# Multi-Head Self-Attention-Based Fully Convolutional Network for RUL Prediction of Turbofan Engines
## 5 Performance Comparison and Discussion
### Ablation Experiments for MHFCN and DMSAM  
This section explores the critical roles of MHFCN and DMSAM in the prediction performance of MSA-FCN through four sets of ablation experiments conducted on the FD002 and FD004 datasets. The neural networks involved in the experiments include MSA-FCN, a neural network without DMSAM_Data (W/O DMSAM_1), a neural network without DMSAM_Features (W/O DMSAM_2), a neural network without the entire DMSAM (W/O DMSAM), and a neural network without MHFCN (W/O MHFCN). All experimental results are detailed in Table 10.  
It can be observed that MSA-FCN significantly outperforms the other four variant neural networks in terms of the average RMSE and Score across all tested datasets. This result confirms that MHFCN and DMSAM (including DMSAM_Data and DMSAM_Features) can capture and emphasize key parts within the sensor data and degradation representations with spatial characteristics, thereby improving RUL prediction performance of MSA-FCN.  
Notably, W/O DMSAM exhibits the highest average values for both RMSE and Score. This phenomenon reveals that the lack of effective enhancement of key degradation information can severely compromise accuracy of RUL predictions. Similarly, it is worth noting that W/O MHFCN also shows a decline in performance compared with MSA-FCN in terms of RMSE and Score. This result suggests that neglecting the spatial characteristics hidden within the monitoring data may lead to an insufficient understanding of the equipment degradation mechanism, further affecting accuracy of RUL predictions.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Variant Model**} & \multicolumn{2}{c}{**RMSE (FD002)**} & \multicolumn{2}{c}{**Score (FD002)**} & \multicolumn{2}{c}{**RMSE (FD004)**} & \multicolumn{2}{c}{**Score (FD004)**} \\ \cline{2-7}  & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** \\ \hline MSA-FCN & **17.165** & 0.213 & **1395.750** & **93.024** & **19.401** & 0.349 & **2184.660** & **158.393** \\ W/O DMSAM\_1 & 17.483 & 0.311 & 1452.621 & 198.692 & 19.502 & 0.596 & 2547.300 & 471.452 \\ W/O DMSAM\_2 & 17.306 & **0.182** & 1494.138 & 183.418 & 20.431 & 0.562 & 3915.280 & 1501.760 \\ W/O DMSAM & 19.835 & 0.622 & 2748.581 & 539.045 & 21.632 & 0.595 & 6034.830 & 1434.710 \\ W/O MHFCN & 18.130 & 0.468 & 1412.704 & 203.923 & 20.241 & **0.336** & 3041.480 & 853.468 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Impact of MHFCN and DMSAM on the prediction performance of MSA-FCN.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Approach**} & \multicolumn{2}{c}{**FD002**} & \multicolumn{2}{c}{**FD004**} \\  & **STD (RMSE)** & **STD (Score)** & **STD (RMSE)** & **STD (Score)** \\ \hline LSTM-INIFR [25] & 0.75 & 203.06 & 0.91 & 649.57 \\ MS-DCNN [26] & **0.08** & 228 & **0.14** & 365 \\ IDMFFN [40] & 0.26 & 289.59 & 0.73 & 492.9 \\ MSA-FCN (ours) & 0.21 & **93.02** & 0.35 & **158.39** \\ \hline \hline \end{tabular}
\end{table}
Table 8: Robustness comparison of MSA-FCN with the other deep neural networks.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Approach**} & \multicolumn{2}{c}{**FD002**} & \multicolumn{2}{c}{**FD004**} \\  & **Training (Seconds/Epoch)** & **Training (Seconds/Epoch)** \\ \hline MS-DCNN [26] & **0.73** & **1.64** \\ AGCNN [28] & 5.40 & 5.79 \\ MSA-FCN (ours) & 4.19 & 4.55 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Computational cost comparison of MSA-FCN with the other deep neural networks.  
Additionally, W/O DMSAM_1 and W/O DMSAM_2 demonstrate moderate performance across all tested datasets. This may be due to their ability to capture and enhance only partial key information, thus preventing further optimization of RUL prediction performance.