﻿ 基于RS-TOPSIS的空中目标威胁评估<sup>*</sup>
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Air target threat evaluation based on RS-TOPSIS
YANG Yuanzhi, YU Lei, ZHOU Zhongliang, RUAN Chengwei
Aeronautics and Astronautics Engineering College, Air Force Engineering University, Xi'an 710038, China
Received: 2017-05-22; Accepted: 2017-06-16; Published online: 2017-05-22 16:24
Foundation item: National Natural Science Foundation of China (61472443)
Corresponding author. YU Lei, E-mail:yl_panda@163.com
Abstract: Air target threat evaluation is the foundation for weapon allocation and resource management within the ground surface air defense system. Aimed at the problems of real-time and human subjectivity for threat evaluation, an air target threat evaluation model based on RS-TOPSIS is established according to combining rough set (RS) theory and technique for order preference by similarity to ideal solution (TOPSIS). RS theory which can avoid the influence of subjective factors and the requirement for prior information is used to determine the weight of target attribute, then close degree is analyzed with TOPSIS, and threat degree of air target is obtained. The model driven with data is easy to implement and has good real-time performance. The simulation results show that this method can effectively evaluate the threat degree and thus provides a new engineering decision-making method for real-time evaluation of air target threat degree.
Key words: rough set (RS)     technique for order preference by similarity to ideal solution (TOPSIS)     threat evaluation     ground surface air defense     air target

1 基于RS的目标属性权重计算

RS理论的概念是由波兰数学家Pawlak[11]于1982年提出来的，基本思想是通过等价关系将信息系统进行分类，实现数据挖掘和知识发现，适用于处理不确定、不完备信息系统，具有较高的实时性，操作简单且易于实现。采用RS理论确定TOPSIS中的权重向量，建立影响空中目标威胁程度的属性集，基于样本数据构建决策信息系统，并通过数据离散和属性约简等步骤构建属性权重计算流程。

1.1 目标属性的确定

1.2 RS基本概念

 (1)

 (2)

RBU上的等价关系，记

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U/RB={[xi]B|xiU}是U上的划分。同理

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1.3 目标属性权重确定流程

 (5)

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B的任何真子集均不为决策协调集时，称B为决策约简集，即可以得到核心属性及其信息系统。

 (7)

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2 基于RS-TOPSIS的空中目标威胁评估模型

TOPSIS是多属性决策问题的一种常用方法。其中心思想是先计算得到一个正理想解和一个负理想解，寻找与正理想解越近且与负理想解越远的解。将RS方法得到的属性权重代入TOPSIS，构建基于RS-TOPSIS的空中目标威胁评估模型。具体模型构建步骤如下[15, 17]

 (11)

H矩阵中目标属性进行量纲归一化处理，消除被评价对象不同属性之间的量纲差异。

 (12)

 (13)

 (14)

 (15)
 (16)

 (17)
 (18)

 (19)

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3 威胁评估处理流程

 图 1 威胁评估处理流程 Fig. 1 Processing flow of threat evaluation

4 仿真分析

 目标 目标类型 目标速度/(m·s-1) 目标航向角/(°) 目标干扰能力 目标高度 目标距离/m 目标威胁值 t1 大型目标 500 130 强 高 360 0.521 2 t2 大型目标 550 90 中 中 160 0.582 8 t3 大型目标 650 110 强 低 280 0.646 5 t4 小型目标 600 50 中 高 160 0.685 3 t5 小型目标 750 150 中 超低 400 0.754 1 t6 小型目标 640 180 强 中 280 0.676 4 t7 直升机 80 6 弱 高 180 0.347 1 t8 直升机 88 140 无 超低 320 0.359 2 t9 直升机 90 180 弱 低 170 0.347 4

1) 目标类型。根据目标特征及其威胁程度，以Miller[19]的人类认知理论为量化依据，对各目标类型的定性描述语言分别作如下量化处理：小型目标(如巡航导弹)、大型目标(如轰炸机)、直升机依次量化为3、2、1。

2) 目标干扰能力。目标具有的干扰能力越强，地面防空系统的电子对抗能力越弱，越容易受到目标的干扰，导致武器系统对目标的命中概率越低，因此将干扰能力的强、中、弱、无依次量化为4、3、2、1。

3) 目标高度。空中目标越高，距离地面防空系统越远，可以采取对抗措施的时间越长，其威胁程度越小，因此将目标高度的高、中、低、超低依次量化为4、3、2、1。

 目标 a1 a2 a3 a4 a5 a6 D t1 2 3 3 4 4 4 2 t2 2 3 2 3 3 2 3 t3 2 4 3 4 2 3 3 t4 3 3 1 3 4 2 4 t5 3 4 3 3 1 4 4 t6 3 4 4 4 3 3 3 t7 1 1 1 2 4 2 1 t8 1 1 3 1 1 4 1 t9 1 1 4 2 2 2 1

 目标 t1 t2 t3 t4 t5 t6 t7 t8 t9 t1 ∅ a3a4a5a6 a2a5a6 a1a3a4a6 a1a2a4a5 a1a2a3a5a6 a1a2a3a4a6 a1a2a4a5 a1a2a3a4a5a6 t2 a3a4a5a6 ∅ ∅ a1a3a5 a1a2a3a5a6 ∅ a1a2a3a4a5 a1a2a3a4a5a6 a1a2a3a4a5 t3 a2a5a6 ∅ ∅ a1a2a3a4a5a6 a1a4a5a6 ∅ a1a2a3a4a5a6 a1a2a4a5a6 a1a2a3a4a6 t4 a1a3a4a6 a1a3a5 a1a2a3a4a5a6 ∅ ∅ a2a3a4a5a6 a1a2a4 a1a2a3a4a5a6 a1a2a3a4a5 t5 a1a2a4a5 a1a2a3a5a6 a1a4a5a6 ∅ ∅ a3a4a5a6 a1a2a3a4a5a6 a1a2a4 a1a2a3a4a5a6 t6 a1a2a3a5a6 ∅ ∅ a2a3a4a5a6 a3a4a5a6 ∅ a1a2a3a4a5a6 a1a2a3a4a5a6 a1a2a4a5a6 t7 a1a2a3a4a6 a1a2a3a4a5 a1a2a3a4a5a6 a1a2a4 a1a2a3a4a5a6 a1a2a3a4a5a6 ∅ ∅ ∅ t8 a1a2a4a5 a1a2a3a4a5a6 a1a2a4a5a6 a1a2a4a5a6 a1a2a4 a1a2a3a4a5a6 ∅ ∅ ∅ t9 a1a2a3a4a5a6 a1a2a3a4a5 a1a2a3a4a6 a1a2a3a4a5 a1a2a3a4a5a6 a1a2a4a5a6 ∅ ∅ ∅

 目标 a1 a2 a3 a4 a5 a6 t1 0.166 7 0 0 0 0 0.055 6 t2 0.166 7 0 0 0 0.111 1 0.333 3 t3 0.166 7 0 0 0 0.222 2 0.166 7 t4 0.333 3 0 0 0 0 0.333 3 t5 0.333 3 0 0 0 0.333 3 0 t6 0.333 3 0 0 0 0.111 1 0.166 7 t7 0 0 0 0 0 0.305 6 t8 0 0 0 0 0.333 3 0.111 1 t9 0 0 0 0 0.222 2 0.319 4

 目标 正理想解距离 负理想解距离 相对贴近度 可能分类 原始分类 t1 0.464 7 0.175 7 0.277 4 1 2 t2 0.277 7 0.388 9 0.583 4 3 3 t3 0.260 5 0.324 0 0.554 3 3 3 t4 0.333 3 0.471 4 0.585 8 4 4 t5 0.333 3 0.471 4 0.585 8 4 4 t6 0.277 7 0.388 9 0.583 4 3 3 t7 0.472 2 0.305 6 0.392 9 1 1 t8 0.400 6 0.351 3 0.467 2 1 1 t9 0.351 6 0.389 1 0.525 3 1 1

 图 2 RS-TOPSIS与TOPSIS相对贴近度对比 Fig. 2 Comparison of relative similarity scale between RS-TOPSIS and TOPSIS

5 结论

1) 本文采用RS理论确定目标属性权重，规避人为主观因素的影响，在一定程度上可以取代专家赋权，结合TOPSIS构建威胁评估模型，得到空中目标的威胁度量值，实现对目标的定量评估，拓宽了TOPSIS的适用范围。

2) RS理论基于数据驱动，减少人为主观因素的影响及对先验信息的需求，且对数据具有一定的容错性，对于战场环境复杂和信息不完备的实际情况具有极强的适用性。模型可为后续的武器配置和资源管理提供支撑，可作为后续使用电子对抗或者采用火力打击决策时的理论依据。

3) 模型运行流程固化，无需人为干预，仿真结果与实际情况相符，验证了本文模型的有效性。且该模型具有较好的实时性，过程简单易于操作，对于指导空中目标威胁评估的工程实践具有极其重要的意义。

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#### 文章信息

YANG Yuanzhi, YU Lei, ZHOU Zhongliang, RUAN Chengwei

Air target threat evaluation based on RS-TOPSIS

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(5): 1001-1007
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0342