# Combined Identification of Vehicle Parameters and Road Surface Roughness Using Vehicle Responses
## 4 Conclusions  
Vehicle responses-based methods for identifying roughness are economical and convenient compared to contact and non-contact measurement methods. However, based on the vehicle response, the vehicle parameters significantly affect the dynamic characteristics of the vehicle and the road surface in the interaction between the vehicle and the road. The coupling of the unknown parameters and the unknown roughness causes difficulties in the combined identification of the vehicle parameters and the roughness, and now there is still a lack of efficient methods for the combined identification of the vehicle parameters and the road roughness.  
Therefore, this paper proposes a combined recognition method for vehicle parameters and roughness. Firstly, the unknown vehicle physical parameters of the part other than the tire stiffness are extended to state vectors, and based on the EKF-UI to identify some vehicle physical parameters and the unknown force on the axle. It is worth noting that the vehicle part above the tire stiffness is the object of study to be analyzed in this study. And then, using the property that the front and rear axles of the vehicle pass through the same road roughness region within a fixed time difference, additional conditions are introduced to construct the joint equation of the front axle position roughness and the rear axle position roughness of the time lag, and the tire stiffness is estimated by nonlinear least squares. Ultimately, the combination of the recognized vehicle parameters with the unknown forces of the axles enables the accurate identification of the roughness surface profile of the road. After numerical validation, the method can accurately and simultaneously identify vehicle physical parameters and road roughness under certain noise levels and different levels of roughness. However, the method still assumes uniform vehicle speeds. Future research will be conducted with additional trials and on more complex complex.  
Conceptualization, L.L. ([PERSON]) and L.L. ([PERSON]); methodology, X.G. and L.L. ([PERSON]); validation, X.G.; investigation, X.G.; data curation, X.G. and X.Y. writing--original draft preparation, X.G. and X.Y.; writing--review and editing, L.L. ([PERSON]) and L.L. ([PERSON]); funding acquisition, L.L. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China through Grant No. 52302441 and the Science and Technology Commission of Shanghai Municipality through Grant No. 22 dz1207500.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Parametric**} & & **Recognition** & **Relative** & **Recognition** & **Relative** \\  & **Real Value** & **Value** & **Error** & **Value** & **Error** \\  & & **(r = 10 m/s)** & **(r = 10 m/s)** & **(r = 20 m/s)** & **(r = 20 m/s)** \\ \hline \(m_{\rm{r}}(\rm{kg})\) & 1400 & 1429 & 2.14\% & 1461 & 4.32\% \\ \(l_{\rm{r}}(\rm{kg}\cdot\rm{m}^{2})\) & 3526 & 3574 & 1.36\% & 3540 & 0.43\% \\ \(k_{\rm{r1}}(\rm{N/m})\) & 92,727 & 92,373 & 0.38\% & 96,746 & 4.33\% \\ \(k_{\rm{r2}}(\rm{N/m})\) & 107,592 & 108,606 & 0.94\% & 114,121 & 6.06\% \\ \(k_{\rm{s4}}(\rm{N/m})\) & 21,284 & 21,541 & 1.21\% & 22,194 & 4.33\% \\ \(k_{\rm{s2}}(\rm{N/m})\) & 28,835 & 29,654 & 2.84\% & 30,015 & 4.13\% \\ \(c_{\rm{s1}}(\rm{N/s}/\rm{m})\) & 2342 & 2353 & 0.46\% & 2390 & 2.00\% \\ \(c_{\rm{2}}(\rm{N/s}\)\(\rm{m})\) & 3795 & 3964 & 4.46\% & 4004 & 5.53\% \\ \(a_{\rm{1}}s\) & 1.65 & 1.659 & 0.57\% & 1.651 & 0.09\% \\ \(a_{\rm{2}}s\) (m) & 1.75 & 1.731 & 1.07\% & 1.712 & 2.16\% \\ Roughness & & & 3.14\% & & 6.74\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Accuracy of vehicle parameters and roughness identification results under different vehicle speeds.