# Research on Lifespan Prediction of Cross-Linked Polyethylene Material for XLPE Cables
## 3 Lifespan Prediction Method
### Analysis of Relative Parameters for Lifespan Prediction  
According to the test results obtained in Section 2, some corresponding parameters which can be used for predicting the lifespan of XLPE cables were studied, as listed in Table 6.  
\begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Parameters** & **Test Methods** \\ \hline
1 & \(C_{gr}\) & Gel content of samples \\
2 & \(X_{C}\) & Crystallinity of samples \\
3 & \(\sigma\) & Tensile strength of samples \\
4 & \(\delta\) & Breaking elongation of samples \\
5 & \(A\) & The hardness of samples \\
6 & \(\varepsilon\) & The dielectric permittivity of samples \\
7 & \(I_{tun}\) & The dielectric loss of samples \\
8 & \(E_{b}\) & The average breakdown strength of samples \\ \hline \end{tabular}
\end{table}
Table 6: Lifespan prediction parameters of samples.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Samples** & **Thickness \(d\)/mm** & \begin{tabular}{c} **Breakdown** \\ **Voltage \(U_{b}\)/kV** \\ \end{tabular} & \
\begin{tabular}{c} **Breakdown Strength** \\ \(E_{b}\)/(kV/mm)** \\ \end{tabular} &
\begin{tabular}{c} **Standard** \\ **Deviation \(a_{E}\)** \\ \end{tabular} \\ \hline A\({}_{1}\) & 0.801 & 5.72 & 7.14 & 0.286 \\ A\({}_{2}\) & 0.806 & 5.72 & 7.10 & 0.291 \\ A\({}_{3}\) & 0.807 & 5.75 & 7.13 & 0.250 \\ A\({}_{4}\) & 0.808 & 5.69 &  
To obtain parameters significantly correlated with the operating time among the lifespan prediction parameters in Table 6, the Pearson correlation analysis method, 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 [17].  
\[r=\frac{\sum\limits_{i=1}^{n}{{{{\left({{{x_{i}}-\overline{x}}\right)}\left({{t_{ i}}-\overline{t}}\right)}}}}}{\sqrt{\sum\limits_{i=1}^{n}{{{{\left({{x_{i}}- \overline{x}}\right)}^{2}}}}}\sqrt{\sum\limits_{i=1}^{n}{{{{\left({{t_{i}}- \overline{t}}\right)}^{2}}}}}}} \tag{6}\]  
where \(x_{i}\) is the lifespan prediction parameters of \(i\)th sample; \(t_{i}\) is the operating time of the \(i\)th sample; \(\overline{x}\) is the mean value of lifespan prediction parameters; \(\overline{t}\) is the mean value of operating time.  
_A T_-test was employed to verify the significance of the correlation coefficient \(r\) of samples and the results of the \(T\)-test were denoted as \(\alpha\). The calculation is expressed in Equation (7).  
\[T=\frac{r\sqrt{n-2}}{\sqrt{1-r^{2}}}\sim t(n-2) \tag{7}\]  
In Equation (7), if the significance value \(\alpha\) is less than 0.05, it indicates that there is a certain correlation between two variables; if \(\alpha\) is larger than 0.01, it indicates that there is a significant correlation between two variables. The test results are listed in Table 7.  
Table 7 shows that parameters including the gel content \(C_{ge}\), the crystallinity \(X_{C}\), tensile strength \(\sigma\), ultimate elongation \(\delta\), the dielectric permittivity \(\varepsilon\) and the dielectric loss \(I_{lam}\) are significantly correlated with the operating time, which can be used to evaluate the aging degree of XLPE cables and propose a lifespan prediction method to determine the operating time of XLPE cables. Moreover, parameters, including the hardness \(A\) and the average breakdown strength \(E_{b}\), are correlated with operating time. On this basis, these parameters can be used as auxiliary indices in evaluating the aging effects on XLPE cables.