Optimization of Active Sonar Buoy Array Deployment Based on Improved Multi-objective Particle Swarm Optimization Algorithm

doi:10.12382/bgxb.2024.0897

Abstract

Abstract:

Active sonar buoy is widely used as a submarine detection equipment for anti-submarine aircraft.It is of great significance to study its deployment optimization method to quickly and effectively complete the anti-submarine tasks and improve the efficiency of anti-submarine combat.The problem in current research lies in the fact that the submarine position distribution model and the simplified search range of active sonar buoys for detecting the submarines are difficult to meet the needs of the actual scenario.A distribution law model of submarines under the conditions of known general heading and unknown speed and an evaluation model of active sonar buoy array search efficiency based on the active sonar equation and the grid method are established.A buoy array deployment optimization method based on improved multi-objective particle swarm optimization algorithm is proposed by introducing Kent mapping,dynamically adjusted inertia weight and learning factor.The simulation verification is carried out in the scene of on-call submarine search.The simulated results show that the proposed algorithm can be used to obtain the optimal deployment scheme in different scenarios,which proves its feasibility and effectiveness.Compared with other algorithms,the proposed algorithm has a larger search probability and a shorter computation time under the condition of the same delivery amount,which proves its superiority.

Key words: active sonar buoy, array deployment optimization, submarine, multi-objective particle swarm optimization, anti-submarine

CLC Number:

TJ301

BI Wenhao, WU Yuxuan, XU Yang, ZHANG An. Optimization of Active Sonar Buoy Array Deployment Based on Improved Multi-objective Particle Swarm Optimization Algorithm[J]. Acta Armamentarii, 2025, 46(9): 240897-.

Figures/Tables 19

Fig.1 Schematic diagram of an underwater search mission

Fig.2 Position dispersion probability distribution of submarine after maneuvering

Fig.3 TS changes of target submarine

Fig.4 Utilizing the grid method to enhance the search efficiency of a single sonar buoy for submariners

Fig.5 Algorithm flowchart

Table 1 Setting of simulation parameters

参数	数值
r_d/km	10.55
v_a/kn	3
σ₀/km	10
σ_α/(°)	20
M	10
t_n/h	2

Table 2 Setting of algorithm parameters

参数	数值
popnum	200
k_max	200
ω_max	0.9
ω_min	0.4
c_max	2.0
c_min	0.2
β	0.7

Fig.6 The minimum,average and maximum search probabilities of different numbers of sonar buoy

Table 3 Optimal solutions for different drop quantities

m	1	2	3	4	5
P_s	0.2268	0.4143	0.5401	0.6215	0.6965
m	6	7	8	9	10
P_s	0.7606	0.8078	0.8446	0.8675	0.8952

Table 4 The coordinates of the optimal scheme delivery points

序号	(x,y)/km
1	(3.53,32.33)
2	(7.13,17.28)
3	(-4.97,20.97)
4	(-9.20,27.18)
5	(-0.79,14.51)
6	(6.81,24.96)

Fig.7 Schematic diagram of the drop point of active sonat buoys

Table 5 The search probability of optimal scheme

概率	t_j/h
概率	0.5	1.0	1.5	2.0
P_tj	0.6998	0.7415	0.7739	0.7606
P_m/%	69.98	92.24	98.25	99.58

Fig.8 Submarine search effect diagram of different deployment schemes at different times

Fig.9 The relationship among the initial dispersion of different submarines and the deployment amount of active sonar buoys and the search probability

Fig.10 Schematic diagram of the influences of different initial position distributions on the position distributions of submarines after a period of maneuvering

Fig.11 The relationship among different approximate courses and active sonar buoy drop amount and search probability

Fig.12 Schematic diagram of the influences of different submarine general courses on the position distribution of submarine after a period of maneuvering

Fig.13 Search probability changes of NSGA-II,the improved MOPSO algorithm and the original MOPSO algorithm for m=6

Fig.14 The maximum search probability and optimization time curves of NSGA-II,the improved MOPSO algorithm and the original MOPSO algorithm under the condition of different delivery amounts

References 27

[28]	LIN Q Z, LIU S B, ZHU Q L, et al. Particle swarm optimization with a balanceable fitness estimation for many-objective optimization problems[J]. IEEE Transactions on Evolutionary Computation, 2018, 22(1):32-46.
[29]	CUI Y Y, MENG X, QIAO J F. Amulti-objective particle swarm optimization algorithm based on two-archive mechanism[J]. Applied Soft Computing, 2022, 119:108532.
[30]	徐海信. 海洋环境中双基地声纳探测范围研究[D]. 长沙: 国防科技大学, 2018.
	XU H X. Research on detection range of bistatic sonar in marine environment[D]. Changsha: National University of Defense Technology, 2018. (in Chinese)
[1]	LIU Y W, LI Y L, SHANG D J. The hydrodynamic noise suppression of a scaled submarine model by leading-edge serrations[J]. Journal of Marine Science and Engineering, 2019, 7(3):68.
[2]	YEO S J, HONG S Y, SONG J H, et al. Analysis of the effect of vortex reduction structures on submarine tonal noise via frequency-domain method employing thickness noise source[J]. Ocean Engineering, 2022, 257:111640.
[3]	REDFORD D. Full spectrum anti-submarine warfare-the historical evidence from a British perspective[J]. Journal of Strategic Studies, 2021, 44:1063-1093.
[4]	IQBAL K, ZHANG M H, PIAO S, et al. Evolution of sonobuoy through history & its applications:a survey[C]// Proceedings of the 2020 17th International Bhurban Conference on Applied Sciences and Technology.Islamabad,Pakistan:IEEE, 2020.
[5]	孙启豪. 航空搜潜阵型及布阵航路优化研究[D]. 成都: 电子科技大学, 2017.
	SUN Q H. Research on the optimization of airborne searching submarine formation routes[D]. Chengdu: University of Electronic Science and Technology of China, 2017. (in Chinese)
[6]	FUGENSCHUH A R, CRAPARO E M, KARATAS M, et al. Solving multistatic sonar location problems with mixed-integer programming[J]. Optimization and Engineering, 2020, 21(1):273-303.
[7]	樊振凯. 固定翼飞机声呐浮标布阵优化研究[J]. 西北工业大学学报, 2017, 35(增刊1):82-87.
	FAN Z K. Study on sonar buoy arraying optimization for fixed wing aircraft[J]. Journal of Northwestern Polytechnical University, 2017, 35(S1):82-87. (in Chinese)
[8]	CRAPARO E M, FUGENSCHUH A, HOF C, et al. Optimizing source and receiver placement in multistatic sonar networks to monitor fixed targets[J]. European Journal of Operational Research, 2019, 272(3):816-831.
[9]	MA Y, MAO Z Y, QIN J, et al. A quick deployment method for sonar buoy detection under the overview situation of underwater cluster targets[J]. IEEE Access, 2020, 8:11-25.
[10]	周旭, 杨日杰, 高学强, 等. 基于遗传算法的被动浮标阵优化布放技术研究[J]. 电子与信息学报, 2008, 30(10):2533-2536.
	ZHOU X, YANG R J, GAO X Q, et al. Analysis of passive sonobuoy array optimal placement based on genetic algorithm[J]. Journal of Electronics & Information Technology, 2008, 30(10):2533-2536. (in Chinese)
[11]	TAYLOR C M, MASKELL S, RALPH J F. Using hybrid multiobjective machine learning to optimise sonobuoy placement patterns[J]. IET Radar,Sonar & Navigation, 2023, 17(3):374-387.
[12]	KARATAS M, CRAPARO E, AKMAN G. Bistatic sonobuoy deployment strategies for detecting stationary and mobile underwater targets[J]. Naval Research Logistics, 2018, 65(4):331-346.
[13]	KIM N H, BAEK D H, KWON J I, et al. Strategy for additional buoy array installation in operational buoy-observation network in Korea[J]. Ocean Engineering, 2022, 266:112746.
[14]	ADEKOYA O, ANEIBA A. An adapted nondominated sorting genetic algorithm III(NSGA-III) with repair-based operator for solving controller placement problem in software-defined wide area networks[J]. IEEE Open Journal of the Communications Society, 2022, 3:888-901.
[15]	HANEEF S, RASHID Z, HAIDER S A, et al. Stochastic optimal PV placement and command based power control for voltage and power factor correction using MOPSO algorithm[J]. Ain Shams Engineering Journal, 2024, 15(11):102990.
[16]	WU H Y, NIU W D, ZHANG Y L, et al. Multidisciplinary optimization-based path planning for underwater gliders executing multi-point exploration missions[J]. Ocean Engineering, 2022, 266:113022.
[17]	LIN Y H, HUANG L C, CHEN S Y, et al. The optimal route planning for inspection task of autonomous underwater vehicle composed of MOPSO-based dynamic routing algorithm in currents[J]. Applied Ocean Research, 2018, 75:178-192.
[18]	TRENTINI E V W, PARSEKIAN G A, BITTENCOURT T N. Multiobjective optimization of bridge and viaduct design:comparative study of metaheuristics and parameter calibration[J]. Engineering Structures, 2024, 312:118252.
[19]	王万良, 金雅文, 陈嘉诚, 等. 多角色多策略多目标粒子群优化算法[J]. 浙江大学学报(工学版), 2022, 56(3):531-541.
	WANG W L, JIN Y W, CHEN J C, et al. Multi-objective particle swarm optimization algorithm with multi-role and multi-strategy[J]. Journal of Zhejiang University(Engineering Science), 2022, 56(3):531-541. (in Chinese)
[20]	MAHMUD S, CHAKRABORTTY R K, ABBASI A, et al. Swarm intelligent based metaheuristics for a bi-objective flexible job shop integrated supply chain scheduling problems[J]. Applied Soft Computing, 2022, 121:108794.
[21]	XI L, LI L, LI L L, et al. Parameter optimization of titanium alloy considering energy efficiency and tool wear based on RBFNN-MOPSO algorithm in milling[J]. Journal of Manufacturing Processes, 2024, 122:97-111.
[22]	KUO R J, MUHAMMAD F L, NUR A M, et al. Application of improved multi-objective particle swarm optimization algorithm to solve disruption for the two-stage vehicle routing problem with time windows[J]. Expert Systems with Applications, 2023, 225:120009.
[23]	ZHANG X Y, ZHENG X T, CHENG R, et al. A competitive mechanism based multi-objective particle swarm optimizer with fast convergence[J]. Information Sciences, 2018, 427:63-76.
[24]	PANG X F, WANG Y B, YANG S X, et al. A bi-objective low-carbon economic scheduling method for cogeneration system considering carbon capture and demand response[J]. Expert Systems with Applications, 2024, 243:122875.
[25]	WANG T Z, TANG J, XIA H, et al. Data-driven multi-objective intelligent optimal control of municipal solid waste incineration process[J]. Engineering Applications of Artificial Intelligence, 2024, 137:109157.
[26]	ZHAO W Z, LUAN Z K, WANG C Y. Parameter optimization design of vehicle E-HHPS system based on an improved MOPSO algorithm[J]. Advances in Engineering Software, 2018, 123:51-61.
[27]	FENG D, LI Y, LIU J C, et al. A particle swarm optimization algorithm based on modified crowding distance for multimodal multi-objective problems[J]. Applied Soft Computing, 2024, 152:111280.