# A Novel Deep Learning Approach for Machinery Prognostics Based on Time Windows
## 3 Experiment and Analysis
### Performance Analysis
#### 3.3.1 Performance of the Results  
The trained model was used to predict the RUL of different aeroengines in the testing set. The testing set FD001, FD002, FD003 and FD004 contain 100, 259, 100 and 248 sets of aircraft engine simulation data from the unknown state of \(t_{1}\) to the unknown state of \(t_{2}\) respectively, and each set of simulation data is truncated to obtain \(T\) consecutive cycles data of the aeroengine. The testing set also gives the actual RUL of aeroengines at \(t_{2}\) to verify the effectiveness of the algorithm. Then, the testing data of \(T\) consecutive time cycles is used to predict the RUL of the aeroengine in the unknown state of \(t_{2}\). Overall, the models achieved accurate results for the prediction of the RUL of aircraft engines in the testing set. Based on the two evaluation functions, Table 5 presents the performance of the trained models on the testing set. The model was trained ten times. Using RMSE as the evaluation function, the model performed best in the FD001 testing set, with a mean score of 12.18, while the model performed the worst in FD004 with a mean score of 22.12. It can be seen from Figure 6 that the prediction results of the FD001 and FD003 were better than those of the FD002 and FD004 due to the multiple simulation conditions of FD002 and FD004. At the same time, the prediction result of the algorithm for FD001 was better than that of FD003, because the failure mode of FD003 included high-pressure compressor degradation and fan degradation, while the failure mode of FD001 was only high-pressure compressor degradation. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Sub-Dataset** & **FD001** & **FD002** & **FD003** & **FD004** \\ \hline RMSE (mean) & 12.18 & 19.58 & 15.67 & 22.12 \\ RMSE (std) & 0.31 & 0.27 & 0.46 & 0.47 \\ RMSE (best) & 11.77 & 19.24 & 14.97 & 21.32 \\ RMSE (worst) & 12.67 & 20.29 & 16.16 & 22.74 \\ S (mean) & 224.16 & 2494.35 & 1279.85 & 4523.32 \\ S (std) & 23.08 & 264.54 & 245.31 & 809.26 \\ S (best) & 200.55 & 2118.57 & 865.06 & 3268.99 \\ S (worst) & 261.69 & 3012.73 & 1620.35 & 6163.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The performance of the model (std: standard deviation). Figure 7 shows the prediction results of the model. For FD001, the model used had seven layers and the size of the time window was selected as 30. For FD002, the model used had three layers and the size of the time window was selected as 20. For FD003, the model used had three layers and the size of the time window was chosen to be 30. For FD004, the model used had two layers and the size of the time window was selected as 15. Since the testing set gives the actual RUL of the aeroengines in the unknown state of \(t_{2}\), the RUL of aeroengines from \(t_{1}\) to \(t_{2}\) can be obtained from this value, e.g., the RUL at time \(t_{1}\) is the actual RUL at time \(t_{2}\) plus \(t_{2}-t_{1}\). The function to calculate the RUL from \(t_{2}\) to \(t_{1}\) can be expressed as  
\[actualRUL\ at\ t=(actualRUL\ at\ t2)+(\ t2-t), \tag{9}\]  
where \(t_{1}+N\leq t<t_{2}\). When the time window is selected as \(N\), the RUL of aircraft engines from \(t_{1}+N\) to \(t_{2}\) can be predicted. Figure 8 shows the predicted results from \(t_{1}+30\) to \(t_{2}\) of two randomly selected aeroengines in the FD001 testing set. The RUL prediction values for the No. 17 and No. 24 aeroengines at time \(t_{2}\) corresponding to the predicted results in Figure 7. In Figure 8, the yellow dashed box represents that the RUL of the aeroengine was a constant value of 125 at the initial stage of aeroengine operation. The predicted result of the No. 17 aeroengine was slightly lower than the actual value at the beginning, but the error was small. With the increasement of the time cycle, the result was more accurate. The predicted result of RUL of the No. 24 aeroengine had slight fluctuations at the initial stage.