## 4 Vibration-Based Road Friction Monitoring
### High Frequency Vibrations  
Besides the methods that focus on the low-frequency range, there are a number of contributions that estimate the tyre-road friction coefficient based on high-frequency vibration information [46; 47; 49; 66; 131; 132]. The assumption behind these methods is that the macro and micro texture of the road surface is influencing heavily the maximum tyre-road friction coefficient. The assumption is supported by several recent contributions. For example, [PERSON] and [PERSON] [133; 134] correlated the texture of the road surface to the friction coefficient. The texture was measured using a CircularTextureMeter and the friction coefficient using a Dynamic Friction Tester. A great number and variety of test track surfaces and lab samples of concrete were used in the test programme. Tests were conducted at 5.55, 11 and 16.66 m/s (20, 40 and 60 km/h). Obviously, the pads used are not designed to dissipate water, and therefore resemble the performance of a tyre with minimum tread depth. The authors applied a signal processing method called HHT (Hilbert-Huang-Transform) to analyse each road surface texture in four Base Intrinsic Mode Functions (IMFs). The Base IMFs were representative of each road surface and described the road texture as a function of road length. [PERSON] and [PERSON] applied the Hilbert Transform to each Base IMF and then for each Base IMF the instantaneous frequencies and amplitudes were averaged. A linear relationship was derived from the characteristic values of the Base IMFs and the measured coefficient of friction. [PERSON] et al. came to the same conclusions from a qualitative point of view [135]. In their study, they characterised different diamond-ground road surfaces using laser scanners and experimentally measured the corresponding tyre-road friction coefficient by locked wheel braking. The locked wheel test was conducted to measure the wet pavement skid resistance in accordance with ASTM E-274 using a standard smooth tyre. As highlighted by [PERSON] et al. friction depended not only on texture depth and shape but also on texture spacing and periodicity. [PERSON] et al. [66] also predicted the tyre-road friction using road surface texture information. All road surfaces samples used in the field trials belonged to asphalt or concrete categories with a maximum aggregate size between 8 and 10 mm. The aggregate types varied between the road sections as well as the age of the surfaces. The texture of the road surfaces was analysed using a laser \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **Hypothesis** & **Method** & **Frequency Range** \\ \hline [PERSON] et al. [51] & Friction influences & Transfer function— & \\  & damping of tyre vibrations & Tyre rotational vibrations & 20–60 Hz \\ \hline [PERSON] et al. [4] & Longitudinal slip & Resonance frequency of the & \\  & stiffness is linearly & driveline of an in-wheel & 15–22 Hz \\  & dependent on friction & motor drive system & \\ \hline [PERSON] and [PERSON] [50] & normalised slip slope factor & Simulations using & 23–36 Hz \\  & LKX is dependent on & MF-Swift type model & \\  & friction coefficient & & \\ \hline  & tyre self-aligning torque (SAT) & Resonance frequency & \\  & stiffness varies linearly with the & of the electric power & 0.5–1.6 Hz \\  & road friction potential & steering system & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of low frequency vibration contributions on friction estimation. scanner and the road friction was measured using two methods; the British pendulum, ASTM E303-93, and skid trailer tests. The skid trailer tests were conducted at constant speed 18.05 m/s (65 km/h) and water was sprayed in front of the tyre. Two tyres were used in the field trials: ASTM F2493 standard reference test tyre (SRTT) of size P225/60R16 and ultra-high performance (UHP) summer tyre with the size P255/40R19.