# Transfer Learning with Deep Recurrent Neural Networks for Remaining Useful Life Estimation
## 3 Experiments and Results  
To verify the performance of our BLSTM-based transfer learning algorithm for RUL estimation, we conducted a series of experiments on the C-MAPSS Datasets. We evaluated the performance of transfer learning over every dataset and studied how different working conditions and the numbers of samples for each pair of source and target datasets affect the performance of the resulting prediction models. We designed four groups of without-transfer learning experiments (E1, E4, E7, E10) and eight groups of transfer learning experiments (E2, E3, E5, E6, E8, E9, E11, E12) involving 4 groups of target datasets (FD001, FD002, FD003, FD004) as shown in Table 2. For each group of target datasets, we randomly selected 10, 20,..., 90, 100 trajectories to generate 10 datasets from which 10 evaluation datasets are generated. This will allow us to evaluate how the number of samples in the target dataset affects the performance of transfer learning. For each transfer experiment, we compared the performance of standard BLSTM models over the target dataset without transfer learning against the performance of the BLSTM models with transfer learning. We repeated each such experiment three times to deal with the randomness of the algorithms. In total, we have conducted 10 \(\times\) 3 \(\times\) (8 + 4) = 360 experiments, where 10 is the number evaluation datasets, each with different numbers of train trajectories; 3 is the number of repeats for each experiment; 8 is the number of transfer experiment pairs; 4 is the number of experiments without transfer. For all experiments, the performances of the experiment were evaluated by score function and RMSE. Note that the experiment group of E2 and E3 have the same target data but different source data, and compare with the experiment group of E1. The same is true for E5 and E6 groups who compare with E4 group, E8 and E9 groups who compare with E7 group, and E11 and E12 groups who compare with E10 group. \begin{table}
\begin{tabular}{c c c c} \hline
**Label** & **Transfer (From To)** & **Operating Conditions** & **Fault Conditions** \\ \hline E1 & FD001 no transfer & 1 & 1 \\ \hline E2 & FD003\(\rightarrow\)FD001 & 1\(\rightarrow\)1 & 2\(\rightarrow\)1 \\ E3 & FD002\(\rightarrow\)FD001 & 6\(\rightarrow\)1 & 1\(\rightarrow\)1 \\ E4 & FD002 no transfer & 6 & 1 \\ E5 & FD004\(\rightarrow\)FD002 & 6\(\rightarrow\)6 & 2\(\rightarrow\)1 \\ E6 & FD001\(\rightarrow\)FD002 & 1\(\rightarrow\)6 & 1\(\rightarrow\)1 \\ E7 & FD003 no transfer & 1 & 2 \\ E8 & FD001\(\rightarrow\)FD003 & 1\(\rightarrow\)1 & 1\(\rightarrow\)2 \\ E9 & FD004\(\rightarrow\)FD003 & 6\(\rightarrow\)1 & 2\(\rightarrow\)2 \\ E10 & FD004 no transfer & 6 & 2 \\ E11 & FD002\(\rightarrow\)FD004 & 6\(\rightarrow\)6 & 1\(\rightarrow\)2 \\ E12 & FD003\(\rightarrow\)FD004 & 1\(\rightarrow\)6 & 2\(\rightarrow\)2 \\ \hline \end{tabular}
\end{table} 
Table 2: Experiments. Figure 5: Piece-wise linear RUL target function. Table 3 shows the results of all experiments in terms of the mean values of the performance scores and RMSE. IMP is the improvement of the models with transfer learning over those without transfer learning. It is defined as \(IMP=(1-(WithTransfer)/(NoTransfer))\times 100\). From the IMP values, we can easily observe that transfer learning made great improvement except for groups E3 and E9, which will be explained in Section 4 (E3 and E9 are multiple operating conditions to 1 condition). For example, when the number of trajectories used is less than or equal to 60, transfer learning has improved the performance scores from 16.41% to 85.12% for group E2. Similar improvements are also observed for groups E5, E6, E8, E11, and E12. In particular, we found transfer learning is more effective in general on models trained with small data sets. For example, it improves the model score by 43.19% for group E5 when only 10 trajectories are used to create the training sets, while the improvement is only 8.29% when 60 trajectories are used as training sets for the same E5 group.