Understanding the chaos of air traffic flow is significant to the achievement of advanced air traffic management, and trajectory data are the basic material for studying the chaotic characteristics. However, at present, there are two main obstacles to this task, namely, large amounts of noise in the measured data and the tedium of existing data processing methods. This paper improves the incorrect trajectory processing method based on ADS-B trajectory data and proposes a method by which to quickly extract the traffic flow through a certain waypoint. Currently, the commonly used theoretical analysis tools for nonlinear complex systems include the classical nonlinear dynamics analysis method and the newly developed complex network-based analysis method. The latter is currently in an exploratory stage because it has just been introduced into the study of air traffic flow. From these two perspectives, the chaotic characteristics of air traffic flow are studied in the present work. From the perspective of nonlinear dynamics, the improved C-C method is used to calculate the reliability parameters, namely, the time delay τ and embedding dimension , of phase-space reconstruction, and the maximum Lyapunov index is calculated by using the small data volume method to prove the existence of chaos in the system. From the perspective of complex networks, the construction of a visibility graph and horizontal visibility graph is used to prove the existence of chaos in the system, and the goodness-of-fit parameters of the degree distributions of two fitting methods under different time scales are evaluated, which provides support for the air traffic flow theory.

中文翻译：

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空中交通流混沌特性的数据驱动分析

了解空中交通流的混乱对实现先进的空中交通管理具有重要意义，而轨迹数据是研究混沌特征的基本材料。但是，目前，该任务存在两个主要障碍，即被测数据中的大量噪声和现有数据处理方法的繁琐。本文改进了基于ADS-B轨迹数据的不正确轨迹处理方法，并提出了一种快速提取通过某个航路点的交通流的方法。当前，用于非线性复杂系统的常用理论分析工具包括经典的非线性动力学分析方法和新开发的基于复杂网络的分析方法。后者目前处于探索阶段，因为它刚刚被引入到空中交通流量的研究中。从这两个角度，本文研究了空中交通流的混沌特性。从非线性动力学的角度出发，采用改进的CC方法来计算可靠性参数，即时延。利用小数据量方法计算出相空间重构的τ和嵌入维数，以及最大李雅普诺夫指数，以证明系统中存在混沌。从复杂网络的角度出发，通过建立能见度图和水平能见度图来证明系统中是否存在混沌，并且两种拟合方法在不同时标下的度分布的拟合优度参数为评估，这为空中交通流量理论提供了支持。