Stochastic duels involving reliability

The reliability of weapons in combat has been treated by Bhashyam in the context of a stochastic duel characterized by fixed ammunition supplies. negative exponentially distributed firing times and weapon lifetimes, and a fixed number of spare weapons for each duelist. The present paper takes a different approach by starting with the fundamental duel of Ancker and Williams, characterized by unlimited ammunition and by ordinary renewal firing times, and adding to it weapon lifetimes which can be functions of time or of round position in the firing sequence. Probabilities of winning and tieing are derived and it is shown that under certain conditions the weapon lifetimes are equivalent to random time and ammunition limits.     

A two-on-one stochastic duel with maneuvering and fire allocation tactics

The large body of work on stochastic duels represents an attempt to model combat situations, or parts of it, by means of formal probability models. Most, but not all, of the existing stochastic duel models, however, relate to static posture and fail to capture dynamic aspects as well as tactical considerations that may be present. In this article we propose a simple model of a two-on-one duel in which dynamic and tactical aspects are considered. The model represents a combat situation that is typical of a battle in which a maneuvering force attacks a smaller defending unit that is static.     

一类搜索型多对二随机格斗的获胜概率

研究搜索型多对二随机格斗战斗模型。假设格斗开始时A方有m件武器,B方有2件武器,B方处于隐蔽状态,格斗开始后B方可以直接对A方进行射击,A方需先搜索到B方后才能进行射击。双方各为同类武器,都是集火射击,所有开火都是独立的,每件武器开火射击直到毁伤对方才重新射击下一个目标。对搜索时间和毁伤间隔时间都服从一般分布的随机格斗模型,通过分析各状态的特征,利用状态概率分析方法和向后递归时间方法建立状态方程,求出了格斗处在各个状态的概率,并得到双方的获胜概率计算公式。     

Stochastic duels with nonrepairable weapons

This paper examines the effect of limitation, regarding weapons that are likely to fail during the period of deployment, on the final outcome in a stochastic duel model. Inter-firing times as well as inter-failure times have been assumed to be exponentially distributed.     

The two-on-one stochastic duel

The one-on-one stochastic duel is extended to the general two-on-one duel for the first time. The state equations, win probabilities, mean value, and variance functions are derived. The case where one side has Erlang (2) firing times and the other is negative exponential is compared with the corresponding “Stochastic Lanchester” and Lanchester models to demonstrate their nonequivalence.     

Optimal force mix in heterogeneous combat

This article presents models for determining the optimum number of Red weapons required to win a heterogeneous combat in which m(m> 1) types of Red weapons face a single type of Blue weapon under a newly defined termination policy. Red aims at either minimizing the total cost or maximizing the aggregated remaining force strength. Kuhn-Tucker and simulated annealing techniques are used for obtaining the optimal solution. The methodology is illustrated by analysing heterogeneous combat to determine (i) the feasibility of introducing new types of weapons and (ii) the number of weapons required to win if a specific type of weapon, say infantry, dominates. © 1995 John Wiley & Sons, Inc.     

Continuous-time markov duels: Theory and application

This article extends the previous research on Markov duels (stochastic duels between weapons with Markov-dependent fire) to situations in which the time between rounds fired by each duelist is a continuous random variable that depends on the state of combat. Three starting conditions for the duels are considered: simultaneous detection, surprise by one duelist with continuous time detection by his opponent, and surprise with discrete time detection. The amount of surprise is treated as both a constant and a random variable. An application of these models to an evaluation of armored vehicles is described. The methods used to consider a variety of engagement ranges, tactical situations, and target types (both lethal and nonlethal) are discussed. The procedure for incorporating nonduel attrition into the analysis is described and the exchange rate (the expected number of enemy targets killed per armored vehicle killed) is derived.     

The stochastic duel with time-dependent hit probabilities

The fundamental stochastic duel considers two opponents who fire at each other at either random continuous or fixed-time intervals with a constant hit probability on each round fired. Each starts with an unloaded weapon, unlimited ammunition, and unlimited time. The first to hit wins. In this article we extend the theory to the case where hit probabilities are functions of the time since the duel began. First, the marksman firing at a passive target is considered and the characteristic function of the time to a hit is developed. Then, the probability of a given side winning the duel is derived. General solutions for a wide class of hit probability functions are derived. Specific examples of both the marksman and the duel problem are given.     

A many-on-many stochastic duel model for a mountain battle

Terrain plays a major role in mountain battle. The advancing (attacking) force is usually restricted to move in a single column—along a narrow, winding, and steep road. The defending force, on the other hand, which is static, can select its positions such that most of its firepower can be effective against the front unit(s) of the attacking force. This combat situation is modeled as a special type of the many-on-many stochastic duel. This duel is a series of many-on-one subduels where at each such subduel the defending force units simultaneously engage the single exposed front unit of the attacking force. This special type of many-on-many stochastic duel demonstrates the possibility of practical applications of stochastic duel theory.     

攻防对抗下防空导弹武器系统作战效能评估

防空导弹武器系统是反空袭作战和国土防空的重要装备,综述了评定武器系统效能的WSEIAC模型,分析了WSEIAC模型的特点,结合攻防对抗下防空导弹武器作战体系作战的过程和对抗的特点,构建了攻防对抗下的防空导弹武器作战体系效能分析指标体系,建立了一种改进的ADC模型,并对模型中每个因素的确定进行了介绍,可为决策部门提供一定的决策预报.     

一种新的超视距空战目标威胁评估距离指标模型

距离指标是进行超视距空战目标威胁评估的重要指标,但当前多数的距离指标模型都过于简单。针对这种不足,在仿真分析当前典型模型的基础上,根据空战的实际情况,首先定性分析了目标位置等因素对于威胁度的影响;然后根据探测距离、导弹射程等参数,将敌我距离分成不同阶段,区分敌我性能强弱的不同情况,分阶段建立了一种新的距离指标模型。最后,针对不同的战场态势,进行了仿真分析,证明了模型的有效性。模型对于提升空战威胁评估的准确性具有积极意义。     

Concentrated firing in many-versus-many duels

A simple stochastic-duel model, based on alternate firing, is proposed. This model is shown to be asymptotically equivalent, for small hit probabilities, to other known models, such as simple and square duels. Alternate firing introduces an interaction between opponents and allows one to consider multiple duels. Conditions under which concentrated firing is better or worse than parallel firing are found by calculation and sometimes by simulation. The only parameters considered are the combat group sizes (all units within a group are assumed identical), the hit probabilities and the number of hits necessary to destroy an opposing unit.     

编队舰空导弹对空拦截综合模型研究

以水面舰艇编队防空为背景,用数学分析法和计算机模拟法对编队防空中预警直升机的配置和探测模型、舰载雷达的探测模型、编队对空导弹的抗击方法、编队对目标的射击能力、转火能力、杀伤概率等问题进行了研究,建立了火力方程等有关数学模型,为定量分析和优化编队对目标的作战能力提供了依据。     

单一流空情生成模型仿真

根据单一流空情的特点,立足贴近实战的要求,分别建立了空袭批数模型、航路生成模型、批次序号模型、类别指数模型、任务指数模型、编队数目模型和干扰模型共7个模型,并且按人工给定航路的方法进行了单一流空情生成的仿真实验,验证了该模型与以往模型相比具有一定的进步性,对防空兵作战仿真系统的开发具有一定的参考价值。     

舰空导弹射击模型优化分析

针对不同情况来袭的反舰导弹,运用系统分析的方法尝试在一定的条件下解决舰空导弹优化射击问题。通过分析,确立了在所假定的情况下选择各自不同的射击方法可以获得最大的抗击效果,从而提高作战的效费比。文中所确立的射击模型有一定的合理性和可行性,在射击方法恰当的情况下,舰空导弹武器系统的战斗可靠性对舰空导弹武器系统的射击效果起着重要作用。     

基于武器协同共用的无人机反潜作战效能研究

在一个暴露时间有限的反潜作战想定背景下,提出了评估该作战过程的效能指标,建立了相应的模型,并把武器协同共用条件下的作战结果与传统作战模式的结果作比较,结论表明,武器协同共用作战模式能够有效改善各项作战效能指标,是提高作战效能的有效手段。     

“simple-approximate” battle-outcome-prediction conditions for variable-coefficient lanchester-type equations of modern warfare

This article considers combat between two homogeneous forces modeled by variable- coefficient Lanchester-type equations of modern warfare and develops new “simple-approximate” battle-outcome-prediction conditions for military engagements terminated by two different types of prescribed conditions being met (fixed-force-level-breakpoint battles and fixed-force-ratio-breakpoint battles). These battle-outcome-prediction conditions are sufficient (but not necessary) to determine the outcome of battle without having to explicitly compute the force-level trajectories, and they are characterized by their simplicity, requiring no advanced mathematical knowledge or tabulations of “special functions” for their application. Integrability properties of the Lanchester attrition-rate coefficients figure prominently in their results, and involved in their development is a generalization of Lanchester's famous square law to variable-coefficient Lanchester-type combat and several other novel mathematical developments for the analysis of ordinary differential equations. Examples are given, with the attack of a mobile force against a static defensive position (both sides armed with weapons whose firepower is range dependent) being examined in detail.     

舰艇编队对空防御火力分配评价模型

未来高技术条件下水面舰艇编队防空作战能力是其生存能力的关键因素.对舰艇编队防空来讲,进行硬抗击的武器主要是舰空导弹和舰炮两种,如何合理地利用这些武器,最大地发挥舰艇编队的防空作战能力,成为舰艇对空防御作战研究的一个重要课题.结合舰艇编队对空防御的实际情况,利用模糊数学的方法,建立了舰艇编队对空防御火力分配方案的模糊综合评价模型.     

数字化步兵作战态势感知建模与仿真研究

通过分析数字化步兵的态势感知需求和信息获取来源以及信息传递方式,建立了数字化步兵单兵和连以下分队的态势感知模型,并进一步讨论了该模型的仿真实现途径。该模型可应用于数字化步兵作战仿真和单兵综合作战系统的效能仿真。     

猎击时敏目标的作战机理分析

美军在第二次对伊战争中,以比第一次对伊战争少得多的兵力,更短的准备时间和更少的消耗取得了更大的胜利,对比两次对伊战争中所用的兵器,坦克、主战飞机、战车、轻兵器等主战装备基本还是上次对伊战争的旧兵器,最大的变化是无人机的大量使用,情报系统、战术网络的提升,使战斗能力有极大的提高,这种由系统整合、提升信息化能力、改进指挥控制所产生的作战效能的提升是显著和有效的,代表发展战争潜力的方向。文中以美军对伊战争中主要的作战样式——打击时敏目标为作战想定,建立作战系统猎击时敏目标作战效能模型,对影响作战系统效能的各种因素作定量的分析,揭示作战效能提升的机理。