## 4 PCI Prediction Model Based on the ISTD-DisNet Outputs
### PCI Prediction Modeling  
(1) Calculation of the distress \(PDR\)  
To establish a PCI prediction model based on the output results of ISTD-DisNet, based on the data in Table 5, we calculated the \(PDR\) and PCI correlation coefficients according to \begin{table}
\begin{tabular}{c c c} \hline \hline
**Evaluation Unit ID** & **PDR** &
\begin{tabular}{c} **PCI (Visual** \\ **Inspection Method**) \\ \end{tabular} & **Type of Pavement** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._Equations (13) and (14) to determine the degree of correlation between the \(PDR\) and PCI indicators and analyze the feasibility of the automated prediction model construction. \[\left\{ \begin{array}{l}s_{PDR}=\sqrt{\frac{\sum\limits_{i=1}^{i=n}(PDR_{i}\ -\ PDR_{ mean})}{n\ -\ 1}}\\ s_{PCI}=\sqrt{\frac{\sum\limits_{i=1}^{i=n}(PCI_{I}\ -\ PCI_{ mean})}{n\ -\ 1}}\\ S_{PDR,PCI}=\frac{\sum\limits_{i=1}^{i=n}(PDR_{i}\ -\ PDR_{ mean})(PCI_{i}\ -\ PCI_{mean})}{n\ -\ 1}\end{array} \right. \tag{13}\]  
where \(n=66\) is the number of evaluation units; \(PDR_{mean}\) and \(PCI_{mean}\) are the arithmetic mean of the two samples, respectively; \(s_{PDR}\) and \(s_{PCI}\) are the standard deviation of the two samples, respectively; and \(S_{PDR,PCI}\) is the covariance of \(PDR\) and \(PCI\). The correlation coefficient \(r_{PDR,PCI}\) is calculated according to Equation (14):  
\[r_{PDR,PCI}=\frac{S_{PDR,PCI}}{s_{PDR}\times s_{PCI}} \tag{14}\]  
From [PERSON] and [PERSON] [65], it can be seen that, when \(1\geq|r_{PDR,PCI}|>0.75\), the two have a strong correlation; when \(0.7\geq|r_{PDR,PCI}|\geq 0.3\), the two have a moderate correlation; and when \(0.25\geq|r_{PDR,PCI}|\geq 0\), the two have a weak correlation. Based on the data in Table 5, we calculated the \(PDR\) and PCI correlation coefficients of the 42 asphalt evaluation units and the 24 cement evaluation units by Equation (14) The results of the calculations are \(r_{Asphalt}=-0.824\) and \(r_{Cement\ concrete}=-0.965\). This indicates that the two have a strong correlation. That is, using the calculation results of ISTD-DisNet to calculate the distress \(PDR\) of the evaluation units and taking it as the independent variable of the pavement damage index calculation can respond to the degree of damage of the pavement and realize the construction of the PCI prediction model. (2) The PCI prediction model  
In this study, based on the \(PDR\) index, linear and nonlinear fitting methods were used to construct the PCI calculation model, and the performance of the model was evaluated using the coefficient of determination, R\({}^{2}\). R\({}^{2}\) can reflect the proportion of all the variations of the dependent variable that can be explained by the independent variable through the regression relationship, where the closer R\({}^{2}\) is to 1, the better the performance of the model. Figure 12 demonstrates the PCI computational model based on the simple linear fitting method, where it can be seen that, for the two types of pavement types, the coefficients of determination of the linear function model constructed based on the \(PDR\) are 0.672 and 0.808, respectively. Nonlinear equations have a wide range of applications in electricity, mechanics, economic management, engineering technology, etc. [66]. It can be seen from Equation (11) that there is a nonlinear relationship between the PCI and the breakage rate DR, which belongs to a kind of exponential function containing two coefficients. Considering the large difference in the size of the \(PDR\) and DR values, we chose Equation (15) as the nonlinear fitting function of the \(PDR\) (independent variable) and PCI (dependent variable), where \(A_{1}\) and \(A_{2}\) are the two coefficients to be solved, and \(\varepsilon\) represents the correction parameters. The Levenberg-Marquardt (LM) algorithm [67] is used to solve the least-squares solution of the nonlinear function coefficients. \[PCI=100-A_{1}\times PDR^{A_{2}}+\varepsilon \tag{15}\]Figure 12 shows the \(PDR\)-based PCI computational model after 29 iterations.