# Aero-Engine Remaining Useful Life Estimation Based on CAE-TCN Neural Networks
## 4 Results and Discussion
### Comparison  
The efficiency and accuracy of the proposed algorithm are compared with other commonly used models, one-dimensional CNN and vanilla LSTM. For the one-dimensional CNN, the same architecture as TCN is used. For vanilla LSTM, generally two to three layers can achieve better learning. Therefore, three layers of LSTM are used. For each layer, the number of neurons is equal to the maximum number of one-dimensional CNN kernel. In addition, the training strategies of the three models are exactly the same. The comparison results are as shown in Tables 5 and 6. As shown in Tables 5 and 6, the proposed algorithm shows great advantages in efficiency and accuracy. It has the shortest training duration and the lowest official score. Since the model structure is mainly based on one-dimensional CNN layer, the proposed algorithm has no obvious advantages over one-dimensional CNN in training duration. In contrast, LSTM needs to iterate on the time dimension, and cannot be implemented in parallel like convolution. Therefore, there is a significant gap between the training \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test score** & **FD001** & **FD002** & **FD003** & **FD004** \\ \hline
**Proposed network** & **3.72** & **26.57** & **7.36** & **56.75** \\ One-Dimensional CNN & 7.22 & 67.32 & 11.04 & 80.24 \\ LSTM & 5.27 & 50.81 & 9.84 & 73.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance comparisons of the score on the CMAPSS datasets. Figure 13: (a) Good result for FD001; (b) Poor result for FD001; (c) Average result for FD001. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **FD001** & **FD002** & **FD003** & **FD004** \\ \hline
**Proposed network** & **0.26 s** & **0.80 s** & **0.31 s** & **0.93 s** \\ One-Dimensional CNN & 0.28s & 1.06s & 0.34s & 1.24s \\ LSTM & 0.62s & 1.64s & 0.75s & 1.95s \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Efficiency comparison of training duration on the CMAPSS datasets. duration of the proposed model and the vanilla LSTM on FD001 to FD004. In other words, the algorithm proposed has a higher application efficiency. In terms of precision comparison, the official scores of the proposed algorithm on the four sub-datasets are smallest. This implies better predictive power. By comparing the results of four sub-datasets, it can be found that the algorithm achieved the best results in FD001 and the worst results in FD004. This is in line with expectations. The prediction effect is negatively correlated with the data complexity. Moreover, the algorithm proposed shows more significant advantages for FD002-FD004. The main reason is that the complexity of the four sub-datasets is different. Compared with FD001, the data from FD002-FD004 is more complex, more operation conditions or more fault modes. Hence, with the same parameters, the RUL prediction model needs to be able to learn the deeper information in the data. For the proposed algorithms, CAE was used to learn the degradation trend. This can reduce the dimension of the data. The key information of degradation was extracted, as well as the noise reduction. To learn the degradation trend and realize time series prediction, TCN was used. Compared with the traditional one-dimensional CNN, TCN is a one-way structure with time constraints. Therefore, TCN is more sensitive to changes in time dimension. LSTM memorizes time information through iteration in time. When the time is longer or the information to be learned is more complex, LSTM is prone to the problem of gradient vanishing. TCN can realize information learning of long time series through the size of dilation and kernels. Meanwhile, it adds skip connection to prevent gradient problems. Therefore, from the perspective of model structure, the proposed model has better learning ability in the face of complex time series information. In summary, as the data situation becomes more complex, the advantages of the proposed model become more obvious. In a word, the proposed algorithm has better robustness in the RUL prediction under complex conditions.