# Research on Clustering-Based Fault Diagnosis during ROV Hovering Control
## 2 Faults and Methods
### [PERSON] et al. divided FD into model and data-based analyses and incorporated both quantitative and qualitative analyses [15]. Quantitative analysis involves mathematical formulas between the system's inputs and outputs, whereas qualitative analysis examines the relationships between different unit elements [16].
If a new point \"\(p\)\" becomes a core point and belongs to the existing cluster (with \(p\) as the core point), the two clusters are considered connected and are merged into one cluster;
5. After completing the clustering process for all points, any point that does not belong to any cluster is considered a noise point. Additionally, points that belong to a cluster but are not core points are called border points. Through iterative processing, adjacent core points form clusters and points not belonging to a cluster are identified as noise. In this study, the focus is on the fault diagnosis of underwater thrusters in ROVs; noise may occur owing to sensor measurement errors and environmental disturbances such as waves and wind in the marine environment, reducing the accuracy of FD. DBSCAN has the advantage of increasing the clustering accuracy because it clusters data while excluding noise. In this study, DBSCAN was applied for FD through the correlation of selected fault features, RPM, and consumption current based on the density in a two-dimensional (2D) Euclidean space. MinPts represents the minimum number of points required within a radius \(\mathcal{E}\) from a point to be considered a core point. With a small MinPts, noise may be included in the clustering process, and data may be misclassified. With large MinPts, parts of the data may be misidentified as noise, and data belonging to the same category may be separated into different clusters. According to [PERSON] et al., a common practice for DBSCAN is to set MinPts to twice the number of dimensions of the dataset [45]. \(\mathcal{E}\) represents the effective radius from the core point. With an excessive \(\mathcal{E}\), distinct datasets may be merged into the same cluster, whereas a small \(\mathcal{E}\) may hinder cluster formation, necessitating the selection of an appropriate. To determine the \(\mathcal{E}\), the elbow method with a sorted k-distance was applied. Arrange This method involves repeatedly calculating the distances between the data points, including the previously selected MinPts, and then sorting them in descending order. Figure 5 is an illustration representing the elbow method with a sorted k-distance. The x-axis represents the sorted points, and the y-axis represents the k-distance. The optimal epsilon is determined as the y-value at the intersection near the elbow point where the dataset calculation ends. Figure 6 shows the anticipated data distribution in situations of breakage and entanglement, as inferred from Equation (3). As the situation approaches breakage, a decrease in the current and an increase in the RPM compared with normal conditions are expected. As the  
Figure 5: Illustration of elbow method with a sorted k-distance. situation approaches entanglement, an increase in the current and a decrease in the RPM are anticipated. As shown in Figure 6, the data distribution for each type of fault will spread diagonally from the normal state, and as the severity of the fault increases, the clusters will form further away from the normal state. Therefore, when applying DBSCAN, the larger the region dominated by the breakage series, the greater the extent of the breakage can be estimated. In the case of entanglement, the impact on the thruster can be inferred. In other words, it is possible to infer which fault has a more dominant influence on the current state of the thruster. It was determined that DBSCAN, which has advantages in nonlinear clustering, can classify faults according to the expected characteristics of the data, even in cases where there is no linear relationship.