信息流介数分布熵测度的C4ISR网络抗毁性

doi:10.19665/j.issn1001-2400.2022.02.014

摘要/Abstract

摘要：

针对当前多数抗毁性研究侧重网络结构进行统计分析,不太适合有特定功能的C4ISR网络的问题,从信息流的功能角度,借鉴“复杂网络介数”和“信息熵”相关理论,提出“信息流介数分布熵”测量C4ISR网络的抗毁性。把侦察节点至火力打击节点的最短信息路径看成一个作战信息链,提出以“信息流介数”测量C4ISR网络中通过某节点的作战信息链数量。以“信息流介数分布熵”测量信息流介数分布的均匀度,分析了该指标反映C4ISR网络功能抗毁性的有效性。在构造一种基本C4ISR网络结构的基础上,仿真分析了网络受随机攻击、度攻击、介数攻击、信息流攻击后的抗毁性表现,以及信息流介数分布熵在提高网络功能抗毁性上的应用。仿真结果表明,文章中提出的测量指标比平均网络效率、自然连通度、度分布熵、介数分布熵等结构上的抗毁性指标更为灵敏与准确,能有效发现C4ISR网络功能失效的临界点,也能为优化提升网络功能上的抗毁能力提供指导。

关键词: 信息流, 介数, 熵, 复杂网络, C4ISR, 抗毁性

Abstract:

Currently,many researches on invulnerability focus on statistical analysis of the network structure which is not suitable for the C4ISR network with specific functions.In view of this problem,this paper proposes “information flow intermediate number centrality distribution entropy” to measure the invulnerability of the C4ISR network.It goes from the perspective of the function of information flow and uses the theory of “intermediate number centrality of complex networks” and “information entropy”.The shortest information path from reconnaissance node to attack node is regarded as an operational information chain,and the “information flow intermediate number centrality ” is proposed to measure the number of operational information chains passing through a node in the C4ISR network.The uniformity of information flow intermediate number centrality is measured by “information flow intermediate number centrality distribution entropy”,and the effectiveness of this index is analyzed which can reflect the invulnerability of the C4ISR network function.Based on a representative C4ISR network structure,the invulnerability of the network after random attack,degree attack,intermediate number centrality attack and information flow attack is simulated,with the application of information flow intermediate number centrality distribution entropy in improving the invulnerability of C4ISR network functions also analyzed.Simulation results show that this indicator is more sensitive and accurate than structural invulnerability indicators such as average network efficiency of complex networks,natural connectivity,degree distribution entropy,intermediate number centrality distribution entropy,and so on and that it can find the critical point of C4ISR network function failure,and can provide guidance for improving the functional invulnerability of the C4ISR network.

Key words: information flow, betweenness centrality, entropy, complex networks, C4ISR, invulnerability

中图分类号:

E917

余昌仁,贾连兴,张斌. 信息流介数分布熵测度的C4ISR网络抗毁性[J]. 西安电子科技大学学报, 2022, 49(2): 116-124.

YU Changren,JIA Lianxing,ZHANG Bin. Invulnerability measurement for the C4ISR network based on information flow betweenness centrality distribution entropy[J]. Journal of Xidian University, 2022, 49(2): 116-124.

图/表 12

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表1

抗毁性系列指标计算公式及符号说明"

抗毁性指标	计算公式	符号说明
复杂网络平均网络效率	E= $2 N (N - 1) ∑ j = i + 1 N ∑ i = 1 N 1 d i j$	N为节点数,d_ij为节点i、j间考虑权重的最短距离
自然连通度	$λ ¯$ =ln $1 N ∑ i = 1 N e λ i$	λ_i为网络邻接矩阵的特征根
复杂网络介数分布熵	E_B=- $S B (v i) ∑ i = 1 N$ lb $S B (v i)$	B(v_i)为节点v_i的介数, $S B (v i)$ =B(v_i) $/ ∑ i = 1 N B (v i)$
度分布熵	E_D=- $S D (v i) ∑ i = 1 N$ lb $S D (v i)$	D(v_i)为节点v_i的度, $S D (v i)$ =D(v_i) $/ ∑ i = 1 N D (v i)$
信息流介数分布熵	E_BI=- $S B I (v k) ∑ k = 1 N$ lb $S B I (v k)$	见式(4)

表1

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