# Combined Identification of Vehicle Parameters and Road Surface Roughness Using Vehicle Responses
## 3 Numerical Validation of Methods
### Verification at Different Noise Levels  
Because the vibration of the vehicle engine generates noise, the impact of noise is therefore included in numerical simulations. Recognition under different noise levels was investigated by previously considering Gaussian white noise with 5% RMS, so in this section, the recognition results will be investigated under noise levels with 10% RMS. The parameter settings are kept the same as in Section 3.1, and the road at class B roughness is studied and discussed.  
Compared to 5% noise level, the recognition error of roughness spatial contour increases to 4.75% at 10% noise level as shown in Figure 10 for the same Class B roughness recognition result. At 10% noise level, the identified road roughness PSD is shown in Figure 11, with more pronounced undulations in the high-frequency part compared to the 5% noise level (e.g., Figure 5). The convergence of vehicle body mass and moment of inertia identification under a 10% noise level is shown in Figure 12. In terms of identifying vehicle parameters, as shown in Table 3, the parameters identified based on the extended Kalman filter with unknown input are still accurate, with an error basically within 3%, while at higher noise levels, the accuracy of the unknown force identification decreases slightly, with an error of 8% in the identification of the unknown force on the front axle and an error of 7% in the identification of the unknown force on the rear axle, which results in a slight decrease in the accuracy of identifying tire stiffness, with an error of identification of around 5%. Thus, it can be seen that the method can accurately identify the physical parameters of the moving vehicle and the roughness of the road at a noise level of 10%, but the recognition accuracy is slightly reduced by the noise.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Parametric**} & \multirow{3}{*}{\begin{tabular}{c} **Real** \\ **Value** \\ **Value** \\ \end{tabular} } & \
\begin{tabular}{c} **Recognized** \\ **Value** \\ **(at Class B** \\ **Roughness)** \\ \end{tabular} & \multicolumn{2}{c}{**Recognized**} & \multirow{3}{*}{
\begin{tabular}{c} **Relative** \\ **Error** \\ **(at Class C** \\ **Roughness)** \\ \end{tabular} } \\ \hline \(m_{\text{c}}(\text{kg})\) & 1400 & 1429 & 2.14\% & 1434 & 2.51\% \\ \(l_{\text{c}}(\text{kg}\cdot\text{m}^{2})\) & 3526 & 3574 & 1.36\% & 3584 & 1.67\% \\ \(k_{\text{11}}(\text{N/m})\) & 92,727 & 92,373 & 0.38\% & 93,617 & 0.96\% \\ \(k_{\text{22}}(\text{N/m})\) & 107,592 & 108,606 & 0.94\% & 111,346 & 3.49\% \\ \(k_{\text{31}}(\text{N/m})\) & 21,284 & 21,541 & 1.21\% & 21,710 & 2.03\% \\ \(k_{\text{32}}(\text{N/m})\) & 28,835 & 29,654 & 2.84\% & 30,062 & 4.27\% \\ \(c_{\text{s1}}(\text{N*s/m})\) & 2342 & 2353 & 0.46\% & 2391 & 2.16\% \\ \(c_{\text{s2}}(\text{N*s/m})\) & 3795 & 3964 & 4.46\% & 3956 & 4.26\% \\ \(a_{\text{1}}\text{s}\;(\text{m})\) & 1.65 & 1.659 & 0.57\% & 1.645 & 0.28\% \\ \(a_{\text{25}}\text{s}\;(\text{m})\) & 1.75 & 1.731 & 1.07\% & 1.731 & 1.04\% \\ Roughness & & & 3.14\% & & 3.73\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Accuracy of vehicle parameters and roughness identification results under different roughness levels.  
Figure 10: Road roughness identified in the spatial domain (10% noise).