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Construction of Driving Condition Based on Discrete Fourier Transform and Improved K-Means Clustering Algorithm

Shuping Xu
Shuping Xu
 and 
Yueqiu Huang
Yueqiu Huang
   | May 31, 2023
International Journal of Advanced Network, Monitoring and Controls's Cover Image
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Published Online: May 31, 2023
Page range: 66 - 74
DOI: https://doi.org/10.2478/ijanmc-2023-0047
Keywords
© 2023 Shuping Xu et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Contrast analysis of speed data filtering
Contrast analysis of speed data filtering

Figure 2.

Schematic diagram of kinematics fragments
Schematic diagram of kinematics fragments

Figure 3.

Time-speed curve of representative working conditions
Time-speed curve of representative working conditions

Figure 4.

Time-acceleration curve of representative working conditions
Time-acceleration curve of representative working conditions

Average feature value of each category after clustering

Clustering categories va Tc vx aa T Ti
Class 1 6.23 0.12 11.06 0.16 26.15 0.59
Class 2 16.25 0.25 18.26 0.59 35.56 0.23
Class 3 23.03 0.49 30.51 0.45 48.12 0.18

Characteristic parameter relative error

Characteristic parameters Overall sample data k-means k-means++ Grid-K-means
Fitted value Relative error/% Fitted value Relative error/% Fitted value Relative error/%
va 18.91 18.11 4.23 18.34 3.01 18.60 1.64
aa 1.85 1.95 5.41 1.88 1.62 1.86 0.54
ad -2.36 -2.45 3.81 -2.43 2.97 -2.39 1.27
Ti 0.52 0.58 11.54 0.55 5.77 0.53 1.92
Ta 0.49 0.41 16.32 0.44 10.20 0.47 4.08
Td 0.26 0.31 19.23 0.29 11.54 0.28 7.69
Es 10.09 5.85 2.86

Principal component load matrix

Characteristic parameters M1 M2 M3
Segment duration T 0.132 0.231 0.745
distance S 0.293 0.134 0.045
Average speed Va 0.719 0.463 -0.025
Average driving speed Vx 0.478 0.615 0.112
Idle time ratio Ti 0.125 -0.351 0.843
Acceleration time ratio Ta 0.694 -0.156 0.060
Deceleration time ratio Td 0.923 0.341 -0.123
Cruising time ratio Tc 0.641 0.435 -0.045
Mean acceleration aa 0.014 0.623 0.033
Mean deceleration ad 0.366 -0.433 -0.052
Standard deviation of acceleration astd 0.445 0.267 -0.067
Standard deviation of speed Vstd 0.387 0.215 0.034

The main eigenvalues represented by the first three principal components

Category Eigenvalue
Primary component principal M1 average speed, acceleration time ratio, deceleration time ratio, cruising time ratio
Secondary component principal M2 average speed, acceleration time ratio, deceleration time ratio, cruising time ratio
Third component principal M3 segment duration, idle time ratio

Kinematics feature parameter values

Fragment number T S Va Vx Ti Ta Td Tc aa ad astd Vstd
1 119 203.29 6.15 7.60 0.06 0.17 0.08 0.03 0.42 -0.66 0.48 5.05
2 319 2320.7 26.19 33.63 0.14 0.26 0.19 0.11 0.30 -0.34 0.37 17.5
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
78 243 346 7.03 12.23 0.04 0.21 0.08 0.04 0.38 -0.61 0.39 5.01
79 167 459.12 5.97 8.04 0.06 0.19 0.05 0.05 0.44 -0.59 0.28 4.91
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
1584 169 829.04 17.66 23.65 0.13 0.19 0.09 0.07 0.36 -0.50 0.48 14.8
1585 486 6799.9 50.37 52.65 0.02 0.18 0.13 0.30 0.19 -0.20 0.29 16.5

Comparison of accuracy and performance of different algorithms

Data set k-means k-means++ Grid-K-means
Accuracy Elapsed time Accuracy Elapsed time Accuracy Elapsed time
20000 92.76% 25.82s 93.16% 34.86s 95.78% 25.83s
80000 88.32% 43.83s 89.32% 49.16s 92.36% 40.69s
100000 87.24% 58.12s 87.65% 67.94s 90.12% 50.38s

Sample K-S Test

Method Acceleration distribution (m/s2)
(-∞,-0.64) [-0.64,0.64] (0.64,+∞)
Grid-K-means K-S value 0.68 0.57 0.53
Similarity level 0.89 0.96 0.99
k-means++ K-S value 0.71 0.26 0.45
Similarity level 0.79 0.44 0.82

Principal component contribution rate and cumulative contribution rate

Serial number eigenvalue contribution/% Cumulative contribution/%
1 5.5605 43.23 43.23
2 3.2315 26.83 70.06
3 1.9901 16.14 86.20
4 1.0434 6.14 92.34
5 0.53476 3.11 95.45
6 0.45796 2.01 97.46
7 0.38341 1.22 98.68
8 0.21525 0.78 99.46
9 0.17450 0.23 99.69
10 0.10126 0.19 99.88
11 0.09324 0.08 99.96
12 0.02532 0.04 100
eISSN:
2470-8038
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Computer Sciences, other
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