## 5 Discussion and Conclusions  
In this paper, we proposed a new PHM methodology for the implementation of fault detection and RUL prediction when there is no prior knowledge regarding the component behavior and only streaming data are available. First, we provided mathematical formulations of the two most promising algorithms for online anomaly detection and data partitioning, which are included in the EDA approach and based on RDE. Subsequently, the main aspects of degradation modelling and RUL prediction are highlighted. These three parts were all included in the proposed methodology, which can be applied from the first data sample that is read. Finally, the new method was applied to a rotating machine operating in a real industrial context. From this application, several considerations have emerged.  
The proposed methodology: (1) recognizes the occurrence of an anomaly in the streaming data collected from the monitored machinery; (2) detects the presence of different HS that are represented by different data clouds; (3) is computationally efficient and able to predict the RUL in real time; and (4) requires little data storage capacity. In addition, if a failure is already known, then it can be represented by an existing cloud, with local parameters being associated with the ADP algorithm, and incremental classification can be included in the methodology.  
Figure 14: Confusion matrix.  
Figure 13: Dynamic degradation modelling and RUL prediction triggered at defined AT.  
As demonstrated in this paper, the first applications of the proposed methodology show interesting results. However, there are some aspects that are related to each step that make its implementation in real industrial contexts challenging.  
Issues related to the online feature extraction can be summarized as:  
* The number \(k\) of data samples included in the time window form where features are extracted has to be known a priori. In addition, a fixed \(k\) might be unsuitable for non-stationary signals.
* The computation time for feature extraction has not to exceed the time available to collect the next \(k\) values.
* Even if time features are suitable for online applications, they may not distinguish different component conditions. Issues that are related to the online anomaly detection can be summarized as:
* Gradual changes are more difficult to recognize than abrupt change.
* The latency time of the algorithm depends on a parameter defined by the user (see Equation (20)). In particular, the switch from one condition to another should be recognized as soon as possible for reducing misclassification errors during data partitioning; at the same time, if the algorithm is too sensitive to an anomalous value, many false alarms will be generated. Issues that are related to the HI construction can be summarized as:
* The HI value used in this paper might be a good solution for avoiding the smoothing technique. However, the recursively computed mean value tends to increase/decrease too slowly, which makes it harder to identify the correct FT. Issue related to RUL prediction can be summarized as:
* Given the dynamic nature of the industrial environment and the possibility of different operating conditions of the component, it would be desirable to have a dynamic FT, computed based on the evolving data structure.
* Given these issues, further research will be dedicated to online feature extraction, anomaly detection algorithm, and the identification of proper HI and FT.  
Conceptualization, F.C. and A.R.; Supervision, A.R. and C.M.; Writing--original draft, L.B.; Writing--review & editing, F.G.G. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.