## 3 Lifespan Prediction Method
### Analysis of Relative Parameters for Lifespan Prediction  
In Section 2, corresponding parameters of composite insulators under different aging years for predicting lifespan were studied, as listed in Table 8.  
In this paper, Pearson correlation analysis, a statistical method, was employed and the correlation coefficient \(r\) was utilized to preliminarily analyze the correlation between each lifespan prediction parameter and the operating year [25]:  
\[r=\frac{\sum\limits_{i=1}^{n}{(x_{i}-\overline{x})(t_{i}-\overline{t})}}{ \sqrt{\sum\limits_{i=1}^{n}{(x_{i}-\overline{x})^{2}}}\sqrt{\sum\limits_{i=1}^{ n}{(t_{i}-\overline{t})^{2}}}} \tag{4}\]  
where, \(x_{i}\) is the lifespan prediction parameters of the \(i\)th sample; \(t_{i}\) is the aging year of the \(i\)th sample; \(\overline{x}\) is the mean value of lifespan prediction parameters of samples aged for different years; \(\overline{t}\) is the mean value of aging time of samples aged for different years.  
The t-test was used to detect the significance of correlation coefficients between lifespan prediction parameters and aging time. The calculation is expressed in Equation (5).  
\[T=\frac{r\sqrt{n-2}}{\sqrt{1-r^{2}}}\ \sim\ t(n-2) \tag{5}\]  
In Equation (5), if the significance value \(\alpha\) is less than 0.05, it indicates that there is a certain correlation between two variables; if \(\alpha\) is less than 0.01, it indicates that there is a significant correlation between two variables. Test results are listed in Table 9.  
\begin{table}
\begin{tabular}{c c l} \hline \hline
**No.** & **Parameters** & **Test Methods** \\ \hline
1 & \(\theta_{ap}\) & CA of the surface of samples \\
2 & \(A\) & Average hardness of the surface of samples \\
3 & \(S_{em}\) & Aging level based on SEM test \\
4 & \(H\) & The ratio of Si-(CH\({}_{3}\))\({}_{2}\) absorption peak altitude to Si-O-Si \\  & & absorption peak altitude \\
5 & \(X_{\text{Si}}\) & Relative content of Si element of samples \\
6 & \(X_{\text{C}}\) & Relative content of C element of samples \\
7 & \(X_{\text{O}}\) & Relative content of O element of samples \\
8 & \(U_{f}\) & Salt spray flashover voltage of samples \\ \hline \hline \end{tabular}
\end{table}
Table 8: Lifespan prediction parameters of samples.  
Table 9 shows the following:  
(1) According to the results of correlation analysis (Table 9), with the increase of aging time, the static contact angle \(\theta_{\text{av}}\), the relative content of Si element \(X_{Si}\) and salt-fog flashover voltage \(U_{f}\) decrease significantly, and the relative content of O element \(X_{O}\) increases significantly. These four parameters are significantly correlated with aging time (\(\alpha<0.01\)). These parameters can be used in evaluating the aging degree of aged composite insulators and proposing a prediction method to determine the aging time of composite insulators.  
(2) With the increase of aging time, the hardness \(A\) and the aging level \(S_{em}\) increase, and the ratio of Si-(CH\({}_{3}\))\({}_{2}\) absorption peak altitude to Si-O-Si absorption peak altitude (\(H\)) and the relative content of C element \(X_{C}\) decrease. These four parameters were correlated with aging time (\(\alpha<0.05\)). On this basis, these parameters can be used as auxiliary indexes in evaluating the aging effects of composite insulators.