# Ride Comfort Prediction on Urban Road Using Discrete
## 4 Results
### Application for Ride Comfort Prediction and Speed Control  
For a given road section with known profiles, we can easily predict the ride comfort based on the DRI calculation and the correlations in Table 2. During the ride comfort prediction, it is necessary to first define the road segmentation method and the vehicle speed. By using the 2 s-MTVV to represent the ride comfort, we can obtain a \"map\"  
Figure 9: Speed-related DRI thresholds: (**a**) 40 km/h, (**b**) 60 km/h, (**c**) 80 km/h, (**d**) 100 km/h. showing how the ride comfort is distributed over the whole section at a fixed speed, as shown in Figure 10.  
Note that the road section in Figure 9 is the same as the road section in Figure 6. The color scale along the distance indicates ride comfort. The ride comfort prediction results can guide us in developing a speed control strategy to avoid severe turbulence. To maintain a good comfort level, vehicles can decelerate on rough road sections and accelerate on flat sections. As the deceleration and acceleration of a vehicle also induce discomfort, we adopted a hyperbolic tangent curve to generate the speed control strategy [26]:  
\[v=-\frac{b}{2}\text{tanh}(k(t-p))-\frac{b}{2}+v_{0} \tag{18}\]  
where \(v_{0}\) indicates the initial speed, t denotes the time, \(v\) is the targeted speed, \(b=v_{0}-v\), \(p\) is a model constant, and \(k\) is the stability coefficient that determines the curve of the speed changes. By calculating the differentiation of Equation (18), the expression of the acceleration of the vehicle is as follows (Figure 10b):  
\[a_{longi}=-\frac{bk}{2}\Big{(}1-(\text{tanh}(k(t-p)))^{2}\Big{)} \tag{19}\]  
\[\text{max}\Big{(}a_{longi}\Big{)}=\frac{b\cdot k}{2} \tag{20}\]  
The hyperbolic tangent curve resembles the process of human deceleration or acceleration, as shown in Figure 11. In practice, we care more about the deceleration stage because vehicles allow us to brake suddenly, but sudden acceleration is usually not allowed. Therefore, we only consider the deceleration stage in this study. Figure 11: The hyperbolic-tangent-based speed control model. Figure 10: Distribution of ride comfort over distance at the speed of: (**a**) 40 km/h, (**b**) 60 km/h, (**c**) 80 km/h, (**d**) 100 km/h. As expressed in Equations (19) and (20), the stability coefficient \(k\) is the key factor that affects the acceleration of vehicles. To maintain a good comfort level during deceleration, vehicles should select a small k to avoid sudden changes in speed and acceleration. Then, combining the vertical acceleration with the longitudinal acceleration, we can calculate the combined maximum transient acceleration (MTVV\({}_{\text{cob}}\)) based on ISO 2631, expressed as follows:  
Figure 9:0  
where \(w_{d}\) and \(w_{k}\) are the weights for the longitudinal and vertical accelerations, respectively. According to the comfort levels in Table 2, the MTVV\({}_{\text{cob}}\) should also meet the ISO comfort standard. Suppose we want to maintain a comfort level under level II (a little uncomfortable), the MTVV\({}_{\text{cob}}\) should not exceed 0.63 m/s\({}^{2}\). Then, we can estimate the \(k\) by solving the inequality:  
Figure 9:1  
then,  
Figure 9:2  
Note that the coefficients \(a_{1}\), \(a_{2}\), \(a_{3}\) are related to vehicle speed, which can refer to the fitting parameters in Figure 9:3 Additionally, the rate of change in a vehicle's longitudinal acceleration, named jerk [27], is also an important factor affecting ride comfort. Research has shown that vehicle jerk significantly affects drivability, which is in accordance with subjective human perception. According to [PERSON]'s research [28], the vehicle jerk should not exceed 2.94 m/s\({}^{2}\) to retain ride comfort.