## 4 Case Study
### Discussion  
In the previous section, we proposed a case study to validate two main parts of the proposed framework. In particular, we used streaming novelty detection and anomaly detection algorithms to perform the OCR and FDA functions. This section summarizes the major outcomes, which are evaluated concerning the stakeholders' requirements (Section 3.1). First, the recognition of the implemented setting would not ideally require data for training. By using an incremental and unsupervised novelty detection algorithm, it is possible to start from scratch. Indeed, the first cluster is initialized when the first observation is available. Thus, the algorithm recursively evaluates if the current point is \"similar\" to the previous point or points belonging to other clusters and assigns it accordingly. Otherwise, a new cluster is created, which will include all the similar observations. Note that the algorithm can initialize more novel clusters. Assuming that each cluster corresponds to a setting, the algorithm corresponds to automatic observation labeling. In the described case study, we initialized two clusters (Cluster 1 and cluster 2), as we were supposed to know the trend of the features in two operating conditions. By extending the streaming analysis to the other two unknown operating conditions, we demonstrate that each observation belonging to a known setting is correctly assigned to the corresponding cluster, a new cluster is created when the third operating condition occurs, and all observations are then correctly assigned to this new cluster. The setting change is detected in 10-15 s. Hence, only 10 or 15 observations will have the wrong label. The second outcome of the presented case study consists of abrupt and unknown fault detection through an anomaly detection algorithm. As no other fault classes were available, no diagnostic model was trained for the real-time inference. However, the anomaly detection algorithm recognizes an anomalous behavior 95 s before the actual fault. Although 95 s are not enough in real industrial applications, an alarm would allow the operator to double-check the machine and eventually stop it. Besides, if the fault would not \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Task** & \begin{tabular}{c} **Total Raw** \\ **Signals (Gb)** \\ \end{tabular} & \begin{tabular}{c} **Raw Signals** \\ **Stored (Gb)** \\ \end{tabular} & \
\begin{tabular}{c} **Feature Matrix** \\ **Stored (Gb)** \\ \end{tabular} &
\begin{tabular}{c} **Total Storage** \\ **Space (Gb)** \\ \end{tabular} \\ \hline Setting 1 & 4.04 & - & 0.34 & 0.34 \\ Setting 2 & 9.63 & - & 0.56 & 0.56 \\ Setting 3 & 3.80 & 3.80 & 0.23 & 4.03 \\ Setting 4 & 0.72 & 0.72 & 0.08 & 0.8 \\ Total & 18.19 & 4.52 & 1.21 & 5.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Memory savings (Gb). Figure 12: Novelty detection for the abrupt fault detection. cause the machine arrest, but just quality issues, then the anomaly would be an alarm for the machine operator, who can intervene for proper tunings. From the producer's point of view, the observations labeled as anomalous make it possible to build a diagnostic model that can recognize the start of a warning Health Stage (Cluster 2) before motor failure [17]. Finally, novelty detection and anomaly detection are not sensitive to point anomalies. An important aspect in PHM industrial applications is represented by false alarms [85]. The integration of anomaly detection and clustering makes it possible to generate an alarm only when the current observation is assigned to a distinct cluster of the previous point instead of when an anomaly is detected. In the OCR function, anomalies are detected more than 12 times (Figure 11). However, only two anomalies correspond to an actual setting change. Indeed, the number of times in which a cluster is created is exactly two. In addition to the performance of the implemented algorithms, there are other aspects to highlight.