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.     

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%.     

导弹单发杀伤概率影响因素分析

提出了进行导弹单发杀伤概率影响因素分析的必要性,进行了大量的导弹单发杀伤概率仿真计算,对作战条件和弹目交会条件等重要影响因素进行了深入地分析研究,并对导弹的作战使用、战术决策和目标机的最佳规避机动策略进行了深入探讨。研究成果给飞行员在导弹作战使用过程中进行战术决策提供了强有力的科学理论依据。     

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     

激光防空武器杀伤概率*

针对高功率防空激光武器的射击特性,运用概率论讨论了激光武器"光弹"的杀伤概率。将单发"光弹"杀伤目标作为一随机事件,按先后分"光弹"击中目标中心点和"光弹"击中目标后对目标的损伤程度两个相互独立的事件,分别用射击误差和目标坐标杀伤概率表示。建立了计算射击误差和目标坐标杀伤概率模型,得到了单发"光弹"的杀伤概率,进而得到了对同一目标连射n发"光弹"的杀伤概率,并根据激光能量饱和密度划分了对目标的杀伤效果,即硬杀伤、软杀伤和干扰,对激光武器研制提供理论参考。     

编队协同反导决策方案优选

为了充分地调度好编队全部的抗导资源,实现抗导弹群的成功概率最大,在利用随机服务系统理论对编队协同反导决策方案各指标值进行计算的基础上,将"模糊优选理论"与"协同学原理"有机地结合起来,求解了在反舰导弹到达强度与舰空导弹的单发杀伤概率在不同值的情况下,编队协同反导决策方案的隶属度,为编队指挥员进行反导决策方案的优选提供了科学依据。     

联合作战的远程火力战法动态分析方法*

用定量动态分析方法开发远程火力战法是联合作战规划中必须解决的重要问题。借助仿真和博弈分析的混合方法,在对博弈效用函数计算的基础上,构建基于识别真目标、假目标以及火力命中目标概率的二人非零和(TPNZS)非合作博弈模型来开发远程火力战法动态分析方法,对两个典型的联合作战远程火力打击战法性能的初步动态分析表明:战场势态的动态变化直接影响定量规划最优战法的结果。     

武器毁伤概率对火力运用的影响

采用离散马尔可夫链概型 ,在符合客观实际的基本假定条件下 ,以毁伤概率为指标 ,定量分析了对抗双方武器毁伤概率的变化对火力运用的影响 ,从而提出了先敌开火时机和火力运用样式转换时机对毁伤概率的要求     

Signal‐to‐interference‐plus‐noise ratio estimation for wireless communication systems: Methods and analysis

The Signal‐to‐Interference‐plus‐Noise Ratio (SINR) is an important metric of wireless communication link quality. SINR estimates have several important applications. These include optimizing the transmit power level for a target quality of service, assisting with handoff decisions and dynamically adapting the data rate for wireless Internet applications. Accurate SINR estimation provides for both a more efficient system and a higher user‐perceived quality of service. In this paper, we develop new SINR estimators and compare their mean squared error (MSE) performance. We show that our new estimators dominate estimators that have previously appeared in the literature with respect to MSE. The sequence of transmitted bits in wireless communication systems consists of both pilot bits (which are known both to the transmitter and receiver) and user bits (which are known only by the transmitter). The SINR estimators we consider alternatively depend exclusively on pilot bits, exclusively on user bits, or simultaneously use both pilot and user bits. In addition, we consider estimators that utilize smoothing and feedback mechanisms. Smoothed estimators are motivated by the fact that the interference component of the SINR changes relatively slowly with time, typically with the addition or departure of a user to the system. Feedback estimators are motivated by the fact that receivers typically decode bits correctly with a very high probability, and therefore user bits can be thought of as quasipilot bits. For each estimator discussed, we derive an exact or approximate formula for its MSE. Satterthwaite approximations, noncentral F distributions (singly and doubly) and distribution theory of quadratic forms are the key statistical tools used in developing the MSE formulas. In the case of approximate MSE formulas, we validate their accuracy using simulation techniques. The approximate MSE formulas, of interest in their own right for comparing the quality of the estimators, are also used for optimally combining estimators. In particular, we derive optimal weights for linearly combining an estimator based on pilot bits with an estimator based on user bits. The optimal weights depend on the MSE of the two estimators being combined, and thus the accurate approximate MSE formulas can conveniently be used. The optimal weights also depend on the unknown SINR, and therefore need to be estimated in order to construct a useable combined estimator. The impact on the MSE of the combined estimator due to estimating the weights is examined. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

毁歼概率积分的高精度计算

精确地计算武器系统对目标的毁歼概率是重要的。在对几种数值积分方案比较的基础上,证明了Ｇａｕｓ－Ｈｅｒｍｉｔ数值积分方案可以最少的积分点达到最高的精度,并以此方案计算了各个参数对毁歼概率的影响     

Using stochastic programming to solve an outpatient appointment scheduling problem with random service and arrival times

We study a stochastic outpatient appointment scheduling problem (SOASP) in which we need to design a schedule and an adaptive rescheduling (i.e., resequencing or declining) policy for a set of patients. Each patient has a known type and associated probability distributions of random service duration and random arrival time. Finding a provably optimal solution to this problem requires solving a multistage stochastic mixed‐integer program (MSMIP) with a schedule optimization problem solved at each stage, determining the optimal rescheduling policy over the various random service durations and arrival times. In recognition that this MSMIP is intractable, we first consider a two‐stage model (TSM) that relaxes the nonanticipativity constraints of MSMIP and so yields a lower bound. Second, we derive a set of valid inequalities to strengthen and improve the solvability of the TSM formulation. Third, we obtain an upper bound for the MSMIP by solving the TSM under the feasible (and easily implementable) appointment order (AO) policy, which requires that patients are served in the order of their scheduled appointments, independent of their actual arrival times. Fourth, we propose a Monte Carlo approach to evaluate the relative gap between the MSMIP upper and lower bounds. Finally, in a series of numerical experiments, we show that these two bounds are very close in a wide range of SOASP instances, demonstrating the near‐optimality of the AO policy. We also identify parameter settings that result in a large gap in between these two bounds. Accordingly, we propose an alternative policy based on neighbor‐swapping. We demonstrate that this alternative policy leads to a much tighter upper bound and significantly shrinks the gap.     

准最优增量搜索效率分析

在对极限搜索圆进行特殊分割的条件下,导出准最优增量搜索和准最优总量搜索发现目标概率的计算公式,并通过对搜索力变化时两种发现概率的比较,得出了准最优增量搜索优于准最优总量搜索的重要结论.     

一种基于蚁群算法的准动态防空武器分配算法

武器目标分配问题是一个典型的限制组合优化问题,旨在得到在整个防御阶段中针对目标函数的最优武器分配方案。分配算法主要分为静态和动态两大类。针对传统静态分配模型中存在的几点问题,提出了基于时间窗的准动态武器目标分配算法,该算法综合考虑拦截概率、拦截时间和武器耗费多个优化指标,并将该算法推广至多类防空武器的优化分配中。通过大量实验验证,该算法在性能、时间复杂度等方面均有较大优势,并且能较好地适应战场态势的变化,及时调整分配方案,具有很好的实用性。     

舰炮武器系统对导弹目标毁伤概率的数字仿真

以某型反导舰炮武器系统为原型,通过分析舰炮武器系统反导作战过程,利用靶场舰炮武器系统的动态精度试验数据,建立了动态精度计算毁伤概率的数学模型,模拟了舰炮武器系统对导弹目标着发射击的毁伤概率,实现了毁伤概率的仿真计算,仿真结果与实弹射击结果接近.结果表明,应用这种方法,可以实现动态精度预估毁伤概率,为射击试验方案制定提供决策依据,也可以为舰炮武器系统射击效力的鉴定和效能评估提供参考.     

Minimizing the false alarm rate in systems with transient abnormality

We consider a stochastic partially observable system that can switch between a normal state and a transient abnormal state before entering a persistent abnormal state. Only the persistent abnormal state requires alarms. The transient and persistent abnormal states may be similar in appearance, which can result in excess false alarms. We propose a partially observable Markov decision process model to minimize the false alarm rate, subject to a given upper bound on the expected alarm delay time. The cost parameter is treated as the Lagrange multiplier, which can be estimated from the bound of the alarm delay. We show that the optimal policy has a control‐limit structure on the probability of persistent abnormality, and derive closed‐form bounds for the control limit and present an algorithm to specify the Lagrange multiplier. We also study a specialized model where the transient and persistent abnormal states have the same observation distribution, in which case an intuitive “watchful‐waiting” policy is optimal. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 320–334, 2016     

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.     

子弹均匀散布子母弹最有利火力分配方法

在将子弹均匀散布的椭圆区域等效转换为矩形区域的基础上,建立了适宽射向射击子母弹对矩形目标毁伤全概率计算的数学模型。通过函数转换和泛函分析给出了子弹均匀散布子母弹理想射击密度,得到了理想射击密度下对目标的毁伤概率计算公式。讨论了最有利火力分配方式的确定方法,给出了最优射向间隔和表尺差的计算公式,为便于实际应用,给出了最优火力分配计算中所需的3个参数的近似计算公式,最后给出了应用算例。     

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。     

The search for an intelligent evader: Strategies for searcher and evader in the two-region problem

This paper considers the search for an evader concealed in one of two regions, each of which is characterized by its detection probability. The single-sided problem, in which the searcher is told the probability of the evader being located in a particular region, has been examined previously. We shall be concerned with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move: his optimal strategy consists of that probability distribution which maximizes the expected time to detection, while the searcher's optimal strategy is the sequence of searches which limits the evader to this expected time. It transpires for this problem that optimal strategies for both searcher and evader may generally be obtained to a surprisingly good degree of approximation by using the optimal strategies for the closely related (but far more easily solved) problem in which the evader is completely free to move between searches.     

电子对抗下防空兵器对空袭目标的杀伤概率计算

研究了雷达受干扰时探测距离及探测区域的变化;分析了情报指挥通信对雷达发现概率以及电子对抗对防空兵合成抗击效能的影响;最后给出了雷达诱饵和距离欺骗干扰时防空兵器一次射击对目标杀伤概率的计算方法。