# A Hybrid Degradation Modeling and Prognostic Method for the Multi-Modal System
## 3 Experiment and Discussion
### Experimental Simulation
#### 3.3.3 Discussion of Results  
The detailed description of the proposed method is given in the Section 2. Here, the processed data features are input into the framework. Then, the long-term cumulative degradation prediction and the latest stage degradation prediction are performed separately and the results are fused. After that, the model performance is evaluated and analyzed according to the evaluation metrics. Since each sub-dataset has larger feature dimensions, considering that there may be a linear correlation between multi-dimensional features, the principal component analysis is used to reconstruct the data to reduce unnecessary calculations. Based that, FD001 retains 27 dimensional features, FD002 retains 14 dimensional features, FD003 retains 23 dimensional features and FD004 retains 14 dimensional features. Then, the multi-objective plan is used to establish health indicators based on monotonicity, threshold similarity and trend similarity. Figure 7 illustrates the comparison of a health indicator and three representative reconstructed features of random samples from different sub-datasets. The points show the data and the solid line is the smoothing data based on moving average smooth method to show the trend of the data more clearly. The experimental results show that the proposed health indicator is more monotonic and better model fitting. Figure 6: Mode labeled from three operational settings based on k-means clustering algorithm, where the data are from the first sample of FD002. Then, the gated recurrent unit model is used to predict remaining useful life for long-term cumulative degradation. Long short term memory network (LSTM) and stacked autoencoders (SAEs) are used to compare predictions. The results are shown in Figure 8, which indicates the proposed CDDHI-GRU mode has a lower RMSE and score values than other algorithms. In addition, it was found that the values of evaluation metrics of FD002 and FD004 are higher than those of FD001 and FD003, indicating that the samples working in multi-modal switching are more challenging for obtaining accurate prediction results than those working in single mode. Figure 8: The values of RMSE and scores of stacked autoencoders (SAEs), long short term memory network (LSTM) and GRU from four sub datasets are on the chart. The differences are plotted in the figure. Figure 7: The comparison of health indicator and three representative reconstructed features of four samples from each sub dataset. **(a)** The comparison of the health indicator and three representative reconstructed features of the sample number 7 in subset FD001. **(b)** The same comparison with the sample number 29 in subset FD002. **(c)** The same comparison with the sample number 96 in subset FD003. **(d)** The same comparison with the sample number 64 in subset FD004. The trend of data is shown more clearly by smoothing data. On the other hand, the time window is used to extract energy and statistical features. It is worth noting that during decomposing the data of the time window based on ensemble empirical mode decomposition, the number of IMF components \(N_{inf}\) is different for different local data. The reason is that the local data of the sample have various fluctuations, and there is noise in the data, so \(N_{inf}\) is added as an energy feature. The size of latest stage sequence \(L\) is a key parameter affecting the performance of model. For the sample with periodic mode switching, a multiple of the period is selected as the time window length. For samples with irregular mode switching, the time window length is selected by traversing. In order to avoid late prediction as much as possible, we use the scores to choose the length of time window. Figure 9 shows the effects of \(L\) on prediction accuracy, and the sizes of the time windows for the sub-datasets are 30, 55, 40 and 45 respectively. The reason is that a larger time window can cover more information to get better results, but extending the window length too much could adversely affect near-term forecasts.