基于改进GRA-TOPSIS的空战威胁评估

奚之飞; 徐安; 寇英信; 李战武; 杨爱武

doi:10.13700/j.bh.1001-5965.2019.0207

基于改进GRA-TOPSIS的空战威胁评估

doi: 10.13700/j.bh.1001-5965.2019.0207

奚之飞¹,
徐安^{1, 2, ,},
寇英信¹,
李战武^{1, 2},
杨爱武¹

1.
空军工程大学航空工程学院, 西安 710038
2.
西北工业大学电子信息学院, 西安 710072

详细信息

作者简介:
奚之飞  男, 硕士研究生。主要研究方向:火力指挥控制原理与技术

徐安  男, 博士, 讲师。主要研究方向:火力指挥控制原理与技术

寇英信  男, 博士, 教授。主要研究方向:火力指挥控制原理与技术

李战武  男, 博士, 教授。主要研究方向:火力指挥控制原理与技术

杨爱武  男, 硕士研究生。主要研究方向:火力指挥控制原理与技术

通讯作者:
徐安, E-mail: xuankgd@163.com

中图分类号: V221⁺.3;TB553
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出版历程
- 收稿日期: 2019-05-05
- 录用日期: 2019-08-03
- 网络出版日期: 2020-02-20

Air combat threat assessment based on improved GRA-TOPSIS

XI Zhifei¹,
XU An^{1, 2
, ,},
KOU Yingxin¹,
LI Zhanwu^{1, 2},
YANG Aiwu¹

1.
Aeronautics Engineering College, Air Force Engineering University, Xi'an 710038, China
2.
College of Electronic Communication, Northwestern Polytechnical University, Xi'an 710072, China

More Information

Corresponding author: XU An, E-mail: xuankgd@163.com

摘要

摘要:
针对在确定空战威胁评估指标权重时，未考虑指标间的耦合性以及客观赋权法不能从逻辑视角体现指标相对评价对象真正的重要程度的问题，提出了一种基于灰色关联度、灰色关联深度的极大熵模型初步确定权值，再根据指标间灰色关联度以及确定的解耦阈值修正权值的方法。为了克服灰色关联分析法（GRA）和理想点接近法（TOPSIS）的缺点，提出了一种基于GRA-TOPSIS的目标威胁评估方法。首先，通过实例对比分析了指标采用数学模型与模糊处理后，对目标威胁评估结果的影响；其次，对比分析了采用GRA、TOPSIS以及GRA-TOPSIS、数学模型得出的目标威胁评估结果；最后，考虑不同决策者的主观偏好，得出不同的目标威胁评估结果。通过仿真验证了所提方法的有效性以及科学性。
- 灰色关联深度 /
- 指标间灰色关联度 /
- 灰色关联分析法-理想点接近法(GRA-TOPSIS) /
- 极大熵 /
- 分辨系数
Abstract:
In order to solve the problem that the coupling between indexes is not considered an the objective weighting method cannot reflect the true importance of indexes relative to evaluation objects from a logical perspective when calculating the weight of indexes in air combat threat assessment, a maximum entropy model based on grey relational degree and grey relational depth is proposed to determine the initial weight, and then the weight is modified according to the grey relational degree among indexes and the decoupling threshold. In order to overcome the shortcomings of grey relational analysis (GRA) and technique for order preference by similarity to solution (TOPSIS), a method of target threat assessment based on GRA-TOPSIS is proposed. First, the influence of mathematical model and fuzzy processing on the target threat assessment is analyzed through example. Second, the results of the target threat assessment using the GRA, TOPSIS, GRA-TOPSIS and mathematical models are compared and analyzed. Finally, different target threat assessment results are obtained by considering the subjective preference of different decision makers. Simulation proved the effectiveness and scientificity of the proposed method.

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图 1 威胁评估处理流程

Figure 1. Threat assessment process

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图 2 各指标之间的关联度

Figure 2. Correlation degree among indexes

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图 3 四种方法相对贴近度对比

Figure 3. Comparison of relative nearness degree calculated by four methods

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图 4 决策者的不同偏好对比

Figure 4. Comparison of different preferences among decision makers

下载: 全尺寸图片幻灯片

表 1 敌机的参数信息

Table 1. Enemy aircraft parameter information

目标	机型	作战意图	q^B/(°)	q^R/(°)	r_r/km	v_r/(m·s^-1)
1	F-16C	攻击	80	-45	50	300
2	F-16C	掩护	45	-45	70	325
3	F-5E	攻击	-60	80	60	320
4	F-15E	干扰	-45	15	60	330

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表 2 灰色关联度

Table 2. Grey relational degree

敌机编号	正理想解灰色关联度	负理想解灰色关联度	相对贴近度
1	0.815 8	0.616 7	0.547 7
2	0.633 1	0.725 3	0.444 1
3	0.783 4	0.605 4	0.542 2
4	0.593 7	0.746 7	0.421 2

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表 3 欧氏距离

Table 3. Euclidean distance

敌机编号	正理想解欧氏距离	负理想解欧氏距离	TOPSIS方法欧氏距离
1	0.353 6	0.629 1	0.394 4
2	0.529 3	0.424 5	0.590 9
3	0.330 3	0.604 1	0.387 8
4	0.543 0	0.521 3	0.546 9

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表 4 无量纲化处理及威胁排序(α=0.5, β=0.5)

Table 4. Dimensionless processing and threat sorting(α=0.5, β=0.5)

敌机编号	正理想解灰色关联度	负理想解灰色关联度	正理想解欧氏距离	负理想解欧氏距离	正理想解贴近度	负理解贴近度	相对贴近度	威胁排序
1	1.000 0	0.825 9	0.651 2	1.000 0	1.000 0	0.738 6	0.574 2	2
2	0.776 0	0.971 4	0.974 7	0.674 9	0.725 5	0.973 1	0.427 1	4
3	0.960 3	0.810 8	0.608 3	0.960 3	0.960 3	0.709 6	0.575 1	1
4	0.727 7	1.000 0	1.000 0	0.828 6	0.778 2	1.000 0	0.437 6	3

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表 5 四种方法相对贴近度与威胁排序比较

Table 5. Comparison of relative nearness degree and threat sorting of four methods

敌机编号	TOPSIS		GRA		GRA-TOPSIS		数学模型
敌机编号	相对贴近度	威胁排序	相对贴近度	威胁排序	相对贴近度	威胁排序	相对贴近度	威胁排序
1	0.394 4	3	0.547 7	1	0.574 2	2	0.610 7	1
2	0.590 9	1	0.444 1	3	0.427 1	4	0.593 0	2
3	0.387 8	4	0.542 2	2	0.575 1	1	0.487 1	3
4	0.546 9	2	0.421 2	4	0.437 6	3	0.452 1	4

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表 6 α，β不同取值时目标威胁排序

Table 6. Target threat sorting at different values of α, β

敌机编号	α=0.2，β=0.8			α=0.4，β=0.6			α=0.7，β=0.3
敌机编号	正理想解贴近度	负理想解贴近度	相对贴近度	正理想解贴近度	负理想解贴近度	相对贴近度	正理想解贴近度	负理想解贴近度	相对贴近度
1	1.000 0	0.825 9	0.547 7	1.000 0	0.756 0	0.569 5	1.000 0	0.703 6	0.575 2
2	0.776 0	0.971 4	0.444 1	0.735 6	0.972 7	0.430 6	0.705 2	0.973 7	0.420 2
3	0.960 3	0.810 8	0.542 2	0.960 3	0.729 8	0.568 2	0.960 3	0.669 1	0.575 1
4	0.727 7	1.000 0	0.421 2	0.768 1	1.000 0	0.434 4	0.798 4	1.000 0	0.443 9
排序	1>3>2>4			1>3>4>2			1>3>4>2

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