## 3 Methodology
### Deep Neural Networks
#### 3.2.2 Recurrent Neural Network and LSTM
It is evident from Tables 2 and 3 and Figure 10 that the accuracy of the proposed scheme is higher than that of the MLP, SVM, CNN, and LSTM in adopted metrics defined in Section 3.5. Particularly, the RMSE values of MLP and SVM are 31.864 and 26.9618, respectively. The RMSE value of the proposed scheme is lower by 4.8072 and 1.5522 compared to the CNN and LSTM models, respectively. Moreover, the MAP values of the MLP and SVM are 24.1433% and 20.4548%, respectively. The MAP value of the proposed scheme is lower by 2.6775% and 0.878% compared to the CNN and LSTM models, respectively. The MAE values of MLP and SVM are 23.6265 and 17.7835, respectively. The MAE value of the proposed scheme is lower by 3.8365 and 0.8 compared to the CNN and LSTM models, respectively. In Figure 10, the average penalty scores for the MLP and SVM are much larger than those of the CNN, LSTM, and the proposed scheme as the automatic feature extraction ability of deep learning methods contributes to a higher prediction accuracy than in traditional data-driven methods. Furthermore, the proposed scheme is slightly better than the CNN and LSTM since the addition of the HI and the hybrid DNN structure extracts high-level spatial features and long-term temporal dependency features. In conclusion, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Metrics**} & \multicolumn{4}{c}{**FD003**} & \multicolumn{4}{c}{**FD004**} \\ \cline{2-9}  & **RMSE** & **MAPE** & **MAE** & **Score** & **RMSE** & **MAPE** & **MAE** & **Score** \\ \hline Model 1 & 31.519 & 19.618\% & 19.644 & \(2.73\times 10^{4}\) & 33.126 & 26.109\% & 23.872 & \(1.08\times 10^{6}\) \\ Model 2 & 26.646 & 16.461\% & 15.245 & \(1.55\times 10^{4}\) & 28.135 & 21.216\% & 18.644 & \(7.81\times 10^{5}\) \\ Model 3 & 21.362 & 16.038\% & 13.147 & \(9.65\times 10^{3}\) & 26.771 & 16.701\% & 13.419 & \(8.46\times 10^{3}\) \\ Model 4 & 17.786 & 13.162\% & 10.297 & \(5.81\times 10^{3}\) & 25.173 & 15.849\% & 12.526 & \(5.56\times 10^{3}\) \\ Proposed & 17.123 & 11.499\% & 8.961 & \(1.42\times 10^{3}\) & 23.256 & 15.211\% & 12.107 & \(4.63\times 10^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of performance on sub-dataset (FD003) and sub-dataset (FD004). Figure 10: Model evaluation. the proposed scheme is superior to other models in prediction accuracy and that is encouraging for RUL prognostics tasks. ## 6 Conclusions

An accurate and reliable RUL prognostic is conducive to equipment management and operation security. On account of the fact that sensor measurement data are highly non-linear and polluted by noise, it is a complex issue to be addressed. In this paper, we proposed a hybrid scheme based on an HI and hybrid DNN model to predict equipment RUL. Differing from preceding methods, hybrid DNNs take full advantage of CNN and LSTM. Specifically, CNN is utilized to extract high-level spatial features, and LSTM is used to learn long-term temporary dependencies. Additionally, the fully connected neural network is modeled to achieve a non-linear regression. Meanwhile, HI describes the equipment's health state, and the preprocessed sensor measurement data are fed into the hybrid DNN, which can further improve the RUL prognostics performance. The proposed scheme was trained on a dataset of equipment degradation from C-MAPSS. The RMSE, MAPE, MAE, and penalty score metrics were adopted to evaluate the models. The simulation results show that the proposed scheme can satisfactorily predict RUL, especially for the late phase close to failure. In contrast to MLP, SVR, CNN, and LSTM models, compared using the same dataset, the proposed scheme possesses higher accuracy and outperforms comparative models. In the field of industrial production lines, aerospace, military, lathe maintenance, computer hardware service, etc., the proposed scheme can contribute to guaranteeing the security of equipment and reduce maintenance costs. [PERSON] proposed the prognostics scheme and drafted the paper. [PERSON] collected the dataset and wrote the paper.