## 5 Prediction of the Remaining Service Life of the Aqueduct  
Based on the time-dependent reliability index of the aqueduct calculated using the proposed method, the fourth-moment method, and the MCS method described in the previous section, the remaining service life of the reinforced concrete aqueduct is accurately predicted. To predict the service life, the target reliability index of 2.7 from the unified standard for the reliability design of building structures (GB50068-2018) [49] is used.  
To predict the remaining service life of the reinforced concrete aqueduct, the fitting results for the lower deterioration case are obtained by fitting the data to the reliability indices of the aqueduct calculated with the proposed method, the fourth-moment method, and the MCS method, as shown in Figures 9-11.  
The functions of time-dependent reliability indices for the different methods are expressed as  
\[\beta_{\mathbf{p}}=4.71\times e^{(-t/20.84)}+1.83 \tag{20}\]  
\[\beta_{\mathbf{dM}}=3.06\times e^{(-t/38.69)}+1.40 \tag{21}\]  
\[\beta_{\mathbf{MCS}}=4.31\times e^{(-t/22.06)}+1.83 \tag{22}\]  
Here, \(\beta_{\mathbf{p}}\), \(\beta_{\mathbf{dM}}\), and \(\beta_{\mathbf{MCS}}\) are the reliability indices obtained from the proposed method, fourth-moment method, and MCS, respectively; t denotes time.  
Figure 8: Comparison of the different methods.  
Figure 7: Reliability index curve.  
The remaining service life of the aqueduct can be obtained by substituting the target reliability index specified in the standard [49] into the fitted expression, as shown in Table 9.  
Figure 11: Curve-fitting results for the MCS method.  
Figure 10: Curve-fitting results for the fourth-moment method.  
Figure 9: Curve-fitting results for the proposed method.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **Remaining Useful Life/a** & **Relative Error/\%/** \\ \hline Proposed method & 35.20 & 0.28 \\ Fourth-moment method & 18.88 & 46.52 \\ MCS & 35.30 & - \\ \hline \hline \end{tabular}
\end{table}
Table 9: Remaining useful life of the different methods.  
From the prediction results in Table 9, it can be seen that the fourth-moment method provides a more conservative prediction with lower estimated results. In comparison, the prediction results from the proposed method and the MCS method are much closer, with a relative error within 0.28%, whereas the relative error of the fourth-moment method is as high as 46.52%. Therefore, the proposed method can efficiently and accurately predict the remaining service life of the aqueduct.  
By using the proposed method, engineers can prioritize maintenance efforts based on the time-dependent reliability of different sections of the aqueduct, optimizing resource allocation and improving the overall efficiency of maintenance operations. The proposed method can be easily integrated into existing asset management systems, where it can be used to inform inspection schedules, identify vulnerable sections, and predict the remaining service life of key components.  
Several challenges may arise when applying this method. First, its accuracy depends on the quality and availability of data, such as environmental records and structural condition data. Limited or unreliable data can reduce the predictive capabilities. The method's complexity also requires specialized knowledge and software, which may hinder adoption by maintenance teams lacking expertise. Additionally, the method assumes stable environmental conditions and degradation mechanisms, but unexpected changes, such as humidity spikes or seismic events, may affect predictions and require frequent updates. Finally, the method does not consider the economic costs of maintenance, which is crucial for decision making in large-scale projects.