# Online Learning Based Underwater Robotic Thruster Fault Detection
## 6 Experimental Results and Analysis
### Sea trial Data Simulation and Analysis  
Firstly, the proposed online learning-based fault detection method was tested using data collected from a sea trial of a human occupied vehicle (HOV). The HOV was named 'SHEN HAI YONG SHI', as shown in Figure 7, specifications of the HOV and its thruster studied in the sea trial are described in Table 1.  
Figure 7: The HOV ‘SHEN HAI YONG SHI’.  
Thruster control variable and propeller speed during sea trial of the HOV is shown in Figure 8, in which the model residual over a certain period of time in the process of fault detection was obtained, as shown in Figure 9. As there were several interfering factors in the sea trial, the model residual fluctuated violently. In order to reduce the number of online model updates and computational burden, the model residual threshold was set to \(|e_{t}|\leq 80\). The range of the modeling data was set as \(w_{\min}=50\), \(w_{\max}=500\). After 500 groups of collection, the thruster fault detection started.  
As can be seen in Figure 9, the model residual exceeded the threshold by a large margin in the 847 th and 868 th sampling periods. However, false alarms were avoided by using the adaptive fault detection strategy based on online model update mechanism. Similarly, the detected model residual exceeded the threshold in the 1357 th sample. Comparably, the residual was below the threshold after online model update in the 1358 th sample. Successive residuals of the model updated in the 1358 th sample keep below the threshold for a longer period of time, which could verify the superiority of the proposed method.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Specifications** & **Value** \\ \hline
1 & Main dimensions of the HOV & 9.3 \(\ast\) 3 \(\ast\) 4 m \\
2 & Weight of the HOV & 20 t \\
3 & Thruster control variable type & Voltage \\
4 & Thruster control variable range & \(-\)5 V\(\rightarrow\)5 V \\
5 & Maximum propeller speed & 700 r/min \\
6 & Propeller speed sensor & Integrated Hall sensor \\
7 & Feedback signal of propeller speed sensor & Voltage pulse \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specifications of the HOV.  
Figure 8: Thruster control variable and propeller speed during sea trial of the HOV.  
It was found that, in the process of fault detection using sea trial data of the HOV, although the model residual fluctuated violently due to various factors, there was no false detection alarm when using the proposed online learning-based method.  
Model residuals of the fixed model-based fault detection method during sea trial of the HOV is shown in Figure 10. As mentioned before, in the fixed-model based method, when a set of runtime work status data is collected, a control variable-speed model will be created in the same way as the proposed online modeling method. After that, the model will be used for propeller speed prediction in the whole fault detection process. If the speed prediction residual of the fixed model exceeds the predefined threshold, a thruster fault was determined to have occurred. For comparison, the predefined threshold and range of the modeling data is the same as that uses in the proposed online learning model-based method.  
Figure 10: Model residuals of the fixed model-based fault detection method during sea trial of the HOV.  
Figure 9: Model residuals of the online learning-based fault detection method during sea trial of the HOV.  
As can be seen in Figure 10, residuals of the fixed model are similar to the online learning-based model after the fixed model has just been established, this is mainly because that the two models are built with the same method and the same data. After the 850 th sampling period, due to the change of thruster work status and environmental factors, residuals of the fixed model become large and exceeds the threshold multiple times, resulting in a series of misdiagnosis.