# Whitening CNN-Based Rotor System Fault Diagnosis Model Features
## 4 Validation of ND for Fault Diagnosis
### Case 2: Azimuth Thruster Fault Detection  
Three azimuth thrusters of a similar configuration of the same drill ship were monitored frequently from mid-2018 to the end of 2019. An azimuth thruster is a rotor system which ships may use for movement or for preserving position. The three thrusters were operated in diverse environments at various rotating speeds and thrusting angles. Figure 9 shows the rotating speed distribution of the vibration samples in the dataset. Each vibration sample in the dataset is a time series sample including four revolutions sampled at 1024 distinct encoder positions totalling 4096 sampling points. Therefore, the time dimension differs between the vibration samples measured at different rotating speeds. The vibration samples were acquired with accelerometers in similar positions near the input shafts (IS) of the thrusters. During the monitoring period, the thrusters were healthy in the beginning but suffered malfunctions in matching components. The faults were related to the bearing near the gear end of the pinion shaft (B) and the gear pinion and the gear wheel (G). Figure 10 shows the thruster assembly, the fault locations and the sensor position. All faults occurred in all three thrusters during the period of observations. The faults in the dataset were recognised by condition monitoring specialists. Some samples with abnormal data were filtered from the dataset with a quality control function. Appendix C describes the quality control function in detail. The resulting dataset is described in Table 5, where the components were either labelled as healthy or faulty. The severity of the faults in a single thruster changes between the samples, due to the long observation period. That is, vibration samples were collected over a long period of time before and after the malfunctions were first noticed. Figure 9: Thruster rotating speed varied between the acquired vibration samples in the range between 100 RPM and 750 RPM. The lowest row in Table 5 shows the number of samples drawn and augmented to training, validation and test datasets. The relatively high number of training, validation and test samples is due to data augmentation with time window division. Each time window was 2048 time steps long. The time windows were overlapped during training data and validation data augmentation, but not overlapped during test data augmentation. The same number of samples were drawn randomly 10 times for each trial consisting of training and evaluation of all models. Furthermore, each set holds an equal number of healthy and faulty samples. The baseline models with BN and the modified models with ND were optimised to recognise faulty behaviour in a specific component. Therefore, the models were subjected to binary classification tasks. All models were trained and then evaluated 10 times for  
Figure 10: The azimuth thruster vibration was measured with an accelerometer sensor near the input shaft. The positions of the sensor and the faulty components are pointed with red lines. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Thruster** & **Condition** & **B** & **G** \\ \hline \multirow{2}{*}{1} & Healthy & 263 & 283 \\  & Faulty & 468 & 448 \\ \hline \multirow{2}{*}{2} & Healthy & 108 & 200 \\  & Faulty & 843 & 751 \\ \hline \multirow{2}{*}{3} & Healthy & 125 & 216 \\  & Faulty & 405 & 314 \\ \hline \multirow{2}{*}{Total} & Healthy & 496 & 699 \\  & Faulty & 1716 & 1513 \\ \hline \multirow{2}{*}{Data splits} & Train & 48,230 & 77,740 \\  & Val & 11,960 & 19,110 \\ \cline{1-1}  & Test & 368 & 592 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Azimuth thruster dataset statistics. each task with the hyperparameters listed in Appendix B. Figure 11 shows the average test classification accuracies of the models in the fault diagnosis tasks. All models achieved similar diagnosis accuracies between 84% and 91% in both tasks. Overall, the modified models with ND performed slightly better.