基于灰主成分的空战目标威胁评估

doi:10.3969/j.issn.1001-506X.2021.01.18

摘要/Abstract

摘要：

由于影响空战目标威胁评估的因素复杂多样,且具有矛盾性、相关性、耦合性等特点,因此利用传统的评估方法无法得到准确客观的评估结果。对此,提出一种基于灰色主成分的目标威胁评估方法。首先,利用主成分分析(principle component analysis, PCA)方法,分析指标之间的相关性,生成指标之间的灰色关联系数矩阵,取代传统的相关矩阵或协方差矩阵,将相互关联的指标转化成相互独立的分量,重构目标威胁评估体系。其次,构建灰色关联深度极大熵模型确定原始评估指标权重。然后,分析以累计贡献率为客观性赋权且没有考虑指标重要性差异的问题,将因子载荷作为主成分权重合成的重要依据。最后,通过仿真案例,对不同的威胁评估方法得出的结果进行对比分析,证明了灰主成分法的有效性和合理性。

关键词: 灰色主成分, 指标相关性, 重构, 灰色关联系数, 因子载荷

Abstract:

Due to the complexity and diversity of the factors affecting the assessment of air combat target threats, which is characterized by contradiction, correlation and coupling. Therefore, the accurate and objective assessment results cannot be obtained using the traditional assessment methods. A target threat assessment method based on gray principal component is proposed. Firstly, the principal component analysis (PCA) method is used to analyze the correlation between indicators, and the grey correlation coefficient matrix between indicators is generated to replace the traditional correlation matrix or covariance matrix. The interrelated indexes are converted into independent components to reconstruct the target threat assessment system. Secondly, a grey correlation depth maximum entropy model is established to determine the original evaluation index weight. Then, the problem that the accumulative contribution rate is used as the objective weight and not taken into account the index importance difference is analyzed, the factor load is used as the important basis for the weight synthesis of main components. Finally, the effectiveness and rationality of grey principal component are illustrated by comparing and analyzing the results of different threat assessment methods through the simulation cases.

Key words: grey principal component, index correlation, reconstruction, grey relational coefficient, factor loading

中图分类号:

奚之飞, 徐安, 寇英信, 李战武, 杨爱武. 基于灰主成分的空战目标威胁评估[J]. 系统工程与电子技术, 2021, 43(1): 147-155.

Zhifei XI, An XU, Yingxin KOU, Zhanwu LI, Aiwu YANG. Air combat target threat assessment based on gray principal component[J]. Systems Engineering and Electronics, 2021, 43(1): 147-155.

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时刻	目标	机型	q^B/(°)	q^R/(°)	r/km	v/(m/s)	导弹射程/km
t-1	1	F－16C	80	-45	80	300	60
	2	F－16C	45	-45	70	325	80
	3	F－5E	-60	80	60	320	50
	4	F－15E	-45	15	60	330	70
t	1	F－16C	78	-52	76	316	60
	2	F－16C	51	-47	74	318	80
	3	F－5E	-57	86	65	332	50
	4	F－15E	-49	21	58	346	70

目标	C	T_A	T_D	T_v	T_I
1	0.85	0.36	0.50	0.487 5	0.126 0
2	0.85	0.27	1.00	0.493 8	0.283 4
3	0.41	0.40	0.50	0.537 5	0.506 9
4	1.00	0.19	0.80	0.581 3	0.329 5

指标	各指标之间的相关系数
指标	z₁	z₂	z₃	z₄	z₅
z₁	1.000 0	0.434 6	0.550 8	0.462 4	0.391 8
z₂	0.436 4	1.000 0	0.514 4	0.101 7	0.699 5
z₃	0.550 8	0.514 4	1.000 0	0.564 5	0.092 5
z₄	0.462 4	0.101 7	0.564 5	1.000 0	0.557 9
z₅	0.391 8	0.699 5	0.092 5	0.557 9	1.000 0

第i主成分	初始特征值
第i主成分	方差大小	方差贡献率	累计贡献率
1	3.405 3	0.681 1	0.681 1
2	1.335 7	0.267 1	0.948 2
3	0.259 0	0.051 8	1.000 0
4	0.000 0	0.000 0	1.000 0
5	0.000 0	0.000 0	1.000 0

序号	评价指标	第1主成分	第2主成分	第3主成分
1	能力	-0.355 4	-0.631 9	0.375 7
2	角度	0.522 7	0.227 0	0.053 1
3	距离	0.346 9	-0.581 6	-0.731 3
4	速度	-0.442 4	0.447 0	-0.507 0
5	意图	0.533 3	0.105 5	0.253 3