考虑节点重要度的反导体系效能评估方法

doi:10.12305/j.issn.1001-506X.2026.02.18

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (2): 569-577.doi: 10.12305/j.issn.1001-506X.2026.02.18

• 系统工程 • 上一篇

考虑节点重要度的反导体系效能评估方法

郝雪婷¹^,*, 方志耕¹, 江安康¹, 张靖如¹, 孙云柯¹^,²

1. 南京航空航天大学经济与管理学院，江苏南京 211106
2. 南京电子设备研究所，江苏南京 210008

收稿日期:2024-07-26 修回日期:2024-09-05 出版日期:2025-04-23 发布日期:2025-04-23
通讯作者: 郝雪婷
作者简介:方志耕（1962—），男，教授，博士研究生导师，博士，主要研究方向为复杂装备研制管理、质量与可靠性
江安康（1999—），男，硕士研究生，主要研究方向为效能评估、可靠性预计
张靖如（1997—），女，博士研究生，主要研究方向为复杂装备研制管理、体系攻防博弈
孙云柯（1996—），女，工程师，硕士，主要研究方向为体系评估
基金资助:
国家自然科学基金（72271124, 52232014, 72071111）资助课题

Method of effectiveness evaluation for anti-missile system of systems based on node importance

Xueting HAO¹^,*, Zhigeng FANG¹, Ankang JIANG¹, Jingru ZHANG¹, Yunke SUN¹^,²

1. College of Economics and Management，Nanjing University of Aeronautics and Astronautics，Nanjing 211106，China
2. Nanjing Institute of Electronic Equipment，Nanjing 210008，China

Received:2024-07-26 Revised:2024-09-05 Online:2025-04-23 Published:2025-04-23
Contact: Xueting HAO

摘要/Abstract

摘要：

反导体系是抵御威胁的重要防线，如何更加准确地描述、评估反导体系的作战效能是一件非常重要而复杂的工作。针对反导体系效能评估问题，分析反导作战体系的特征，结合图示评审技术(graphical evaluation and review technique, GERT)，首先构建反导作战GERT网络，为效能评价提供模型框架；其次引入节点重要度思想，通过分析装备自身属性和关联装备的重要性，修正装备能力，并利用梅森公式和矩母函数的优良性质，解决基于节点重要度的反导体系作战效能评估问题；最后通过算例研究，说明基于节点重要度的反导体系效能评估方法的实用性和有效性。结果表明，基于节点重要度的效能评估方法能够有效量化装备异质性及网络结构对整体效能的影响，充分考虑关键节点对体系效能的影响，为反导体系的效能评估与优化提供了一种更贴合实际的新思路。

关键词: 节点重要度, 效能评估, GERT网络, 反导, 作战体系

Abstract:

The anti-missile system of systems serves as a crucial defense line against hostile threats, how to exactly describe the anti-missile system of systems and evaluate its combat effectiveness is a significant and complex task. Aimming at the issue of effectiveness evaluation of anti-missile systems, the characteristics of the anti-missile combat system of systems are analyzed. Combining with graphical evaluation and review technique （GERT）, anti-missile combat GERT network is firstly constructed to provide a modeling framework for effectiveness evaluation. Secondly, the node importance idea is introduced. The correction of equipment abilities involves evaluating the significance of both the equipment itself and its related equipment. Based on this, the challenge of determining the combat effectiveness for an anti-missile system of systems based on the node significance is resolved by utilizing the superior qualities of Mersenne’s formula and the mother-of-moments function. Finally, a case study illustrates the efficiency and effectiveness of the effectiveness evaluation model for anti-missile system of systems based on node importance. The results demonstrate that the effectiveness evaluation method based on node importance can effectively quantify the impacts of equipment heterogeneity and network structure on overall effectiveness. This method fully accounts for the influence of critical nodes on system effectiveness. It provides a more practical approach for the effectiveness evaluation and optimization of anti-missile system of systems.

Key words: node importance, effectiveness evaluation, graphical evaluation and review technique (GERT) network, anti-missile, combat system of systems

中图分类号:

N 945

郝雪婷, 方志耕, 江安康, 张靖如, 孙云柯. 考虑节点重要度的反导体系效能评估方法[J]. 系统工程与电子技术, 2026, 48(2): 569-577.

Xueting HAO, Zhigeng FANG, Ankang JIANG, Jingru ZHANG, Yunke SUN. Method of effectiveness evaluation for anti-missile system of systems based on node importance[J]. Systems Engineering and Electronics, 2026, 48(2): 569-577.

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作战活动(i，j)	活动概率p_ij	活动效果E_ij	执行装备i	装备能力
$({\mathrm{Start}},{O_1})$	0.33	0	−	−
$({\mathrm{Start}},{O_2})$	0.33	0
$({\mathrm{Start}},{O_3})$	0.33	0
$({O_1},{O_2})$	0.5	0.7924	${O_1}$	0.8452
$({O_1},{P_2})$	0.5	0.8979	${O_1}$	0.8452
$({O_2},{P_1})$	0.49	0.8268	${O_2}$	0.8204
$({O_2},{P_2})$	0.49	0.8474	${O_2}$	0.8204
$({O_3},{P_1})$	0.49	0.8077	${O_3}$	0.8002
$({O_3},{P_2})$	0.49	0.8253	${O_3}$	0.8002
$ ({P_1},{P_2}) $	0.33	0.8777	$ {P_1} $	0.8657
$ ({P_1},{D_1}) $	0.33	0.8678
$ ({P_1},{D_2}) $	0.33	0.8778
$ ({P_2},{D_1}) $	0.5	0.9505	$ {P_2} $	0.9559
$ ({P_2},{D_2}) $	0.5	0.9613	$ {P_2} $	0.9559

节点$i$	位置重要度	关联节点		关联重要度	节点重要度	归一化节点重要度
节点$i$	位置重要度	入节点	出节点	关联重要度	节点重要度	归一化节点重要度
$ {T_1} $	0.5	$ {A_1} $,$ {A_2} $	${O_1}$,${O_2}$,${O_3}$	0.8316	0.4158	0.0903
$ {T_2} $	0.4	$ {A_2} $	${O_1}$,${O_2}$,${O_3}$	0.6965	0.2786	0.0605
${O_1}$	0.4	$ {T_1} $,$ {T_2} $	${O_2}$,$ {P_2} $	0.8391	0.3356	0.0728
${O_2}$	0.5	$ {T_1} $,$ {T_2} $,${O_1}$	$ {P_1} $,$ {P_2} $	1.0194	0.5097	0.1106
${O_3}$	0.4	$ {T_1} $,$ {T_2} $	$ {P_1} $,$ {P_2} $	0.8504	0.3402	0.0738
$ {P_1} $	0.5	${O_2}$,${O_3}$	$ {P_2} $,$ {D_1} $,$ {D_2} $	1.0646	0.5323	0.1155
$ {P_2} $	0.6	${O_1}$,${O_2}$,${O_3}$,$ {P_1} $	$ {D_1} $,$ {D_2} $	1.1632	0.6979	0.1515
$ {D_1} $	0.5	$ {P_1} $,$ {P_2} $	$ {D_2} $,$ {A_1} $,$ {A_2} $	1.0092	0.5046	0.1095
$ {D_2} $	0.5	$ {P_1} $,$ {P_2} $,$ {D_1} $	$ {A_1} $,$ {A_2} $	1.0048	0.5024	0.1090
$ {A_1} $	0.3	$ {D_1} $,$ {D_2} $	$ {T_1} $	0.8253	0.1862	0.0404
$ {A_2} $	0.4	$ {D_1} $,$ {D_2} $	$ {T_1} $,$ {T_2} $	0.8253	0.3039	0.066 0

作战活动$(i,j)$	活动概率${p_{ij}}$	活动效果$E_{ij}^{'}$	等价传递函数${W_{ij}}$
$({\mathrm{Start}},{O_1})$	0.33	0	0.33
$({\mathrm{Start}},{O_2})$	0.33	0	0.33
$({\mathrm{Start}},{O_3})$	0.33	0	0.33
$({O_1},{O_2})$	0.5	0.7632	$0.5{\mathrm{Exp}}(0.763\;2s)$
$({O_1},{P_2})$	0.5	0.8648	$0.5{\mathrm{Exp}}(0.864\;8s)$
$({O_2},{P_1})$	0.49	0.8270	$0.49{\mathrm{Exp}}(0.827s)$
$({O_2},{P_2})$	0.49	0.8476	$0.49{\mathrm{Exp}}(0.847\;6s)$
$({O_3},{P_1})$	0.49	0.7787	$0.49{\mathrm{Exp}}(0.778\;7s)$
$({O_3},{P_2})$	0.49	0.7957	$0.49{\mathrm{Exp}}(0.795\;7s)$
$ ({P_1},{P_2}) $	0.33	0.8821	$0.33{\mathrm{Exp}}(0.882\;1s)$
$ ({P_1},{D_1}) $	0.33	0.8721	$0.33{\mathrm{Exp}}(0.872\;1s)$

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考虑节点重要度的反导体系效能评估方法

Method of effectiveness evaluation for anti-missile system of systems based on node importance

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