﻿ 基于数据链的空战对抗建模及增援决策分析
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1. 空军工程大学 理学院, 西安 710051;
2. 空军工程大学 装备管理与安全工程学院, 西安 710051

Modeling and reinforcement decision analysis in air force combat based on data link
NIU Dezhi1, CHEN Changxing1 , XU Haoxiang2, LI Yongbin2, WANG Zhuo1, CHEN Qiang1
1. Science College, Air Force Engineering University, Xi'an 710051, China;
2. Equipment Management and Safety Engineering College, Air Force Engineering University, Xi'an 710051, China
Abstract:Force change problem during air combat course was studied. First of all, operation ability index of aircraft was converted to average combat level. Furthermore, in view of data link's influence on air combat and reinforcement force's joining to original force, differential equation model of every force changing which was represented by variety of aircraft number was set up based on Lanchester equation. Then numerical computation method of the model was given, and what time step should meet in discrete computation was pointed out. According to different reinforcement mode, the model was extended to different representation forms. Simulation experiment shows there is effective reinforcement time range if reinforcement force was joined in air combat, reinforcement only in one time and reinforcement with constant deceleration have merits on time. High reinforcement efficiency of the two reinforcement mode was illustrated by constructing the judgment function, which provides one new thought for air combat application and decision making.
Key words: average combat level     Lanchester equation     data link     judgment function     reinforcement efficiency     decision making

1 飞机作战效能

2 空战力量对比的建模分析 2.1 数据链体制下的动态力量变化微分模型

2.2 模型离散化和数值计算方法

2.3 增援作战时的模型分类

μ(n)=c匀速增援

3 仿真实验分析

3.1 匀速增援时不同起始时间下的动态损耗关系

 图 1 3种状态下的双方动态损耗Fig. 1 Dynamic exhaustion under three statuses

 图 2 红军不同增援时刻时双方的动态损耗图Fig. 2 Dynamic exhaustion in different reinforcement time from Red

 图 3 有效增援起始范围内不同时刻时的动态损耗Fig. 3 Dynamic exhaustion at different time among effective reinforcement beginning range

3.2 3种匀速增援状态时的动态损耗关系

 图 4 3种匀速增援模式时的动态损耗关系Fig. 4 Dynamic exhaustion curve of three constant velocity reinforcement mode

3.3 变速增援时的动态损耗关系

 图 5 变速增援模式时的双方动态损耗Fig. 5 Dynamic exhaustion curve of varied velocity reinforcement mode

4 增援方式优劣的评判准则制定

 增援模式 战斗时间 增援飞机数 损失飞机数 归一化增效因子 1.匀速增援 4.525 9.1 14.704 2 0.347 9 2.匀速一段时间 5.8 6.5 15.309 0.467 9 3.一次性增援 3.975 4 11.639 1 4.匀加速增援 3.575 9.1 12.882 3 0.397 1 5.匀减速增援 3.2 7.553 9 11.521 2 0.534 9

 图 6 不同增援模式时的增援效率Fig. 6 Reinforcement efficiency in different reinforcement mode

5 结 论

1) 建立了空中对抗作战的数学模型,指出了离散计算的时间步长所应满足的条件.将战机效能评估的结果(平均战斗力水平)作为其毁伤效率,并考虑在数据链环境下的平均战斗力水平的相对变化情况,建立表示双方作战单位数量变化的微分方程模型.为便于仿真实现和研究战斗变化规律,给出了所建模型的数学求解方法.

2) 给出了不同增援方式的优劣结论.在不同增援方式的空战对抗数学模型中,进行了3种不同情形下的空战对抗实验,分别是匀速增援时起始时间不同的双方动态损耗实验、3种不同类型匀速增援的双方动态损耗实验、变速增援的双方动态损耗实验.在第1种实验中得出结论为增援时间越早,损失的战机数量越少.在后2种实验中,通过构造增援效率评价函数进行有效度量,得出结论为一次性增援和匀减速增援方案的性能较优.实验结论为空战指挥和决策提供了依据.

 [1] Zhou L,Zhang H Y,Wang T,et al.Static check of WS-CDL documents [J].IEEE International Symposium on Service-Oriented System Engineering,2008,8:142-147. Click to display the text [2] 贺刚,柏鹏,彭卫东,等.数据链中基于动态博弈的联合功率与速率控制[J].西南交通大学学报,2013,48(3):473-480.He G,Bai P,Peng W D,et al.Joint rate and power control based on dynamic game theory in data link system[J].Journal of Southwest Jiaotong University,2013,48(3):473-480(in Chinese). Cited By in Cnki (1) | Click to display the text [3] 魏嘉利,贾云峰,谢树果,等.航空电子系统电磁环境复杂度量化评估方法[J].航空学报,2014,35(2):487-496.Wei J L,Jia Y F,Xie S G,et al.Complexity assessment method of electromagnetic environment for avionic systems[J].Acta Aeronautica et Astronautica Sinica,2014,35(2):487-496(in Chinese). Cited By in Cnki [4] 林琪,李智.基于拓扑特征的卫星网络效能评估[J].中南大学学报:自然科学版,2013,44(增刊2):368-371.Lin Q,Li Z.Performance evaluation of satellite-network based on topologic characteristics[J].Journal of Central South University:Science and Technology,2013,44(S2):368-371(in Chinese). Cited By in Cnki (2) [5] Liu H,Xu M,Chen N Y,et al.Task effectiveness evaluation on anti-ship attack of fighter aircraft[J].Transactions of Nanjing University of Aeronautics & Astronautics,2012,29(2):164-170. [6] Lee J,Kang S H,Rosenberger J,et al.A hybrid approach of goal programming for weapon systems selection[J].Computers & Industrial Engineering,2010,58(3):521-527. Click to display the text [7] Chen J,Mu Y P,Li D F.Study on effect evaluation of weapon coordinated use of fleet[J].Military Operations Research and Systems Engineering,2009,23(3):66-71. [8] Johnson I R,Mackay N J.Lanchester models and the battle of Britain[J].Naval Research Logistics,2011,58(3):210-222. Click to display the text [9] Yan J J,Wang Y,Wang X Y.Modeling and simulation of Lanchester equation based on game theory[C]//Proceedings of International Conference on the Business Management and Electronic Information.New York:IEEE,2011:212-214. Click to display the text [10] Yang F,Yang C C,Liang L,et al.New approach to determine common weights in DEA efficiency evaluation model[J].Journal of Systems Engineering and Electronics,2010,21(4):609-615. Click to display the text [11] 冯忠华,王新龙,王彬.一种数据链传输延迟建模及其补偿方法[J].北京航空航天大学学报,2012,38(8):1106-1110.Feng Z H,Wang X L,Wang B.Transfer time delay model of data link and its compensation[J].Journal of Beijing University of Aeronautics and Astronautics,2012,38(8):1106-1110(in Chinese). Cited By in Cnki (1) | Click to display the text [12] 陈向勇,井元伟,李春吉.基于Lanchester方程的作战混合动态系统最优变招控制[J].控制理论与应用,2012, 29(6):773-777.Chen X Y,Jing Y W,Li C J.Optimal variable tactic control of warfare hybrid dynamic system based on Lanchester equation[J].Control Theory & Applications,2012,29(6):773-777(in Chinese). Cited By in Cnki (2) | Click to display the text [13] Chen H M.An optimal control problem in determining the optimal reinforcement schedules for the Lanchester equations[J].Computers and Operations Research,2003,30(7):1051-1066. Click to display the text [14] Draguna V,Frank L.Adaptive dynamic programming for online solution of a zero-sum differential game[J].Journal of Control Theory and Applications,2011,9(3):353-360. Click to display the text [15] 朱宝鎏,朱荣昌,熊笑非.作战飞机效能评估[M].2版.北京:航空工业出版社,2006:184-185.Zhu B L,Zhu R C,Xiong X F.Aircraft effectiveness evaluation[M].2nd ed.Beijing:Aviation Industry Press,2006:184-185(in Chinese). [16] 谭东风.基于网络整体效能的战斗毁伤模型[J].系统工程理论与实践,2013,33(2):521-528.Tan D F.An attrition model with global network efficiency[J].Systems Engineering-Theory & Practice,2013,33(2): 521-528(in Chinese). Cited By in Cnki (1) | Click to display the text [17] 黄金才,张勇,杨磊,等.战术数据链作战效能定量评估方法[J].火力与指挥控制,2010,35(12):66-69.Huang J C,Zhang Y,Yang L,et al.A quantitative evaluation method for operation efficiency of tactical data link[J].Fire Control & Command Control,2010,35(12):66-69(in Chinese). Cited By in Cnki (3) [18] 牛德智,陈长兴,班斐,等.基于效能评估的航空作战进程预测[J].航空学报,2014,35(5):1416-1423.Niu D Z,Chen C X,Ban F,et al.Prediction on force in air combat process based on effectiveness evaluation[J].Acta Aeronautica et Astronautica Sinica,2014,35(5):1416-1423(in Chinese) Cited By in Cnki

#### 文章信息

NIU Dezhi, CHEN Changxing, XU Haoxiang, LI Yongbin, WANG Zhuo, CHEN Qiang

Modeling and reinforcement decision analysis in air force combat based on data link

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(1): 102-109.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0130