Data-Driven Analysis of the Chaotic Characteristics of Air Traffic Flow

Abstract

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 m, 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.

Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs

“…In the case of the networks constructed using the visibility methods, the degree distribution may also be interpreted as following an exponential law. We demonstrated (Section 5.1) that the λ-exponent criterion applied to HVG (Section 3.1) [16,[50][51][52][53][54][55][56] cannot reliably distinguish chaos from randomness since practically indistinguishable exponents are found for both chaotic and random processes. Therefore, the distinction cannot rely only on the λ-exponent criterion.…”

“…Specifically, in [52], the λ-exponent criterion is applied to the HVG [16] to characterize magnetic fluctuation time series obtained from PIC simulations. Also, the time series of streamflow [53], air traffic flow [54], cryptocurrencies price [55], and the air mean temperature [56] are characterized as chaotic or stochastic depending on the exponent λ.…”

“…However, the arguments presented in [50,51] referred only to the case of HVG and, specifically, the λ-criterion proposed by Lacasa and Toral [16]. The idea that chaos can be discriminated from randomness via complex networks was discussed without reservation [52][53][54][55][56]. We explored all other cases which claim the possibility of the distinction of chaos from randomness using the degree distribution of the associated VGs and PSRGs.…”