Buoy broken line interception array optimization laying method based on particle swarm optimization

Abstract

The invention discloses a buoy broken line interception array optimization laying method based on a particle swarm algorithm, and relates to the technical field of buoy broken line interception arrays, and the method comprises the following steps: 1, initialization: setting algorithm parameters, including the number of particles, the maximum number of iterations, speed limitation and learning factors; 2, evaluating particles: calculating the fitness value of each particle; and step 3, individual updating and global optimum: for each particle, if the fitness value of the current position is better than the optimal position (individual optimum, pbest) found so far, the individual optimum is updated. According to the buoy broken line interception array optimization laying method based on the particle swarm optimization, the smaller the interval coefficient is, the larger the overlapping area between the buoys is, the larger the number of the laid buoys is, and the smaller the escape possibility of the submarine is; the larger the interval coefficient is, the smaller the overlapping area between the buoys is, the smaller the number of the thrown buoys is, and the larger the escape possibility of the submarine is.

Description

Technical Field

[0001] The invention relates to the technical field of buoy broken line interception arrays, and in particular to an optimized deployment method of buoy broken line interception arrays based on a particle swarm algorithm. Background Art

[0002] How to use sonar buoys to find enemy submarines in the shortest time with the highest search probability is an urgent problem to be solved in the field of aviation anti-submarine search, which has great military significance. An efficient buoy array method is the basis and prerequisite for the deployment and tactical use of anti-submarine aircraft. Therefore, the optimized array method of sonar buoys is of great significance to effective search operations, which can ensure the rapid formation of combat effectiveness and improve the combat effectiveness of our anti-submarine aircraft. In foreign countries, the details of combat research and application at the tactical level of aviation anti-submarine search are difficult to understand due to military confidentiality. Research on the submarine search process is generally limited to qualitative and rough descriptions. In China, due to the short development time of aviation anti-submarine equipment and technology, basic theoretical research started late and invested little, especially the basic theoretical research related to the combination of combat skills, so there is even less research on the optimization theory of aviation sonar buoy submarine search array in China. At present, the traditional sonar buoy array has the problems of low search probability and low search efficiency. Based on this, this paper takes the sonar buoy zigzag array as an example, uses the optimization characteristics of the particle swarm algorithm to optimize it, and verifies the optimality of the algorithm through simulation. Summary of the invention

[0003] The present invention provides a buoy broken line interception array optimization deployment method based on particle swarm algorithm to solve the problems raised in the above background technology.

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0005] A buoy broken line interception array optimization deployment method based on particle swarm algorithm includes the following steps:

[0006] Step 1: Initialization: Set the algorithm parameters, including the number of particles, maximum number of iterations, speed limit, and learning factor;

[0007] Step 2: Evaluate particles: calculate the fitness value of each particle;

[0008] Step 3: Update individual and global optimality: For each particle, if the fitness value of the current position is better than the best position (individual optimality, pbest) found so far, update its individual optimality;

[0009] Step 4: Particle position update: According to the individual optimum and global optimum, as well as the current speed of the particle, a specific formula is used to update the speed and position of each particle;

[0010] Step 5: Check termination conditions: The algorithm will check whether the termination conditions are met, which may be reaching the maximum number of iterations, finding a good enough solution, or the fitness value has not improved significantly in a certain number of iterations;

[0011] Step 6: Output results: Once the termination condition is met, the algorithm will output the optimal solution currently found, which is the global optimal solution or the optimal solution in the last generation of particles.

[0012] Preferably, initialization includes the following:

[0013] A1: Initialization parameters: define the input parameters such as the number of buoys and the angle between buoys.

[0014] A2: Initialize particles: Initialize the position and velocity of each particle through a loop, ensure that each particle is within the given area, and add it to the particle group.

[0015] Preferably, the fitness function is designed as:

[0016] The approximate position and course of the target disappearance are known. When the target speed is unknown, it is assumed that the target speed obeys the economic speed v e is the Rayleigh distribution with mean, and the heading follows N(0,σ 0 2 ) Normal distribution; the calculation method of the search probability at this time is as follows:

[0017]

[0018] Directly call this formula to calculate the fitness of individuals in the population: where l = 2R + 2k (n-1) R is the length of the buoy interception array, R is the detection range of the buoy, k is the buoy spacing coefficient, n is the number of buoys in the interception array, t is the call time of the anti-submarine patrol aircraft (the time required for the anti-submarine aircraft to receive the mission and arrive at the mission area), σ 0 is the mean square error of the target heading error.

[0019] Preferably, update the particle position and velocity:

[0020] After the update, the fitness value of each particle is calculated, and then the global optimal solution is updated according to the fitness value;

[0021] At each iteration, the algorithm evaluates each particle and compares it with the global optimal solution; if a particle's fitness is better than the global optimal solution, the global optimal solution will be updated to that particle; the algorithm updates the speed and position of each particle based on the inertia weight and learning factor (individual learning factor and social learning factor); when updating the speed, the particle's own speed and its position in the search space relative to the individual optimal solution and the global optimal solution are considered to adjust the direction and size of the speed; finally, when updating the position, the particle's position is updated based on its current speed, so that the particle moves in a more favorable direction;

[0022] The speed update formula is:

[0023]

[0024] In the formula, k is the number of iterations, i is the particle number, d is the dimension number, ω is the inertia weight, c 1 is the individual learning factor, c 2 is the group learning factor, r 1 、r 2 is a random number in [0, 1], v is the velocity vector of the particle, x is the position vector, p pbest is the individual optimum, p gbest Optimal for the group;

[0025] The position update formula is:

[0026]

[0027] In the formula, is the current position of the particle, is the velocity of the particle at the next moment, is the position of the particle at the next moment.

[0028] Due to the adoption of the above technical solution, the present invention has the following technical advances compared with the prior art:

[0029] 1. The present invention provides a method for optimizing the deployment of a buoy zigzag interception array based on a particle swarm algorithm. The interval coefficient between two buoys in the buoy zigzag interception array is generally 1.5-2. It is necessary to ensure that there is no gap between two adjacent buoys to minimize the possibility of enemy submarines escaping. The smaller the interval coefficient, the larger the overlapping area between buoys, the larger the number of buoys deployed, and the smaller the possibility of submarine escape; the larger the interval coefficient, the smaller the overlapping area between buoys, the smaller the number of buoys deployed, and the greater the possibility of submarine escape. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a schematic diagram of the position model of the folded line array of the present invention;

[0031] Figure 2 The particle swarm algorithm flow chart of the present invention. DETAILED DESCRIPTION

[0032] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further explained below in conjunction with specific implementation methods.

[0033] like Figure 1-2 As shown in the figure, a method for optimizing the deployment of a buoy curved interception array based on a particle swarm algorithm is shown. The interval coefficient between two buoys in the buoy curved interception array is generally 1.5 to 2. It is necessary to ensure that there is no gap between two adjacent buoys to minimize the possibility of enemy submarines escaping. The smaller the interval coefficient, the larger the overlapping area between buoys, the greater the number of buoys deployed, and the smaller the possibility of submarine escape; the larger the interval coefficient, the smaller the overlapping area between buoys, the smaller the number of buoys deployed, and the greater the possibility of submarine escape. It can be seen that there is a contradiction between the number of buoys deployed and the probability of submarine search in the traditional buoy array.

[0034] Particle Swarm Optimization (PSO) is a search algorithm that simulates the predation of bird flocks and fish schools in nature. It is used to solve the Traveling Salesman Problem (TSP). After years of development, it has become a popular global optimization algorithm.

[0035] When the particle swarm algorithm is applied to the buoy array route planning in the field of aviation anti-submarine, the calculation of fitness value and the update of particle position are the core parts of the whole algorithm. The calculation of fitness value determines the quality of the solution, while the update of position is the way for particles to explore new solutions in the optimization process, including the following steps:

[0036] Step 1: Initialization: Set the algorithm parameters, including the number of particles, maximum number of iterations, speed limit, and learning factor; randomly initialize the position and speed of the particle swarm, with each particle representing a potential solution;

[0037] Step 2: Evaluate particles: Calculate the fitness value of each particle; in particle swarm optimization, the fitness value is usually determined by the objective function of the problem, and this value represents the quality of the particle's current position;

[0038] Step 3: Update individual and global optimality: For each particle, if the fitness value of the current position is better than the best position it has found so far (individual optimality, pbest), update its individual optimality; at the same time, find the particle with the best fitness value from all particles and update the global optimality (group optimality, gbest);

[0039] Step 4: Particle position update: Based on the individual optimum and global optimum, as well as the current speed of the particle, a specific formula is used to update the speed and position of each particle; the updated position needs to be evaluated for fitness again;

[0040] Step 5: Check termination conditions: The algorithm will check whether the termination conditions are met, which may be reaching the maximum number of iterations, finding a good enough solution, or the fitness value has not improved significantly in a certain number of iterations;

[0041] Step 6: Output results: Once the termination condition is met, the algorithm will output the optimal solution currently found, which is the global optimal solution or the optimal solution in the last generation of particles.

[0042] Among them, initialization includes the following:

[0043] A1: Initialization parameters: define the input parameters such as the number of buoys and the angle between buoys.

[0044] A2: Initialize particles: Initialize the position and velocity of each particle through a loop, ensure that each particle is within the given area, and add it to the particle group.

[0045] Among them, the fitness function is designed as:

[0046] The approximate position and course of the target disappearance are known. When the target speed is unknown, it is assumed that the target speed obeys the economic speed v e is the Rayleigh distribution with mean, and the heading follows N(0,σ 0 2 ) Normal distribution; the calculation method of the search probability at this time is as follows:

[0047]

[0048] Directly call this formula to calculate the fitness of individuals in the population: where l = 2R + 2k (n-1) R is the length of the buoy interception array, R is the detection range of the buoy, k is the buoy spacing coefficient, n is the number of buoys in the interception array, t is the call time of the anti-submarine patrol aircraft (the time required for the anti-submarine aircraft to receive the mission and arrive at the mission area), σ 0 is the mean square error of the target heading error.

[0049] Among them, update the particle position and velocity:

[0050] After the update, the fitness value of each particle is calculated, and then the global optimal solution is updated according to the fitness value;

[0051] At each iteration, the algorithm evaluates each particle and compares it with the global optimal solution; if a particle's fitness is better than the global optimal solution, the global optimal solution will be updated to that particle; the algorithm updates the speed and position of each particle based on the inertia weight and learning factor (individual learning factor and social learning factor); when updating the speed, the particle's own speed and its position in the search space relative to the individual optimal solution and the global optimal solution are considered to adjust the direction and size of the speed; finally, when updating the position, the particle's position is updated based on its current speed, so that the particle moves in a more favorable direction;

[0052] The speed update formula is:

[0053]

[0054] In the formula, k is the number of iterations, i is the particle number, d is the dimension number, ω is the inertia weight, c 1 is the individual learning factor, c 2 is the group learning factor, r 1 、r 2 is a random number in [0, 1], v is the velocity vector of the particle, x is the position vector, p pbest is the individual optimum, p gbest Optimal for the group;

[0055] The position update formula is:

[0056]

[0057] In the formula, is the current position of the particle, is the velocity of the particle at the next moment, is the position of the particle at the next moment.

[0058] in Figure 1 In: d is the distance between the first buoy and the initial approximate position of the submarine; α Li (i=1,2) are the directions of the two linear arrays respectively; Assuming the approximate heading of the submarine is η, according to the statistical law of error, it can be known that the actual heading obeys the heading dispersion σ with η as the mean η is a normal distribution with standard deviation, then the minimum heading angle can be considered to be η min =η-3σ η , the maximum heading angle is η max =η+3σ η , let η 0 =(η max -η min ) / 2, φ is the opening angle of the broken line buoy array, then α L1 =η+φ / 2,α L2=η+π-φ / 2.

[0059] The buoy position at the minimum heading angle of each linear array is:

[0060]

[0061] Where: d = R / cosη 0 .

[0062] The buoy position at the maximum heading angle of each straight buoy array is:

[0063]

[0064] set up If d 1 ≤d 2 ,but If d 1 >d 2 ,but

[0065] Depend on Figure 1 It can be seen that the position of the i-th buoy is:

[0066]

[0067] The buoy line interception array is mainly a buoy array method for the case where the approximate position and approximate heading of the target are known to disappear. The simulation conditions in this section are the sound source frequency of 500Hz and the sound source depth of 200m. It is assumed that the submarine search mission is carried out in a rectangular sea area with a length of 80 nautical miles and a width of 50 nautical miles. The initial position of the target is assumed to obey the circular normal distribution, that is:

[0068]

[0069] Assume that the initial standard deviation is σ=20 nautical miles, the initial heading is uniformly distributed within (0, 2ω), and the target is in uniform linear motion. The sound source depth of the target submarine is 200m. The number of buoys used in the array is 9, and the effective detection radius of the sonar buoy is calculated based on the current ocean environment in the deep sea. When arranging the zigzag array, the buoy spacing coefficient is set to 1.8. The call time is 1 hour.

[0070] The specific parameter settings of the particle swarm algorithm are shown in Table 1. The maximum number of iterations is set to 200 generations.

[0071] Table 1 Parameter settings

[0072] Parameter name Parameter Value Parameter name Parameter Value Particle swarm size 50 Inertia Weight 0.8 Individual learning factor 0.5 Social Learning Factor 0.5

[0073] Simulation 1: Sonar buoy range estimation:

[0074] Calculate the propagation loss according to the BELLHOP model: Assume that the sound source level is 140dB, the noise level is 80dB, the sonar directivity index is 10dB, and the sonar detection threshold is 5dB. The calculated FOM value is 65dB. Based on the propagation loss obtained by BELLHOP, the detection radius of the sonar is approximately obtained by comparing the FOM value with the TL.

[0075] The horizontal coordinate of the last intersection of the FOM value and the TL curve is the maximum detection radius of the sonar at this time. It can be seen from the figure that in this simulation scenario, the detection range is approximately 4km.

[0076] Simulation 2: Simulation process of buoy interception array deployment based on particle swarm algorithm

[0077] According to the simulation input conditions, the position, heading and speed of the simulation target are randomly generated based on the target position following the circular normal distribution, the heading following the uniform distribution and the speed following the Rayleigh distribution, and the algorithm planning of the buoy array is carried out accordingly.

[0078] After determining the target position, heading and speed, the particle swarm algorithm will initialize and randomly generate the positions and speeds of 50 particles, and then Calculate the fitness of each individual, and update the optimal solution of the entire particle swarm and each particle at any time, and save them to p gbest and p pbest middle.

[0079] The position information of the particle is:

[0080] x=[(20.5,29.5), (26.5,34.5), (33,36.5), (38.9,39.55), (45.5,42.5), (51.5,36.5), (55.5,31.5), (60.6,26.5), (65.7,21.3)]

[0081] The speed information is:

[0082] v=[0.71289323, -6.55822045, -8.73794366, -5.45762503, -3.52721158, 9.64428848, 4.04296415, 5.61280894, 9.62429758]

[0083] According to the formula After one iteration, its position information becomes:

[0084] x′=[(15.5, 36.2), (20.7, 31.9), (35.8, 39.3), (42.0, 46.2), (52.3, 43.6), (55.9, 41.8), (54.4, 37.1), (69.8, 22.9), (58.6, 30.7)]

[0085] According to the formula The speed information becomes:

[0086] v′=[1.82372884, -3.37567582, -4.62427878, -1.22499287, -3.01633543, 0.30793569, 2.29008917, -3.10665031, 4.28426293]

[0087] According to this rule, the position and velocity information of each particle is continuously updated, and the individual optimal and group optimal solutions are continuously updated; after reaching the maximum number of iterations, the optimal solution to the problem is selected.

[0088] According to the initial conditions of the simulation and the propagation loss and sonar detection capability calculated during the simulation, the planning is carried out through the particle swarm algorithm;

[0089] After about 150 iterations, the search probability is close to 80%. The algorithm reaches convergence in 192.7 seconds; according to the search probability calculation formula, the detection probability that can be achieved at this time is 79.8%.

[0090] This paper conducted a total of 10 simulation experiments, and the specific results are shown in Table 2. From the results in the table, it can be seen that for the case of a sound source frequency of 500 Hz and a sound source depth of 200 m, the longest planning time used in the 10 simulations is 201.5 seconds, and the shortest planning time is 177.8 seconds; the highest submarine search probability is 79.8%, and the lowest submarine search probability is 74.6%; the average planning time used for the 10 simulation results is 191.54 seconds, and the average submarine search probability is 77.41%.

[0091] Table 2 Planning results of particle swarm algorithm for 500Hz / 200m

[0092]

[0093]

[0094] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A buoy line interception array optimization deployment method based on particle swarm algorithm, characterized by: The following steps are involved: Step 1: Initialization: Set the algorithm parameters, including the number of particles, maximum number of iterations, speed limit, and learning factor; Step 2: Evaluate particles: calculate the fitness value of each particle; Step 3: Update individual and global optimality: For each particle, if the fitness value of the current position is better than the optimal position it has found so far, update its individual optimality; Step 4: Particle position update: According to the individual optimum and global optimum, as well as the current speed of the particle, a specific formula is used to update the speed and position of each particle; Step 5: Check termination conditions: The algorithm will check whether the termination conditions are met, which may be reaching the maximum number of iterations, finding a good enough solution, or the fitness value has not improved significantly in a certain number of iterations; Step 6: Output results: Once the termination condition is met, the algorithm will output the optimal solution currently found, which is the global optimal solution or the optimal solution in the last generation of particles.

2. According to the particle swarm algorithm-based buoy line interception array optimization deployment method of claim 1, it is characterized by: Initialization includes the following: A1: Initialization parameters: define the input parameters such as the number of buoys and the angle between buoys. A2: Initialize particles: Initialize the position and velocity of each particle through a loop, ensure that each particle is within the given area, and add it to the particle group.

3. The particle swarm algorithm-based buoy line interception array optimization deployment method according to claim 1 is characterized by: The fitness function is designed as: The approximate position and heading of the target disappearance are known. When the target speed is unknown, it is assumed that the target speed follows the economic speed v e is the Rayleigh distribution with mean, and the heading follows N(0,σ0 2 ) Normal distribution; the calculation method of the search probability at this time is as follows: Directly call this formula to calculate the fitness of individuals in the population: where l = 2R + 2k(n-1) R is the length of the buoy interception array, R is the detection range of the buoy, k is the buoy spacing coefficient, n is the number of buoys in the interception array, t is the call time of the anti-submarine patrol aircraft, and σ0 is the mean square error of the target heading error.

4. The particle swarm algorithm-based buoy line interception array optimization deployment method according to claim 1 is characterized by: Update particle positions and velocities: After the update, the fitness value of each particle is calculated, and then the global optimal solution is updated according to the fitness value; At each iteration, the algorithm evaluates each particle and compares it with the global optimal solution; if a particle's fitness is better than the global optimal solution, the global optimal solution will be updated to that particle; the algorithm updates the speed and position of each particle based on the inertia weight and learning factor; when updating the speed, the particle's own speed and the position of the individual optimal solution and the global optimal solution in the search space are considered to adjust the direction and size of the speed; finally, when updating the position, the particle's position is updated according to its current speed, so that the particle moves in a more favorable direction; The speed update formula is: Where k is the number of iterations, i is the particle number, d is the dimension number, ω is the inertia weight, c1 is the individual learning factor, c2 is the group learning factor, r1 and r2 are random numbers in [0,1], v is the particle velocity vector, x is the position vector, and p is the particle position vector. pbest is the individual optimum, p gbest Optimal for the group; The position update formula is: In the formula, is the current position of the particle, is the velocity of the particle at the next moment, is the position of the particle at the next moment.

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