## 5 Case Study
### Pavement Performance Clustering of Unit Road Sections  
After the road segment clustering is completed, further detailed analysis can be carried out on the road segments with low road performance levels or by selecting specific road segments according to project requirements. In this section, R4 is used as an example to cluster unit road segments.  
R4 has a total length of 48.32 km and a total of 48 units to evaluate the road sections. Based on its PCI measured data in 2019, a PCI cumulative distribution evaluation model was established through the sampling theorem. The value of the independent variable is set to [0, 100], the sampling point N is set to 1000, and the sampling interval is set to 0.1. The discrete cumulative frequency distribution data of pavement performance indexes are continuous.  
\[F(x)=F(0.1)\sin c(10\times(x-0.1))+\ldots+F(100)\sin c(10\times(x-100))\]  
The continuation function of the measured value of PCI cumulative distribution and Equation (5) is plotted in Figure 6a. It can be seen from the figure that the PCI cumulative  
Figure 4: The clustering pedigree obtained by using the K-means algorithm based on the road segment pavement performance distribution.  
Figure 5: Clustering diagram obtained using K-means algorithm based on road performance distribution of road sections: (**a**) K = 5; (**b**) K = 8.  
distribution continuity function completely coincides with the field measured value, that is, the modeling fit is very high. By substituting any road performance index level into the function through the continuity equation, the proportion of road sections below the performance index level can be obtained. Similarly, the RQI cumulative distribution evaluation model is established by the sampling theorem, and the fitting result is also high, as shown in Figure 6b below.  
The K-means algorithm was used to cluster the R4 unit evaluation road segments. The input observation value is a two-dimensional vector constructed by the R4 unit evaluation road section pavement performance indexes PCI and RQI. There are 48 unit road segment vectors \(v_{i}{=}\left[\text{PCI}_{(i)},\text{RQI}_{(i)}\right]\) with the station number \(i\).  
The calculated K value and its corresponding error sum of squares are shown in Figure 7. It can be seen from the figure that the error sum of squares decreases rapidly from class 1 to class 5, and then decreases slowly, indicating that the ideal K value appears at 5.  
Set K = 5, the initial cluster center point is randomly selected from the observation vector, and K-means clustering is performed. The results of the unit evaluation road segment based on PCI and RQI clustering are plotted in Figure 8. The figure takes PCI as the abscissa and RQI as the ordinate. It can be clearly seen that all the observation unit road sections are divided into five categories.  
Figure 6: Continuity graph of the cumulative distribution of R4 pavement performance: (a) PCI; (b) RQI.  
Figure 7: The relationship between SSE and the number of classes for R4.  
The cumulative distribution continuation functions for PCI and RQI are plotted in Figure 9. Combining Figures 8 and 9, it can be seen that the PCI index of the two-unit road sections whose RQI index is lower than 70 is also lower than 80, which can be classified into one category, and similar maintenance measures are taken during maintenance. Most of the road sections are in the horizontal range of PCI and RQI of 70-90. According to the clustering results, these road sections can be divided into three categories for research. For the sections with a PCI index higher than 90, the RQI is also higher than 90. These sections with better performance are concentrated in the upper right corner of the cluster map.