## 5 Conclusions  
In this paper, a novel framework based on an edge-cloud infrastructure and novel functional and logical architectures for a semi-supervised and partially online PHM applications to industrial equipment is introduced. It aims to address the requirements collected from machine producers through several interviews. The motivations behind the paper are the great interest in PHM systems shown by companies that produce machines for several industrial sectors, such as packaging and pharmaceutical industries. Major industrial requirements are related to the difficulties in data collection. To address these issues, an edge-cloud-based framework is introduced. The idea is to compute streaming analysis at the edge node installed on users' machines. Then, data extracted from edge nodes are sent to the cloud through proper policies, and the cloud is accessible only by the machine producer. Here, he or she can gather data of better quality, increasing data availability and reducing their quantity. Indeed, raw signals are processed at the edge, and only relevant information (features) are transmitted to the cloud. In addition, the two layers of the infrastructure allow differentiating the information shown to the client and the producer so that confidential data can be protected. Given the framework, novel functional and logical architectures are also introduced. Contrary to existing PHM frameworks in other sectors, the proposed functional architecture includes the Operating Condition Recognition (OCR) function, which uses a novelty detection algorithm to discover new settings as new data are available. In addition, the proposed architecture also includes the feature extraction at two levels: system-levelfeatures, which feed the OCR function, and component-level features, which feed the Fault Diagnosis Assessment (FDA) function and the Prognostic Assessment (PA) function, where models trained on the available data in the cloud are used to make inference on streaming data. Finally, anomaly detection algorithms are also applied to component-level features to detect abrupt faults and determine the RUL prediction trigger point. A case study shows the potential of the proposed functional framework. The study focuses on the OCR function and abrupt fault detection. Vibration signals are collected from an experimental platform under two operating conditions. During the training phase, system-level features and component-level features are extracted and selected. Then, the system-level features are used as input of the novelty detection algorithm (OCR function) to obtain local parameters of the clusters corresponding to the known operating conditions while component-level features are used for the fault diagnosis and detection (FDA function). Finally, the methodology is implemented for streaming data, collected under four different operating conditions, two known and two unknown. At the end of the experiment, an abrupt fault also occurred. Results show the proposed architecture recognized the setting change in three out of four cases with a maximum latency of 15 s. In addition, it detected two anomalous behaviors 1380 s and 90 s before the occurrence of the failure. Finally, as only features are sent to the cloud when the machinery behavior is known, the space needed for keeping these data in memory was reduced by 68.5%. Despite the advantages of OCR and abrupt fault detection, there are some limitations of the proposed methodology. The first limitation is related to the system-level feature extraction. For the case study, the data were collected under stable conditions. This means that components such as gearboxes were not subject to any degradation during data collection. However, when a gearbox degrades, the vibration level increases. Hence, the values of the extracted features in a specific operating condition may be different depending on whether degradation occurs.