# Multi-Head Self-Attention-Based Fully Convolutional Network for RUL Prediction of Turbofan Engines
## 5 Performance Comparison and Discussion  
### Comparison with Other Models  
In this section, MSA-FCN is compared with 11 existing deep neural networks for the RUL prediction of turbofan engines, including DSCN [30], MS-DCNN [26], LTSM-Attention [27], AGCNN [28], LSTM-INIFR [25], MCLSTM [29], Bi-level LSTM Scheme [24], LSTM Model [37], SMDN [38], BiGRU-TSAM [39], and IDMFFN [40]. The experimental results are summarized in Table 7 where N/A represents results that are not reported in the corresponding paper; underlined values indicate sub-optimal results; and bold values represent the optimal results. It should be noted that the experimental results of MSA-FCN in Section 4.5 are presented in this section with two decimal places kept for comparison with the other networks. Overall, MSA-FCN performs best on all performance metrics for both the FD002 and FD004 datasets. Specifically, compared with the sub-optimal results, MSA-FCN achieves a reduction of 3.10% and 6.45% in RMSE and Score, respectively, on the FD002 dataset. On the FD004 dataset, it attains a decrease of 5.04% and 28.11% in RMSE and Score, respectively. We additionally calculated the sum (sum) and average (average) of RMSE and Score across all networks. Compared with the sub-optimal outcomes, MSA-FCN reduces both the sum and average of RMSE by 4.14% and lowers the sum and average of Score by 23.61%. These results indicate that, compared with the other 11 approaches, MSA-FCN can achieve more accurate and timely RUL prediction, demonstrating superior overall prediction performance. Table 8 demonstrates a comparison of the robustness of MSA-FCN and the other models in RUL prediction. As shown in the table, MSA-FCN achieved the best results in all Score STDs, and it obtained the second-best results in all RMSE STDs. Overall, compared with the other models, MSA-FCN exhibits superior stability and robustness in multiple experimental tests, both in terms of prediction accuracy and timeliness. Table 9 compares the computational cost of training among MSA-FCN and the other models. As shown in the table, MSA-FCN does not achieve the minimum training time per epoch. Therefore, compared with other models, MSA-FCN does not have a significant advantage in terms of computational cost for RUL prediction, which will be a focus of improvement in future research work. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Approach**} & \multicolumn{2}{c}{**FD002**} & \multicolumn{2}{c}{**FD004**} & \multicolumn{2}{c}{**Sum**} & \multicolumn{2}{c}{**Average**} \\ \cline{2-9}  & **RMSE** & **Score** & **RMSE** & **Score** & **RMSE** & **Score** & **RMSE** & **Score** \\ \hline DSCN [30] & 20.47 & 4367.56 & 22.64 & 5168.45 & 43.11 & 9536.01 & 21.56 & 4768.01 \\ MS-DCNN [26] & 19.35 & 3747.00 & 22.22 & 4844.00 & 41.57 & 8591.00 & 20.79 & 4295.50 \\ LSTM-Attention [27] & N/A & N/A & 27.08 & 5649.14 & N/A & N/A & N/A & N/A \\ AGCNN [28] & 19.43 & 1492.00 & 21.50 & 3392.00 & 40.93 & 4884.00 & 20.47 & 2442.00 \\ LSTM-INIFR [25] & 17.72 & 1647.93 & 20.43 & 3038.84 & 38.15 & 4686.77 & 19.08 & 2343.39 \\ MCLSTM [29] & N/A & N/A & 23.81 & 4826.00 & N/A & N/A & N/A & N/A \\ Bi-level LSTM [24] & 23.14 & 3771.00 & 23.38 & 3492.00 & 46.52 & 7263.00 & 23.26 & 3631.50 \\ LSTM Model [37] & 26.48 & 4060.00 & 27.91 & 8600.00 & 54.39 & 12,660.00 & 27.20 & 6330.00 \\ SMDN [38] & N/A & N/A & 23.40 & 4302.00 & N/A & N/A & N/A & N/A \\ BiGRU-TSAM [39] & 18.94 & 2264.13 & 20.47 & 3610.34 & 39.41 & 5874.47 & 19.71 & 2937.24 \\ IDMFFN [40] & 19.17 & 1819.42 & 21.72 & 3338.34 & 40.89 & 5158.47 & 20.45 & 2579.13 \\ MSA-FCN (ours) & **17.17** & **1395.75** & **19.40** & **2184.66** & **36.57** & **3580.41** & **18.29** & **1790.21** \\ \hline _Reduction_ & 3.10\% & 6.45\% & 5.04\% & 28.11\% & 4.14\% & 23.61\% & 4.14\% & 23.61\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance comparison of MSA-FCN with other deep neural networks.