Identification Method for Key Nodes in En-Route Network
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摘要:
有效辨识关键节点对增强网络韧性、提高运行能力具有重要意义，为提高航路网络关键节点识别的准确性，提出基于TOPSIS（technique for order preference by similarity to an ideal solution，TOPSIS）-灰色关联分析法的综合评价方法和航路网络节点分级方法. 首先，从复杂网络统计特性、交通流量特性、脆弱性3个方面构建航路网络关键节点评价指标体系；通过引入相对熵改进逼近理想值排序法，并结合灰色关联分析法综合评价航路点重要程度，采用基于K-means聚类方法有效划分航路节点等级；最后，以民航空管实际运行数据为实例，开展关键节点识别. 研究表明：相较于单一指标，所建航路网络节点评价指标体系获得的评价结果更加全面；改进TOPSIS-灰色关联分析方法相较于传统TOPSIS法评价结果更加准确；本研究所提识别方法发现了我国华东地区典型繁忙航路网络中有29个关键节点，其在网络结构及交通流量方面具有关键作用.
Abstract:Accurate identification of key nodes is of great significance for enhancing network resilience and improving operational capabilities. In order to improve the identification accuracy of key nodes in the en-route network, a comprehensive evaluation method based on the technique for order preference by similarity to an ideal solution (TOPSIS)-grey correlation analysis method and a node classification method for the en-route network were proposed. Firstly, an evaluation index system of key nodes in the en-route network was constructed from three perspectives: complex network characteristics, traffic volume, and vulnerability. Then, the relative entropy was introduced to improve the TOPSIS method, and the importance of en-route waypoints was comprehensively evaluated by combining this method with the grey correlation analysis method. The K-means clustering method was used to effectively divide the levels of en-route waypoints. Finally, key node identification was carried out based on the actual operation data of civil air traffic management. It finds that the results obtained by the constructed evaluation index system of key nodes in the en-route network are more comprehensive than the evaluation results of a single index. The improved TOPSIS-grey correlation analysis is more accurate than the traditional TOPSIS method. The proposed identification method finds that there are 29 key nodes in the typical busy en-route network in Eastern China, which play a key role in the network structure and traffic volume.
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Key words:
- complex networks /
- TOPSIS /
- relative entropy /
- grey relational degree /
- K-means clustering
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图 2 航路点重要程度综合评估流程
Figure 2. Comprehensive evaluation process of importance of en-route waypoints
图 3 华东地区各航路点小时航班量变化情况
Figure 3. Changes in hourly flight volume at each en-route waypoint in Eastern China
图 5 华东地区航路点的综合接近度
Figure 5. Comprehensive proximity of en-route waypoints in Eastern China
表 1 华东地区航路点评价指标规范化数值
Table 1. Normalized values of evaluation indexes for en-route waypoints in Eastern China
航路点序号 Z1,1 Z1,2 Z1,3 Z1,4 Z2,1 Z2,2 Z2,3 Z3,1 Z3,2 Z3,3 1 0.222 0.095 0.610 0.095 0.533 0.354 0.447 0.000 0.097 0.897 2 0.111 0.018 0.794 0.077 0.000 0.000 0.000 0.000 0.068 0.831 3 0.444 0.130 0.871 0.130 0.733 0.459 0.505 0.000 0.134 0.789 4 0.111 0.391 0.691 0.012 0.667 0.078 0.107 0.000 0.130 0.838 5 0.111 0.114 0.765 0.032 0.333 0.131 0.184 0.000 0.089 0.835 6 0.111 0.055 0.251 0.005 0.533 0.158 0.175 0.500 0.242 0.869 7 0.111 0.027 0.847 0.086 0.733 0.231 0.243 0.000 0.085 0.850 8 0.556 0.604 0.924 0.153 0.600 0.208 0.252 0.000 0.407 0.892 9 0.111 0.103 0.613 0.007 0.200 0.024 0.058 0.000 0.129 0.811 10 0.111 0.031 0.285 0.000 0.267 0.010 0.029 0.000 0.061 0.840 
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表 2 航路网络排名前二十的评价结果
Table 2. Evaluation results of top 20 points in en-route network
排名 $ {G_i} $ TOPSIS $ G_{{\mathrm{C}}i} $ 值 航路点 值 航路点 值 航路点 1 0.703 TOL 0.867 TOL 0.697 TOL 2 0.685 HFE 0.759 HFE 0.687 DST 3 0.639 JTN 0.729 ELNEX 0.641 DO 4 0.620 ELNEX 0.726 P215 0.617 SHZ 5 0.603 P215 0.724 JTN 0.612 OF 6 0.602 SHR 0.699 DST 0.603 HFE 7 0.601 DST 0.692 SHR 0.593 JTN 8 0.588 DO 0.612 KAKIS 0.536 SUPAR 9 0.563 BK 0.608 BK 0.519 BK 10 0.561 AND 0.605 AND 0.500 P215 11 0.559 SHZ 0.552 SHZ 0.495 ELNEX 12 0.551 KAKIS 0.541 NINAS 0.488 BZ 13 0.533 NINAS 0.533 LASAN 0.472 LYG 14 0.531 LASAN 0.533 DO 0.449 SHR 15 0.511 UGAGO 0.526 UGAGO 0.433 PK 16 0.508 BZ 0.509 SASAN 0.431 YCH 17 0.504 P263 0.509 XUVGI 0.429 RUPUD 18 0.503 PINOT 0.499 OF 0.424 UGAGO 19 0.502 JDZ 0.498 MADUK 0.424 OSIKI 20 0.493 SASAN 0.497 PINOT 0.412 NOBEM
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