## 4 Case Study
For the fault detection goal, the impulse factor of signal 2 (y axis of the first accelerometer) was selected, as it was independent of the implemented setting (Figure 8b). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Condition** & \begin{tabular}{c} **Distance** \\ **between** \\ **Pulleys (mm)** \\ \end{tabular} & \begin{tabular}{c} **Braking Torque** \\ **(Nm)** \\ \end{tabular} & \
\begin{tabular}{c} **Duration (min)** \\ \end{tabular} &
\begin{tabular}{c} **Rotation Speed** \\ **(rpm)** \\ \end{tabular} \\ \hline Setting 1 & 27.33 & 0.1 & 82.8 & 660 \\ Setting 2 & 27.33 & 0.5 & 184.2 & 660 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Operating conditions implemented during the collection of the Training Data. Figure 7: Features extracted from signal 1 in setting 1 (blue) and setting 2 (orange). Then, the novelty detection algorithm was trained on extracted features to initialize the parameters of known conditions. The novelty detection consists of two parts:  
1. The anomaly detection algorithm, which determines if a point is normal or anomalous according to the algorithm developed in [83]
2. The clustering algorithm, which is inspired by the clustering algorithm developed in [84]. It automatically assigns the current point [58]: 1. To the current cluster if the feature vector does not determine a change in the system's state (from normal to anomalous and vice versa). 2. To an existing cluster if the feature vector determines a change in the system's state and is considered similar to a known operating condition. 3. To a novel cluster if the feature vector determines a change in the system's state and is far from all existing clusters. The results of the novelty detection algorithm trained on the first set of features (for the OCR task) and the second feature (for the abrupt fault detection) are shown in Figures 9 and 10, respectively. As expected, for the OCR task, the algorithm creates two clusters. In Figure 9, the blue dots correspond to the first setting, while the orange dots to the second one. Note that anomalies, represented by red crosses, that do not determine a system's state change and are assigned to the current cluster can be considered measurement errors or anomalous peaks in the signal. For the fault detection task, only one cluster was created (it is represented by black dots in Figure 10). Hence, the extracted component-level features are not sensitive to the setting change and are thus appropriate for the FDA task. At this point, the extracted feature matrix containing labeled observations belonging to two different classes is stored. These data can be used to train classification models. Local parameters of the created clusters are also stored. They are used when the algorithm is executed in streaming to initialize the clusters that correspond to the known machinery settings. Figure 8: (**a**) Features selected for condition recognition; (**b**) Feature selected for fault detection. Finally, the algorithm is executed in streaming. During the experiment, four settings were implemented. Setting values are summarized in Table 3. In particular, the first two settings are the same as those in the previous training phase. At the end of the fourth experiment, a motor fault occurred. Table 4 shows results for the OCR task. Points belonging to settings 1 and 2 are correctly assigned to the initialized clusters. The algorithm detects the second setting change after 15 s and the third setting change after 10 s. However, the fourth setting is not detected (Figure 11). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & **Distance** & **Breaking** & **Duration (min)** & **Rotation Speed** (rpm) \\ \cline{2-5}  & **Pulleys (mm)** & **Torque (Nm)** & **Duration (min)** & **Rotation Speed** (rpm) \\ \hline Setting 1 & 27.33 & 0.1 & 82.8 & 660 \\ Setting 2 & 27.33 & 0.5 & 184.2 & 660 \\ Setting 3 & 27.54 & 0.1 & 77.4 & 660 \\ Setting 4 & 27.54 & 0.328 & 25.8 & 660 \\ \hline \hline \end{tabular}
\end{table}