DOI: 10.2478/oszn-2026-0005 ISSN: 2353-8589
Assessment of Vehicle Operational Properties Using Stochastic Models of Driving Velocity Processes
Paulina Luiza Grzelak, Zdzisław Chłopek, Katarzyna Bebkiewicz, Dagna Zakrzewska, Jakub Lasocki Abstract
This article investigates the use of stochastic driving velocity processes
Driving velocity processes are time-dependent functions or stochastic processes that describe the instantaneous velocity of a vehicle as it evolves during real-world operation. They represent the dynamic behaviour of vehicle motion and capture the variability resulting from driver actions, traffic conditions, road infrastructure and environmental influences.
as a basis for evaluating vehicle operational properties and their potential environmental implications. Driving velocity processes were modelled as sets of empirical process representations-velocity courses-recorded under four characteristic traffic conditions: urban driving with congestion, urban driving without congestion, rural driving and fast-road driving (on highways and expressways). Zero-dimensional statistical characteristics were determined for each representation and sets with similar mean values, maximum values and coefficients of variation were selected as stochastic models of the underlying processes. The low non-repeatability of these characteristics confirms the statistical stability of the representations.
The analyses were conducted in the domain of time, process value and frequency, including probability density estimation and power spectral density
The power spectral density (PSD) is a function that describes the distribution of the power of a signal or stochastic process across individual frequencies. It is defined as the Fourier transform of the autocorrelation function and makes it possible to identify which frequency components dominate the signal and how intense its temporal variations are.
analysis. The results show that urban driving exhibits the strongest dynamic properties, while fast-road driving is characterised by the weakest dynamics. None of the analysed sets followed a normal distribution, as confirmed by the Kolmogorov-Smirnov, Lilliefors and Shapiro-Wilk tests.
Treating driving tests as stochastic velocity processes provides a more realistic representation of real-world driving variability. This approach enhances the understanding of vehicle operational behaviour and supports more accurate assessment of environmental impacts, particularly fuel consumption and pollutant emissions under dynamic driving conditions.