# A Sparse Autoencoder-Based Unsupervised Scheme for Pump Fault Detection and Isolation
## 4 Results and Discussion  
### Case One: Detection of a Misalignment Fault  
In order to demonstrate the effectiveness of the proposed approach, the traditional PCA method is also applied to process the data set. In this case, both models (PCA and SAE) for the pump anomaly detection were trained on the data acquired in a quarter of the year period from 10 March 2013 to 21 June 2013, where no abnormal events were recorded in the pump. The models were then used to assess the health condition after 22 June 2013. In this period, the pump worked under working conditions: speed around 90-105 rpm with suction pressure 10-12 bar, discharge pressure around 226-230 bar, and flow fluctuates between 850 to 1250 km\({}^{3}\)/d. The MD thresholds for PCA and SAE are calculated based on the training data. The results are presented in Figure 4, in which the blue points under the threshold are healthy data, and the red points above the threshold are viewed as anomaly data. The reference thresholds (\(d_{PCA}\) and \(d_{SAE}\)) for these two models were calculated based on Equation (7) with confidence level \(\alpha=0.01\)[30]. For the PCA model, the number of principal components is determined when the cumulative variance contribution \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ID** & **Variable Name** & **ID** & **Variable Name** & **ID** & **Variable Name** \\ \hline
1 & Speed & 2 & Suction pressure & 3 & Discharge pressure \\ \hline
4 & Discharge temperature & 5 & Actual flow & 6 & Radial vibration overall X1 \\ \hline
7 & Radial vibration overall Y1 & 8 & Radial bearing temperature 1 & 9 & Radial vibration overall X2 \\ \hline
10 & Radial vibration overall Y2 & 11 & Radial bearing temperature 2 & 12 & Thrust position axial probe1 \\ \hline
13 & Thrust position axial probe 2 & 14 & Active thrust bearing temperature 1 & 15 & Inactive thrust bearing temperature 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measurement variables in the pump monitoring system. rates exceed 95%. For the SAE model, the number of nodes in the hidden layer was set as 11. Later in this case study, the influence of parameter selection is evaluated by ROC and AUC. The anomaly detection results for the pump from 22 June 2013 to 6 July 2013 are shown in Figure 5. As can be seen, no anomalies were detected until 3 July for both SAE and PCA models, because no continuous anomalies were found during that period. It is in consistence with the fact that no failure was recorded in the historical maintenance log, and no obvious changes in original signals can be observed in bearing temperatures from 22 June to 3 July in Figure 6.  
Moreover, it can be observed in Figure 5 that the SAE model generated continuous alarm after 4:00 pm on 3 July, and the PCA model generated continuous alarm after 6:00 am on 4 July. The maintenance log recorded a maintenance action on 7 July of misalignment fault in the pump system with four bearing temperatures changed altogether. The SAE anomaly detection models detected the fault four days before the maintenance actions being carried out. Contrastingly, in Figure 6, there was no obvious increasement in the bearings' measurements from 3 July to 4 July. After 4 July, four bearing temperatures increased altogether (see Figure 6), and both the SAE and PCA models showed an obvious increase in MD values. The two-dimensional Q statistic contribution map of PCA from 22 July to 6 July is presented in Figure 7. A contribution map shows the contribution of each input variable to the anomaly that detected. By contrast, the contribution of each variable calculated by SAE from 22 July to 6 July is presented in Figure 8.  
Figure 4: Mahalanobis distance (MD) fault detection thresholds calculated during the training stage from 10 March 2013 to 21 June 2013. (**a**) MD threshold calculated by principal component analysis (PCA). (**b**) MD threshold calculated by sparse autoencoder (SAE). (Blue points: healthy data; red points: anomalies; magenta line: reference MD thresholds.).