FOURIER ANALYSIS OF THE TRAFFIC FLOW INTENSITY
M. G. Boyarshinov, A. S. Vavilin, A. G. Shumkov
Perm National Research Polytechnic University, Perm, Russia
e-mail: atm@pstu.ru
Abstract. The relevance of this work is determined by the need to find modern ways to process the information about traffic flows for regulating and controlling the movement of transport and pedestrians, to reduce congestion, road accidents, etc. The object of study is a part of road with heavy two-way traffic, equipped with a software and hardware complex that allows to measure the characteristics of the transport flow. The subject of the study is the daily intensity of the cars flow during the week, from Monday to Sunday.
The purpose of this study is to analyze the amplitudes, frequencies, and periods of harmonic functions obtained by decomposing the time series of road traffic intensities to identify the main patterns of traffic flow formation. As a theoretical and methodological approach, the decomposition of the function of the traffic flow intensity in the Fourier series with respect to harmonic functions is used. The approach developed by the authors using the fast Fourier transform procedure made it possible to determine the amplitude-frequency characteristics of the time series under consideration, which is a scientific novelty of the analysis. It is proposed to use the «period-amplitude» characteristics as physically more meaningful instead of the «frequency-amplitude» dependencies traditionally used for the analysis.
The processing of data obtained from software and hardware complexes allowed us to determine dependences of the car flow intensity on the road of the Perm city at different averaging intervals, to describe the features of the motor transport movement on the road under consideration. As a result of the study, the amplitude-frequency characteristics of time series are obtained. It is shown that the individual harmonics of the Fourier series expansion of the traffic flow intensity, which exhibits the properties of a random function, duplicate the periodicity of the global, local, and intermediate extremes of the original function and have similar periods.
The practical significance consists in the use of the decomposition of the function of the traffic flow intensity in the Fourier series of harmonic functions for predicting traffic flows, controlling the operation of traffic lights, monitoring the operation of equipment, as well as in the reconstruction, design and construction of roads and road objects. The study will continue in the direction of obtaining, processing and determining the «period-amplitude» characteristics for time series of traffic flow intensity for other road networks.
Key words: traffic flow intensity, harmonic set, Fourier series, amplitude-frequency characteristics.
Cite as: Boyarshinov, M. G., Vavilin, A. S., Shumkov, A. G. (2021) [Fourier analysis of the traffic flow intensity]. Intellekt. Innovatsii. Investitsii [Intellect. Innovations. Investments]. Vol. 4, pp. 46–59. DOI: 10.25198/2077-7175-2021-4-46.
