Explicit modeling of detection within a stochastic duel

Many mathematical models have been formulated to describe combat between two weapon systems. However, until recently duel models did not explicitly represent target detection within a duel, leading to the necessity for the development of new model for each tactical situation. An earlier article by two of the authors described a duel between weapons with constant firing times and explicit modeling of detection. This article enhances the study of this form of duel between weapons by introducing a variable parameter for firing times. This enhancement removes the discontinuities evident during parametric analysis of the earlier model and hence provides a more coherent model of this combat situation. © 1993 John Wiley & Sons, Inc.     

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.     

一类多对二随机格斗中的最优射击策略

射击策略的选择在随机格斗中是一重要战术问题,当一方武器面临多个武器目标时,如何确定射击目标顺序的研究,显然是具有实际意义的。依据发射间隔服从负指数分布的多对一随机格斗中最优策略应满足的条件,推出求解此类多对一格斗最优策略的方法。进而研究了射击间隔服从此类分布的多对二随机格斗中处于劣势一方的射击策略选择问题,得出寻求最优射击策略的一般方法。     

The many-on-one stochastic duel

The general many-on-one stochastic duel conditioned on the order in which targets are attacked is investigated, and the state probabilities are derived for the first time. The results are illustrated by an example of a three-on-one stochastic duel with negative exponential interfiring times. Some aspects of the tradeoff between individual firepower and the nominal size of a force are investigated.     

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.     

CEC网络—实现海上战斗兵力群战术协同作战的关键

在夺取制海权的作战中,海上战斗兵力群是最重要的。群内各兵力的战术协同是提高兵力群整体作战能力的关键,当然也是最难实现的。美国海军正加紧研制、试验和发展的战术协同作战网络,简称ＣＥＣ网络,极大地提高了由水面舰艇和飞机组成的兵力群战术协同作战能力,代表了兵力群战术协同作战的最高水平,将对海军的作战方法和样式产生重大影响。介绍了ＣＥＣ网络要实现的目的、组成、工作原理、特点、试验和发展情况     

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.     

微分对策在动态评价舰艇作战能力中的应用

作战能力是表征战斗舰艇战术技术性能的一项重要指标,如何正确评价舰艇的作战能力一直是舰载武器系统配置研究的重点,也是军事系统工程的重要研究方向。该文应用微分对策理论提出了一种动态评价舰艇作战能力的思想,首次定量研究了舰艇机动性与舰炮武器系统毁伤概率之间的关系,为综合评价舰艇的作战能力提供了一条可行途径。     

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.     

空战关键信息与战术规则提取算法

将粗糙集理论引入到空战研究中 ,提出了一种通过属性约简提取空战决策的关键信息和战术规则的算法 ,以便对空战过程中的冗余信息进行约简 ,提高决策实时性。通过一个空战战术选择示例对该算法进行了验证 ,结果表明 :在保证空战战术分类结果不变的情况下 ,该算法可提取出对空战决策起关键作用的信息以及最小简化战术规则。     

改进的遗传算法在导弹火力分配中的应用

弹道导弹系统是一个非常复杂的系统,有其自身的特点,其造价昂贵,数量有限,发射点也很分散.因此,火力分配问题在弹道导弹射击中具有极为重要的地位.尤其对于常规战术弹道导弹,火力分配的合理与否将直接影响作战效果与战斗力的发挥.根据地地战术导弹的作战运用特点,建立了导弹火力分配的优化模型;详细介绍了一种改进的遗传算法,将其应用于火力分配优化模型的求解,通过算例比较,证明该改进算法更能有效快速地找到最优解.     

基于模糊综合评价法的装甲团城市市区进攻战斗部署方案优化研究

战斗部署的内容是决心方案的主体部分,战斗部署确定的合理与否,将会直接影响到战斗方案的质量。因此,准确的评估战斗部署方案,对提高作战指挥决策的科学性,保障指挥员定下正确、合理的战斗决心具有重要意义。论文根据战斗部署的定义和战斗部署的要求,建立了城市市区进攻战斗部署的评价指标体系,并采用层次分析法确定其权重,最后使用模糊综合评价法对战斗部署方案进行评估。     

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.     

Stochastic duels with displacements (suppression)

The stochastic duel is extended to include the possibility of a near-miss on each round fired, which causes the opponent to displace. During displacement, the displacing contestant cannot return the fire but is still a target for his opponent. An alternative interpretation of this model is to consider the displacement time as the time a contestant's fire is suppressed by his opponent's fire and that he does not move, but merely ceases fire temporarily. All times are exponentially distributed.     

基于双向启发式属性约简的战术决策建模研究

从预警机指挥引导的多机协同空战原则分析出发,针对超视距协同空战决策过程中的不确定性和不完备性问题,提出了一种不完备信息系统中的基于双向启发式属性约简的战术粗决策建模方法。首先考虑粗糙集决策过程中条件属性发生缺失或不确定的情况,根据扩展不完备信息概念建立了不完备决策信息系统的最优完备选择;其次基于分辨矩阵的属性约简算法,以属性频度的大小作为启发信息进行决策信息系统约简的双向选择,得出决策信息系统的最佳约简集合;然后依据使决策最有可能发生的原则,给出决策信息系统的最优选择,以该最优选择为代表提取出决策规则;最后根据软、硬杀伤结合使用的CGF实体超视距协同空战作战想定,建立了CGF实体综合战术决策模型,并通过作战决策实例对该方法的正确性和有效性进行了验证。结果表明：该方法能在作战态势信息不完备的情况下正确给出CGF实体综合战术行为。     

基于仿真的水面舰艇作战能力评价研究

水面舰艇作战能力评价研究目前多沿用静态分析的综合指数法,应用作战仿真可以对装备作战能力进行全面的动态分析.提出了基于作战想定和其仿真结果的评价体系,构建了水面舰艇作战仿真模型体系,并给出调用关系.介绍了以STAGE为平台进行作战仿真开发的用户模型开发和脚本开发方法,建立了基于仿真统计结果的作战能力计算模型.最后,以一组服役驱逐舰作战能力分析的仿真实例验证了评价方法,结果表明该评价方法是合理的.     

General solution to many-on-many heterogeneous stochastic combat

Stochastic combat models are more realistic than either deterministic or exponential models. Stochastic combat models have been solved analytically only for small combat sizes. It is very difficult, if not impossible, to extend previous solution techniques to larger-scale combat. This research provides the solution for many-on-many heterogeneous stochastic combat with any break points. Furthermore, every stage in stochastic combat is clearly defined and associated aiming and killing probabilities are calculated. © 1996 John Wiley & Sons, Inc.     

基于MAS的末端防御网络化作战系统指控网

在简要介绍末端防御防空导弹网络化作战系统的基础上,分析了其指控网的结构和功能,并利用多智能体系统中的BD I模型对指控网的单个智能体进行描述,并重点研究了基于BD I结构的智能体的环境感知模型、作战意图模型、决策模型和通讯行为。     

基于模糊综合评价法的装甲团城市 市区进攻战斗部署方案优化研究

战斗部署的内容是决心方案的主体部分,战斗部署确定的合理与否,将会直接影响到战斗方案的质量。因此,准确的评估战斗部署方案,对提高作战指挥决策的科学性,保障指挥员定下正确、合理的战斗决心具有重要意义。论文根据战斗部署的定义和战斗部署的要求,建立了城市市区进攻战斗部署的评价指标体系,并采用层次分析法确定其权重,最后使用模糊综合评价法对战斗部署方案进行评估。     

A Lanchester-type aggregated-force model of conventional ground combat

This article develops a Lanchester-type model of large-scale conventional ground combat between two opposing forces in a “sector”. It is shown that nonlinear Helmbold-type equations of warfare with operational losses may be used to represent the loss-rate curves that have been used in many aggregated-force models. These nonlinear differential equations are used to model the attrition of combat capability (as quantified by a so-called firepower index) in conjunction with a rate-of-advance equation that relates motion of the contact zone (or FEBA) between the opposing forces to the force ratio and tactical decisions of the combatants. This simplified auxiliary model is then used to develop some important insights into the dynamics of FEBA movement used in large-scale aggregated-force models. Different types of behavior for FEBA movement over time are shown to correspond to different ranges of values for the initial force ratio, for example, an attack will “stall out” for a range of initial force ratios above a specific threshold value, but it will “break out” for force ratios above a second specific threshold value. Such FEBA-movement predictions are essentially based on being able to forecast changes over time in the force ratio.