火力对抗条件下防空导弹作战有效性分析

针对火力对抗条件下空中来袭目标对国土或岛屿进行轰炸的情况,通过分析作战双方兵力兵器的变化关系,建立了轰炸机——防空导弹对抗的确定型Lanchester方程,并以此方程为基础,导出随机类型的Lanchester方程。结合基于随机服务系统理论的作战有效性分析的排队论模型及方法,获得在来袭目标有火力对抗条件下防空武器的作战有效性分析方法。     

火力和机动对作战毁伤的影响

火力和机动的密切结合才能产生强大的战斗力,对信息化条件下的现代战争进行建模和仿真分析,就必须考虑这两个要素。针对传统Lanchester方程不能描述火力和机动因素的限制,采用了基于Agent的作战模拟系统——EINSTein系统,探讨了火力和机动因素对作战毁伤的影响。     

正规战中作战效率变化初探

本文以描述常规战最基本的模型——Lanchester方程为基础,就影响作战效率的一些因素进行了分析并定量化地表现在作战模型中,然后运用有关系统学理论讨论了作战效率变化对战斗进程的影响程度。     

隐身武器与现代作战

隐身武器出现并应用于现代高技术局部战争,对现代作战尤其是空中作战产生了重大影响。在海湾战争中,美国使用了42架F-117A隐身战斗轰炸机,用来突袭伊拉克防空火力密集的国家军事指挥中心、重要设施以及防空指挥机构等,出动架次虽然只占多国部队飞机总     

基于兰彻斯特方程的大区域防空作战效能评估模型

针对大区域防空参战兵力多,体系结构、交战过程复杂的特点,引入作战效能、战斗编组、火力毁伤及任务分配等矩阵,建立了基于兰彻斯特方程的大区域防空作战效能评估模型,包括战斗力指数、战斗编组、毁伤指数、任务分配、指挥控制和作战实力损耗等部分。每个模型的建立均通过设定相应矩阵,分析战斗力指数,得出其计算模型。并以相关抗击率以及安全率表征总体效能指标,较好地解决了对大区域防空作战效能的评估问题。模型简洁,便于理解,易于计算。     

战役优势参数及其应用研究

数学分析方法在军事行动计划中扮演着越来越显著的角色。对以兰彻斯特作战模型为基础的描述诸兵种合成作战的矩阵微分方程，以及由方程的控制矩阵和状态变量初值，在不解方程的情况下导出的战役优势参数进行了研究；以空战为例讨论了预测战役结局、辅助军事决策、优化兵力部署和规划火力分配等战役优势参数的主要应用；给出了对战役优势参数和数学模型的评价。     

一种舰载多武器火力兼容优先级控制模型和方法

分析了美海军先进驱逐舰的武器配置,给出了舰载两两武器间动态火力散布体交叉的时空模型,提出了一种舰载多武器火力兼容优先级控制数学模型,并给出计算实例。     

基于地面目标群的陆战武器火力指数模型

给出了基于地面目标群的陆战武器火力指数模型,该模型与作战时节(持续的时间)、所要达成的作战目的、火力打击距离(射程)、发射的弹药量、目标性质(重要性)及毁伤效能有关,便于计算陆军参战武器的个体火力指数和战役总火力指数,并且能够计算对应于战场目标分布、重要目标分布的相应距离上的火力指数分布,从而便于武器对目标分配的战役估...     

合成坦克分队最佳火力分配模型

实际战斗中敌我双方均以多兵种进行交战,在兰切斯特方程基础上,利用不同作战单位的相对作战指数,以及各种作战单位之间的交战强度、掩护强度和循环交战强度,建立合成坦克分队最佳火力分配算法,并应用该算法定量计算二对二作战中坦克分队火力最佳分配的方案,为定量研究合成坦克分队火力运用打下了基础。     

一种基于随机映射的战斗效能模型

利用随机映射概念提出了一种新的战斗毁伤模型形式———Lanchester战斗网络模型。模型是由一个阶递减的随机映射序列组成的随机有向二部图,它明确、形式地描述了战争整体行为与局部作用之间的关系。理论分析和计算获得的结论表明,模型描述的整体作战效能符合Lanchester平方律,其网络拓扑结构是非同质的,出度和入度分布服从指数幂律。应用模型定量对比了“对称”与“非对称”战斗中全局信息因素对战斗系统整体效能的影响。初步讨论了网络模型研究在战争建模理论、实证和计算方法论上的意义。     

Force-annihilation conditions for variable-coefficient lanchester-type equations of modern warfare

This paper develops a mathematical theory for predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type “square-law” áttrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients). It introduces a canonical auxiliary parity-condition problem for the determination of a single parity-condition parameter (“the enemy force equivalent of a friendly force of unit strength”) and new exponential-like general Lanchester functions. Prediction of force annihilation within a fixed finite time would involve the use of tabulations of the quotient of two Lanchester functions. These force-annihilation results provide further information on the mathematical properties of hyperbolic-like general Lanchester functions: in particular, the parity-condition parameter is related to the range of the quotient of two such hyperbolic-like general Lanchester functions. Different parity-condition parameter results and different new exponential-like general Lanchester functions arise from different mathematical forms for the attrition-rate coefficients. This theory is applied to general power attrition-rate coefficients: exact force-annihilation results are obtained when the so-called offset parameter is equal to zero; while upper and lower bounds for the parity-condition parameter are obtained when the offset parameter is positive.     

Target selection in lanchester combat: Heterogeneous forces and time-dependent attrition-rate coefficients

We develop solutions to two fire distribution problems for a homogeneous force in Lanchester combat against heterogeneous enemy forces. The combat continues over a period of time with a choice of tactics available to the homogeneous force and subject to change with time. In these idealized combat situations the lethality of each force's fire (as expressed by the Lanchester attrition-rate coefficient) depends upon time. Optimal fire distribution rules are developed through the combination of Lanchester-type equations for combat attrition and deterministic optimal control theory (Pontryagin maximum principle). Additionally, the theory of state variable inequality constraints is used to treat the nonnegativity of force levels. The synthesis of optimal fire distribution policies was facilitated by exploiting special mathematical structures in these problems.     

The salvo combat model with area fire

This article analyzes versions of the salvo model of missile combat where area fire is used by one or both sides in a battle. Although these models share some properties with the area fire Lanchester model and the aimed fire salvo model, they also display some interesting differences, especially over the course of several salvos. Although the relative size of each force is important with aimed fire, with area fire, it is the absolute size that matters. Similarly, although aimed fire exhibits square law behavior, area fire shows approximately linear behavior. When one side uses area fire and the other uses aimed fire, the model displays a mix of square and linear law behavior. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 652–660, 2013     

海战中信息支援的影响分析

进入信息时代,信息成为作战取胜的第一要素,信息的作用与运行流程的掌握也就成为现代作战分析与决策的重要任务。以信息在作战应用中的特点进行分类为基础,建立了新的作战信息指标体系;想定了具体的典型海战对抗模式,通过构建基于信息支援的兰彻斯特方程模型,经作战仿真模拟,定量描述了在现代海战中信息支援能力的增强对作战能力的提升的显著程度;信息支援能力的提高使敌方损耗呈指数曲线上升。     

“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.     

Fitting Lanchester equations to the battles of Kursk and Ardennes

Lanchester equations and their extensions are widely used to calculate attrition in models of warfare. This paper examines how Lanchester models fit detailed daily data on the battles of Kursk and Ardennes. The data on Kursk, often called the greatest tank battle in history, was only recently made available. A new approach is used to find the optimal parameter values and gain an understanding of how well various parameter combinations explain the battles. It turns out that a variety of Lanchester models fit the data about as well. This explains why previous studies on Ardennes, using different minimization techniques and data formulations, have found disparate optimal fits. We also find that none of the basic Lanchester laws (i.e., square, linear, and logarithmic) fit the data particularly well or consistently perform better than the others. This means that it does not matter which of these laws you use, for with the right coefficients you will get about the same result. Furthermore, no constant attrition coefficient Lanchester law fits very well. The failure to find a good‐fitting Lanchester model suggests that it may be beneficial to look for new ways to model highly aggregated attrition. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

88B坦克分队与M60A3坦克分队随机火力对抗

以 8 8 B坦克分队进攻防御阵地之 M6 0 A3坦克分队为立足点 ,建立双方随机对抗时的兰彻斯特平方律模型 ,结合战场实际 ,得出 88B坦克分队取得最大作战效能时的最佳兵力比 ,及其运用火力的几点结论。     

Establishment,simulation and verification of firepower safety control model

On a narrow warship platform, the coordinated use of shipborne weapon systems may cause firepower conflicts, which seriously endangers the ship safety. Meanwhile, with directed-energy weapons mounted on ships, firepower conflicts between weapons become a “high probability event”. Aiming at the problem of firepower safety control, based on the research about the collision probability model of air crafts and space targets and according to the cone of fire model of conventional weapons and directed-energy weapons, this paper solved the firepower conflict probabilities between conventional weapons as well as between conventional weapons and directed-energy weapons respectively using the methods of probability theory, and established the firepower safety control model. Then the calculation of firepower conflict probability was carried out using the dimensionality reduction method based on the equivalent conversion of polar coordinates and the power series method based on Laplace transform. The simulation results revealed that the proposed model and calculation methods are effective and reliable, which can provide theoretical basis and technical support for resolution of firepower conflicts between weapons.     

Theoretical analysis of lanchester-type combat between two homogeneous forces with supporting fires

This paper studies combat between two homogeneous forces modelled with variable-coefficient Lanchester-type equations of modern warfare with supporting fires not subject to attrition. It shows that this linear differential-equation model for combat with supporting fires may be transformed into one without the supporting fires so that all the previous results for variable-coefficient Lanchester-type equations of modern warfare (without supporting fires) may be invoked. Consequently, new important results for representing the solution (i.e. force levels as functions of time) in terms of canonical Lanchester functions and also for predicting force annihilation are developed for this model with supporting fires. Important insights into the dynamics of combat between two homogeneous forces with such supporting fires are discussed.