# Whitening CNN-Based Rotor System Fault Diagnosis Model Features
## 4 Validation of ND for Fault Diagnosis
### Case 1: Bearing Fault Diagnosis under Varied Load Conditions  
The CWRU bearing fault dataset [33] is a well-established machine fault classification benchmark. The vibration dataset includes samples of healthy and faulty bearings placed in the test rig in Figure 6. There are four different bearing health conditions in the dataset: healthy (H), ball fault (B), inner race fault (I) and outer race fault (O). Each fault type was machined with three different diameters: 0.1778 mm (*\({}_{L}\)), 0.3556 mm (*\({}_{M}\)) and 0.5334 mm (*\({}_{H}\)). Thus, the number of different health states in the dataset is 10. Each fault type was measured at three different motor loads: 0.746 kW (1 hp), 1.491 kW (2 hp) and 2.237 kW (3 hp). Each time series sample was measured with two accelerometers at the drive-end and the fan-end of the motor. The sampling frequency was 12 kHz. Earlier related studies have mostly trained the fault diagnosis models with the vibration data acquired with the drive-end sensor only [15; 18; 19]. However, often condition monitoring systems include multiple sensors. Therefore, this subsection also presents the fault diagnosis experiments employing both, the drive-end and the fan-end sensor data as model inputs. Figure 5: Time series sample consisting of two input signals divided to overlapping training samples. Table 4 shows the details related to the bearing fault dataset. The training samples were acquired by sampling overlapping time windows from the 10 time series samples corresponding to the health states. Each training sample is 2048 timesteps long. The shift between adjacent training samples is 32 timesteps. Test samples share the length with training samples, however, they do not overlap. The baseline models with BN and the modified models with ND were trained to recognise the health state of the bearing from the vibration data. Every model was trained on each motor load domain and then evaluated on the other motor load domains. These tests were repeated 10 times for each model and load domain. Furthermore, these experiments were conducted with data from both accelerometers and with data from the drive-end accelerometer only. Figure 7 presents the means and standard deviations of the model accuracies when only the data from the drive-end accelerometer was available. Figure 8 presents the results from repeated experiments with data from both accelerometers. Figure 7 shows that all models diagnose the bearing health states with over 80% accuracy on average from the drive-end accelerometer data. In the same experiments, the modified WDCNN and SRDCNN models achieve more than 5 percentage points (pp) better average classification accuracies than the corresponding baseline models. The accuracy of the modified [PERSON]'s model is 0.35 pp less than the corresponding baseline. Overall the modified models achieve similar or significantly better diagnosis accuracies than the corresponding baselines in these experiments. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Load** & **Split** & **H** & **B\({}_{L}\)** & **B\({}_{M}\)** & **B\({}_{H}\)** & **I\({}_{L}\)** & **I\({}_{M}\)** & **I\({}_{H}\)** & **O\({}_{L}\)** & **O\({}_{M}\)** & **O\({}_{H}\)** \\ \hline \multirow{2}{*}{1 hp} & Train & 1980 & 1980 & 1980 & 1980 & 1980 & 1980 & 1980 & 1980 & 1980 & 1980 & 1980 \\  & Test & 59 & 59 & 59 & 59 & 59 & 59 & 59 & 59 & 59 & 59 & 59 \\ \multirow{2}{*}{2 hp} & Train & 1980 & 1980 & 1980 & 1980 & 1980 & 1980 & 1980 & 1980 & 1980 & 1980 \\  & Test & 59 & 59 & 59 & 59 & 59 & 59 & 59 & 59 & 59 & 59 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Number of training and test samples per bearing health state and motor load. Figure 6: Bearing fault test rig [33]. Figure 8 shows that the average diagnosis accuracies of the models decreased after introducing data from both accelerometers to the task.