# 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
In breakage conditions (a), (b) and (c), the influence of RPM on the first principal component was significant, and the effects of vibration and current were apparent on the second and third principal component axes. In the (d) condition, which \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **1 st PC Axis** & **2 nd PC Axis** & **3 rd PC Axis** \\ \hline Normal & RPM & Current & Input voltage \\ \hline
1 cm breakage & RPM & Current & Vibration \\ \hline
2 cm breakage & RPM & Vibration & Current \\ \hline
3 cm breakage & RPM & Current & Vibration \\ \hline Thin rope & Current & RPM & Vibration \\ \hline Thick rope & Vibration & Current & Input voltage/RPM \\ \hline Net & Current & Vibration & Input voltage/RPM \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Types of vectors with significant influence on each principal component under different conditions. Figure 9: Visualized 3D PCA result of the normal condition. was the thin-rope entanglement, the influence of current was observed on the first principal component axis owing to the influence of the consumed current. Figure 11: Visualized 3D PCA results for cases with small changes in data under fault conditions. (**a**) One-centimeter breakage condition; (**b**) Two-centimeter breakage condition; (**c**) Three-centimeter breakage condition; (**d**) Thin-rope entanglement condition. Figure 10: Visualized 3D PCA results for fault conditions associated significant data changes. (**a**) Thick-rope entanglement condition; (**b**) Net entanglement condition. For these conditions, by examining the vibration and current planes, the faults could be diagnosed by classifying each condition. The planes of each condition are illustrated in Figure 12.  
Figure 12 shows the 1 cm breakage (a), 2 cm breakage (b), 3 cm breakage (c) and thin-rope entanglement (d) conditions, respectively, and shows the data distributions for the planes of vibration and current. In the breakage conditions (a), (b) and (c), it can be observed that the data distributions formed a circular shape, which is the first characteristic of breakage conditions. Furthermore, it can be observed that the circular shape disappeared with the increasing severity of breakage. In the entanglement condition, it can be observed that the distribution exhibited an angular shape in the form of a rectangle. Under the breakage condition, the data showed more sensitive changes for vibration than for the consumed current, which, upon analysis, was found to be because vibration tended to oscillate around an equilibrium point either periodically or randomly, thus forming a circular shape in the data distribution. In addition, the current data were examined under the breakage condition in Table 2, and it was found that the consumed current decreased with increasing length of breakage. This was found to be because the consumed current decreased owing to a decrease in the diameter and area pushing away  
Figure 12: Visualized 2D PCA results for cases with small changes in data under fault conditions (vibration and current planes). (**a**) One-centimeter breakage condition; (**b**) Two-centimeter breakage condition; (**c**) Three-centimeter breakage condition; (**d**) Thin-rope entanglement condition. the water; because this characteristic was very pronounced, with the increasing severity of breakage, the influence of current increased, leading to loss of the circular distribution of data. In the case of thin-rope entanglement, the consumed current data revealed a sensitive change, as a result of which the data distribution was angular in shape. Therefore, for the cases with relatively small changes in data under the fault conditions, the shapes in the planes of the vibration and current could be examined, and if the distribution was circular, the fault could be classified as breakage, and as thin-rope entanglement if it was rectangular.