## 3 The Relay Experiment and Parameters Analysis
### Simulation Test Data and Evaluation Index  
The relay lifetime prediction is based on multi-dimensional GM, GNN model, FWA-GNN model, and the IFWA-GNN model. The corresponding performance parameters and the final lifetime of each relay are recorded at different temperatures. The GM, GNN, FWA-GNN, and IFWA-GNN models were trained with the data in Tables 2-4. The four models were tested with the data in Table 8.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**Y**} & **Algorithm** & **Optimal Value** & \begin{tabular}{c} **The Worst** \\ **Value** \\ \end{tabular} & \
\begin{tabular}{c} **Average Value** \\ \end{tabular} &
\begin{tabular}{c} **Average Running** \\ **Time of Program (s)** \\ \end{tabular} \\ \hline \multirow{2}{*}{Y\({}_{1}\)} & FWA & \(4.51\times 10^{-21}\) & \(2.88\times 10^{-6}\) & \(2.11\times 10^{-7}\) & \(1.14\) \\ \cline{2-6}  & IFWA & \(2.20\times 10^{-32}\) & \(8.59\times 10^{-25}\) & \(5.81\times 10^{-26}\) & \(0.86\) \\ \hline \multirow{2}{*}{Y\({}_{2}\)} & FWA & \(7.79\times 10^{-10}\) & \(1.51\times 10^{-5}\) & \(4.21\times 10^{-6}\) & \(0.98\) \\ \cline{2-6}  & IFWA & \(1.74\times 10^{-16}\) & \(1.69\times 10^{-13}\) & \(2.07\times 10^{-14}\) & \(0.77\) \\ \hline \multirow{2}{*}{Y\({}_{3}\)} & FWA & \(1.77\times 10^{-15}\) & \(5\times 10^{-2}\) & \(3.8\times 10^{-3}\) & \(1.01\) \\ \cline{2-6}  & IFWA & \(0\) & \(0\) & \(0\) & \(0.88\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Test results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**Lifetime**} & **Temperature** & \(\mathbf{t_{T}}\) **(ms)** & \(\mathbf{t_{D}}\) **(ms)** & \(\mathbf{V_{m}}\) **(V)** & \(\mathbf{V_{C}}\) **(V)** \\ \hline
612 & \(-20\) & \(0.54\) & \(0.63\) & \(0.67\) & \(0.90\) \\
693 & \(-20\) & \(0.71\) & \(0.20\) & \(0.91\) & \(0.88\) \\
752 & \(-20\) & \(0.43\) & \(0.69\) & \(1.12\) & \(0.88\) \\
788 & \(-20\) & \(0.92\) & \(0.69\) & \(1.61\) & \(0.88\) \\
900 & \(-20\) & \(1.89\) & \(0.69\) & \(2.58\) & \(0.91\) \\
689 & \(20\) & \(0.95\) & \(0.20\) & \(1.15\) & \(0.04\) \\
711 & \(20\) & \(0.71\) & \(0.48\) & \(1.19\) & \(0.13\) \\
755 & \(20\) & \(0.55\) & \(0.84\) & \(1.39\) & \(0.18\) \\
807 & \(20\) & \(1.01\) & \(0.88\) & \(1.89\) & \(0.40\) \\
834 & \(20\) & \(0.73\) & \(1.30\) & \(2.03\) & \(0.22\) \\
807 & \(55\) & \(0.50\) & \(0.25\) & \(0.75\) & \(1.02\) \\
827 & \(55\) & \(0.40\) & \(0.62\) & \(1.02\) & \(1.02\) \\
837 & \(55\) & \(0.34\) & \(0.86\) & \(1.20\) & \(0.96\) \\
913 & \(55\) & \(0.36\) & \(1.39\) & \(1.75\) & \(1.05\) \\
919 & \(55\) & \(0.59\) & \(1.29\) & \(1.88\) & \(1.00\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: The initial performance parameters of relay and its lifetime.  
The average deviation (\(AD\)) and root mean square error (\(RMSE\)) are used as the evaluation index of model prediction error. The decision coefficient (\(R2\)) is used as the evaluation index of model fitting effect.  
\[AD=(\sum_{j=1}^{m}\left|v_{j}-v_{j}^{*}\right|)/m \tag{23}\]  
\[RMSE=\sqrt{\left[\sum_{j=1}^{m}\left(v_{j}-v_{j}^{*}\right)^{2}\right]/m} \tag{24}\]  
\[R2=\frac{\left(m\sum vv^{*}-\sum v\sum v^{*}\right)^{2}}{\left(m\sum\left(v^{* }\right)^{2}-\sum\left(v^{*}\right)^{2}\right)\left(m\overline{\sum\left(v \right)^{2}-\sum\left(v\right)^{2}}\right)} \tag{25}\]  
where \(m\) is the number of samples; \(v\) is the actual value of the sample; and \(v^{*}\) is the prediction value of the sample. The range of decision coefficient \(R2\) is between 0 and 1. When the decision coefficient \(R2\) is closer to 1, the input and output of the model are better fitted.