# 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]. 1. Quantitative model-based analysis often utilizes mathematical modeling techniques, such as Kalman filters for state estimation and regression analysis for parameter estimation. For instance, [PERSON] et al. employed a Gaussian particle filter to estimate the failure model and motion state of the thruster of an autonomous underwater vehicle (AUV) to diagnose faults [40], and [PERSON] applied an Adaptive Kalman filter for the parameter estimation of a thruster [41];
2. Qualitative model-based analysis typically employs causal models such as fault trees or uses abstraction layers for FD. [PERSON] et al. defined a fault tree based on predetermined fault types for diagnosing faults in underwater thrusters [42];
3. Quantitative data-based analyses generally employ statistical methods, such as principal component analysis (PCA) and neural networks (NNs). For example, Choo  
Figure 3: RPM and current by control input (PWM). (**a**) RPM of T200; (**b**) current of T200; (**c**) RPM of T60-30; (**d**) current of T60-30. et al. used PCA to diagnose faults, such as blade breakage and entanglement, in underwater thrusters [34], and [PERSON] et al. utilized a model-free pattern recognition neural network (PRNN) to detect and isolate external thruster faults in ROVs [12]. In the study by [PERSON] et al., an enhanced CNN was applied to detect defect patterns on the wafer surface by improving the traditional CNN and selectively restricting learning on important weights [43];
4. Qualitative data-based analyses use methods such as fuzzy logic, pattern recognition, and frequency analysis for FD. [PERSON] et al. applied possibilistic fuzzy C-means (PFCM) to classify the types and degrees of faults that can occur in the underwater thrusters of an AUV [44]. In this study, considering the performance degradation due to the long-term use of underwater thrusters, data on normal and faulty states were collected to diagnose faults. The RPM and current consumption of underwater thrusters were selected as fault features, and a qualitative data-based approach was used to analyze the relationship between faults and normal conditions. To classify the thruster faults during hovering, DBSCAN--a pattern recognition technique--was employed in this study. DBSCAN recognizes clusters based on a core point, including the minimum number of points (MinPts) within a radial epsilon (\(\mathcal{E}\)). \[N_{Eps}(p)=D\mid\text{dist}(p,q)\leq Eps \tag{4}\]  
Here, \(D\) represents the dataset, and \(\text{dist}(p,q)\) represents the distance between two points \(p\) and \(q\). If the distance between \(p\) and \(q\) is within the radius \(\mathcal{E}\), these points are considered neighbors. As illustrated in Figure 4, when drawing a circle of radius \(\mathcal{E}\) from a point, if there are at least MinPts within the circle, that point is recognized as the core point. Points within \(\mathcal{E}\) of a core point become border points, whereas those outside points are considered noise points. Through iterative processing, adjacent core points form clusters and points not belonging to a cluster are identified as noise. The process of DBSCAN is as follows:  
1. Set an arbitrary point \(p\) and count the number of points within the radius \(\mathcal{E}\) of the given cluster that includes \(p\);
2. If the number of points within this radius is at least MinPts, consider point \(p\) as a core point and group the points within the radius into a cluster;
3. If the number of points within the radius is less than MinPts, pass it;  
Figure 4: Diagram of DBSCAN. 4. Repeat steps 1 to 3 for all points.