Nonlinear Fractal Characteristics of Air Traffic Flow

To provide scientific evidence for traffic flow modeling and prediction, the nonlinear characteristics of air traffic flow were studied based on fractal. First, 4 time series were constructed, and their nonlinearities were tested by the surrogate data method, and the 5-minute-scale time series was determined as the subsequent research object. Then, the wavelet decomposition method was used to study the self-similarity of time series. The global and local Hurst exponents were calculated by R/S method to study the long-range correlation characteristics. Next, scale-free ranges of time series were calculated using second-order difference of correlation integral. Then, the multi-fractal characteristics of time series were studied by multi-fractal spectrum method. Finally, the correlation dimensions of time series were calculated by Grassbeger-Procaccia method. The results show that the probability of the nonlinearity of 5-min-scale time series is 99.2%, and the nonlinearities of the other 3 time series are not clear. It is qualitatively observed that the time series has strong self-similarity. The global Hurst exponent is 0.756 5, and the local Hurst exponents are all more than 0.5, which indicate that the time series has a long-range correlation. The second-order difference of the correlation integral can effectively identify scale-free ranges, which shows that the time series has scale-free property and the scale-free ranges are different corresponding to different embedding dimensions. The bell-shaped multi-fractal spectrum shows the time series has multi-fractal characteristics. The correlation dimension is 6.89, indicating that at least 7 variables are needed to clearly describe the corresponding air traffic flow.