Research On Complexity Of The Sectors Based On Lyapunov Exponents

With the rapid development of the air transport industry, air traffic flow is increasing,stretched airspace resources cannot meet the increasing air traffic demand, and the flights are facing serious risk of conflicts. Air traffic complexity evaluation as an important tool of air traffic management thus become a new research hot spot.In this thesis we research the complexity of the sector, summarizing the research results domestic and international, based on a detailed analysis of the advantages and disadvantages of complexity studies clearly establish the need for objective indicators of the complexity of the sector, to explore the relationship between the Lyapunov exponent and the complexity of transportation systems sector.This paper builts a dynamic model of the transportation sector using time series analysis to conduct nonlinear analysis on the system, detailed analysis of the relationship between trajectory element, raised the concept of timing distance between aircraft pair, using element of the aircraft trajectory to calculate the timing distance between the aircraft pair,and use the timing distance parameter to solve Lyapunov exponent.Using the rush hour of one sector in Xiamen, we calculate the timing distance between aircraft pairs in this sector and using this as a parameter to solve the Lyapunov exponent,analyzing the relationship between the Lyapunov exponent, the timing distance and the sector air traffic situation. The results indicates valid correspondences of these factors thus verified the feasibility of using the Lyapunov exponent as an indicator for the complexity evaluation of the air traffic sector.In this article we analyzed the relationship between the complexity of the sector air traffic and the sensitivity of the controller, suggests during the implement of control, we should adjust the distance between aircraft pairs, heading differences, vector velocity differences etc. to adjust the complexity of the sector to a level that's acceptable to the controller to ensure the sector's safety and efficiency.