基于多矩形饼切函数的弹药毁伤效能评估方法

代权; 李向东; 周兰伟; 纪杨子燚

doi:10.11883/bzycj-2023-0316

基于多矩形饼切函数的弹药毁伤效能评估方法

doi: 10.11883/bzycj-2023-0316

南京理工大学机械工程学院，江苏南京 210094

详细信息

作者简介:
代　权（2001－　），男，硕士研究生，daiquan@njust.edu.cn

通讯作者:
李向东（1969－　），男，博士，教授，lixiangd@njust.edu.cn

中图分类号: O389
计量
- 文章访问数: 215
- HTML全文浏览量: 66
- PDF下载量: 100
- 被引次数: 0
出版历程
- 收稿日期: 2023-08-31
- 修回日期: 2023-12-22
- 网络出版日期: 2023-12-25
- 刊出日期: 2024-03-14

An assessment method for ammunition damage effectiveness based on multiple rectangular cookie cutter function

School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China

摘要

摘要: 为了快速准确地评估弹药对目标的毁伤效能，提出了一种基于多矩形饼切函数的弹药毁伤效能评估方法。该方法采用梯形法则、分区等效的思想，可以较大程度地保留实际毁伤区域中毁伤概率值的分布规律，从而保证计算的准确度。通过算例分析，研究了弹药落角和投放精度对目标平均毁伤概率的影响，并与基于矩形饼切和卡尔顿毁伤函数方法的结果进行了比较。结果表明，在弹药落角范围为30°~75°及弹药投放精度（circular error probable, CEP）范围为5~50 m时，与矩形饼切毁伤函数相比，基于多矩形饼切毁伤函数的计算方法使毁伤效能计算精度最大提高了26.4%；同时，与卡尔顿毁伤函数相比，计算效率提高了518倍。
- 毁伤效能 /
- 毁伤函数 /
- 梯形法则 /
- 计算精度
Abstract: When assessing the damage effectiveness of blast-fragmentation ammunitions against ground targets, the traditional approach involves calculating the overall target damage probability based on component damage criteria. Typically, the shooting line tracing method is used to determine the specific location on the target where fragments from the munition hit. However, this computation process is time-consuming. Therefore, to rapidly and accurately evaluate the ammunition damage effectiveness on the target, this study proposes a method called the multiple rectangular cookie cutter damage function. This method adopts the concept of the trapezoidal rule and performs equivalent processing on different regions corresponding to different damage probability intervals based on the gradient of damage probability changes within the actual damage area. This method can effectively retain the distribution pattern of damage probability values in the practical damage area, thus ensuring the accuracy of the computations. When describing ammunition delivery accuracy, a two-dimensional normal distribution is commonly employed to simulate the impact point locations of projectiles. Therefore, when calculating the mean of damage probability of the ammunition on the target, integration operations on the normal distribution function are necessary. However, due to the absence of an analytical solution for integrating the normal distribution function, polynomial equations are introduced as substitutes to enhance computational efficiency. The effects of ammunition drop angle and accuracy on the mean of damage probability of the target were investigated through example analysis, and the results were compared with those of methods based on the rectangular cookie cutter and Carlton damage function. The results show that within the ammunition drop angle range from 30° to 75°, and the circular error probable (CEP) precision range from 5 m to 50 m, compared with the rectangular cookie cutter damage function, the calculation method based on the multiple rectangular cookie cutter damage function improves the accuracy of damage effectiveness calculation by up to 26.4%. At the same time, the computational efficiency is improved by a factor of 518 compared with the Carlton damage function.
- damage effectiveness /
- damage function /
- trapezoidal rule /
- calculation accuracy

HTML全文

图 1 地面坐标系

Figure 1. Ground coordinate system

下载: 全尺寸图片幻灯片

图 2 卡尔顿毁伤函数图形

Figure 2. The graph of the Carlton damage function

下载: 全尺寸图片幻灯片

图 3 椭圆函数图形

Figure 3. The graph of the elliptical cookie cutter damage function

下载: 全尺寸图片幻灯片

图 4 矩形与椭圆区域关系

Figure 4. Relationship between rectangular and elliptical kill zone

下载: 全尺寸图片幻灯片

图 5 矩形函数图形

Figure 5. The graph of rectangular cookie cutter damage function

下载: 全尺寸图片幻灯片

图 6 毁伤矩阵等效为多矩形饼切毁伤函数示意图

Figure 6. Schematic diagram of the damage matrix equivalent to the multiple rectangular cookie cutter damage function

下载: 全尺寸图片幻灯片

图 7 平均毁伤概率计算流程

Figure 7. Flow chart for calculating mean damage probability

下载: 全尺寸图片幻灯片

图 8 概率分区数对平均毁伤概率和计算时间的影响

Figure 8. Influences of the number of probability divisions on mean damage probability and computation time

下载: 全尺寸图片幻灯片

图 9 平均毁伤概率随蒙特卡罗抽样次数的变化

Figure 9. Variation of mean damage probability with Monte-Carlo sampling number

下载: 全尺寸图片幻灯片

图 10 弹药落角为30°时基于3种毁伤函数计算的弹药毁伤效能对比

Figure 10. Comparison of ammunition damage effectiveness calculated based on three damage functions while the ammunition drop angle is 30°

下载: 全尺寸图片幻灯片

图 11 弹药落角为45°时基于3种毁伤函数计算的弹药毁伤效能对比

Figure 11. Comparison of ammunition damage effectiveness calculated based on three damage functions while the ammunition drop angle is 45°

下载: 全尺寸图片幻灯片

图 12 弹药落角为60°时基于3种毁伤函数计算的弹药毁伤效能对比

Figure 12. Comparison of ammunition damage effectiveness calculated based on three damage functions while the ammunition drop angle is 60°

下载: 全尺寸图片幻灯片

图 13 弹药落角为75°时基于3种毁伤函数计算的弹药毁伤效能对比

Figure 13. Comparison of ammunition damage effectiveness calculated based on three damage functions while the ammunition drop angle is 75°

下载: 全尺寸图片幻灯片

表 1 基于3种毁伤函数的计算时间

Table 1. Computational time consumption based on three damage functions

毁伤函数计算时间/μs

卡尔顿毁伤函数 2174

矩形饼切毁伤函数 0.2

多矩形饼切毁伤函数 4.2

下载: 导出CSV

参考文献(21)

[1]	徐豫新, 蔡子雷, 吴巍, 等. 弹药毁伤效能评估技术研究现状与发展趋势 [J]. 北京理工大学学报, 2021, 41(6): 569–578. DOI: 10.15918/j.tbit1001-0645.2020.194. XU Y X, CAI Z L, WU W, et al. Current research and development of ammunition damage effect assessment technology [J]. Transactions of Beijing Institute of Technology, 2021, 41(6): 569–578. DOI: 10.15918/j.tbit1001-0645.2020.194.
[2]	曾松林, 韩玉龙, 陈榕, 等. 一种评估航空炸弹对集群目标毁伤效能的新方法 [J]. 航空兵器, 2023, 30(1): 25–30. DOI: 10.12132/ISSN.1673-5048.2022.0037. ZENG S L, HAN Y L, CHEN R, et al. A new method to evaluate aerial bomb damage effectiveness hitting cluster targets [J]. Aero Weaponry, 2023, 30(1): 25–30. DOI: 10.12132/ISSN.1673-5048.2022.0037.
[3]	徐文旭, 李召, 陆凡东. 基于状态空间的反坦克导弹毁伤效能精准评估方法 [J/OL]. 兵工学报[2023-08-23]. DOI: 10.12382/bgxb.2022.0686. XU W X, LI Z, LU F D. Accurate evaluation method of antitank missile damage effectiveness based on state space [J/OL]. Acta Armamentarii[2023-08-23]. DOI: 10.12382/bgxb.2022.0686.
[4]	赵晓旭, 韩旭光, 吴浩, 等. 制导杀爆弹毁伤效能评估的应用研究 [J]. 北京理工大学学报, 2019, 39(6): 551–557. DOI: 10.15918/j.tbit1001-0645.2019.06.001. ZHAO X X, HAN X G, WU H, et al. Applied research on damage effectiveness evaluation of guided explosive bomb [J]. Transactions of Beijing Institute of Technology, 2019, 39(6): 551–557. DOI: 10.15918/j.tbit1001-0645.2019.06.001.
[5]	田浩成, 卢芳云, 李志斌, 等. 基于改进毁伤矩阵的人员目标毁伤效能评估 [J]. 兵器装备工程学报, 2022, 43(7): 101–108. DOI: 10.11809/bqzbgcxb2022.07.015. TIAN H C, LU F Y, LI Z B, et al. Evaluation of damage effectiveness of personnel target based on improved damage matrix [J]. Journal of Ordnance Equipment Engineering, 2022, 43(7): 101–108. DOI: 10.11809/bqzbgcxb2022.07.015.
[6]	KATSEV I, EVLOGIEV S. Damage functions evaluation coherent to weapon target interaction [J]. Machines, Technologies, Materials, 2019, 13(3): 124–126.
[7]	DRIELS M R. Weaponeering: conventional weapon system effectiveness [M]. Reston: American Institute of Aeronautics and Astronautics, 2004.
[8]	CHUSILP P, CHARUBHUN W, NILUBOL O. Effects of the cookie cutter function shapes on Monte Carlo simulations of weapon effectiveness [C]//2014 Seventh IEEE Symposium on Computational Intelligence for Security and Defense Applications (CISDA). Cau Giay: IEEE, 2014: 1–7. DOI: 10.1109/CISDA.2014.7035622.
[9]	ECKLER A R, BURR S A. Mathematical models of target coverage and missile allocation: DTIC: AD-A953517 [R]. Alexandria: Military Operations Research Society, 1972.
[10]	ANDERSON C M. Generalized weapon effectiveness modeling [D]. Monterey: Naval Postgraduate School, 2004.
[11]	MOON S H. Weapon effectiveness and the shapes of damage functions [J]. Defence Technology, 2021, 17(2): 617–632. DOI: 10.1016/j.dt.2020.04.009.
[12]	KLOPCIC J T. A comparison of damage functions for use in artillery effectiveness codes: DTIC_ADA222589 [R]. Maryland: Army Ballistic Research Laboratory, Aberdeen Proving Ground, 1990.
[13]	CHUSILP P, CHARUBHUN W, KOANANTACHAI P. Monte Carlo simulations of weapon effectiveness using Pk matrix and Carleton damage function [J]. International Journal of Applied Physics and Mathematics, 2014, 4(4): 280–285. DOI: 10.7763/IJAPM.2014.V4.299.
[14]	李向东, 周兰伟, 纪杨子燚. 目标易损性评估及应用 [M]. 北京: 北京理工大学出版社, 2022: 372-373.
[15]	丁贵鹏, 陶钢, 庞春桥, 等. 基于卡尔顿毁伤函数的杀伤榴弹效能评估模拟 [J]. 兵器装备工程学报, 2021, 42(8): 8–13. DOI: 10.11809/bqzbgcxb2021.08.002. DING G P, TAO G, PANG C Q, et al. Evaluation simulation of grenade effectiveness based on Carleton damage function [J]. Journal of Ordnance Equipment Engineering, 2021, 42(8): 8–13. DOI: 10.11809/bqzbgcxb2021.08.002.
[16]	WANG H Y, LABARIA G, MOTEN C, et al. Average damage caused by multiple weapons against an area target of normally distributed elements [J]. American Journal of Operations Research, 2017, 7(5): 289–306. DOI: 10.4236/ajor.2017.75022.
[17]	WANG H Y, MOTEN C, DRIELS M, et al. Explicit exact solution of damage probability for multiple weapons against a unitary target [J]. American Journal of Operations Research, 2016, 6(6): 450–467. DOI: 10.4236/ajor.2016.66042.
[18]	LEE J H, CHOI W J. Assessment of vulnerable area and naval ship’s vulnerability based on the Carleton damage function [J]. Journal of the Society of Naval Architects of Korea, 2018, 55(3): 274–280. DOI: 10.3744/SNAK.2018.55.3.274.
[19]	GALLAGHER M A, HORTA M C. Cyber joint munitions effectiveness manual (JMEM) [J]. American Intelligence Journal, 2013, 31(1): 73–81.
[20]	宋谢恩, 宋卫东, 宋高兴. 弹道修正火箭弹对面目标射击的最佳CEP研究 [J]. 弹道学报, 2014, 26(4): 51–55. DOI: 10.3969/j.issn.1004-499X.2014.04.010. SONG X E SONG W D, SONG G X. Research on the best CEP of ballistic correction rocket firing on surface target [J]. Journal of Ballistics, 2014, 26(4): 51–55. DOI: 10.3969/j.issn.1004-499X.2014.04.010.
[21]	ABRAMOWITZ M, STEGUN I A. Handbook of mathematical functions with formulas, graphs, and mathematical tables [M]. Washington: Government Printing Office, 1967.