Abstract：This paper introduces the concept of operation loop, and a network model of combat networks of Weapon System-of-systems based on operation loop. Then the concept of directed natural connectivity is proposed and is used to investigate the robustness of combat networks. To verify the feasibility and effectiveness of directed natural connectivity in evaluating the robustness of combat networks, three scenarios are designed: edge destruction, edge increasing and connection probability increasing. The robustness of combat networks measured by spectral radius of Laplacian matrix and directed natural connectivity are compared under the three scenarios. The results suggested that the directed natural connectivity allows a sensitive and precise quantitative analysis for the robustness of combat network. It is also showed that robust of combat networks will decrease dramatically if intelligence reconnaissance and acquisition capabilities of sensor nodes are restrained. Our results may lead to useful insights on designing a more robust combat networks, such as improving the accuracy of intelligence acquisition, ensuring instructions delivered accurately, strengthening the capability of precision strike, and enhancing communication capabilities of armaments etc.
李际超, 吴俊, 谭跃进, 张小可, 杨克巍. 基于有向自然连通度的作战网络抗毁性研究[J]. 复杂系统与复杂性科学, 2015, 12(4): 25-31.
LI Jichao, WU Jun, TAN Yuejin, ZHANG Xiaoke, YANG Kewei. Robustness of Combat Networks Based on Directed Natural Connectivity[J]. Complex Systems and Complexity Science, 2015, 12(4): 25-31.
[1] 谭跃进,张小可,杨克巍. 武器装备体系网络化描述与建模方法[J]. 系统管理学报, 2012, 21 (6): 781-786. Tan Yuejin, Zhang Xiaoke, Yang Kewei. Research on networked description and modeling methods of armament system-of-systems[J]. Journal of Systems & Management, 2012, 21 (6): 781-786. [2] Hu B, Li F, Zhou H S. Robustness of complex networks under attack and repair[J]. Chinese Physics Letters, 2009, 26 (12): 1-4. [3] Herrmann H J, Schneider C M, Moreira A A, et al. Onion-like network topology enhances robustness against malicious attacks[J]. Journal of Statistical Mechanics: Theory and Experiment, 2011, 2011 (1): 1-9. [4] Zeng A, Liu W P. Enhancing network robustness against malicious attacks[J]. Physical Review E, 2012, 85 (6): 066130. [5] 汤浩锋, 张琨, 郁楠, 等. 有向加权复杂网络抗毁性测度研究[J]. 计算机工程, 2013, 39 (1): 23-28. Tang Haofeng, Zhang Kun, Yu Nan, et al. Research on invunnerability measure of directed and weighted complex network[J]. Computer Engineering, 2013, 39 (1): 23-28. [6] Jeffrey R C. An information Age Combat Model[M]. Newport: Alidade, 2004. [7] Dekker A H. Measuring the agility of networked military forces[J]. Journal of Battlefeild Technology, 2006, 9 (1): 19–24. [8] 金伟新, 肖田元. 基于特征谱的作战体系网络脆性研究[J]. 系统仿真技术及其应用, 2012, 14 (1): 11-15. Jin Weixin, Xiao Tianyuan. Research on the vulneralbility of the SoS network with spectral analysis of its Laplacian matrix eigenvalues[J]. System Simulation Technology & Application, 2012, 14 (1): 11-15. [9] 狄鹏, 胡涛, 胡斌, 等. 基于复杂网络的作战网络模型抗毁性研究[J]. 系统仿真学报, 2011, 23 (1): 56-60. Di Peng, Hu Tao, Hu Bin, et al. Research on invulnerability of combat net model based on complex networks[J]. Journal of System Simulation, 2011, 23 (1): 56-60. [10] 齐燕博, 刘忠, 许江湖. 作战体系网络模型与网络化效能分析[J]. 火力指挥与控制, 2013, 38 (5): 66-69. Qi Yanbo, Liu Zhong, Xu Jianghu. Combat system of systems network modeling and networked effects analysis[J]. Fire Control &Command Control, 2013, 38 (5): 66-69. [11] Li D Y, Xiao L P, Han Y N, et al. Network thinking and network intelligence[J]. Proceedings of Lecture Notes of Artificial Intelligence, 2007, 4845: 36-58. [12] 谭东风. 基于网络整体效能的战斗毁伤模型[J]. 系统工程理论与实践, 2013, 33 (2): 522-527. Tan Dongfeng. An attrition model with global network efficiency[J]. Systems Engineering Theory & Practice, 2013, 33 (2): 522-527. [13] 王斌, 谭东风, 凌云翔. 基于复杂网络的作战描述模型研究[J]. 指挥控制与仿真, 2007, 29 (4): 11-16. Wang Bin, Tan Dongfeng, Ling Yunxiang. Research on combat description model based on complex networks[J]. Command Control & Simulation, 2007, 29 (4): 11-16. [14] 王庆功, 沈寿林, 袁昌平. 基于复杂网络的作战体系网络模型分析[J]. 指挥控制与仿真, 2013, 35 (1): 6-10. Wang Qinggong, Shen Shoulin, Yuan Changping. Combat system network model analysis based on complex network[J]. Command Control & Simulation, 2013, 35 (1): 6-10. [15] 黄仁全, 李为民, 董雯, 等. 不同攻击策略下作战体系网络抗毁性研究[J]. 复杂系统与复杂性科学, 2012, 9 (3): 64-72. Huang Renquan, Li Weimin, Dong Wen, et al. Research on the invulnerability of combat SoS under different attack strategies[J]. Complex Systems and Complexity Science, 2012, 9 (3): 64-72. [16] Wu J, Barahona M, Tan Y J, et al. Natural connectivity of complex networks[J].Chinese Physics Letters, 2010, 27 (7): 1-4. [17] Shang Y L. Local natural connectivity in complex networks[J]. Chinese Physics Letters, 2011, 28 (6): 68903-68906. [18] Wu J, Mauricio B, Tan Y J, et al. Spectral measure of structural robustness in complex networks[J]. IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans, 2011, 41 (6): 1244-1252. [19] Wu J, Mauricio B, Tan Y J, et al. Robustness of regular ring lattices based on natural connectivity[J]. International Journal of Systems Science, 2011, 42: 1085-1092.
