# Measurement Model of Full-Width Roughness Considering Longitudinal Profile Weighting
## 1 Introduction
With the advancement of science and technology, numerous three-dimensional point cloud measurement devices have been applied in the field of road surface elevation measurement [2; 17; 18]. These devices, typically utilizing laser scanning technology, are capable of rapidly acquiring large amounts of high-precision point cloud data, enabling accurate measurement of road surface elevation and precise calculation of the IRI. [PERSON] et al. [19] extracted and computed road surface roughness at 1 m from the outer edge of the road using road slice segmentation and K-means clustering methods. [PERSON] et al. [20] processed three-dimensional point cloud data using ordinary Kriging and inverse distance weighting methods to extract road surface elevation changes for calculating IRI values. [PERSON] et al. [21] proposed determining roughness from point cloud data by establishing the standard deviation of elevation relative to an interpolated planar surface. [PERSON] and [PERSON] [13] developed a segmentation algorithm based on point cloud voxelization to estimate road surface roughness. [PERSON] et al. [22] utilized point cloud data acquired from three-dimensional stationary terrestrial laser scanning (STLS) to process and extract road surface roughness characteristics. [PERSON] et al. [23] used unmanned aerial vehicles (UAVs) and photogrammetry to obtain the IRI of roads. These studies demonstrate that three-dimensional measurement technology has proven to be a reliable means in the field of road surface roughness detection. Despite technological advancements, existing research still exhibits deficiencies in data analysis methods [20]. Specifically, numerous studies predominantly focus on calculating the IRI through single longitudinal profile elevation assessments, neglecting the lateral distribution variations of road surface roughness [14]. While this singular or fixed measurement line selection simplifies data processing, it fails to fully utilize the rich information provided by three-dimensional point cloud data, resulting in limitations for comprehensive road surface roughness evaluations. [PERSON] et al. [14] employed UAVs equipped with LiDAR technology to collect road surface elevation data. Through an analysis of the lateral distribution of the IRI, they discovered significant differences among various measurement lines. Based on experimental results, they advocated for consideration of the lateral distribution of roughness. [PERSON] et al. [24] made progress in evaluating airport runway surface roughness using three-dimensional point cloud data, taking a step forward by refining the lateral impact of multiple measurement lines on roughness distribution. These studies reveal that, compared to traditional measurement tools, methods based on point cloud data offer more diversified research perspectives for road surface IRI analysis [14]. However, without in-depth application of these massive elevation point cloud data, their potential value cannot be fully exploited. Therefore, there is an urgent need to adopt more scientific and reasonable data analysis techniques to enhance the accuracy and completeness of road surface roughness evaluations. Given the randomness of vehicle trajectories and the fact that contact points with the road surface are distributed across the entire lane, it is scientifically reasonable to incorporate elevation data from the full lane into IRI calculations. However, efficiently integrating elevation data from the entire roadway width poses a new challenge. Fortunately, British Standard BS 5400-10 [25] records the frequency of lateral distribution of vehicle centerlines based on bridge traffic observation data. Although these data are specific to bridges, they provide a valuable reference for constructing new roughness measurement models. [PERSON] et al. [14] found that the lateral distribution of asphalt pavement roughness follows a normal distribution. These research findings reinforce the idea of establishing a lateral distribution model of wheel trajectories in this study.