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

Abstract

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

CLC Number:

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.

Figures/Tables 13

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References 30

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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

Air combat target threat assessment based on gray principal component

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敌方目标	正理想解灰关联度	负理想解灰关联度	相对贴近度	威胁排序
1	1.000 0	0.856 0	0.538 8	1
2	0.791 7	1.000 0	0.441 9	4
3	0.858 0	0.808 5	0.514 9	2
4	0.852 2	0.869 6	0.495 0	3

编号	灰色关联	威胁排序	灰主成分	威胁排序	文献[26-27] 方法	文献[28] 方法
1	0.538 8	1	0.718 4	2	2	2
2	0.441 9	4	-0.309 6	3	1	3
3	0.514 9	2	0.846 7	1	4	1
4	0.495 0	3	-1.255 5	4	3	4

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目标	第1主成分	第2主成分	第3主成分	综合值
1	1.706 9	-1.306 4	0.173 8	0.718 4
2	-1.186 4	0.596 5	0.637 7	-0.309 6
3	1.436 8	1.274 9	-0.332 5	0.846 7
4	-1.957 2	-0.565 0	-0.479 0	-1.255 5

敌方目标	正理想解灰关联度	负理想解灰关联度	相对贴近度	威胁排序
1	1.000 0	0.697 3	0.582 9	2
2	0.797 2	0.785 0	0.503 9	3
3	0.994 9	0.672 5	0.596 7	1
4	0.611 5	1.000 0	0.379 5	4