Damage accumulation and probability of kill for gun and target engagements

Determination of the gunfire probability of kill against a target requires two parameters to be taken into consideration: the likelihood of hitting the target (susceptibility) and the conditional probability of kill given a hit (vulnerability). Two commonly used methods for calculating the latter probability are (1) treating each hit upon the target independently, and (2) setting an exact number of hits to obtain a target kill. Each of these methods contains an implicit assumption about the probability distribution of the number of hits‐to‐kill. Method (1) assumes that the most likely kill scenario occurs with exactly one hit, whereas (2) implies that achieving a precise number of hits always results in a kill. These methods can produce significant differences in the predicted gun effectiveness, even if the mean number of hits‐to‐kill for each distribution is the same. We therefore introduce a new modeling approach with a more general distribution for the number of hits‐to‐kill. The approach is configurable to various classes of damage mechanism and is able to match both methods (1) and (2) with a suitable choice of parameter. We use this new approach to explore the influence of various damage accumulation models on the predicted effectiveness of weapon‐target engagements.     

Weapon effectiveness and the shapes of damage functions

This paper provides a review of methods of assessing a fragmentation weapon's effectiveness against a point target or an area target with keeping the focus on the necessity of using the Carleton damage function with the correct shape factor.First,cookie-cutter damage functions are redefined to preserve the shape factor of and to have the same lethal area as the corresponding Carleton damage function.Then,closed-form solutions of the effectiveness methods are obtained by using those cookie-cutter damage functions and the Carleton damage function.Finally,the closed-form solutions are applied to calculate the probability of damaging a point target and the expected fractional damage to an area target for several attack scenarios by using cookie-cutter damage functions and the Carleton damage functions with different shape factors.The comparison of the calculation results shows that using cookie-cutter damage functions or the Carleton damage function with a wrong shape factor results in quite signifi-cant differences from using the original Carleton damage function with a correct shape factor when weapon's delivery error deviations are less than or comparable to the lengths of the lethal area and the aim point is far from a target.The effectiveness methods improved in this paper will be useful for mission planning utilizing the precision-guided munitions in circumstances where the collateral damage should be reduced.     

考虑目标定位误差的点目标毁伤概率求解

根据射击毁伤理论和概率统计学,在现有点目标毁伤概率求解方法基础之上提出考虑目标定位误差的解析法和仿真法.计算结果表明2种方法均准确可行.通过对比分析得出不同弹药量、不同目标特性条件下,定位误差对毁伤概率的影响程度.运用解析法得出点目标的单发命中概率服从χ2分布,通过大量仿真得出目标定位误差可忽略的条件为WmaxRCEP/ω.     

A method to determine the shell layout scheme for equipment battlefield damage tests under artillery fire

In this paper,a new method for determining the shell layout scheme is proposed,which can make the equipment damage data by the battlefield damage test resemble as close as possible the actual combat data.This method is based on the analysis of the impact point distribution and effective damage area of equipment.In order to obtain the position of the impact points,an impact point distribution model under artillery fire was established.Similarly,in order to obtain the effective damage area of equipment,the concepts of generalized damage area and task-based equipment functional damage probability were demonstrated,and the corresponding calculation model was established.Through case analysis,the shell layout scheme was effectively obtained,verifying the correctness of the proposed method.     

导弹装备战场损伤预测仿真研究

装备的战场损伤、损耗预测是作战保障的基础。文中构建了导弹装备损伤预测的马尔可夫Markov模型,导弹装备战场损伤部件数量动力学预测模型,并针对战场损伤强度和维修强度对损伤概率和部件损伤数量进行了仿真。对导弹作战计划以及装备保障与维修计划的制定具有指导意义。     

舰炮对海上集群小目标射击的毁伤概率

海上集群小目标是水面舰艇面临的主要威胁之一。以单管大口径舰炮对海上集群小目标射击作为研究对象,对集群目标进行了等效处理,分析了弹种、引信和装药的选择以及效力射中的表尺分配问题,提出多表尺效力射方法,利用该方法对海上集群小目标射击的毁伤概率进行了分析。结果表明,采用该方法并使用空炸榴弹或杀伤爆破弹,可有效破坏敌运输工具,杀伤其有生力量。     

Realignment in the National Football League: Did they do it right?

The National Football League (NFL) in the United States expanded to 32 teams in 2002 with the addition of a team in Houston. At that point, the league was realigned into eight divisions, each containing four teams. We describe a branch‐and‐cut algorithm for minimizing the sum of intradivisional travel distances. We consider first the case where any team can be assigned to any division. We also consider imposing restrictions, such as aligning the AFC (American Football Conference) and the NFC (National Football Conference) separately or maintaining traditional rivalries. We show that the alignment chosen by the NFL does not minimize the sum of intradivisional travel distances, but that it is close to optimal for an alignment that aligns the NFC and AFC separately and imposes some additional restrictions. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 683–701, 2003.     

A proportional defense model

This paper considers the problem of defending a set of point targets of differing values. The defense is proportional in that it forces the offense to pay a price, in terms of reentry vehicles expended, that is proportional to the value of the target. The objective of the defense is to balance its resources so that no matter what attack is launched, the offense will have to pay a price greater than or equal to some fixed value for every unit of damage inflicted. The analysis determines which targets should be defended and determines the optimal firing doctrine for interceptors at defended targets. A numerical example is included showing the relationship between the total target damage and the size of the interceptor force for different values of p, the interceptor single shot kill probability. Some generalizations are discussed.     

空空导弹对目标的毁伤计算与仿真

根据空空导弹破片式战斗部对空中目标的毁伤特点,对战斗部对空中目标的毁伤过程进行分析.在分析研究的基础上,建立了计算空空导弹单发杀伤概率的数学模型,设计了空空导弹对空中目标毁伤过程的仿真流程,研究了基于OpenGL的空空导弹对目标毁伤过程的可视化仿真实现,为正确评估空空导弹武器系统的作战效能提供了依据和手段.最后,给出了基于OpenGL的空空导弹毁伤空中目标过程的仿真实例.     

Upper and lower bounds for a pattern bombing problem

This paper includes two simple analytic formulas for kill probability that are applicable in circumstances where shots should be fired in a pattern. The two formulas bracket the maximum kill probability achievable with an optimal pattern. The upper bound corresponds to an optimal nonfeasible pattern, and the lower bound to a nonoptimal feasible pattern.     

连续波强激光武器动态毁伤概率的非毁检测法

给出一种强激光武器与目标存在相对运动时的毁伤概率(动态毁伤概率)在非致毁条件下的检测方法。该方法是在已知强激光对目标的致毁时间、一次发射时间的基础上,在武器的跟瞄子系统对目标无毁的跟踪试验中,通过检测跟踪误差在射击门内外交替出现的时间间隔,给出动态毁伤概率的点估计,以及在既定置信度下,动态毁伤概率的置信区间,同时还能判断所测毁伤概率是否处于最佳状态,为进一步优化动态毁伤概率提供依据。     

New results on a stochastic duel game with each force consisting of heterogeneous units

Two forces engage in a duel, with each force initially consisting of several heterogeneous units. Each unit can be assigned to fire at any opposing unit, but the kill rate depends on the assignment. As the duel proceeds, each force—knowing which units are still alive in real time—decides dynamically how to assign its fire, in order to maximize the probability of wiping out the opposing force before getting wiped out. It has been shown in the literature that an optimal pure strategy exists for this two‐person zero‐sum game, but computing the optimal strategy remained cumbersome because of the game's huge payoff matrix. This article gives an iterative algorithm to compute the optimal strategy without having to enumerate the entire payoff matrix, and offers some insights into the special case, where one force has only one unit. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 56–65, 2014     

The stochastic single resource service‐provision problem

The service‐provision problem described in this paper comes from an application of distributed processing in telecommunications networks. The objective is to maximize a service provider's profit from offering computational‐based services to customers. The service provider has limited capacity and must choose which of a set of software applications he would like to offer. This can be done dynamically, taking into consideration that demand for the different services is uncertain. The problem is examined in the framework of stochastic integer programming. Approximations and complexity are examined for the case when demand is described by a discrete probability distribution. For the deterministic counterpart, a fully polynomial approximation scheme is known 2 . We show that introduction of stochasticity makes the problem strongly NP‐hard, implying that the existence of such a scheme for the stochastic problem is highly unlikely. For the general case a heuristic with a worst‐case performance ratio that increases in the number of scenarios is presented. Restricting the class of problem instances in a way that many reasonable practical problem instances satisfy allows for the derivation of a heuristic with a constant worst‐case performance ratio. Worst‐case performance analysis of approximation algorithms is classical in the field of combinatorial optimization, but in stochastic programming the authors are not aware of any previous results in this direction. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

基于作战环的单目标毁伤概率分析

针对现代化战争的特点,基于作战环的思想,将整个作战环分成几个不同的环节进行分析,并提出了一种求解武器装备对于单目标毁伤概率的计算方法。该方法考虑了不同环节对于目标毁伤的影响,定量计算了武器装备对敌方目标的毁伤概率,既从宏观层面上考虑了武器装备的涌现性,又从底层分析了影响目标毁伤的参数。最后通过示例分析验证了方法的可行性和有效性。     

Non‐zero‐sum nonlinear network path interdiction with an application to inspection in terror networks

A simultaneous non‐zero‐sum game is modeled to extend the classical network interdiction problem. In this model, an interdictor (e.g., an enforcement agent) decides how much of an inspection resource to spend along each arc in the network to capture a smuggler. The smuggler (randomly) selects a commodity to smuggle—a source and destination pair of nodes, and also a corresponding path for traveling between the given pair of nodes. This model is motivated by a terrorist organization that can mobilize its human, financial, or weapon resources to carry out an attack at one of several potential target destinations. The probability of evading each of the network arcs nonlinearly decreases in the amount of resource that the interdictor spends on its inspection. We show that under reasonable assumptions with respect to the evasion probability functions, (approximate) Nash equilibria of this game can be determined in polynomial time; depending on whether the evasion functions are exponential or general logarithmically‐convex functions, exact Nash equilibria or approximate Nash equilibria, respectively, are computed. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 139–153, 2017     

弹炮结合防空武器系统毁伤概率分析与仿真

针对弹炮结合防空武器系统毁伤概率是决定系统效能的关键问题,分析了决定系统精度和毁伤概率的主要因素及其相互关系.以单枚导弹对目标的毁伤概率和高炮一次点射对目标的毁伤概率为目的,建立了弹炮结合系统毁伤概率分析模型.通过计算机仿真得出了一定航路条件下对典型目标射击,高炮一个2S长的36发点射的平均毁伤概率为40%,单枚导弹的平均毁伤概率为63%.在2枚导弹和2个点射的情况下,系统总的毁伤概率可达97.8%.     

机场跑道毁伤效果评估系统研究

开展对机场跑道的毁伤效果评估研究在战效评估领域具有重要的现实意义。针对机场跑道目标的特点,提出了一种机场跑道毁伤效果评估方法,即以毁伤效果评估数据为基础,在机场跑道区域内寻找飞机的最小起降窗口,以此判断机场跑道是否被封锁,实现对机场跑道的物理毁伤评估和功能毁伤评估。仿真实验结果表明该方法能够合理地评估机场跑道的毁伤效果,对打击方案优化比对具有重要意义。     

基于等效电路和点电流源的潜艇水下腐蚀电场估算

为了对潜艇涂层破损状态的水下腐蚀电场进行快速评估,基于电化学腐蚀原理和潜艇结构特点,建立潜艇涂层局部破损时的腐蚀电流等效电路,对潜艇涂层局部破损时的腐蚀电流强度进行估算,并基于点电流源对潜艇腐蚀电场建模,将潜艇涂层破损部位和裸露螺旋桨等效为点电流源,利用点电流源在分层介质中的电场计算公式对潜艇涂层破损时的腐蚀稳恒电场进行估算。与某型潜艇腐蚀电场商业有限元软件COMSOL仿真结果对比表明：该估算方法得到的潜艇表面腐蚀电流和不同路径电场分布曲线规律与COMSOL仿真结果基本一致,电流估算值相对误差不超过6.5%,电场各分量峰峰值相对误差不超过18%。     

动能拦截弹弹目碰撞概率仿真建模技术

针对目前研究反导拦截的主要方式——直接碰撞杀伤技术,提出了一种动能拦截弹弹目碰撞计算模型用以进行动能拦截弹与目标碰撞的概率计算,拦截弹碰撞目标的要害部位分析以及不同交会姿态对碰撞概率的影响分析.此模型是直接动能杀伤目标毁伤评估建模的基础,也可用于对拦截弹最佳碰撞方式的研究等方面.     

联合火力毁伤下炮兵连阵地配置与被毁伤概率

现代战场威胁炮兵的火力与弹药种类更加丰富,如何根据它们的特点选择恰当的阵地配置队形与火炮间隔,以最大限度地降低被毁伤概率就显得尤为重要.以自行炮兵连为研究对象,依据射击效率评定理论.结合几种典型的配置队形和红蓝双方的主要装备,对不同攻击方式下的被毁伤概率进行了模拟分析,得到了在阵地地形允许的情况下,应采用半圆形配置;普通榴弹射击时火炮配置间隔以200 m为宜,子母弹射击时如果要避免一半以上的火炮被毁伤,配置间隔也应至少达到200 m的结论.