# Ride Comfort Prediction on Urban Road Using Discrete
## 4 Results
### Correlations between DRI and MTVV
#### 4.2.4 Correlation Development  
In previous studies, it was widely accepted that the IRI has a good linear relation with the WRMSA. The DRI is more sensitive to the local unevenness than the IRI; however, the linear relation may not be suitable for developing correlations between the DRI and the MTVV. Therefore, we adopted the power function regression (MTVV = a\({}_{1}\)DRI\({}_{right}^{a_{2}}\)DRI\({}_{left}^{a_{3}}\), a\({}_{1}\), a\({}_{2}\), a\({}_{3}\) are fitting parameters) to develop the correlations, summarized in Table 2, and the regressed correlations between the IRI and the MTVV were also calculated and summarized for comparison. Once the correlations were developed, we could easily predict the ride comfort on the road sections with the given profile. From Table 2, we can see that the performance of the DRI-based prediction method outperforms the IRI-based method. The R-squares of the DRIavg vs. MTVV are mostly higher than those of the IRI, especially at a high speed. This indicates that the DRI is more \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Time Period** & **Speed** & **DRI vs. MTVV** & **IRI vs. MTVV** \\ \hline \multirow{4}{*}{1 s} & 40 km/h & MTVV = 0.23 DRI\({}_{left}^{0.62}.DRI\)\({}_{right}^{0.22}\) & \(R^{2}=0.63\) & MTVV = 0.221\(R_{left}^{0.54}.IR\)\({}_{right}^{0.25}\) & \(R^{2}=0.62\) \\  & 60 km/h & MTVV = 0.37 DRI\({}_{left}^{0.67}.DRI\)\({}_{right}^{0.25}\) & \(R^{2}=0.76\) & MTVV = 0.341\(R_{left}^{0.66}.IR\)\({}_{right}^{0.21}\) & \(R^{2}=0.74\) \\  & 80 km/h & MTVV = 0.49 DRI\({}_{left}^{0.62}.DRI\)\({}_{right}^{0.29}\) & \(R^{2}=0.74\) & MTVV = 0.481\(R_{left}^{0.62}.IR\)\({}_{right}^{0.18}\) & \(R^{2}=0.65\) \\  & 100 km/h & MTVV = 0.60 DRI\({}_{left}^{0.56}.DRI\)\({}_{right}^{0.35}\) & \(R^{2}=0.72\) & MTVV = 0.601\(R_{left}^{0.55}.IR\)\({}_{right}^{0.22}\) & \(R^{2}=0.60\) \\ \hline \multirow{4}{*}{2 s} & 40 km/h & MTVV = 0.26 DRI\({}_{left}^{0.23}.DRI\)\({}_{right}^{0.20}\) & \(R^{2}=0.72\) & MTVV = 0.231\(R_{left}^{0.27}.IR\)\({}_{right}^{0.17}\) & \(R^{2}=0.71\) \\  & 60 km/h & MTVV = 0.41 DRI\({}_{left}^{0.27}.DRI\)\({}_{right}^{0.24}\) & \(R^{2}=0.80\) & MTVV = 0.371\(R_{left}^{0.80}.IR\)\({}_{right}^{0.14}\) & \(R^{2}=0.78\) \\  & 80 km/h & MTVV = 0.57 DRI\({}_{left}^{0.66}.DRI\)\({}_{right}^{0.32}\) & \(R^{2}=0.78\) & MTVV = 0.551\(R_{left}^{0.50}.IR\)\({}_{right}^{0.36}\) & \(R^{2}=0.70\) \\  & 100 km/h & MTVV = 0.69 DRI\({}_{left}^{0.57}.DRI\)\({}_{right}^{0.40}\) & \(R^{2}=0.76\) & MTVV = 0.681\(R_{left}^{0.41}.IR\)\({}_{right}^{0.40}\) & \(R^{2}=0.64\) \\ \hline \multirow{4}{*}{4 s} & 40 km/h & MTVV = 0.29 DRI\({}_{left}^{0.28}.DRI\)\({}_{right}^{0.22}\) & \(R^{2}=0.76\) & MTVV = 0.271\(R_{left}^{0.67}.IR\)\({}_{right}^{0.27}\) & \(R^{2}=0.74\) \\  & 60 km/h & MTVV = 0.47 DRI\({}_{left}^{0.82}.DRI\)\({}_{right}^{0.24}\) & \(R^{2}=0.83\) & MTVV = 0.421\(R_{left}^{0.57}.IR\)\({}_{right}^{0.43}\) & \(R^{2}=0.80\) \\  & 80 km/h & MTVV = 0.64 DRI\({}_{left}^{0.72}.DRI\)\({}_{right}^{0.29}\) & \(R^{2}=0.78\) & MTVV = 0.591\(R_{left}^{1.15}.IR\)\({}_{right}^{0.23}\) & \(R^{2}=0.72\) \\  & 100 km/h & MTVV = 0.81 DRI\({}_{left}^{0.66}.DRI\)\({}_{right}^{0.34}\) & \(R^{2}=0.76\) & MTVV = 0.771\(R_{left}^{0.72}.IR\)\({}_{right}^{0.16}\) & \(R^{2}=0.67\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlations of DRIavg vs. MTVV and IRI vs. MTVV. Figure 8: Relations between the DRI\({}_{left}\) and DRI\({}_{right}\): (**a**) length = 100 m, (**b**) length = 40 m, (**c**) length = 20 m, (**d**) length = 10 m.  
applicable to predict ride comfort. The exponents of the DRIleft and the DRIright indicate how significant their effects are. It is observed that the exponents in the correlations of the DRI vs. MTVV follow this trend: as the vehicle speed increases, the exponent of the DRIright grows continuously. It can be concluded that the left and right wheel paths both have a significant effect on the ride comfort at a high speed, while the ride comfort is mainly affected by the closest wheel path at a low speed.