# Measurement Model of Full-Width Roughness Considering Longitudinal Profile Weighting
## 5 Experimental Verification and Analysis
### Experimental Data Analysis  
Figure 6 provides a visual representation of the original elevation point cloud data collected along a 600 m section of the tested roadway. Upon observation, it is evident that the difference between the maximum and minimum elevations exceeds 200 mm, and the uneven color distribution indicates significant surface irregularities. The regions with higher elevations are predominantly concentrated on the left side (upper left), while those with lower elevations are located on the right side (upper right). This phenomenon of higher elevation on the left and lower elevation on the right is intentionally designed to facilitate road surface drainage. Two cross-sections at H\({}_{1}\) = 150 m and H\({}_{2}\) = 450 m were randomly selected for analysis. The cross-slope elevations of these two cross-sections were 103.37 mm and 143.09 mm, respectively, and both were higher on the left and lower on the right. Similarly, two longitudinal profiles at V\({}_{1}\) = \(-\)0.9 m and V\({}_{2}\) = 0.9 m were randomly chosen for analysis. The elevation change rates of these two longitudinal profiles were relatively flat, and their slopes met the requirements of high-grade road design specifications. It was assumed that the V\({}_{1}\) and V\({}_{2}\) longitudinal profiles corresponded to the two desired measurement trajectories within the left and right wheel trajectories, respectively. In early road surface roughness measurements, the elevations of these two longitudinal profiles were used to calculate the roughness value of the road. However, this method ignored the road surface elevation data outside the two longitudinal profiles, limiting the comprehensiveness and scientific rigor of the road performance evaluation. Assuming that the tested road was a mixed traffic lane, \(L\) = 1.8 m and \(\mu\) = 0.9 m were selected as the parameters for the lateral distribution of vehicle trajectories within the lane, and the weighting model of the longitudinal profile \(f_{\mathrm{norm}}(x)\) was obtained. Subsequently, the weighted elevation point cloud data \(P_{2}(x_{i},\,n)\) were obtained, presented in Figure 7. The characteristics of the 'M' shape indicated that the proposed weighting model \(f_{\mathrm{norm}}(x)\) effectively highlighted the elevations within the left and right wheel trajectories while suppressing the elevations along the lane centerline and both boundaries. This outcome aligned with the expectations of the study. Figure 5: Experimental testing roads with various specifications of standard blocks. Continuing the elevation analysis of the two cross-sections at specific locations H\({}_{1}\) = 150 m and H\({}_{2}\) = 450 m, the results clearly showed higher peaks within the wheel trajectory zones. Furthermore, the peak values in the left wheel trajectory were higher than those in the right wheel trajectory. This finding indicated that the weighted allocation of cross-sectional point cloud data did not alter the established function of the lane draining toward the right side, thus providing initial validation for the rationality of the weighting model. Moving forward, elevation analysis of the two longitudinal profiles at V\({}_{1}\) = \(-\)0.9 m and V\({}_{2}\) = 0.9 m was conducted. The results revealed that, compared with the curves presented in Figure 6, the elevation amplitude of these two longitudinal profiles was not significantly reduced, and the elevation change trend along the driving direction was consistent. This is because the two longitudinal profiles were at the \(L/2\) position and were least affected by \(f_{\text{norm}}(x)\). Notably, within the interval of 500 m to 600 m, multiple points with pronounced elevation fluctuations were observed. These fluctuations may have indicated local variations in road surface roughness. Upon verification, these locations corresponded precisely to the multiple sets of standard test blocks laid within the wheel trajectories during the experiment, further validating the close correlation between our analysis and actual road conditions.