## 7 Conclusions  
To address the challenges in predicting the RUL for turbofan engines under multi-operational conditions, characterized by difficulties and low accuracy, this paper proposed an Adam-optimized SAM-TCN neural network for engine RUL prediction. After experimental verification, the following conclusions have been obtained:  
1. The Adam-SAM-TCN method introduces an SAM module on top of the TCN neural network for prediction modeling. This neural network structure enables the model to focus on local patterns during training while effectively capturing global patterns in data.
2. The method utilizes the Adam to optimize the prediction model, which adaptively adjusts the learning rate based on historical gradient information. The algorithm swiftly and accurately minimizes the loss function, thereby effectively enhancing the training effectiveness and generalization capability of the neural network.
3. By conducting training and testing on four datasets, experimental results show that the RMSE values for this paper came out to 11.50, 16.45, 11.62, and 15.47 respectively.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **FD001** & **FD002** & **FD003** & **FD004** & **Year** \\ \hline LSTM [34] & 14.18 & 25.25 & 12.79 & 27.63 & 2021 \\ CNN-BGRU-SA [35] & 13.88 & 17.25 & 14.85 & 19.39 & 2022 \\ TaFCN [36] & 13.99 & 17.06 & 12.01 & 19.79 & 2022 \\ Multi-attention-TCN [37] & 13.25 & 19.57 & 13.43 & 21.69 & 2022 \\ RCNN-Abi-LSTM [38] & 12.98 & 19.16 & 13.24 & 22.29 & 2023 \\ GATA-TCN [39] & 12.80 & 17.61 & 13.16 & 21.04 & 2024 \\ Adam-SAM-TCN & 11.50 & 16.45 & 11.62 & 15.47 & 2024 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of RMSE values of other RUL prediction methods on the C-MAPSS dataset.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **FD001** & **FD002** & **FD003** & **FD004** & **Year** \\ \hline CNN-BGRU-SA [35] & 248 & 1140 & 295 & 1840 & 2022 \\ TaFCN [36] & 336 & 1946 & 251 & 3671 & 2022 \\ Multi-attention-TCN [37] & 235 & 1655 & **239** & 2415 & 2022 \\ RCNN-Abi-LSTM [38] & 258 & 2980 & 246 & 3795 & 2023 \\ GATA-TCN [39] & 234.31 & 1361.23 & 290.63 & 2303.42 & 2024 \\ Adam-SAM-TCN & 225.32 & 1136.27 & 259.79 & 1365.40 & 2024 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of Score values of other RUL prediction methods on the C-MAPSS dataset.  
Compared to existing prediction models, the evaluation metrics of the proposed method were consistently lower, demonstrating the effectiveness of the Adam-SAM-TCN prediction model proposed in this study.  
Conceptualization, H.W. and Y.L.; methodology, D.L.; software, D.L.; validation, D.L.; formal analysis, G.Z.; investigation, D.L., Y.L. and G.Z.; resources, H.W.; data curation, D.L.; writing--original draft preparation, D.L.; writing--review and editing, D.L.; visualization, G.Z. and R.L.; supervision, H.W.; project administration, Y.L. and R.L.; funding acquisition, H.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Funding Number: 61863016).  
Not applicable.  
The datasets used in this study are openly available in the NASA repository, and they are called Turbofan Engine Degradation Simulation Dataset and PHM08 Challenge Dataset: ([[https://www.nasa.gov/intelligent-systems-division](https://www.nasa.gov/intelligent-systems-division)]([https://www.nasa.gov/intelligent-systems-division](https://www.nasa.gov/intelligent-systems-division)), accessed on 16 February 2023).  
The authors declare no conflicts of interest.