# Battery Life Prediction for Ensuring Robust Operation of IoT Devices in Remote Metering
## 5 Experimental Results and Discussion
In Table 6, the C-SDFormer outperforms the other models on all performance metrics, generally, with RMSE being the best performer for all test sets. The average MAE of C-SDFormer is 4.021, showing that on average, the SOC estimates are closest to the actual values. The average RMSE is 5.186, indicating that large errors occur less frequently. The average SMAPE is 7.072, highlighting the model's reduced sensitivity to relative differences, which underscores its robustness. The average R\({}^{2}\) is 0.965, demonstrating the model's ability to accurately capture the patterns and variability in the data. Specifically, the average MAE and RMSE values demonstrate over 1% better performance compared to existing models, with the average RMSE showing a difference of approximately 1%, and the average R\({}^{2}\) value exhibiting a difference of over 0.02. In addition, C-SDFormer shows competitive results, with an MAE difference of only 0.003 compared to CNN-LSTM-DNN [16] for #2, and an R\({}^{2}\) difference of 0.02 compared to LSTM [14] for #1. These results highlight the effectiveness of the C-SDFormer model in enabling real-time SOC estimation and providing accurate and robust predictions without relying on discharge capacity as an input. The proposed battery life prediction method is particularly suitable for practical applications such as remote metering. It addresses critical considerations, including minimizing hardware costs and ensuring robust operation. The model demonstrates high prediction accuracy while processing data such as voltage, temperature, and communication count. This capability highlights its potential for deployment in real-world scenarios. Additional performance evaluations and extended analyses are provided in Table A1 in the appendix, offering further insights into the model's robustness and superiority. We recommend replacing the battery as soon as it reaches the primary point, ensuring a sufficient maintenance margin for life prediction stability. To validate this approach, we evaluated the SOC estimation error at the primary point. Figure 8 illustrates the SOC estimation error rates at the primary point for the C-SDFormer model compared to other methods. Our results show that the C-SDFormer model achieves the lowest error rates, with values of 0.27, 0.25, and 0.01, respectively. These findings demonstrate the superior \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Ablated**} & \multicolumn{4}{c}{**MAE (\%)**} & \multicolumn{4}{c}{**RMSE (\%)**} & \multicolumn{4}{c}{**SMAPE (\%)**} & \multicolumn{4}{c}{**R\({}^{2}\)**} \\ \cline{2-13}  & **\#1** & **\#2** & **\#3** & **Average** & **\#1** & **\#2** & **\#3** & **Average** & **\#1** & **\#2** & **\#3** & **Average** \\ \hline w/o CNN & 4.764 & 6.822 & 7.907 & 6.497 & 6.177 & 8.628 & 9.525 & 8.110 & 7.977 & 12.92 & 12.86 & 11.21 & 0.947 & 0.871 & 0.882 & 0.900 \\ Embedding & & & & & & & & & & & & & & & \\ \hline w/o CNN & 4.524 & **4.634** & 7.064 & 5.407 & 5.597 & 6.447 & 7.064 & 6.369 & 7.235 & **8.431** & 11.49 & 9.052 & 0.954 & 0.933 & 0.915 & 0.934 \\ Output & & & & & & & & & & & & & & & \\ \hline w/o Transformer & 5.273 & 6.816 & 5.644 & 5.911 & 6.178 & 8.338 & 6.777 & 7.097 & 10.33 & 10.89 & 9.117 & 10.11 & 0.928 & 0.854 & 0.928 & 0.903 \\ \hline w/o Series Decomposition & 4.641 & 4.966 & 4.500 & 4.702 & 6.236 & 6.652 & 5.973 & 6.287 & 6.714 & 9.790 & 6.323 & 7.609 & 0.949 & 0.944 & 0.958 & 0.950 \\ \hline C-SDFormer (Ours) & **3.408** & 5.123 & **3.534** & **4.021** & **4.602** & **6.391** & **4.567** & **5.186** & **5.070** & 11.60 & **4.547** & **7.072** & **0.972** & **0.950** & **0.974** & **0.965** \\ \hline \hline \end{tabular}  
**Note: Bold values indicate the best performance among the ablated layers.**  
\end{table} 
Table 5: Ablation study of C-SDFormer. predictive accuracy and robustness of the C-SDFormer model in estimating battery SOC.