Research on the performance of multi-base buoy arrays under the condition of on-called anti-submarine and warship-helicopter cooperation

In order to improve the performance of traditional on-called Anti-submarine, the method of combining the towed sonar and helicopter deployment with traditional buoy arrays for multi-base searching is proposed. Combining the acoustics principle and the actual movement characteristics of warships and helicopters, model of naval movement and multi-base passive circular buoy arrays,square buoy arrays, and triangle buoy arrays deployed by a helicopter were established. The Monte Carlo method was used to simulate and analyse the effect of the initial distance from the call point, the initial position of the submarine, the speed of the submarine economy, the size parameters of the float array and the number of deployments on the multi-base search performance under each formation. The simulation results show that the search performance of the three multi-base arrays decreases with the increase of the initial distance, the initial position of the submarine, and the speed of the submarine economy; the circular multi-base array has the best search performance, and the appropriate deployment radius and the number of passive buoys to be deployed can be selected according to different search requirements and actual operational conditions. This method is suitable for on-called anti-submarine within a certain distance, and has certain military significance for anti-submarine warfare.


Introduction
With the development of submarine in terms of noise reduction, speed increase, and anti-submarine exploration [1] , it is increasingly difficult to meet the needs of anti-submarine warfare by relying solely on single-base sonar. Therefore, it is important to seek multi-base collaborative search methods in various forms. At present, the synergy between surface ships and antisubmarine helicopters is mostly parallel inspection or patrol search. With the continuous updating of the submersible equipment, on the basis of solving the problem of consistent frequency of synergy, the towed sonar of the surface ship can be combined with the passive buoy array to form a multi-base search submerged array. Based on the traditional buoy array method, this paper combines the factors such as acoustic attenuation and helicopter coordinated turning, and innovatively combines the moving surface ship with the anti-submarine helicopter to set up the intercepting buoy array. The multi-base sonar buoy array model of arc, straight line and polyline is established, and the simulation results of three multi-base array search potentials under different conditions are simulated and compared. Let the distance between 0 P and 1 P be o L ,the total number of passive buoys placed is n , the position of each buoy point is i P , the flight distance from .Then the total time from the acquisition of submarine information to the end of the anti-submarine helicopter deployment buoy is: The surface ship departs from 0 P at a speed of nav v and heads in direction 0

Buoy array and size requirements for arcs, straight and broken lines
When the anti-submarine helicopter receives the order, it starts from 0 P and arrives at 1 P to place the first buoy, and then lays the buoy i P in turn. Fig. 2, Fig. 3 and Fig.  4 [2] are ship route diagrams of the arc buoy array, the linear buoy array and the three-fold line buoy array respectively.
When the buoy array is deployed, the rough heading of the submarine is generally used as the central axis of the formation, so that the angular division of the detection angle ω coincides with the central axis, and the buoys are arranged at equal intervals according to the array in the detection angle range. The key to deployment is to determine the size parameter R of the interception array and the placement of the first buoy. The size parameter R must be satisfied that the submarine cannot escape the buoy array even if it is evaded by its maximum maneuverer speed max sub V before the buoy array is released. Then: Through the geometric relationship of each formation, the relationship between o L , i L and size parameter R can be obtained, and the value of R needs to satisfy these relations. The placement of the first buoy is determined by o L and the initial heading angle 2 β of the helicopter [3] . R can be obtained according to the geometric relationship ， the triangle sine theorem ， the triangle cosine theorem and the induction formula [4] . For arc multi-base buoy array, the corresponding radius of the arc is the size parameter R , then: ( ) For straight line multi-base buoy array, 0 sub P to the linear array distance is the size parameter R , then: For polyline multi-base buoy array, the distance from 0 sub P to the edge of any line is the size parameter R , and the opening and closing angle of the line array is γ , then:

Model of potential search probability for multi-base sonar array
Assume that the warship and the submarine operate independently, and the depth of the submarine is consistent with the depth of the multi-base sonar buoy array and the towed sonar. The initial position distribution of the submarine satisfies the normal distribution, and the speed of the submarine satisfies the Rayleigh distribution with the average economic speed. The heading is equally probable in a certain range of directions [5] . The anti-submarine helicopter deployed a multi-base sonar buoy array, and at this time the towed sonar began to work. In the effective working time of the sonar array,  19) is satisfied [6] , then: It is considered that the multi-base sonar buoy array searches for the submarine. According to the Monte Carlo method if the total number of times the submarine is searched is M , the probability of searching for the multi-base sonar buoy array P is:

Simulation and analysis
In order to visually and accurately reflect the solution gap, the ocean area covered by the three multi-base sonar buoy arrays is equal when comparing the potentials of the schemes [7] . Set , the average speed of the anti-submarine helicopter to the calling area, the buoy and the monitoring search is150 / km h , the surface speed of the surface ship is 20 knots, the search speed is 12 knots, and the gravity acceleration in the sea area is For each coordinated turning time 1.5min , the buoy is passively omnidirectional, the effective working distance is 3km , 45 β =  , 90 ω =  , 120 γ =  , and the submarine's heading distribution is 8  , and R is taken as 35km .In order to simplify the analysis, the probability density of the target strength of the submarine is as follows [8] : ) The multi-base search potential pattern of the three buoy arrays is simulated and the potential of the search potential is simulated to analyse the influence of different conditions on the search potential.

Analysis and conclusion
It can be seen from Fig. 5 that under the same conditions, the search performance of the arc multi-base array is better than that of the straight line array and the polyline array. And the search efficiency of the three multi-base sonar buoy arrays decreases with the initial distance, the initial position distribution of the submarine, and the initial speed of the submarine, and increases with the initial heading angle of the submarine. At the same time, it can be seen in the figure that when the number of passive buoys is fixed, the probability of searching for each formation will increase and then decrease with the increase of the size parameter. under the condition that the size parameter is certain, the search potential probability first increases with the number of layouts, and gradually becomes gentle. Therefore, for different search requirements, combined with actual combat conditions, it is necessary to select the appropriate deployment radius and number of placements, so as to improve the search potential while ensuring better economy.

Conclusion
This paper proposes a method of dragging sonar and helicopter deployment of traditional buoy array combined multi-base search potential to improve the potential of search potential. Based on the actual movement characteristics of surface ships and helicopters, this paper establishes a multi-base passive buoy array model for ship motion and helicopter deployment, and establishes a multi-base joint search potential model under arc array, linear array and polygonal line array respectively. The simulation analyzes the influence of six factors on the multi-base search potential performance under each formation. The method is applicable to the call search potential within a certain distance range, and has certain military significance for anti-submarine warfare.