## 4 Results
### Recurrent Neural Network: Long Short-Term Memory (DL)  
The results of the DL method of predictive maintenance are also presented by calculating the empirical probability from Equation (17).  
Again, it is checked which runs are best suited for training normal data. For a classification task, it may be useful to use the same number of data sequences for both classes for training. For this reason, the last ten runs before the failure of the differential are used as abnormal data for the training process. Regarding the data of the abnormal class, this means that the LSTM network is trained on local tooth damage or heavy wear. Figure 11 shows the results of the 1 st DUT of the LSTM network. The runs used to train the network will have a slight influence on the result. Considering the running-in behavior and the occurrence of initial signs of wear, runs 30-40 are again selected for training.  
Figure 10: Result series of the anomaly detection of the OSVM considering the features \(f_{2}\pm f_{2}\) and \(f_{2}\pm 2f_{2}\). All tests were taught on the model of the first DUT. First DUT (**a**), fourth DUT (**b**), seventh DUT (**c**), and ninth DUT (**d**).  
Figure 12 shows the result series of the LSTM network classification, in which a model was trained for each DUT and applied to its own test. The result of the first DUT is shown in Figure 12a. The empirical probability starts to increase from run 305 onwards, indicating a change in transmission. From there on, the torque sequences are no longer classified as normal. From run 450 on, the values are permanently in the range around 1. The method fulfills the classification task exactly as it was designed and recognizes the abnormal data sequences for the last runs. Early signs of wear are irrelevant to the LSTM network and are of little consequence. The results of the other tests are similarly good. In Figure 12b-d, the values rise continuously towards the end and reach an empirical probability of 1 shortly before the DUTs fails. The LSTM network does not provide any indications of abnormal components on the test bench, as the OSVM does. Another special feature is that the fourth test in Figure 12b was taught to recognize a combinatorial abnormality with damage to the gears and bearings. Here too, the LSTM network finds a good solution for the classification task of distinguishing the features in the measured values.  
Figure 13 shows the results when a model trained on the first DUT is applied to the other tests, which follows the approach of statistical PdM. Graphs (a) and (c) in Figures 12 and 13 show a high degree of correlation. The visible difference in (b) is because the model of the first DUT was trained on a missing tooth. When applied to the measure  
Figure 11: Result of the classification with the LSTM network on the first DUT for testing different runs for learning normal measurement data.  
Figure 12: Result series of the LSTM network. All tests were trained on their own model. First DUT (**a**), fourth DUT (**b**), seventh DUT (**c**), and ninth DUT (**d**).  
ment data from the fourth test, in which no tooth was missing, the empirical probability in Figure 13b does not reach a value of 1 at the end of the test. The result of the ninth test in Figure 13d differs greatly from the condition-based PdM approach in Figure 12d. Obviously, the data at the beginning are too different to use the model of the first DUT. The behavior of the graph only normalizes from run 165 onwards. This is where the abnormal bellows was replaced. After that, the values of the empirical probability slowly increase with an increased spread and reach values around 1 from run 300 on.