after each autonomous underwater vehicle moves and obtain the real-time position of each autonomous underwater vehicle.

[0062] The present invention uses the movement model to generate the real-time position of the autonomous underwater vehicle, which specifically includes the following sub-steps:

[0063] S21. Use the random walk model as the movement model to simulate the underwater environment affected by various environmental factors;

[0064] S22. Randomly generate the initial positions of the autonomous underwater vehicles, make them evenly distributed in the environment, and set factors such as water flow speed, energy consumption, and obstacle distribution;

[0065] S23, iteratively updating the position of the autonomous underwater vehicle at fixed time intervals, adding the influence of the above-mentioned random disturbance factors into the position update formula;

[0066] S24. Directly read the current coordinates of the autonomous underwater vehicle through its attributes, so as to achieve the purpose of obtaining the position of the autonomous underwater vehicle in real time.

[0067] In step S3, the present invention redesigns the cellular space and transformation rules of the cellular automaton, wherein the cellular space is no longer limited to a fixed number of cells, but instead integrates these cells into an overall abstract space, and all nodes can move in the entire space, rather than limiting cells to individual cells. At the same time, the neighborhood definition of the cellular automaton should also be changed accordingly. Now the definition of the neighborhood is changed to nodes that exist within the communication radius of the current node. Therefore, when the communication radius of the node is r, the division of the cellular space in CA is πr 2 , so that the communication process of the network can be closer to the real situation.

[0068] The updating process of constructing the cellular automaton model of the present invention specifically includes the following steps:

[0069] S31, setting the size and boundary conditions of the cellular automaton cell space, and assigning an initial state value to each cell;

[0070] S32. Clarify how the state of the cell in the current state will change at the next moment;

[0071] S33, determining the range of the cellular neighborhood, and performing statistics on the states of all cells in each cellular neighborhood;

[0072] S34, traverse all cells, use the rules to generate new state values ​​according to the number of states counted in step S33, and then replace all old states with the new states;

[0073] S35. When the fixed number of time steps is reached, the iteration is stopped.

[0074] In step S4, the present invention sets the propagation model of malicious programs of cellular automata: for cellular automata, it is mainly composed of cellular space, cellular state and conversion rules. The present invention uses mathematical language to set cellular automata, and cellular automata can be represented by a four-tuple: A = {C, S, V, f}, where A represents the cellular automata system; C represents the divided cellular space; S represents a finite set of cellular states; V represents the neighborhood cell set of the cell. Assuming that a cell i has k neighbors, the neighborhood node set of cell i at time t is represented as V t,i ={S t,1 ,S t,2 ,…,St,k}; f represents the transformation rule of the cell. The state of cell i at time t is determined based on the neighborhood state at time t - 1, which can be expressed as:

[0075] S t,i = f(V t-1,i );

[0076] In the present invention, the transformation rule of malicious program propagation in the cellular automaton model can be expressed as: when node_state = 0, the underwater sensor node N U is in the susceptible state S; when node_state = 1, the underwater sensor node N U is in the exposed state E; when node_state = 2, the underwater sensor node N U is in the infected state I; when auv_state = 0, the autonomous underwater vehicle N A is in the susceptible state S; when auv_state = 1, the autonomous underwater vehicle N A is in the exposed state E; when auv_state = 2, the autonomous underwater vehicle N A is in the infected state I.

[0077] The state variables node_state and auv_state are used to describe the states of the underwater sensor node and the autonomous underwater vehicle during the propagation process, which are expressed as:

[0078]

[0079]

[0080] As Figure 2 shown, it is the state transition schematic diagram of the design method of the underwater wireless sensor network propagation model based on cellular automata of the present invention. The upper part of the picture refers to the state transition schematic of the underwater sensor node, and the lower part is the state transition schematic of the autonomous underwater vehicle. In addition to the malicious program propagation within the underwater sensor node and the autonomous underwater vehicle systems themselves, there is also a propagation path for mutual propagation between the two types of nodes.

[0081] Based on the above steps, the present invention provides a mathematical expression for the iterative process of the underwater sensor node based on probability theory:

[0082] P(S i (t + ΔT + 1)=1)

[0083] = 1 - P(S i (t + ΔT + 1)=0)-P(S i (t + ΔT + 1)=2)

[0084] = 1 - P(S i (t + ΔT + 1) = 0 | S i (t) = 0)P(S i (t) = 0)

[0085] - P(S i (t + ΔT + 1) = 2 | S i (t) = 1)P(S i (t) = 1)

[0086] - P(S i (t + ΔT + 1) = 2 | S i (t) = 2)P(S i (t) = 2);

[0087] The state of a specific node i at time t can be obtained through the total probability as follows:

[0088]

[0089] According to the time dependence and local spatial dependence between node i and its neighboring nodes, the present invention gives the following iterative process:

[0090]

[0091] where the vector is the state vector of the neighbors of the underwater node i at time t, and the vector represents 's state parameter, i.e., s j (t) = 0, 1, or 2. β ji = p1p2 is the probability that an infected node j with state parameter 1 or 2 infects its already infected neighbor i, where p1 represents the probability of successfully infecting a healthy node when an infected node communicates with an uninfected node, and p2 represents the probability of a healthy node being infected during the spread of a malicious program.

[0092] Similarly, subsequent mathematical expressions can also be derived based on the local spatial dependence and the state of node i at time t + 1. The specific process can be expressed as:

[0093]

[0094] where γ ji represents the probability that an infected node j with state I successfully infects another communicating healthy node i, which has already been infected but has not yet received an attack command. Finally, the conversion rule can be expressed as:

[0095]

[0096] where the state transition function indicates whether the healthy node i will transition to state E after time t+T. It then indicates whether the underwater node i changes its state after receiving an attack command from a communicable node in state E. Finally, f random (x) represents the recovery function, which reflects that the probability of node i changing its state after receiving an attack command is δ i , and random is a randomly generated decimal between 0 and 1.

[0097] The mathematical expression of the iterative process within the autonomous underwater vehicle system is similar to that of the underwater sensor node iterative process, so the corresponding derivation will not be carried out.

[0098] The present invention uses a two-dimensional cellular automaton model to construct a propagation model of malicious programs in UWSN, and uses A={C,S,V,f} to represent the propagation model of malicious programs.

[0099] The present invention adopts S U (t), E U (t), I U (t) to represent the number of underwater sensor nodes in the susceptible state S, exposed state E, and infected state I at time t respectively, and S A (t), E A (t), I A (t) to represent the number of autonomous underwater vehicles in the susceptible state S, exposed state E, and infected state I respectively. The constructed propagation model of the underwater wireless sensor network based on cellular automata is expressed as:

[0100]

[0101] The system is constructed to run the method of this application. Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course also by hardware. Based on such an understanding, the above technical solution, in essence, or the part that makes a contribution to the prior art can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0102] Those skilled in the art can easily understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for constructing a propagation model of underwater wireless sensor networks based on cellular automata, characterized in that: The following steps are involved: S1. The space where the underwater wireless sensor network is located is abstracted into a gridless two-dimensional space, a cellular automaton model of the underwater wireless sensor network is established, and all nodes are divided into two categories: sensor nodes and autonomous underwater vehicles; S2. Generate the position of each autonomous underwater vehicle after movement using the mobile model, and obtain the real-time position of each autonomous underwater vehicle; S3. Redesign the cell space and conversion rules according to the characteristics of underwater wireless sensor networks, and continuously update the status of underwater nodes and autonomous underwater vehicles according to the redesigned conversion rules; Cellular space: Set a whole space as the cellular space of cellular automaton; Conversion rule: Use the node as the center of the circle and determine whether there are nodes within the communication radius as cell neighbors; S4. Based on the mutual influence of two types of nodes, a cellular automaton-based underwater wireless sensor network propagation model is constructed.

2. The method for constructing an underwater wireless sensor network propagation model based on cellular automata according to claim 1, characterized in that: Step S1 establishes a cellular automaton model of the underwater wireless sensor network, specifically: abstract the space where the underwater wireless sensor network is located into a cell-free two-dimensional space of size L×L. The above space can also be set as an irregular two-dimensional figure, but in order to facilitate subsequent calculations, the space here is set as a square space that is convenient for calculation. N underwater sensor nodes and M autonomous underwater vehicles are evenly distributed in the two-dimensional space. All sensor nodes and autonomous underwater vehicles can communicate with each other, but there are slight differences in communication performance, and the sensor nodes are relatively fixed, while the autonomous underwater vehicles have strong mobility. Generally speaking, the communication range of a node is fixed. If the node leaves the communication range of the node during movement, it will cause communication interruption.

3. The method for constructing an underwater wireless sensor network propagation model based on cellular automata according to claim 1, characterized in that: The specific steps of step S2 are as follows: S21. Using a random walk model as a movement model of an autonomous underwater vehicle to simulate an underwater environment affected by multiple environmental factors; S22. Randomly generate the initial positions of the autonomous underwater vehicles and so that they are evenly distributed in the environment, and set external influencing factors; S23. Iteratively update the position of the autonomous underwater vehicle at fixed time intervals, and add the influence of external factors such as water flow speed, energy consumption and obstacle distribution into the position update formula; S24. Read the current coordinates of the autonomous underwater vehicle and obtain the position of the autonomous underwater vehicle in real time.

4. The method for constructing an underwater wireless sensor network propagation model based on cellular automata according to claim 1, characterized in that: In step S3, the redesigned cellular space and transformation rules are used to implement the iterative update of the cellular automaton model, which specifically includes the following steps: S31. Setting the size range and boundary conditions of the underwater wireless sensor network cell space, and assigning initial states and initial positions to all nodes, and also distinguishing between sensor nodes and autonomous underwater vehicles in terms of their characteristic attributes; S32. Setting specific requirements for the transformation between different states of the cell, when certain space and neighbor requirements are met, the cell can be transformed from one state to another, and it can be transformed according to the transformation rules; S33. Determine the judgment method of the cell neighbors, that is, take the cell as the center and calculate the number of different types of cells within the communication radius; S34. Traverse all cells, use the state number counted in step S33 to generate a new state value of this cell according to the conversion rule, and then replace all old state values ​​with new state values; S35. Detect the number of time steps, and stop iterating if the fixed time step is reached, otherwise continue iterating.

5. The method for constructing an underwater wireless sensor network propagation model based on cellular automata according to claim 1, characterized in that: In step S4, the different types of cells in the cellular automation model are defined as follows: when node_state=0, the underwater sensor node N U The state is susceptible state S; when node_state=1, the underwater sensor node N U The state is exposed state E; when node_state=2, the underwater sensor node N U The state is infection state I; when auv_state=0, the autonomous underwater vehicle N A The state is susceptible to the state S; when auv_state = 1, the autonomous underwater vehicle N A The state is exposed state E; when auv_state = 2, the autonomous underwater vehicle N A The status is infection status I.

6. The method for constructing an underwater wireless sensor network propagation model based on cellular automata according to claim 1, characterized in that: The cellular automaton model in step S4 is specifically: A={L,S,T,N,V,f}; Assuming that a cell i has k neighbors, the set of neighboring nodes of cell i at time t is represented by V t,i ={S t,1 ,S t,2 ,…,S t,k }; f represents the transformation rule of cell redesign. The state of cell i at time t is determined based on the state of its neighborhood at time t-1, which is expressed as: S t,i =f(V t-1,i ); N represents the new neighborhood function. The number of neighboring nodes of cell i at time t is based on whether the distance between it and other cells j is less than the communication radius r of the cell, expressed as: Among them, A represents the cellular automaton system; L represents the divided cellular space; S represents a finite set of cellular states; T represents the time set; and V represents the neighborhood cell set of the cell.

7. The method for constructing an underwater wireless sensor network propagation model based on cellular automata according to claim 1, characterized in that: The underwater wireless sensor network propagation model based on cellular automata is as follows: S U (t), E U (t), I U (t) represents the number of underwater sensor nodes in susceptible state S, exposed state E and infected state I at time t, respectively. A (t), E A (t), I A (t) represents the number of autonomous underwater vehicles in susceptible state S, exposed state E and infected state I at time t, respectively.

8. The method for constructing an underwater wireless sensor network propagation model based on cellular automata according to claim 1, characterized in that: The iterative process of underwater sensor nodes is: P(S i (t+ΔT+1)=1) =1-P(S i (t+ΔT+1)=0)-P(S i (t+ΔT+1)=2) =1-P(S i (t+ΔT+1)=0|S i (t)=0)P(S i (t)=0) -P(S i (t+ΔT+1)=2|S i (t)=1)P(S i (t)=1) -P(S i (t+ΔT+1)=2|S i (t)=2)P(S i (t)=2) Through the state of a specific node i at time t, the total probability can be obtained: According to the temporal dependency and local spatial dependency between node i and its neighboring nodes, the subsequent iterative process is: where the vector is the state vector of the neighbors of underwater node i at time t, and the vector express The state parameter, s j (t) = 0, 1 or 2; β ji =p1p2 is the probability that an infected node j with state parameter 1 or 2 infects its infected neighbor i, where p1 represents the probability of successfully infecting a healthy node when the infected node communicates with an uninfected node, and p2 represents the probability of a healthy node being infected when a malicious program spreads.

9. The method for constructing an underwater wireless sensor network propagation model based on cellular automata according to claim 1, characterized in that: According to the dependency of the local space and the state of node i at time t+1, the iterative expression of state I is derived. The specific process can be expressed as: where γ ji It represents the probability that the infected node j in state I successfully infects the other communicating healthy node i, which has been infected but has not received the attack command. Finally, the conversion rule can be expressed as: The state transition function Indicates whether the healthy node i will be converted to state E after time t+T; It indicates whether the underwater node i changes its state after receiving the attack command to the communicable node in state E; f random (x) represents the recovery function, which reflects the probability that the state of node i changes after receiving the attack command is δ i , random is a randomly generated decimal between 0 and 1.

Images