Node importance Evaluation in Air Traffic Control Equipment Based on Topological Potential

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2017 2nd International Conference on Computational Modeling, Simulation and Applied Mathematics (CMSAM 2017) ISBN: 978-1-60595-499-8

Node-importance Evaluation in Air Traffic Control Equipment

Based on Topological Potential

Wei-jun PAN, Xiao-lin LI

*

, You-jun YE, Bin RAN and Jie REN

Civil Aviation Flight University of China, Guanghan City, Sichuan, China

*Corresponding author

Keywords: Air traffic control equipment, Complex network, Topological potential.

Abstract. The navigation equipment in the air traffic control (ATC) navigation equipment network is important for the protection of air traffic services. Identifying the key nodes in the network can provide an effective theoretical basis for the operational continuity of the air traffic control system. This paper designs a complex network model of civil aviation air traffic control equipment with flight traffic flow on the route as the network side weights, analysis and evaluation the importance of ATC equipment by the node importance evaluation algorithm of the topology potential. In this paper, taking the Chengdu control area in the southwest as an example, evaluate the key nodes in the ATC navigation network, and sort the importance of navigation equipment. The results can be used as a relative performance index for the reliability and survivability of the navigation equipment network.

Introduction

Civil aviation air traffic control equipment is of great significance to the protection of air traffic services. Although the civil aviation navigation equipment are independence in the space, in the provision of navigation support services need cooperation, and air traffic control navigation equipment network there is a certain growth and connectivity preferences, which conforms to the complex network of non-scale network characteristics. With the increasing traffic volume of civil aviation airspace, the air navigation and navigation equipment network is constantly planning and the network degree is increasing. The key navigation equipment also plays an increasingly important role in the civil aviation navigation equipment network. In order to enhance the air traffic service capability of the aviation network and avoid the "Matthew effect", it is necessary to evaluate the vulnerability of the network nodes and the sustainability of the business in order to identify the key nodes in the network and then to add and plan equipment, which is to enhance the sustainability of civil aviation security system business is of great significance.

It has been a long time to research the theory of complex network at home and abroad. The domestic complex network in the civil aviation operation support system also made some research. Kui Huang combined with complex network theory, modeling from two aspects of navigation equipment and radar monitoring equipment, research expansion planning of security system respectively[1]; Xiaojia Feng used the complex network theory to study the network of aviation security system for the prevention of major disasters from the perspective of network structure and function, and established the service continuity assessment model of civil aviation security system [2]. The non-homogeneous topological characteristic structure of complex networks means that the importance of each node in the network is different, so it is very important to evaluate the importance of nodes in complex networks. Corley and Shade first studied important nodes in the network [3]; Rui Su, Yong Wang, Zhihui Yang through the data mining method using PPHM algorithm to simulate the real Internet to identify important nodes [4].

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navigation station of the navigation equipment network and determine the key navigation equipment, provides an effective theoretical basis for the research on the service continuity of the air traffic control system.

Node Importance Evaluation Algorithm for Topology Potential

The potential field is a kind of physical field, and its main characteristic is that the scalar potential function and the vector intensity function of the description field can be connected with each other through the differential operator. The potential value of any point in the potential field is inversely proportional to the distance from that point to the field source. Inspired by this, a topological network is regarded as a virtual physics field that includes several nodes and their interactions with each other. The topology network has the characteristics of growth and connection preference, which indicates that the virtual influence field of each node will be weakened with the increase of network distance. In this case, the Gaussian potential function is used to characterize the interaction between nodes. The topological network is the topological potential field.

Given a network G(V,E)of n nodes, m edge, m weight set, build the following weighted network model:

) , (V E

G _. (1)

} ,..., ,

{v₁ v₂ v_n

V  is a collection of nodes, E{e₁,e₂,...,e_m} is a set of edges. The concept of the topological potential of any node in the topological network is introduced here [5]:



     n j d j j i ij e m m v 1 ) ( 2

1 ) ]

[( ) ( 2  

. (2) Among them, dij means the distance between nodes; the influencing factor  represents the range of action of each node; mj1 and mj2 represent the inherent properties of each node with different physical meanings; dij represents the distance matrix of the topological network. Where dij use Floyd algorithm to determine. The greater the potential of the node topology is, the greater the importance of it in the whole topology network system.

) ) ( log( ) ( 1 Z v Z v H i n i i  



   . (3)



  n i i v Z 1 ) ( 

is the normalization factor. The size of the H represents the network uncertainty.

Example Analysis

Establish a Complex Network of Navigation Equipment in Southwest Region

Southwest navigation equipment network mainly consists of the navigation station and the air route which connecting these stations. Based on the complex network theory, the navigation equipment is abstracted as a complex network node, here does not take into account the flight direction of the flight in the air traffic control route, as long as the aircraft in turn accept any two navigation equipment provide services, then considers the sides of the two navigation stations to form sides

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[image:3.595.206.419.68.231.2]

Figure 2. Southwest Network Topology.

Node-importance of the Topology Potential Evaluation Algorithm Parameters

Node Inherent Attributes of Navigation Equipment Network. In this paper, we collected the flight planning data of Chengdu for one week in 2016 to analyze and research the important navigation stations of Chengdu control area. In the route network, the 24 nodes of the equipment refer to the number of routes connected between the equipment node and the neighboring equipment node. Table 1 summarizes the degree mj1 of the route network. According to the node strength formula, the average daily security flight volume mj2 of 24 navigation stations in Chengdu control area is counted. The data statistics are shown in Table 1:

Table 1. Statistical Data of Inherent Attribute Data of the Network Node in Chengdu Control Area.

Navigation Station DCH JZH AHY GYN MYG GAO JTG CZH

Degree mj1 2 5 3 4 5 6 6 6

Day Guarantee Sorties mj2 4 45 0 21 57 323 370 67 Navigation Station WFX CTU FJC BHS ZYG KDJ YBN LZH

Degree mj1 7 7 7 3 5 3 4 2

Day Guarantee Sorties mj2 447 18 362 0 252 12 262 31 Navigation Station XYO MYD CKG QJG FLG DAX WZH ENH

Degree mj1 3 3 2 4 2 3 2 3

Day Guarantee Sorties mj2 343 8 93 292 198 16 10 5

The greater the degree of navigation nodes, indicating that these naval nodes in the network position is relatively important. The more day guarantee sorties of navigation station, the heavier the mission of the navigation station.

Influencing Factors of Network Nodes of Navigation Equipment

[image:3.595.53.546.391.504.2]

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[image:4.595.198.397.72.197.2]

Figure 3. Chengdu Control Area Network Node Impact Factor.

The maximum value of the potential close to Hmaxlog(n) _{, where n = 24, that is} 18

. 3 ) 24 log(

max  

H _{. Here the impact factor} _{increases, potential entropy from the approaching}

max

H _{first decrease and then increase to infinity close to} Hmax_{. When}_{=0.32, the corresponding}

potential entropy is the smallest, H = 2.8921.

[image:4.595.56.549.332.546.2]

Analysis of Network Node Topological Potential Result of Navigation Equipment

Table 2. Chengdu Control Area Navigation Equipment Network Node Topology Statistics.

Navigation Station DCH JZH AHY GYN MYG GAO JTG CZH

Topological Potential 6.001 50.031 3.008 25.026 62.071 329.033 376.054 73.041

Navigation Station WFX CTU FJC BHS ZYG KDJ YBN LZH

Navigation Station XYO MYD CKG QJG FLG DAX WZH ENH

Figure 4. Distribution Map of the Topology of the Navigation Area in Chengdu.

From the table analysis, we get the topological potential of WFX (Wufengxi), FJC (Fujiatang), JTG (Jintang) and several navigation stations. It is proved that these navigation stations are more important in Chengdu control area, and it is easier to become a weak link in the network. The importance of the navigation station is sorted by the topological potential data of the navigation station of the Chengdu navigation area navigation equipment network in Table 2. As shown in Figure 4, the linear trend in the graph also presents a power-law distribution, which is consistent with complex network characteristics.

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network, so as to give the necessary support and protection to the important nodes and improve the overall business continuity of the equipment network.

Acknowledgement

This research was sponsored by National Nature Science Foundation of China (Project No. 71573184).

References

[1] Huang K. Research on Air Traffic Control Equipment Support Planning Based on Complex Network Theory.[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2013.

[2] Feng X J. Flight planning for aviation security system for major disaster prevention [D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2016.

[3] Corley H W, Sha D Y. Most vital links and nodes in weighted networks.[M]. Elsevier Science Publishers B. V. 1982.

[4] Su R, Wang Y, Yang Z H. Based on the topology potential of the network topology modeling method [J]. Computer Engineering, 2010,36 (5): 109-113.