Fractal characteristics analysis on driving behavior time series: Example with speed data as vehicle driving towards an intersection

In this paper, we use the fractal theory to analyze the characteristics of driving behavior time series. Three types of driving behavior such as driving a vehicle towards an intersection for turn-left, driving for turn-right, and driving for go-straight are designed as a set of real vehicle driving experiments to be carried out. The speed data collected by a real vehicle driving experimental platform are arranged into speed time series. Those time series corresponding to the three types of driving behavior had the same number of data and the equal time intervals. To analyze whether the speed time series varying randomly or having a bias, the method of rescaled range analysis is introduced and the degrees of correlation quantized as H-values are resolved and mapped to the fractal characteristics. Then, to search the further characteristics as if the speed time series would be multi-fractal, analysis with a partition function for transformation where real value q as the exponent value, and the τ(q) regarded as a quality index function are applied. As all the curves trends of the three types of driving behavior met the requirement of a multi-fractal object, the multi-fractal spectrums of each speed time series of the corresponding driving behavior are drawn out. The relevant indexes of those spectrums could be regarded as characteristic values for describing or predicting a specific type of driving behavior in the given traffic environment.