# A Research on Fault Diagnosis of a USV Thruster Based on PCA and Entropy
## 5 Analysis of the Fault Diagnosis Algorithm
### Fault Diagnosis through Visualization  
Figure 9 shows the visualized results obtained after reducing the dimensionality of the data acquired under normal conditions to 3D through PCA. Each blue dot indicates existing data expressed in the reduced principal component dimension. The axes represent each principal component and contain many features of the data in the order of the principal components. The data expressed in the text indicate that the fault feature vectors had significant influence on each principal component axis. In this study, considering the characteristics of the data and the changes in them under the fault condition analyzed in Section 3, the types of vectors with significant influences on each principal component were adjusted such that they became the fault features. Through this adjustment, it was possible to perform visual classification by examining the symptoms of the faults using the types of fault feature vectors with significant influence on the principal components. In the data preprocessing process, scaling parameters were adjusted to highlight the feature factors to enable visual classification, and the scaling parameter values applicable to all conditions were derived through trial and error. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Case 1**} & \multicolumn{2}{c}{**Case 2**} \\ \cline{2-5}  & **Range** & **Average** & **Range** & **Average** \\ \hline Normal & 0.8649–0.9301 & 0.9035 & 0.8484–0.8991 & 0.8837 \\ \hline
1 cm breakage & 1.6153–1.3526 & 1.3355 & 1.3078–1.3385 & 1.3263 \\ \hline
2 cm breakage & 1.4818–1.5010 & 1.4908 & 1.4822–1.5334 & 1.5204 \\ \hline
3 cm breakage & 1.3711–1.4173 & 1.3861 & 1.3349–1.3752 & 1.3542 \\ \hline Thin rope & 1.4682–1.5381 & 1.5028 & 1.2010–1.3204 & 1.2718 \\ \hline Thick rope & 1.8853–2.0438 & 1.9488 & 2.0706–2.0794 & 2.0758 \\ \hline Net & 1.7219–2.0934 & 1.9448 & 1.6069–1.6595 & 1.6379 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ranges of values and mean values of entropy for the planes of vibration and current for each condition. From the normal condition in Figure 9, it can be observed that the RPM vector had the most significant influence on the first principal component axis, and the consumed current and input voltage had a significant influence on the next principal component axes. The effect of input voltage had little correlation with the fault conditions; thus, the intention of the visualization was to enable clear visual distinction of the normal condition. For the rest of the results, the types of vectors with significant influence on each principal component axis were visually expressed, and the types of fault feature vectors with significant influence on each principal component axis are summarized in Table 4.  
Upon detection, a fault was classified according to whether the change in data was significant or not under the fault condition based on the entropy value. The entropy value was larger than 1.6 under the thick-rope and net conditions, fault conditions under which the vibration and current data changed significantly, as shown in Figure 10.  
Considering relatively significantly changes in the data, the visualization shows features appearing on the first and second principal component axes. In addition, as shown in Table 2, in the case of the thick rope, owing to greater sensitivity to vibration than to the current, it can be observed that vibration had a more significant influence on the first principal component axis. In the case of the net, owing to greater sensitivity to the consumed current than to vibration, the current had a more significant influence on the first principal component axis. The results in Figure 11 represent cases where changes in data were relatively small. With reference to Table 4, these results show that, similar to the normal condition, the effects of RPM and current on the principal component axes were significant. Further, unlike the results for the normal condition, the effect on the principal component owing to the increase in vibration was evident.