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Assessment of Vehicle Operational Properties Using Stochastic Models of Driving Velocity Processes Cover

Assessment of Vehicle Operational Properties Using Stochastic Models of Driving Velocity Processes

Open Access
|Aug 2026

Figures & Tables

Figure 1.

Representations of the velocity process (v) in the CT test in the time domain (t)

Figure 2.

Representations of the velocity process (v) in the UT test in the time domain (t)

Figure 3.

Representations of the velocity process (v) in the RT test in the time domain (t)

Figure 4.

Representations of the velocity process (v) in the HT test in the time domain (t)

Table 1.

Statistical zero-dimensional characteristics of the CT test process

CT
1234
AV8.68.58.58.4
M7.68.07.37.4
D6.334.865.374.75
K−0.213−0.145−0.025−0.169
S0.7840.4190.7480.687
R26.423.424.422.7
Min0.00.00.00.0
Max26.423.424.422.7
W0.7370.5710.6290.563
Q13.95.14.34.6
Q310.911.611.911.6
RQ2.82.32.82.5
DQ1.41.11.41.2
WQ0.18130.14370.19240.1694
Table 2.

Statistical zero-dimensional characteristics of the UT test process

UT
1234
AV36.036.036.036.0
M40.537.339.739.9
D18.7326.2221.4223.17
K−1.232−1.525−1.332−1.358
S−0.285−0.009−0.181−0.180
R65.773.370.874.2
Min0.00.00.00.0
Max65.773.370.874.2
W0.5200.7280.5950.643
Q117.410.915.611.3
Q351.462.954.056.3
RQ3.05.83.55.0
DQ1.52.91.72.5
WQ0.03660.07710.04370.0624
Table 3.

Statistical zero-dimensional characteristics of the RT test process

RT
1234
AV70.770.669.670.7
M76.472.376.177.3
D28.0924.4321.4621.40
K0.6621.3461.9482.000
S−1.170−1.181−1.440−1.445
R104.1106.098.297.0
Min0.00.00.00.0
Max104.1106.098.297.0
W0.3970.3460.3080.303
Q159.161.461.360.8
Q392.589.884.886.0
RQ1.61.51.41.4
DQ0.80.70.70.7
WQ0.01020.01010.00910.0091
Table 4.

Statistical zero-dimensional characteristics of the HT test process

HT
1234
AV122.5121.4121.4117.9
M129.9124.7124.7122.2
D22.6420.8320.8319.00
K8.78412.97712.97710.287
S−2.745−3.182−3.182−2.393
R141.8152.0152.0143.8
Min0.00.00.00.0
Max141.8152.0152.0143.8
W0.1850.1720.1720.161
Q1120.4119.7119.7108.9
Q3135.3131.5131.5131.3
RQ1.11.11.11.2
DQ0.60.50.50.6
WQ0.00430.00440.00440.0049

[i] Note: AV: average value; M: median (second quartile Q2); D: standard deviation; DQ: quartile deviation; K: kurtosis; S: skewness; Min: minimum value; Max: maximum value; Q1: first quartile; Q3: third quartile; R: range; RQ: interquartile range; W: coefficient of variation; WQ: quartile coefficient of variation.

Figure 5.

Average value (AV) of the CT, UT, RT and HT velocity process representation

Figure 6.

Median (M) of the CT, UT, RT and HT velocity process representation

Figure 7.

Maximum value (Max) of the CT, UT, RT and HT velocity process representation

Figure 8.

Standard deviation (D) of the CT, UT, RT and HT velocity process representations

Figure 9.

Quartile deviation (DQ) of the CT, UT, RT and HT velocity process representations

Figure 10.

Coefficient of variation (W) of the CT, UT, RT and HT velocity process representations

Figure 11.

Quartile coefficient of variation (WQ) of the CT, UT, RT and HT velocity process representations

Figure 12.

Kurtosis (K) of the CT, UT, RT and HT velocity process representations

Figure 13.

Skewness (S) of the CT, UT, RT and HT velocity process representation

Figure 14.

The uniqueness (U) of the zero-dimensional characteristics of the CT, UT, RT and HT velocity process representations

Figure 15.

The uniqueness (U) of the average value, maximum value and coefficient of variation of the CT, UT, RT and HT velocity process representations

Figure 16.

Probability density (g) of the CT process representations depending on the standardized velocity (vs)

Figure 17.

Probability density (g) of the UT process representations depending on the standardized velocity (vs)

Figure 18.

Probability density (g) of the RT process representations depending on the standardized velocity (vs)

Figure 19.

Probability density (g) of the HT process representations depending on the standardized velocity (vs)

Figure 20.

Power spectral density of the CT process representations and the average value (AV) for all representations in the frequency domain (f)

Figure 21.

Power spectral density of the UT process representations and the average value (AV) for all representations in the frequency domain (f)

Figure 22.

Power spectral density of the RT process representations and the average value (AV) for all representations in the frequency domain (f)

Figure 23.

Power spectral density of the HT process representations and the average value (AV) for all representations in the frequency domain (f)

Figure 24.

The joint power spectral density of the CT, UT, RT and HT process representations in the frequency domain (f)

DOI: https://doi.org/10.2478/oszn-2026-0005 | Journal eISSN: 2353-8589 | Journal ISSN: 1230-7831
Language: English
Page range: 24 - 35
Published on: Aug 12, 2026
Published by: National Research Institute, Institute of Environmental Protection
In partnership with: Paradigm Publishing Services
Related subjects:

© 2026 Paulina Luiza Grzelak, Zdzisław Chłopek, Katarzyna Bebkiewicz, Dagna Zakrzewska, Jakub Lasocki, published by National Research Institute, Institute of Environmental Protection
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.