## 3 Application for Failure-Recall Data with DCLNN Method
### Results of LSTM and DCLNN  
It is easy to see that no straightforward rules can be found directly from the failure time curve in Figure 10. The LSTM is used directly to train and predict the data in Figure 10. During the training process, the prediction goal is the failure time of the last day. Among them, about 90% of the time series data are used to train the LSTM NN, and the last 10% of the data are used to test the model and predict the failure time. The specific architecture and hyperparameters of CLNN can be found in Figure 12. Tensorflow was used to build the above neural networks. A related repository was stored in the link (the same name with paper) on github. Figure 11: Comparison of comprehensive selection indicator (CSI) before and after DTW pre-processing. Figure 12: Specific architecture and hyper-parameters. Taking into account the time cost and prediction accuracy of network training, the recommended training epochs is around 200. Before data training and testing using a neural network, data normalization using Equation (18) is necessary. \[xn(i)=\frac{x(i)-x_{\min}}{x_{\max}-x_{\min}} \tag{18}\]  
Then, the original failure time series of six escalators are first trained by the CLNN. The training process and prediction result are shown in Figure 13. Training loss and testing loss are also given in Figure 14.  
Figure 13: Training process and prediction result using CLNN directly. Black lines are the true value of the failure time curve, green lines indicate the training process, and the red point shows the prediction result. All escalators except the third one have poor predictions that can be seen from Figure 13 directly. The results are consistent with the result of CSI. The reason for the poor prediction of other escalators are: 1) The length of the data sequence is short, and the number of data used for CLNN model training and testing are also small; 2) the trend of the third escalator is stable with no obvious disturbance, while there are more or less disturbances in the time series data of the other five escalators. In addition, those disturbances make a big difference on modeling accuracy of the CLNN. Then, DTW is used to warp other failure time curves with the data of the third escalator as a reference. Using new data for training and prediction of the DCLNN, the results are shown in Figure 15. Training loss and testing loss are also given in Figure 10.0  
The prediction accuracy after pre-processing is significantly improved compared to the direct use of the original data. Here, the root-mean-square error (RMSE) is chosen to assess the prediction accuracy of escalators. The RMSE can measure the difference between two time series. The mathematical formula is:  
Figure 10.1  
Figure 10.2 Loss of 6 escalators using CLNN for training and prediction. (**a**) Escalator #1. (**b**) Escalator #2. (**c**) Escalator #3. (**d**) Escalator #4. (**e**) Escalator #5. (**f**) Escalator #6. The comparison results are summarized in Tables 3 and 4. Table 3 shows the RMSE of the training process between the original data and warping data. Table 4 shows the RMSE of the prediction process between the original data and warping data. Although the RMSE in the training process changes a little, the RMSE has been reduced a lot in the prediction process. After pre-processing by DTW, the accuracy of the DCLNN is improved. Figure 10.3 Training process and prediction using DCLNN. With DCLNN, the RMSE of the escalator can be reduced by an average of 83.96%. From Figure 15, the accuracy of the prediction result can be reduced from a few hundred days to less than one month, in order to compare the accuracy of the proposed DCLNN model for failure time prediction of escalators. For a better explanation about the effectiveness of the DCLNN, the other three classical time series prediction methods (Kalman Filter, Nonlinear Auto Regressive Neural Network, Elman RNN, LSTM) are applied for data analysis of the third escalator.