﻿ 基于蒙特卡罗法的舰船目标毁伤概率分析
 舰船科学技术  2023, Vol. 45 Issue (23): 1-6    DOI: 10.3404/j.issn.1672-7649.2023.23.001 PDF

1. 江苏科技大学 船舶与海洋工程学院，江苏 镇江 212100;
2. 江南造船（集团）有限责任公司，上海 201913

Damage probability analysis of ship target based on the Monte Carlo method
LI Dong-qin1, ZHANG Yu1, LIU Jia-hao2
1. School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212100, China;
2. Jiangnan Shipyard(Group) Co., Ltd., Shanghai 201913, China
Abstract: A new formula for calculating the damage probability of the semi-armor-piercing warhead penetrating the ship target is presented. The penetration probability, the probability of the projectile's stability meeting the requirements, the damage probability of shock wave and the hit probability are analyzed and calculated respectively. Based on the Monte Carlo method, the attack of the semi-armor-piercing warhead on the ship target was simulated, and 100 independent repeated simulation tests were carried out and 1000 simulated strikes were carried out each time to obtain the probability of each device being hit. Based on the Latin hypercube random sampling method, the effectiveness of the related parameters in the damage probability formula is verified. The verification results show that the error between the fitted function relationship and the simulation result is within the allowable range of the project.
Key words: ship target     probability of damage     Monte Carlo method
0 引　言

1 舰船目标模型的建立 1.1 典型舰船目标概况

1.2 易损性模型的构建

 图 1 典型舰船的易损性可视化模型 Fig. 1 A visual model for the vulnerability of the typical ship
2 毁伤概率计算方法

 $P_{q}(x) =P_q(x) \cdot P_a(s)\cdot P_c(x)\cdot P_j(x)。$ (1)

 $P_{q}(x)=\left\{\begin{array}{ll} 0, & v \leqslant 0，\\ 1, & v>0。\end{array}\right.$ (2)

 $P_{a}(x)=\left\{\begin{array}{ll} 1, & \sigma<\sigma_{\max } ，\\ 0, & \sigma \geqslant \sigma_{\max }。\end{array}\right.$ (3)

 $r_{\alpha}=k_{\alpha} \sqrt{w}，$ (4)
 $r_{b}=k_{b} \sqrt{w} 。$ (5)

 $\Delta P_{m}=0.084 \frac{\sqrt[3]{m_{T}}}{R}+0.27\left(\frac{\sqrt[3]{m_{T}}}{R}\right)^{2}+0.7\left(\frac{\sqrt[3]{m_{T}}}{R}\right)^{3}({\rm{M P a}})。$ (6)

$\dfrac{R}{\sqrt[3]{{m}_{T}}} <$ 0.35时：

 $\Delta P_{m}=0.0106 \frac{\sqrt[3]{m_{T}}}{R}+0.43\left(\frac{\sqrt[3]{m_{T}}}{R}\right)^{2}+1.4\left(\frac{\sqrt[3]{m_{T}}}{R}\right)^{3}({\rm{M P a}})。$ (7)

 $P_{c}(x)=\left\{\begin{array}{lc} 0 ，& r(x)>r_{b}，\\ \dfrac{\Delta P_{m}(x)-\Delta P_{m b}(x)}{\Delta P_{m a}-\Delta P_{m b}} ，& r_{a}(x)r_{a}。\end{array}\right.$ (8)

${P}_{j}\left(x\right)$ 的计算通过蒙特卡罗法进行仿真模拟得到。

3 侵彻概率的分析及基于蒙特卡罗法的击中概率计算 3.1 半穿甲战斗部侵彻概率分析

 图 2 船体舷侧防护液舱有限元模型图 Fig. 2 Finite element modelling of the protective fluid tanks on the side of the hull

 图 3 弹体打击液舱侵彻深度 Fig. 3 Depth of penetration of a projectile against a liquid chamber

 图 4 初速度与剩余速度关系图 Fig. 4 Diagram of the relationship between initial velocity and residual velocity

 图 5 攻角与剩余速度的关系 Fig. 5 The relationship between angle of attack and residual velocity

 图 6 拟合函数三维关系图 Fig. 6 Three-dimensional plot of the fitted function
3.2 基于蒙特卡罗法的击中概率计算

 图 7 坐标系图 Fig. 7 Coordinate system

 图 8 标准正态分布函数图 Fig. 8 Graph of a function of the standard normal distribution

 图 9 蒙特卡罗仿真模拟流程图 Fig. 9 Flowchart of the Monte Carlo simulation

1）将舰船模型图导入程序中，并建立以2层甲板中点为原点的X-Z坐标系；

2）利用random库中的内置正态分布函数生成随机xz值，并根据模型尺寸转换为准确的（XZ）位置坐标；

3）利用turtle库生成对应（XZ）的像素点，从而在模型图上确定其具体的打击位置，对于未命中的坐标位置记作黑像素点，命中记为红像素点；

4）利用循环语句进行多次重复的随机像素点生成；

5）通过if条件语句统计舰船目标各个设备位置的打击次数，以此计算出各个设备的打击概率。

 图 10 随机样本点生成的弹体打击分布图 Fig. 10 Distribution of projectile strikes generated from random sample points

3.3 毁伤概率计算结果的验证

 图 11 拉丁超立方抽样方法示意图 Fig. 11 Schematic diagram of the Latin hypercube sampling method

1）确定样本元素集，同时对元素集进行等概率分区；

2）从各等概率分区中随机抽取样本点；

3）将各个分区的样本点进行随机组合成一个样本；

4）重复步骤3，直到得到完整的样本集合，结束抽样。

4 结　语

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