An assessment method for ammunition damage effectiveness based on multiple rectangular cookie cutter function
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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。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.
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Key words:
- damage effectiveness /
- damage function /
- trapezoidal rule /
- calculation accuracy
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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
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
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
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°
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°
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°
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°
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 
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