## 3 Experimental Study
### Experimental Results and Discussion
#### 3.2.1 Prediction Performance Comparison of Different Neural Network Architectures  
The prediction results of the 1D-CNN-LSTM hybrid network were compared with its base versions of a 1D-CNN and LSTM network separately. Also, the proposed hybrid network was compared with the well-known traditional machine learning methods, such as k-NN [66], RF [33], and GBM [44]. Additionally, one of the earliest deep learning methods, namely, the group method of data handling (GMDH) [67; 68; 69], was used for comparison. Each experiment was repeated ten times to alleviate the impact of randomization, and the mean values were reported. The trained model was used to predict the RUL values for test engines. The performances of the proposed 1D-CNN-LSTM hybrid model and its base versions, namely, a 1D-CNN and LSTM network, for the same engine on the training set are depicted in Figure 16.  
Figure 16: Training results of a randomly selected engine: (**a**) 1D-CNN; (**b**) LSTM; (**c**) 1D-CNN-LSTM. From Figure 16, it can be observed that the prediction errors were minor when the engine was closer to failure because the system accumulated more degradation information as time passed. In addition, we deduce from Figure 16 that each neural network model successfully detected the change point of the engines because the breakpoints of the actual and predicted signals were very close to each other. The RUL prediction results using the test data for the eight-network architectures are displayed in Table 7 with and without the new difference feature. The best performances for RMSE and score function are presented in bold. The results shown are the average of the ten repeated experiments and their standard deviation. In the results, first, only the fused sensor values of the relevant network are included, and just below, the values of the newly added difference feature combined with the fused sensor values are included. The RUL prediction performances of the proposed 1D-CNN-LSTM hybrid network using the base variants 1D-CNN and LSTM network with the difference feature in terms of score function were 437.2, 498.9, and 1176.5, respectively. The average score of the 1D-CNN-LSTM model with the difference feature was 14% better than that of the 1D-CNN model with the difference feature added, and 169% better than that of the LSTM model with the difference feature added. Additionally, the standard deviation of the 1D-CNN-LSTM model was 126.4, that of the 1D-CNN model was 170, and that of the LSTM model was 1368.6. The standard deviation of the proposed 1D-CNN-LSTM model was the smallest among them, providing more robust prediction results. Also, the 1D-CNN increased the network's performance by providing helpful information to LSTM thanks to its robust feature extraction capability within the 1D-CNN-LSTM hybrid network for both cases. Compared with one of the pioneers of deep learning methods, namely, GMDH, the proposed hybrid 1D-CNN-LSTM network demonstrated superior performance, outperforming GMDH's score of 542.1, and it also excelled in terms of the RMSE. When comparing deep learning methods and traditional machine learning methods for solving the turbofan RUL prediction problem, it was observed that the performance of the 1D-CNN-LSTM hybrid network was notably strong in comparison with the LSTM network, which exhibited lower performance. The test data set of the FD001 input into the trained 1D-CNN-LSTM network and the positive and negative difference between the actual and the predicted RUL values in time steps for each engine are shown in Figure 17. Negative values indicate early predictions, while positive values indicate late predictions.