# Measurement Model of Full-Width Roughness Considering Longitudinal Profile Weighting
## 1 Introduction  
In modern transportation systems, highways utilize traffic signs and markings to scientifically delineate lanes, effectively regulating vehicle travel and enhancing traffic capacity and the driving experience [1, 2]. However, with continuous increase in traffic load, the road surface experiences uneven subsidence and wear, altering its elevation and operational performance [3]. From the perspectives of road maintenance, improving passenger comfort, and reducing dynamic loads on vehicles and roadways, evaluating road roughness is a crucial area of research [4]. The International Roughness Index (IRI) stands as a prevalent metric in the global evaluation and management of road systems [5]. Considerable research efforts have been dedicated to this indicator by scholars worldwide. [PERSON] et al. [6] compared and analyzed three different methods for evaluating road roughness and explored the influence of vehicle speed on the roughness threshold. [PERSON] et al. [7] monitored road conditions using cost-effective MEMS accelerometers and GPS sensors, calculating the IRI from road surface elevation data. [PERSON] et al. [8] introduced new IRI thresholds based on riding comfort, comprehensively assessing the impact of road roughness on driving comfort using three distinct evaluation techniques. [PERSON] et al. [9] proposed an IRI prediction model leveraging multiple linear regression analysis and artificial neural networks (ANNs) for flexible road condition forecasting, achieving high prediction accuracy. Similar predictive work on IRI models was also conducted by [PERSON] et al. [10]. [PERSON] et al. [11] developed a deterioration model for IRI, integrating empirical mechanical methods withregression-based approaches. These investigations highlight the effective application of IRI in assessing road roughness, thereby providing valuable data support for road management departments in formulating maintenance strategies. From the perspective of data acquisition and processing, early studies typically relied on devices like laser profilometers [12] and 3D LiDAR [13] to record road surface elevation changes [14], enabling road roughness evaluation. It is worth noting that these IRI calculations were primarily based on elevation data from single or a few longitudinal profiles, without establishing direct connections to other profiles. In actual roadways, vehicle trajectories exhibit relative randomness, and the distribution of road surface elevations is unpredictable. Based on the computational principles of IRI, variations in elevation across different longitudinal profiles can lead to disparities in IRI values. Hence, selecting longitudinal profiles scientifically and reasonably is crucial for accurately assessing the roughness of a given roadway. However, there is currently no unified standard for choosing longitudinal profiles [15], and existing methods often lack scientific rigor [14]. [PERSON] [15] provided a comprehensive overview and tabular presentation of the differences in the number (1, 2, or multiple) and position (0.75 m, 0.79 m, 0.8 m, 0.9 m, 1.0 m, 1.2 m, etc. from the centerline of the roadway) of longitudinal profiles. Under actual road conditions, the elevation of each profile may vary. Additionally, the trajectories of inspection vehicles and other road users are not always confined to the same longitudinal profile. Consequently, relying solely on elevation data from a few longitudinal profiles to evaluate the performance of the entire roadway raises questions about scientific validity and accuracy. This limitation is primarily attributed to the technical constraints of early instrumentation, particularly the limited number of ranging sensors available [16], which hindered large-scale and wide-ranging road surface measurement efforts. Therefore, to more accurately evaluate the performance of a given roadway, comprehensive measurement and analysis of road surface elevations are necessary to obtain precise IRI values.