基于节点重要性和改进效能环的防空反导预警体系能力评估

doi:10.12382/bgxb.2022.0488

摘要/Abstract

摘要：

针对防空反导预警体系能力评估中存在的现实性较弱、考虑异质特性较少和能力计算不够全面等问题,提出基于节点重要性和改进效能环的体系能力评估方法。依托超网络模型对体系结构进行抽象建模,给出具有现实意义的效能环模型。从网络全局和局部节点的重要性出发,根据节点之间相互影响关系对效能边进行分析,并结合节点的重要性和可靠性提出体系的能力期望,从而改进基于效能环的体系能力评估方法。反导预警作战的案例仿真分析结果表明:新方法具有可行性与合理性,充分考虑了防空反导预警体系的现实特性和装备的异质特征,能够较全面地评估体系作战能力,为体系的能力评估和结构优化提供理论支撑。

关键词: 防空反导预警体系, 效能环, 节点重要性, 能力评估

Abstract:

A capability evaluation method of air defense and anti-missile early warning system-of-systems (SOS) based on the node importance and improved effectiveness loop (EL) is proposed to address the problems in the capability evaluation of air defense and anti-missile SOS, such as weak realism, less consideration of heterogeneous characteristics and incomplete calculation of capabilities. The structure of the SOS is abstractly modeled based on the super-network model, and a more realistic EL model is proposed. The importance of nodes is calculated from the global and local aspects of the network. Then the effectiveness edges are analyzed according to the mutual influence relations among nodes. In addition, the capability expectation of the SOS is presented to improve the evaluation method by combining the node importance and reliability with the capability of the edge. Finally, the feasibility and rationality of the method are verified through the simulation analysis of anti-missile early warning combat example. The proposed method fully takes the realistic characteristics of the air defense and anti-missile early warning SOS and the heterogeneous features of the equipment into account, and can assess the capability of SOS in a more comprehensive manner, which provides theoretical support for the capability evaluation and structural optimization of SOS.

Key words: air defense and anti-missile early warning system-of-systems, effectiveness loop, node importance, capability evaluation

中图分类号:

E917

俞锦涛, 肖兵, 崔玉竹. 基于节点重要性和改进效能环的防空反导预警体系能力评估[J]. 兵工学报, 2024, 45(1): 328-338.

YU Jintao, XIAO Bing, CUI Yuzhu. Capability Evaluation of Air Defense and Anti-missile Early Warning System-of-systems Based on Node Importance and Improved Effectiveness Loop[J]. Acta Armamentarii, 2024, 45(1): 328-338.

图/表 10

图1 防空反导基本作战过程示意图

Fig.1 Basic combat process of air defense and anti-missile

图2 广义效能环

Fig.2 General ELs

表1 作战体系中效能环的类型和意义

Table 1 Types and meanings of ELs in combat SOS

效能环	含义
T-O-P-D-A-T	标准的效能环
T-O-O-P-D-A-T	具有协同探测的效能环
T-O-P-P-D-A-T	具有信息交互的效能环
T-O-P-D-D-A-T	具有协同指控的效能环
T-O-O-P-P-D-A-T	具有协同探测和信息交互的效能环
T-O-O-P-D-D-A-T	具有协同探测和指控的效能环
T-O-O-P-P-D-D-A-T	具有协同探测、指控和信息交互的效能环

图3 防空反导预警体系能力指标

Fig.3 Capability indexes of air defense and anti-missile early warning SOS

图4 防空反导预警体系作战能力评估流程

Fig.4 Combat capability evaluation process of air defense and anti-missile early warning SOS

图5 反导预警体系作战网络结构图

Fig.5 Combat network structure diagram of anti-missile early warning SOS

表2 体系网络中节点的重要性和可靠性

Table 2 Importance and reliability of nodes in SOS network

节点	节点重要性	归一化节点重要性	节点可靠性
$T o u t (1)$	4.1984		1
$T o u t (2)$	4.1984		1
O⁽¹⁾	5.5105	0.1050	1
O⁽²⁾	6.1077	0.1164	0.98
O⁽³⁾	5.1870	0.0989	0.98
P⁽¹⁾	6.4870	0.1236	1
P⁽²⁾	7.0945	0.1352	1
D⁽¹⁾	6.4502	0.1229	1
D⁽²⁾	6.4605	0.1231	1
A⁽¹⁾	4.1490	0.0791	0.99
A⁽²⁾	5.0225	0.0957	0.99
$T i n (1)$	3.1394
$T i n (2)$	2.3291

表2 体系网络中节点的重要性和可靠性

Table 2 Importance and reliability of nodes in SOS network

节点	节点重要性	归一化节点重要性	节点可靠性
$T o u t (1)$	4.1984		1
$T o u t (2)$	4.1984		1
O⁽¹⁾	5.5105	0.1050	1
O⁽²⁾	6.1077	0.1164	0.98
O⁽³⁾	5.1870	0.0989	0.98
P⁽¹⁾	6.4870	0.1236	1
P⁽²⁾	7.0945	0.1352	1
D⁽¹⁾	6.4502	0.1229	1
D⁽²⁾	6.4605	0.1231	1
A⁽¹⁾	4.1490	0.0791	0.99
A⁽²⁾	5.0225	0.0957	0.99
$T i n (1)$	3.1394
$T i n (2)$	2.3291

表3 体系效能边的能力值

Table 3 Capability value of SOS effectiveness edge

效能边	能力值	效能边	能力值
T⁽¹⁾-O⁽¹⁾	0.7489	P⁽¹⁾-D⁽¹⁾	0.8678
T⁽¹⁾-O⁽²⁾	0.7113	P⁽¹⁾-D⁽²⁾	0.8778
T⁽¹⁾-O⁽³⁾	0.8618	P⁽²⁾-D⁽¹⁾	0.9505
T⁽²⁾-O⁽¹⁾	0.7489	P⁽²⁾-D⁽²⁾	0.9613
T⁽²⁾-O⁽²⁾	0.7113	D⁽¹⁾-D⁽²⁾	0.8328
T⁽²⁾-O⁽³⁾	0.8618	D⁽¹⁾-A⁽¹⁾	0.8132
O⁽¹⁾-O⁽²⁾	0.8457	D⁽¹⁾-A⁽²⁾	0.8284
O⁽¹⁾-P⁽²⁾	0.9583	D⁽²⁾-A⁽¹⁾	0.8256
O⁽²⁾-P⁽¹⁾	0.9020	D⁽²⁾-A⁽²⁾	0.8426
O⁽²⁾-P⁽²⁾	0.9244	A⁽¹⁾-T⁽¹⁾	0.9099
O⁽³⁾-P⁽¹⁾	0.8234	A⁽²⁾-T⁽¹⁾	0.9096
O⁽³⁾-P⁽²⁾	0.8414	A⁽²⁾-T⁽²⁾	0.7300
P⁽¹⁾-P⁽²⁾	0.8777

表4 针对目标1的效能环及能力值

Table 4 Effectiveness loop and corresponding capability value for Target 1

序号	效能环路径	能力值
1	T⁽¹⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽¹⁾-D⁽²⁾-A⁽¹⁾-T⁽¹⁾	0.2892
2	T⁽¹⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽¹⁾-D⁽²⁾-A⁽²⁾-T⁽¹⁾	0.2951
3	T⁽¹⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽¹⁾-A⁽¹⁾-T⁽¹⁾	0.3421
4	T⁽¹⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽¹⁾-A⁽²⁾-T⁽¹⁾	0.3483
︙	︙	︙
59	T⁽¹⁾-O⁽³⁾-P⁽²⁾-D⁽²⁾-A⁽¹⁾-T⁽¹⁾	0.5080
60	T⁽¹⁾-O⁽³⁾-P⁽²⁾-D⁽²⁾-A⁽²⁾-T⁽¹⁾	0.5183
	平均值	0.4052

表5 针对目标2的效能环及能力值

Table 5 Effectiveness loop and corresponding capability value for Target 2

序号	效能环路径	能力值
1	T⁽²⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽¹⁾-D⁽²⁾-A⁽²⁾-T⁽²⁾	0.2368
2	T⁽²⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽¹⁾-A⁽²⁾-T⁽²⁾	0.2796
3	T⁽²⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽²⁾-A⁽²⁾-T⁽²⁾	0.2876
4	T⁽²⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-D⁽¹⁾-D⁽²⁾-A⁽²⁾-T⁽²⁾	0.2463
︙	︙	︙
29	T⁽²⁾-O⁽³⁾-P⁽²⁾-D⁽¹⁾-A⁽²⁾-T⁽²⁾	0.4043
30	T⁽²⁾-O⁽³⁾-P⁽²⁾-D⁽²⁾-A⁽²⁾-T⁽²⁾	0.4160
	平均值	0.3284

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