Time-series Characteristics of Unsafe Events in Air Traffic Based on Visibility Graph

Time series characteristics of traffic accidents is crucial for understanding air traffic safety. To analyze the characteristics of air-traffic-accident time series, a visual graph (VG) method is proposed. The unsafe-event time series (UETS) are mapped into complex network via the VG, and then the static characteristics of the UETS are described by the topological indicators such as degree distribution and clustering coefficient. Considering the higher-order influences and interaction modes between events, a visual circle ratio index is developed to evaluate the impacts of each event on the entire safety level. A third-order temporal structure representing temporal evolution is proposed based on the sequential model from the VG, describing the dynamic micro- characteristics of the UETS. To demonstrate the proposed method, an empirical analysis is conducted based on 578 unsafe air traffic events that occurred in the United States from 2007 to 2021, and the results indicate that: ① the VG of the UETS exhibit a long-tail degree distribution at both macroscopic and microscopic scales, with clustering coefficients all greater than 0.7; ② the VG network of the UETS possesses small-world characteristics, and the macroscopic sequence-degree distribution follows the power-law distribution with a coefficient of 1.852, indicating scale-free properties of the network; ③ the visibility graphs of different regions also exhibit the characteristics of small-world networks, with significant differences in network size and density among regions, revealing the spatial heterogeneity in the frequency of unsafe events. The visual circle index of the network reaches 33.2%, the circle ratio structural indicator has a significant impact on network robustness, demonstrating that the circle ratio index can be used to identify the effects of different events on the overall safety level. ④ the third-order temporal structure shows significant transition characteristics when the step size is 1 and 2. In summary, this paper reveals that the occurrence of unsafe air traffic events has complex pattern that differs from randomness and periodicity patterns, The safety levels among different regions exhibit spatial heterogeneity and temporal evolution characteristics. Considering the impact of higher-order network structures, managing a minority of nodes with high circle ratios can enhance the overall safety level from a macro perspective. Analyzing the transfer patterns and trend preferences of temporal structures can reveal the intrinsic laws of how air traffic unsafe events evolve over time from a micro perspective. This is conducive to predicting potential risk points, thereby providing a scientific basis for formulating effective preventive measures and safety management decisions.