﻿ 基于压缩粒子群算法的水雷策略优化研究
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 哈尔滨工程大学学报  2019, Vol. 40 Issue (7): 1230-1237  DOI: 10.11990/jheu.201807016 0

引用本文

LIU Qiqing, LI Qiang, CAI Shang, et al. Optimization study of the mine-laying strategy on the basis of the particle swarm optimization algorithm with compression factor[J]. Journal of Harbin Engineering University, 2019, 40(7), 1230-1237. DOI: 10.11990/jheu.201807016.

文章历史

1. 哈尔滨工程大学 船舶工程学院, 黑龙江 哈尔滨 150001;
2. 北京航天长征飞行器研究所, 北京 100076;
3. 中集海洋工程有限公司, 广东 深圳 518000

Optimization study of the mine-laying strategy on the basis of the particle swarm optimization algorithm with compression factor
LIU Qiqing 1, LI Qiang 2, CAI Shang 1, WANG Shiping 1, KANG Youwei 3
1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China;
2. Beijing Institute of Space Long March Vehicle, Beijing 100076, China;
3. China International Marine Containers Offshore Engineering Co. Ltd., Shenzhen 518000, China
Abstract: To analyze the blockage probability of a minefield with a finite number of mines in the target water area, the particle swarm optimization algorithm was used to optimize the mine-laying strategy. A mathematical model of the blockage probability of a minefield, which accounts for the dispersion characteristic of a mine, was established, and the validity of the mathematical model was verified. For the finite target water area, the particle swarm optimization algorithm with compression factor (CFPSO) was used to optimize the number and launch coordinates of mines. The research results show that, when the target warship passes through a minefield under the uniform probability method, the mine-laying method optimized by the CFPSO algorithm can improve the blockage probability compared with two traditional mine-laying methods. For a single target warship, the minefield based on the CFPSO algorithm can reach the expected blockage probability of 0.6 with only seven mines, and the mine utilization rate is increased by 12.5% compared with the uniform mine-laying method. For a fleet with 3 warships, the minefield based on the CFPSO algorithm can reach the expected blockage probability with 30 mines, and the mine utilization rate is increased by 14.3% compared with the uniform mine-laying method.
Keywords: mine-laying strategy    particle swarm optimization algorithm    probability model    dispersion characteristic    launch coordinate    target warship    damage probability

1 数学模型 1.1 水雷布放模型

 Download: 图 2 目标舰船以攻角α驶入雷区 Fig. 2 The target warship enters the mine barrier at the angle of attack α
 Download: 图 3 投影后的雷线示意 Fig. 3 Schematic diagram of projected mine line

 Download: 图 4 水雷布设散布误差椭圆示意 Fig. 4 The error ellipse diagram of dispersion during the laying of mine

 $\left\{\begin{array}{l}{f_{1} \sim N\left(\overline{x}, \sigma_{a}^{2}\right)} \\ {f_{2} \sim N\left(\overline{x}, \sigma_{b}^{2}\right)}\end{array}\right.$ (1)

σaσb主要受航程的影响较大，一般认为它们与水雷航程之间存在线性关系[17]

 $\left\{\begin{array}{l}{\sigma_{a}=K_{a} S_{0}} \\ {\sigma_{b}=K_{b} S_{0}}\end{array}\right.$ (2)

 $f \sim N\left(\overline{x}, \sigma_{m}^{2}\right)$ (3)

1.2 雷阵封锁概率评估模型

 $\left\{\begin{array}{l}{p_{f i}=\delta \eta} \\ {\delta=\frac{1}{\sqrt{2 {\rm{ \mathsf{ π} }}} \sigma_{i m}}} \\ {\eta=\exp \left(\frac{-\left(x_{i}-\overline{x}_{i}\right)^{2}}{2 {\sigma_{i m}}^{2}}\right)}\end{array}\right.$ (4)

 $\sigma_{i m}^{2}=\sigma_{i a}^{2} \cos ^{2} \theta+\sigma_{i b}^{2} \sin ^{2} \theta$
 $\overline{x}_{i}=L i /(N+1)-L / 2$

 $\left|x_{\mathrm{s}}-x_{\mathrm{i}}\right| \leqslant W_{r}$

 $p_{\mathrm{g} i}\left(x_{\mathrm{s}}\right)=p_{\mathrm{r}} p_{\mathrm{b}} \int_{x_{\mathrm{s}}-W_{\mathrm{r}}}^{x_{\mathrm{s}}+W_{\mathrm{r}}} p_{\mathrm{f}i} \mathrm{d} x_{i}$ (5)

 $p_{\mathrm{h}i}\left(x_{\mathrm{s}}\right)=p_{\mathrm{g} i}\left(x_{\mathrm{s}}\right) p_{\mathrm{m}}$ (6)

 $\sigma_{1 a} \approx \sigma_{i a} \cdots \approx \sigma_{n a}$
 ${\sigma}_{1 b} \approx {\sigma}_{i b} \cdots \approx {\sigma}_{n b}$

 $p_{n}=1-\prod\limits_{i=1}^{n}\left(1-p_{\mathrm{h}i}\right)$ (7)

 $P=\int_{-\frac{L}{2}}^{\frac{L}{2}} p_{n} p_{x_{s}} \mathrm{d} x_{s}$ (8)

 $P_{\mathrm{u}}=\frac{1}{L} \int_{-\frac{L}{2}}^{\frac{L}{2}} p_{n} \mathrm{d} x_{s}$ (9)
1.3 数学模型仿真验证

 Download: 图 5 理论与仿真结果对比 Fig. 5 Comparison of theoretical and simulated results
2 粒子群优化算法

 $v_{i d}^{k+1}=\varphi\left\{v_{i d}^{k}+c_{1} r_{1}\left(p_{i d}-x_{i d}^{k}\right)+c_{2} r_{2}\left(p_{g d}-x_{i d}^{k}\right)\right\}$ (10)
 $\varphi=\frac{2}{\left|2-C-\sqrt{C^{2}-4 C}\right|}, \quad C=c_{1}+c_{2}$

3 水雷布阵策略优化 3.1 水雷布阵方位优化

 Download: 图 6 3种布设方案结果对比 Fig. 6 Comparison of the results of three deployment schemes
3.2 水雷布阵数量优化 3.2.1 单雷线数量优化

 Download: 图 7 不同水雷数目下3种方案结果对比 Fig. 7 Comparison of the results of three deployment schemes with different numbers of mines

3.2.2 多雷线数量优化

 Download: 图 8 多雷线示意 Fig. 8 The diagram of multi mine lines

 $\sum\limits_{k=m}^{n} C_{k-1}^{m-1} P^{m}(1-P)^{k-m} \geqslant 0.6, \quad n \geqslant m$ (11)

 $P_{3}=\sum\limits_{k=3}^{n} C_{k-1}^{2} P^{3}(1-P)^{k-3}, \quad 3 \leqslant n \leqslant 8$ (12)

 Download: 图 9 不同雷线数目下的水雷总数 Fig. 9 The total number of mines based on different numbers of mine lines

N=30时，有2种布设方案，方案1为n=5时，即有5条雷线，每条雷线有6枚水雷；方案2为n=6时，即布设6条雷线，每条雷线有5枚水雷。由表 8的2种布设方案的雷阵封锁概率可知，在相同水雷数目情况下，方案1雷阵的封锁概率为0.628，方案2雷阵的封锁概率为0.667。故为能达到目标水域期望封锁概率0.6且使水雷总数最少，优先选择方案2的布阵方式。其中方案2中每条雷线上水雷的发射坐标x1~x5分别为-133.8、-133.8、0.04、133.8、133.8。

4 结论

1) 针对单雷线模型，选取雷位散布均方差作为变量时，CFPSO算法对雷线上水雷发射坐标优化后的雷线封锁概率均比均匀布设和集中布设的方式高；选取水雷数目作为变量时，基于CFPSO算法优化后的布雷策略能够在较少的水雷数目下达到期望封锁概率。

2) 针对多雷线水雷数量优化，采用多条雷线等间距分布且每条雷线均利用CFPSO算法优化后的单雷线布雷策略进行布设，可使目标水域达到期望封锁概率的基础上，得出水雷总数最少的布设方案，节约了布设成本。

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