# A Sparse Autoencoder-Based Unsupervised Scheme for Pump Fault Detection and Isolation
## 4 Results and Discussion
### Case Two: Detection of a Misalignment Fault and Bearing Fault  
From 1 st September 2015 to 11 July 2016, the pump worked under another condition, with speed around 95-105 rpm, discharge pressure around 203-220 bar, and flow fluctuate around 1000-1400 km\({}^{3}\)/d. The training data were selected via setting thresholds for shaft speed, discharge pressure and flow, to make sure that the selected training data had the same working condition with monitoring data. Then, the trained models were applied to check the health condition after 12 July 2016. The MD thresholds calculated during the training stage by PCA and SAE anomaly detection models, respectively, are presented in Figure 10a,b. As shown in the figure, the blue points under the threshold are regarded as healthy data, and the red points are viewed as abnormal data. Same as in case one, during the training stage, the reference thresholds (\(d_{PCA}\) and \(d_{SAE}\)) were calculated via Equation (7), with a confidence level \(\alpha=0.01\)[30]. For the PCA model, the number of principal components is determined when the cumulative variance contribution rates exceed 95%. For the SAE model, the number of nodes in the hidden layer was set as 11. The fault detection results from 12 July 2016 to 23 August 2016 are shown in Figure 11, and, as a comparison, the measurements of bearings are shown in Figure 12. As can be seen in Figure 12, from the 12 July to 17 July, there was no obvious changes in original data, and, after 17 July, four bearings' temperature increased, resulting from a misalignment fault. In Figure 11a,b, both the PCA and SAE models indicated the pump worked healthily from the 12 July to 17 July. The PCA generated continuous alarms after 22:00 on 18 July. By contrast, the SAE discovered some anomalous and generated continuous alarms after 16:00 on 17 July. Figure 9: ROC curves and average AUC values: (**a**) ROC curves for the PCA model with a different number of principal components; (**b**) ROC curves for the SAE model with different number nodes in the hidden layer; (**c**) average AUC values of PCA and SAE models. Figure 11: Anomaly detection from 12 July 2016 to 23 August 2016. (**a**) Anomaly detection by PCA. (**b**) Anomaly detection by SAE. Figure 10: MD fault detection thresholds calculated during the training stage from 1 September 2015 to 11 July 2016 of the pump. (**a**) MD threshold calculated by PCA. (**b**) MD threshold calculated by SAE. (Blue points: healthy data; red points: anomalies; magenta line: reference MD thresholds.). Contribution maps for PCA and SAE models are presented in Figures 13 and 14, respectively. In Figure 13, the anomalies in the PCA model are mainly contributed by bearing 1 and 2, and the contribution map failed to indicate changes in thrust bearings' temperatures. In Figure 14, it shows that the anomalies in the SAE model were caused by the temperature changes in four bearings, which was inconsistent with the observations in Figure 12.  
From 20 July to 23 August 2016, it can be seen in Figure 11a,b that continuous anomalous points were detected with both PCA and SAE models. Both Figures 13 and 14 clearly show that it was bearing 2's vibration amplitude that mainly contributed to the fault. This consisted of the performance showed in Figure 12b that the bearing 2's vibration amplitude kept increasing in this period. To evaluate the performance of PCA and SAE for fault detection, the ROC curves and AUC values are calculated and shown in Figures 15 and 16. The models' performance, influenced by the number of PCA components and the number nodes in hidden layers of SAE, was explored. Figure 15 is the ROC curves and average AUC values for the detection of the misalignment, and Figure 16 is for the detection of the bearing fault. As can be seen in both figures, the SAE model had higher AUC value than the PCA model, especially when detecting the misalignment fault. Figure 12: Measurements of the pump from 12 July to 23 August 2016. (**a**) The increase in the pump bearings’ temperature due to misalignment.