# 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 calculated results are shown in Table 4 and Figure 12.  
Table 4 indicates that variations in the starting and ending positions lead to differences in the calculated IRI results within each statistical interval. Figure 12 further illustrates this trend, indicating that as the offset distance increases, the differences in the IRI results within each interval decrease, resulting in a more concentrated roughness distribution. This may be attributed to the fact that the roughness in the middle section is generally less discrete compared to the two extremities. However, it is worth noting that the mean of the IRI results remained relatively constant, suggesting that the conventional method of using the mean value to represent the roughness of the entire road section is reasonably reliable to some extent. In view of the volatility, it was found that offsetting the starting point has a significant impact on the roughness, while offsetting the ending point has a minimal effect. Specifically, when the offset distance of the starting point exceeded 30 m, the volatility of the roughness became statistically significant (\(\mu>1.96\)). This demonstrates that an unreasonable offset of the starting point may obscure the local abnormal areas in these road sections. On the other hand, changing the position of the ending point primarily affected the IRI result of the last statistical interval, resulting in a minimal overall influence. Consequently, the risk \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Offset Position** & **Offset Distance (m)** & **IRI Results (m/km)** & **Mean of the IRI (m/km)** & \(\mu\)**Value** \\ \hline No offset & 0 & 5.60, 5.07, 6.14, 5.19, 4.36, 6.51, 3.50 & 5.196 & 1.78 \\ Starting point & 10 & 5.50, 5.02, 6.06, 5.15, 4.34, 6.57, 3.85 & 5.213 & 1.88 \\ Starting point & 20 & 4.88, 5.03, 6.15, 5.10, 4.35, 6.57, 4.32 & 5.200 & 1.93 \\ Starting point & 30 & 4.69, 5.15, 6.04, 5.10, 4.36, 6.67, 4.67 & 5.240 & **2.02** \\ Starting point & 40 & 4.09, 5.63, 5.82, 5.30, 4.62, 6.07, 4.85 & 5.197 & **2.11** \\ Starting point & 50 & 4.12, 5.74, 6.19, 4.82, 5.33, 5.54, 4.79 & 5.219 & **2.13** \\ Starting point & 60 & 5.12, 5.69, 5.25, 4.66, 5.50, 5.26, 5.02 & 5.214 & **2.49** \\ Ending point & 10 & 5.34, 5.12, 6.05, 5.13, 4.25, 6.61, 4.25 & 5.250 & 1.83 \\ Ending point & 20 & 5.02, 5.13, 6.12, 5.21, 4.22, 6.45, 4.11 & 5.180 & 1.89 \\ Ending point & 30 & 5.24, 5.34, 5.94, 4.97, 4.54, 6.21, 4.26 & 5.214 & 1.91 \\ Ending point & 40 & 4.95, 5.49, 5.78, 5.24, 5.02, 5.46, 4.52 & 5.209 & 1.82 \\ Ending point & 50 & 5.48, 5.61, 6.01, 4.98, 4.51, 5.29, 4.57 & 5.207 & 1.87 \\ Ending point & 60 & 4.35, 5.27, 6.06, 5.41, 4.17, 6.48, 4.73 & 5.210 & 1.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: IRI results under different starting and ending point offsets. Figure 12: IRI results and \(\mu\) values under different starting point offsets. of roughness variation caused by offsetting the ending point was deemed to be lower than offsetting the starting point. Therefore, it is advisable to prioritize controlling the recording position of the starting point during the actual detection process. The analysis of the influence of the starting and ending positions on the roughness revealed that increasing the offset distance significantly increases the volatility of the roughness results. To further evaluate the sensitivity of the road sections with different lengths to the offset distance, 700 road sections with various lengths were selected for analysis. The offset distances that caused significant changes in the roughness results were identified for each road section. In light of the above findings, the volatility evaluation result was used to determine noticeable changes in roughness, considering only the offset of the starting point. These results are presented in Table 5.  
Based on the consistent findings, it can be concluded that the average offset distance threshold causing a significant change in roughness results is less than 30 m, regardless of the variation in the road length.