Identification of Road Profile Parameters from Vehicle Suspension Dynamics for Control of Damping
Abstract
:1. Introduction
2. Materials and Methods
3. Results and Discussion
- (1)
- Using Equation (4) without smoothing; w1 in frequency range from 0.0557 to 0.21 cycles/m; w2 in frequency range from 0.21 cycles/m up to 1.22 cycles/m or max value; w3 in frequency range from 1.22 cycles/m up to max value.
- (2)
- Using Equation (4) but after smoothing.
- (3)
- After smoothing along a straight line using Equation (3), starting from octave with lower cut-off frequency 0.0557 cycles/m and centre frequency 0.0625 cycles/m up to octave with max value.
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Speed, km/h (N; x, m) | Window | w1, w2, w3 (Case 1) | w1, w2, w3 (Case 2) | w (Case 3) | |||
---|---|---|---|---|---|---|---|
Buffer | Buffer | Buffer | |||||
1000 m | 100 m | 1000 m | 100 m | 1000 m | 100 m | ||
20 (18000; 1000) (1800; 100) | Hamming | 2.5, 2.1, 2.4 | 2.4, 2.0, 2.4 | 2.3, 2.0, 2.4 | 2.1, 1.9, 2.3 | 2.1 | 2.1 |
Hanning | 2.5, 2.1, 2.4 | 2.5, 2.0, 2.4 | 2.3, 2.0, 2.4 | 2.1, 1.9, 2.3 | 2.1 | 2.1 | |
Bartlett | 2.5, 2.1, 2.4 | 2.4, 2.0, 2.5 | 2.3, 2.0, 2.4 | 2.1, 1.9, 2.4 | 2.1 | 2.1 | |
Rectangular | 2.1, 2.0, 2.4 | 2.2, 2.0, 2.3 | 2.1, 2.0, 2.4 | 2.0, 1.9, 2.2 | 2.1 | 2.0 | |
50 (7200; 1000) (720; 100) | Hamming | 2.5, 2.1, 1.5 | 2.4, 1.9, 1.6 | 2.3, 2.0, 1.7 | 2.1, 1.9, 1.7 | 1.9 | 1.9 |
Hanning | 2.6, 2.1, 1.6 | 2.4, 1.9, 1.6 | 2.3, 2.0, 1.7 | 2.1, 1.9, 1.7 | 1.9 | 1.9 | |
Bartlett | 2.5, 2.1, 1.5 | 2.4, 1.9, 1.6 | 2.3, 2.0, 1.7 | 2.1, 1.9, 1.7 | 1.9 | 1.9 | |
Rectangular | 2.1, 2.0, 1.5 | 2.2, 2.0, 1.6 | 2.1, 2.0, 1.7 | 2.0, 1.9, 1.6 | 1.9 | 1.9 | |
70 (5142; 999.8) (514; 99.94) | Hamming | 2.5, 2.0, 1.2 | 2.4, 1.9, 1.4 | 2.3, 1.9, 1.1 | 2.1, 1.8, 1.3 | 1.9 | 1.9 |
Hanning | 2.5, 2.0, 1.2 | 2.5, 1.9, 1.4 | 2.3, 1.9, 1.1 | 2.1, 1.8, 1.3 | 1.9 | 1.9 | |
Bartlett | 2.4, 2.0, 1.2 | 2.4, 1.9, 1.4 | 2.3, 1.9, 1.1 | 2.2, 1.9, 1.3 | 1.9 | 1.9 | |
Rectangular | 2.1, 2.1, 1.2 | 2.3, 2.0, 1.3 | 2.1, 1.9, 1.2 | 2.0, 1.8, 1.2 | 1.9 | 1.8 | |
90 (4000; 1000) (400; 100) | Hamming | 2.6, 1.9, 0.3 | 2.4, 1.9, 0.5 | 2.3, 1.9, 0.4 | 2.1, 1.8, 0.8 | 1.8 | 1.8 |
Hanning | 2.6, 2.0, 0.4 | 2.5, 1.9, 0.6 | 2.3, 1.9, 0.3 | 2.2, 1.8, 0.8 | 1.8 | 1.8 | |
Bartlett | 2.6, 1.9, 0.2 | 2.4, 1.9, 0.5 | 2.3, 1.8, 0.4 | 2.2, 1.8, 0.8 | 1.8 | 1.8 | |
Rectangular | 2.2, 1.9, 0.3 | 2.3, 1.9, 0.8 | 2.1, 1.9, 0.7 | 2.0, 1.8, 0.8 | 1.8 | 1.8 | |
130 (2768; 999.6) (276; 99.67) | Hamming | 2.5, 1.7, −3.0 | 2.4, 1.7, −0.1 | 2.3, 1.7, -- | 2.1, 1.6, -- | 1.8 | 1.8 |
Hanning | 2.5, 1.7, −3.2 | 2.4, 1.7, 0.0 | 2.3, 1.7, -- | 2.2, 1.6, -- | 1.8 | 1.8 | |
Bartlett | 2.5, 1.7, −3.4 | 2.4, 1.7, −0.4 | 2.3, 1.7, -- | 2.2, 1.6, -- | 1.8 | 1.8 | |
Rectangular | 2.1, 1.8, 0.2 | 2.2, 1.8, −1.3 | 2.1, 1.7, -- | 1.9, 1.6, -- | 1.8 | 1.8 |
Profile and Waviness | Speed, km/h | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
20 | 50 | 70 | 90 | 130 | ||||||||||||
Min Max NRMSE | Min Max NRMSE | Min Max NRMSE | Min Max NRMSE | Min Max NRMSE | ||||||||||||
pr111 | w1 | 2.3 | 5.7 | 197 | 2.6 | 6.5 | 214 | 2.0 | 5.5 | 212 | 2.3 | 6.0 | 251 | 1.4 | 5.1 | 216 |
w2 | 0.7 | 1.7 | 50 | 0.8 | 2.2 | 64 | 0.4 | 1.5 | 46 | 0.5 | 1.4 | 49 | −0.3 | 0.8 | 70 | |
pr112 | w1 | −0.3 | 4.6 | 129 | −0.4 | 4.1 | 128 | 0.2 | 3.7 | 93 | 1.1 | 3.1 | 104 | −0.7 | 3.1 | 74 |
w2 | 0.7 | 1.5 | 35 | 0.6 | 1.7 | 32 | 0.5 | 1.4 | 32 | 0.6 | 1.4 | 26 | 0.3 | 1.6 | 36 | |
pr122 | w1 | −0.2 | 4.3 | 118 | 0.4 | 3.7 | 112 | 0.0 | 3.3 | 91 | 1.1 | 3.1 | 101 | −0.8 | 3.1 | 75 |
w2 | 1.7 | 2.5 | 14 | 1.6 | 2.7 | 17 | 1.6 | 2.4 | 15 | 1.4 | 2.4 | 13 | 0.9 | 2.4 | 17 | |
pr132 | w1 | −0.1 | 4.2 | 114 | 0.4 | 3.7 | 109 | 0.0 | 3.2 | 92 | 1.1 | 3.1 | 100 | −0.3 | 3.1 | 72 |
w2 | 2.6 | 3.5 | 9 | 2.3 | 3.6 | 12 | 2.2 | 3.2 | 9 | 1.8 | 2.9 | 11 | 1.0 | 2.4 | 18 | |
pr212 | w1 | 0.7 | 4.6 | 57 | 0.2 | 4.3 | 62 | 0.7 | 4.2 | 56 | 1.2 | 3.6 | 47 | 0.3 | 3.8 | 40 |
w2 | 0.7 | 1.4 | 36 | 0.7 | 1.6 | 34 | 0.5 | 1.4 | 32 | 0.6 | 1.4 | 27 | 0.4 | 1.5 | 35 | |
pr222 | w1 | 0.4 | 4.6 | 53 | 0.3 | 4.2 | 56 | 0.6 | 3.8 | 56 | 1.1 | 3.6 | 46 | 0.1 | 3.9 | 39 |
w2 | 1.7 | 2.4 | 15 | 1.6 | 2.7 | 18 | 1.4 | 2.4 | 16 | 1.4 | 2.4 | 13 | 1.0 | 2.3 | 16 | |
pr232 | w1 | 0.7 | 4.4 | 50 | 0.3 | 4.1 | 57 | 0.6 | 3.6 | 56 | 1.1 | 3.6 | 45 | 0.1 | 3.9 | 38 |
w2 | 2.6 | 3.4 | 10 | 2.2 | 3.6 | 13 | 2.2 | 3.2 | 9 | 1.8 | 2.9 | 12 | 1.1 | 2.4 | 18 | |
pr312 | w1 | 1.8 | 5.5 | 30 | 1.7 | 5.2 | 36 | 1.6 | 4.6 | 30 | 1.5 | 4.3 | 32 | 1.4 | 4.7 | 28 |
w2 | 0.8 | 1.4 | 29 | 0.6 | 1.6 | 27 | 0.6 | 1.4 | 25 | 0.7 | 1.4 | 21 | 0.5 | 1.5 | 27 | |
pr322 | w1 | 1.8 | 5.1 | 29 | 1.4 | 4.9 | 35 | 1.5 | 4.5 | 30 | 1.3 | 4.2 | 33 | 1.4 | 4.8 | 28 |
w2 | 1.8 | 2.4 | 13 | 1.6 | 2.6 | 15 | 1.5 | 2.4 | 12 | 1.6 | 2.4 | 12 | 1.2 | 2.2 | 16 | |
pr332 | w1 | 1.7 | 4.7 | 27 | 1.4 | 5.0 | 36 | 1.5 | 4.6 | 31 | 1.2 | 4.2 | 33 | 1.4 | 4.8 | 27 |
w2 | 2.6 | 3.4 | 9 | 2.3 | 3.6 | 14 | 2.2 | 3.3 | 12 | 1.9 | 2.8 | 12 | 1.3 | 2.3 | 20 | |
pr333 | w1 | 1.9 | 4.6 | 24 | 1.8 | 4.6 | 26 | 1.7 | 4.7 | 26 | 1.6 | 4.5 | 27 | 1.9 | 4.5 | 28 |
w2 | 2.7 | 3.5 | 8 | 2.6 | 3.5 | 13 | 2.6 | 3.5 | 13 | 2.6 | 3.5 | 13 | 2.4 | 3.4 | 15 |
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Čerškus, A.; Lenkutis, T.; Šešok, N.; Dzedzickis, A.; Viržonis, D.; Bučinskas, V. Identification of Road Profile Parameters from Vehicle Suspension Dynamics for Control of Damping. Symmetry 2021, 13, 1149. https://doi.org/10.3390/sym13071149
Čerškus A, Lenkutis T, Šešok N, Dzedzickis A, Viržonis D, Bučinskas V. Identification of Road Profile Parameters from Vehicle Suspension Dynamics for Control of Damping. Symmetry. 2021; 13(7):1149. https://doi.org/10.3390/sym13071149
Chicago/Turabian StyleČerškus, Aurimas, Tadas Lenkutis, Nikolaj Šešok, Andrius Dzedzickis, Darius Viržonis, and Vytautas Bučinskas. 2021. "Identification of Road Profile Parameters from Vehicle Suspension Dynamics for Control of Damping" Symmetry 13, no. 7: 1149. https://doi.org/10.3390/sym13071149