# Combined Identification of Vehicle Parameters and Road Surface Roughness Using Vehicle Responses
## 3 Numerical Validation of Methods
### Verification at Different Speeds  
The identification of different vehicle speeds is investigated, and previously considering \(v=10\) m/s. Therefore, in this section, the identification results under \(v=20\) m/s will be investigated. The parameter settings are kept in line with Section 3.1, and the road at class B roughness is investigated and discussed.  
Compared to the vehicle speed \(v=10\) m/s, at \(v=20\) m/s, level B roughness recognition results, as shown in Figure 13, the recognition error of roughness spatial contour increases to 6.74% because the unknown force recognition accuracy decreases at too fast vehicle speed, and the recognition results of roughness decrease by the unknown force recognition accuracy. At the vehicle speed 20 m/s, the identified road roughness PSD is shown in Figure 14 and the results are generally accurate. The convergence of suspension damping identification at vehicle speed 20 m/s is shown in Figure 15. In terms of recognizing vehicle  
Figure 11: Identified road roughness PSD (10% noise).  
Figure 12: Convergence of some parameters (10% noise). (**a**) Body mass M\({}_{v}\); (**b**) body moment of inertia I\({}_{v}\).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parametric**} & **Real** & \multicolumn{2}{c}{**Recognized**} & \multirow{2}{*}{**Relative**} & **Recognized** & \multirow{2}{*}{**Relative**} \\  & **Value** & **Value** & & **Error** & **Value** & **Error** \\ \hline \(m_{v}(\text{kg})\) & 1400 & 1429 & 2.14\% & 1425 & 1.78\% \\ \(l_{v}(\text{kg}\cdot\text{m}^{2})\) & 3526 & 3574 & 1.36\% & 3556 & 0.85\% \\ \(k_{t1}(\text{N/m})\) & 92,727 & 92,373 & 0.38\% & 97,750 & 5.41\% \\ \(k_{t2}(\text{N/m})\) & 107,592 & 108,606 & 0.94\% & 113,789 & 5.76\% \\ \(k_{s1}(\text{N/m})\) & 21,284 & 21,541 & 1.21\% & 21,469 & 0.86\% \\ \(k_{s2}(\text{N/m})\) & 28,835 & 29,654 & 2.84\% & 29,652 & 2.83\% \\ \(c_{s1}(\text{N/s/m})\) & 2342 & 2353 & 0.46\% & 2346 & 0.19\% \\ \(c_{s2}(\text{N/s/m})\) & 3795 & 3964 & 4.46\% & 3917 & 3.20\% \\ \(a_{15}(\text{m})\) & 1.65 & 1.659 & 0.57\% & 1.658 & 0.54\% \\ \(a_{25}(\text{m})\) & 1.75 & 1.731 & 1.07\% & 1.736 & 0.80\% \\ Roughness & & & 3.14\% & & 4.75\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Accuracy of vehicle parameters and roughness identification results under different noise levels.  
parameters, as shown in Table 4, the parameters recognized based on the extended Kalman filter with unknown input are still accurate, with the error basically within 5%. At higher speeds, the recognition accuracy of tire stiffness decreases slightly, with a recognition error of around 6%. Therefore, it can be seen that the method can accurately identify the physical parameters of the moving vehicle and the roughness of the road when \(v\) = 10 m/s or \(v\) = 20 m/s. However, as the speed of the vehicle is too high, the identification accuracy decreases and the problem can be solved by increasing the sampling frequency.  
Figure 14: Identified road roughness PSD (under 20 m/s vehicle speed).  
Figure 13: Road roughness identified in the spatial domain (under 20 m/s vehicle speed).  
Figure 15: Convergence of some parameters (under 20 m/s vehicle speed). (a) Front suspension damping cs\({}_{1}\); (b) rear suspension damping cs\({}_{2}\).