# Measurement Model of Full-Width Roughness Considering Longitudinal Profile Weighting
## 5 Experimental Verification and Analysis
### IRI Comparison  
The vehicle-mounted laser profiler selects the elevation data from the V\({}_{1}\) longitudinal profile for analysis, and the output result is labeled as IRI\({}_{0}\). The vehicle-mounted three-dimensional point cloud measurement device utilizes both the V\({}_{1}\) longitudinal profile and the equivalent longitudinal profile V\({}_{\text{F}}\) for computational analysis, with the output results denoted as IRI\({}_{\text{V}}\) and IRI\({}_{\text{F}}\), respectively. V\({}_{\text{F}}\) represents the equivalent longitudinal profile, and its elevation corresponds to \(P_{4}(n)\). It should be noted that although the vehicle-mounted laser profiler aims to use the V\({}_{1}\) longitudinal profile as the measurement trajectory, various factors may cause the actual measurement trajectory to deviate from the expected one, which will ultimately be reflected in the output IRI\({}_{0}\). On the other hand, for the vehicle-mounted three-dimensional point cloud measurement device, the V\({}_{1}\) longitudinal  
Figure 8: Curve of cumulative elevation \(P_{3}\). Figure 9: Elevation comparison between equivalent profile V\({}_{\text{F}}\) and profile V\({}_{1}\). profile is extracted strictly based on the distance from the point cloud data within the lane, providing high certainty and independence from the actual driving trajectory of the vehicle. Figure 10 presents the roughness results of IRI\({}_{0}\), IRI\({}_{V}\), and IRI\({}_{F}\), calculated based on the elevation data from two V\({}_{1}\) longitudinal profiles and the equivalent longitudinal profile V\({}_{F}\), with each section measured every 100 m. Initially, comparing the measurement results of the V\({}_{1}\) longitudinal profiles from the two types of equipment, it is evident that the curves of IRI\({}_{0}\) and IRI\({}_{V}\) exhibited significant consistency, although there were some local differences. This suggested that there were indeed variations in the elevations collected by the two devices. Due to the absence of a standard IRI, it remained uncertain which measurement result was optimal. However, from the perspective of acquiring longitudinal profile data, the method employed by IRI\({}_{V}\), which determines a fixed measurement line based on the lane edge and subsequently extracts elevation values and calculates roughness, aligned more closely with expectations. Furthermore, the roughness indicators IRIV and IRIF, both derived from point cloud data, exhibited strong consistency with a correlation coefficient of 0.996. However, it is noteworthy that the IRI\({}_{F}\) values were generally higher than the IRI\({}_{V}\) values. This phenomenon arose from the more complex and comprehensive composition of the equivalent elevation \(P_{4}(n)\), which encompasses not only the elevations from the V\({}_{1}\) longitudinal profile but also integrates the elevations from multiple other longitudinal profiles within the lane. Therefore, compared to relying solely on elevation data from a single longitudinal profile, the equivalent elevation \(P_{4}(n)\) undoubtedly provides richer and more comprehensive road surface elevation information. This information gain is reflected in the calculation of roughness indicators, resulting in relatively larger IRI values. The coefficient of variation (\(Cv\)) was employed to analyze the repeatability of the IRI, and the results are presented in Figure 11. The \(Cv\) indicator has demonstrated effective application in the field of engineering survey [31,32]. When using the vehicle-mounted laser profiler to measure the V\({}_{1}\) longitudinal profile, the results exhibited significant variability, particularly within the road segment of 500-600 m, where the coefficient of variation \(Cv_{0}\) even exceeded 9%. By contrast, the coefficients of variation for IRI\({}_{V}\) and IRI\({}_{F}\) based on 3D point cloud data, namely \(Cv_{V}\) and \(Cv_{F}\), remained at relatively low levels, not exceeding 3.0% and 4.0%, respectively.