# Differences Evaluation of Pavement Roughness Distribution Based on Light Detection and Ranging Data
## 5 Volatility Evaluation of the Pavement Roughness under Different Detection Lengths  
The volatility of the pavement roughness can be categorized into two aspects: natural volatility and artificial volatility. The former is associated with the lateral variation of pavement roughness that is influenced by various environmental factors, such as the road material condition, traffic volume, and climatic conditions. On the other hand, the latter refers to the longitudinal variation in the repeated roughness detection results, which is mainly influenced by the data collection methodology. While the previous section discussed the analysis of lateral volatility, this section will primarily concentrate on investigating artificial volatility. Since the detection vehicle encounters a red light at the intersection, requiring it to decelerate to a stationary state, the IRI results around the intersection area significantly differ from those of the other areas. Therefore, the invalid detection results of the low-speed area were generally excluded from further analysis. However, given that a red light is a random event, a discrepancy existed between the detection length and the actual road length in multiple detections, with variations of up to 70 m having been observed in the detection data. This discrepancy arises from the fluctuation of the starting and ending points during each IRI calculation, leading to the repeated detection results volatility. Thus, this study provides insights into the influence of the variation in the starting and ending points on the roughness results, which is essential for ensuring the reliability of the results under different detection lengths. In accordance with the repeatability test method specified in the standard [27], the variation coefficient was chosen to evaluate the roughness volatility. It was calculated as shown in Equation (9) and is required to be within 5%. To further assess the significance of the results, the Mann-Whitney U test was employed. It is a non-parametric test that is typically utilized to determine whether two independent sequential data samples originated from the same population. Since minimal roughness volatility was expected within one road section during detection, the original hypothesis assumed that the variation coefficient was less than or equal to the maximum threshold \(C_{v0}\) (\(C_{v0}=5\%\)). The hypotheses and test statistics of the one-tailed test are presented in Formulas (18)-(20) [29]:  
\[\left\{ \begin{array}{l}S=\sqrt{\frac{\sum\limits_{i=1}^{\overline{c}}(x_{i}- \overline{x})^{2}}{n-1}}\\ C_{v}=\frac{5}{\overline{x}}\cdot 100\%\end{array} \right. \tag{18}\]  
\[H_{0}:C_{v}\leq C_{v0};H_{1}:C_{v}>C_{v0} \tag{19}\]  
\[\mu=\frac{\sqrt{n-1}|C_{v}-C_{v0}|}{C_{v0}\sqrt{0.5+C_{v0}^{2}}} \tag{20}\]  
where \(S\) is the standard deviation of repeatability, \(x_{i}\) is the \(i\)th roughness result, \(\overline{x}\) is the average of roughness results, \(n\) is the total number of samples, \(C_{v0}\) is the variation coefficient calculated for the sample, and \(\mu\) is the test statistics. At a 95% confidence level, if \(\mu\) is less than 1.96, the result is considered insignificant, and the original hypothesis \(H_{0}\) is rejected. If \(\mu\) is greater than or equal to 1.96, the result is considered statistically significant, and the original hypothesis \(H_{0}\) can thereby be accepted, and when \(\mu\) is greater than 2.58, the result is considered very significant. The primary length range of the road section fell between 100 and 500 m, respectively. Given that the statistical interval was generally taken as 100 m, the shorter road was not conducive to analysis. Therefore, a 672 m long road section on the Cao'an Highway was utilized as the test section. The starting and ending points were offset to calculate the roughness for analyzing the influence of the different detection lengths. In order to ensure comparability, the pavement roughness was calculated using the elevation data obtained from the road wheel track.