# Research on Clustering-Based Fault Diagnosis during ROV Hovering Control
## 4 Performance Evaluation of FD  
### Water-Tank Test Results  
To validate the FD, experiments were conducted in an engineering water tank with dimensions of \(4.5\times 2.5\times 2.8\) m\({}^{3}\) (L \(\times\) W \(\times\) H). Data were collected at a 10 Hz sampling rate while changing the fault situations of vertical thruster TH4. Various fault situations were applied to the thruster, as shown in Figure 15. For both the normal and fault situations, the ROV was placed at the bottom of the tank (2.8 m), ascended to a target depth of 2 m, and maintained that target depth while keeping the roll and pitch angles at 0\({}^{\circ}\) through hovering control. Figure 16 presents the results of hovering under normal conditions, including the depth and attitude outcomes. Figure 16a shows the depth and attitude data during hovering, and Figure 16b shows the normal distribution of the depth data during hovering control from the bottom of the tank to the target depth of 2 m. Typically, in control theory, the settling time is defined as the duration within which a system's response remains within \(\pm 2\%\) or \(\pm 5\%\) of the reference value once it reaches the steady state. However, in cases of entanglement, inconsistent thrust due to the entangled thruster can lead to an imbalance in attitude. To resolve this imbalance, thrusters generate thrust to stabilize the attitude, causing the ROV to hover in a tilted position without reaching the target depth. Therefore, in this study, the \"hovering time\" is defined as the time for which the depth data remain within one standard deviation (\(\pm\sigma\)) from the target depth during hovering. As illustrated in Figure 15, fault data were collected by changing the fault situations based on the hovering gain values of a normally operating propeller. Figure 15: Tank experiment conditions: Alternating between normal and faulty situations of thruster TH4. Figure 17 presents the depth and attitude data for each fault situation of TH4, including one-blade breakage (a), two-blade breakage (b), rope (c), and net (d). Breakage situations, such as (a) and (b), resulted in delayed hovering times owing to the weaker thrust relative to a normal thruster, with two-blade damage reaching hovering time later than one-blade damage. In contrast to entangled thrusters, breakage thrusters, which have weaker self-thrust, do not cause a significant change in the attitude rate. In entanglement situations, such as (c) and (d), the thrust exceeds than breakage situations; thus, the hovering time is reached more quickly. However, inconsistent thrust due to debris entanglement causes an imbalance in attitude, and maintaining hovering control in a tilted position makes it difficult to reach a target depth of 2 m.  
Table 3 presents the average current consumption and RPM data during the hovering period after the target depth was reached. As shown, the current decreases and the RPM increases in breakage situations compared with normal conditions, whereas in entanglement situations, the current increases and the RPM decreases or remains similar. These results validate the selected fault features (consumption current and RPM of the thruster) based on the torque equation of the thruster. Figure 16: Depth and attitude results of hovering after reaching the target depth from the bottom of the engineering water tank under normal conditions: (**a**) Depth and attitude data acquired during hovering; (**b**) normal distribution of depth data during hovering; (**a**) hovering time: the time for which hovering around the target depth did not exceed \(\pm\sigma\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Conditions** & **Battery Voltage (V)** & **Current (A)** & **RPM** & **Control Input** \\ \hline Normal & 22.9 & 0.6648 & 1766 & 1630 \\ One-blade breakage & 22.58 & 0.5371 & 1809 & 1635 \\ Two-blades breakage & 22.70 & 0.4294 & 1954 & 1638 \\ Rope & 22.78 & 2.1645 & 1802 & 1658 \\ Net & 22.99 & 2.7734 & 1708 & 1666 \\ \hline \hline \end{tabular}
\end{table}