-
摘要:
管制员和航空器是管制系统的关键所在,两者紧密关联、相互依存,分析其间的相互关系,能够加深对管制系统的理解,更好地维护其运行效率。为此,首先构建了一种由飞行状态网络和管制网络相耦合所组成的相依网络模型。其中,飞行状态网络由空中的航空器和彼此之间位置关系决定;管制网络由管制扇区及其之间的移交关系确定。然后根据管制员对航空器的调配难度确定依存边的权重。最后依据构建原则模拟生成人造网络,对该网络的节点度、点强和加权聚类系数以及网络效率和鲁棒性进行了分析。分析结果表明:所构建的相依网络模型能够反映管制员和航空器之间的相互关系,管制节点重要程度高于航空器节点。
Abstract:The controller and aircraft are the key of the control system. They are closely related and interdependent. Analyzing the relation of them can deepen the comprehension of the control system and maintain the operation efficiency better. For this purpose, an interdependent network model coupled by aircraft state network and control network is established. In the model, aircraft state network is composed of the aircraft and their relative position. The control network is made up of the control sectors and their handover relationship. And the weights of the edges between the networks are calculated according to the control difficulty. On this basis, an artificial network is generated according to construction principle. The node degree, node weight, weighted clustering coefficient, network efficiency and network robustness of the interdependent network are analyzed. The analysis results show that the constructed interdependent network model can reflect the relationship between the controllers and the aircraft and the importance degree of the control nodes is higher than that of the aircraft nodes.
-
表 1 节点度的数值
Table 1. Numerical value of node degree
节点编号 度 1 9 2 9 3 9 4 9 5 7 48 5 49 5 50 5 51 18 52 24 53 19 54 23 55 37 56 29 57 14 58 25 59 16 表 2 节点点强的数值
Table 2. Numerical value of node weight
节点编号 点强/104 1 0.086 2 0.028 3 3.45 4 3.60 5 0.019 48 0.034 49 0.057 50 0.057 51 0.079 52 0.829 53 0.138 54 7.179 55 12.56 56 0.307 57 0.10 58 1.391 59 0.548 表 3 节点加权聚类系数的数值
Table 3. Numerical of weighted clustering coefficient of node
节点编号 加权聚类系数 1 0.921 2 0.870 3 0.925 4 0.925 5 0.910 48 0.966 49 0.965 50 0.965 51 0.298 52 0.297 53 0.278 54 0.333 55 0.311 56 0.277 57 0.388 58 0.278 59 0.368 表 4 相依网络拓扑指标
Table 4. Topological index of interdependent network
节点状态 网络效率 鲁棒性 正常情况 0.1946 0.8561 55号管制节点失效 0.179 0.7683 59号管制节点失效 0.1903 0.8474 54号管制节点失效 0.1798 0.7885 56号管制节点失效 0.1845 0.8366 -
[1] 丁连红, 孙斌, 时鹏.知识图谱复杂网络特性的实证研究与分析[J].物理学报, 2019, 68(12):128902. http://d.old.wanfangdata.com.cn/Periodical/wlxb201912034DING L H, SUN B, SHI P.Empirical study of knowledge network based on complex network theory[J].Acta Physica Sinica, 2019, 68(12):128902(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/wlxb201912034 [2] 陈单, 石丹丹, 潘贵军.复杂网络电输运性能与通信序列熵之间的关联[J].物理学报, 2019, 68(11):118901. http://d.old.wanfangdata.com.cn/Periodical/wlxb201911035CHEN D, SHI D D, PAN G J.Correlation between the electrical transport performance and the communicability sequence entropy in complex networks[J].Acta Physica Sinica, 2019, 68(11):118901(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/wlxb201911035 [3] 王立夫, 赵云康, 段乐, 等.割点失效对复杂网络可控性的影响[J].控制与决策, 2019, 34(11):2310-2316. http://d.old.wanfangdata.com.cn/Periodical/kzyjc201911006WANG L F, ZHAO Y K, DUAN L, et al.Effect of cut vertexes-removal on controllability of complex networks[J].Control and Decision, 2019, 34(11):2310-2316(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/kzyjc201911006 [4] 赵昱, 惠晓滨, 高杨军, 等.基于复杂网络的机群作战建模与仿真[J].火力与指挥控制, 2017, 42(5):10-13. http://d.old.wanfangdata.com.cn/Periodical/hlyzhkz201705003ZHAO Y, HUI X B, GAO Y J, et al.Fleet combat modeling and simulation based on complex networks[J].Fire Control & Command Control, 2017, 42(5):10-13(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/hlyzhkz201705003 [5] JIANG X R, WEN X X, WU M G, et al.A complex network analysis approach for identifying air traffic congestion based on independent component analysis[J].Physica A:Statistical Mechanics and Its Applications, 2019, 523:364-381. https://www.sciencedirect.com/science/article/abs/pii/S0378437119301360 [6] 武喜萍, 杨红雨, 韩松臣.基于复杂网络的空中交通特征与延误传播分析[J].航空学报, 2017, 38(S1):721473. http://d.old.wanfangdata.com.cn/Periodical/hkxb2017z1015WU X P, YANG H Y, HAN S C.Analysis of properties and delay propagation of air traffic based on complex network[J].Acta Aeronautica et Astronautica Sinica, 2017, 38(S1):721473(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/hkxb2017z1015 [7] 陈才龙.基于复杂网络的航路汇聚点布局优化方法研究[D].合肥: 中国科学技术大学, 2011. http://cdmd.cnki.com.cn/Article/CDMD-10358-1011284057.htmCHEN C L.Research on optimization method based on complex network for crossing waypoints location[D].Hefei: University of Science and Technology of China, 2011(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-10358-1011284057.htm [8] 吴小欢.航线网络鲁棒优化设计及其复杂性问题研究[D].南京: 南京航空航天大学, 2012. http://cdmd.cnki.com.cn/Article/CDMD-10287-1014059509.htmWU X H.Robust optimization design and complexity analysis for airline network[D].Nanjing: Nanjing University of Aeronautics and Astronautics, 2012(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-10287-1014059509.htm [9] 黄洋, 汤俊, 老松杨.基于复杂网络的无人机飞行冲突解脱算法[J].航空学报, 2018, 39(12):322222. http://d.old.wanfangdata.com.cn/Periodical/hkxb201812023HUANG Y, TANG J, LAO S Y.UAV flight conflict resolution algorithm based on complex network[J].Acta Aeronautica et Astronautica Sinica, 2018, 39(12):322222(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/hkxb201812023 [10] WANG X H, ZHANG Y, WANG L Z, et al.Robustness evaluation method for unmanned aerial vehicle swarms based on complex network theory[J].Chinese Journal of Aeronautics, 2020, 33(1):352-364. http://d.old.wanfangdata.com.cn/Periodical/hkxb-e202001027 [11] 王兴隆, 高经东, 赵末.空中交通管制扇区复杂网络建模与特性分析[J].中国民航大学学报, 2019, 37(1):7-11. http://d.old.wanfangdata.com.cn/Periodical/zgmhxyxb201901002WANG X L, GAO J D, ZHAO M.Construction and characteristics analyses of ATC sector complex network[J].Journal of Civil Aviation University of China, 2019, 37(1):7-11(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/zgmhxyxb201901002 [12] 朱新平, 潘卫军, 韩松臣.民航空管陆基导航保障体系的复杂网络模型[J].火力与指挥控制, 2018, 43(3):48-53. http://d.old.wanfangdata.com.cn/Periodical/hlyzhkz201803011ZHU X P, PAN W J, HAN S C.Complex network of land-base navigation system for air traffic management of civil aviation[J].Fire Control & Command Control, 2018, 43(3):48-53(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/hlyzhkz201803011 [13] 涂从良, 吴明功, 温祥西.基于接近度与评价矩阵的关键机场节点识别[J].火力与指挥控制, 2017, 42(10):172-176. http://d.old.wanfangdata.com.cn/Periodical/hlyzhkz201710036TU C L, WU M G, WEN X X.Identification of key airport nodes based on closeness sorting algorithm and evaluation matrix[J].Fire Control & Command Control, 2017, 42(10):172-176(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/hlyzhkz201710036 [14] BULDYREV S V, PARSHANI R, PAUL G, et al.Catastrophic cascade of failures in interdependent networks[J].Nature, 2010, 464(7291):1025-1028. http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_0907.1182 [15] PARSHANI R, BULDYREV S V, HAVLIN S.Interdependent networks:Reducing the coupling strength leads to a change from a first to second order percolation transition[J].Physical Review Letters, 2010, 105(4):048701. doi: 10.1103-PhysRevLett.105.048701/ [16] SHAO J, BULDYREV S V, HAVLIN S, et al.Cascade of failures in coupled network systems with multiple support-dependence relations[J].Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 2011, 83(3 Pt 2):036116. doi: 10.1103-PhysRevE.83.036116/ [17] 王兴隆, 潘维煌, 赵末.空中交通相依网络的脆弱性研究[J].航空学报, 2018, 39(12):322235. http://d.old.wanfangdata.com.cn/Periodical/hkxb201812024WANG X L, PAN W H, ZHAO M.Vulnerability of air traffic interdependent network[J].Acta Aeronautica et Astronautica Sinica, 2018, 39(12):322235(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/hkxb201812024 [18] 王兴隆, 潘维煌, 赵末.华北航空相依网络统计特征与鲁棒性分析[J].科学技术与工程, 2018, 18(13):180-185. http://d.old.wanfangdata.com.cn/Periodical/kxjsygc201813029WANG X L, PAN W H, ZHAO M.Analysis of network characteristics and robustness of aeronautical interdependent network in North China[J].Science Technology and Engineering, 2018, 18(13):180-185(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/kxjsygc201813029 [19] WANG Z K, WEN X X, WU M G.Identification of key nodes in aircraft state network based on complex network theory[J].IEEE Access, 2019, 7:60957-60967. [20] 老松杨, 王竣德, 白亮.相依网络研究综述[J].国防科技大学学报, 2016, 38(1):122-128. http://d.old.wanfangdata.com.cn/Periodical/gfkjdxxb201601020LAO S Y, WANG J D, BAI L.Review of the interdependent networks[J].Journal of National University of Defense Technology, 2016, 38(1):122-128(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/gfkjdxxb201601020