## 2 PHM: Reference Methodologies, Frameworks, and Architectures  
In this section, existing methodologies, frameworks, and architectures for PHM systems design are briefly reviewed. From the methodology point of view, in [8] a complete process for the PHM architecture definition is proposed. According to the authors, the first step is the definition of the stakeholders' expectations and requirements, which represents the input of the process, together with constraints. The second step is the framework definition, which is a layered structure of the system built according to the requirements. It includes the functions, performance, operational conditions, and project constraints that will influence the architecture. Finally, three architectures need to be built: the functional architecture, which is defined as the set of functions and sub-functions that have to be performed to achieve the desired system objective; the logical architecture, which is defined as the set of related technical concepts and principles that represent the logical operation of the system; the physical architecture, which is defined as the set of physical elements, such as equipment made of hardware, software, and/or human roles, that can perform the system functions. Regarding the framework definition, technologies such as Cyber-Physical Systems (CPS), IIoT, edge computing, and cloud computing are receiving more and more attention for PHM systems in industries [18]. Indeed, machine producers could take advantage of these technologies for collecting the data they need, when they need them, from the machines they want [19]. In literature, there are several examples of PHM frameworks based on these technologies. The basic idea is to exploit edge computing to perform the PHM tasks that have to provide real-time feedback while leaving in the cloud the data storage and batch analysis for more complex and accurate results. In [20,21], a cloud architecture for PHM is described. It consists of at least two clouds: the first one is the service provider and includes several PHM units; the second cloud offers expert service. In this way, the provider offers shared software for PHM, and the client can create its maintenance applications and methods with the tools provided by the provider; finally, storage and networking resources are available for implementing the maintenance solutions. In [22], a framework for Edge Computing-based fault diagnosis of rotating machinery is proposed, where edge computing is preferred to global or offline approaches performed in a centralized cloud server because of the following reasons: first, it reduces the storage and computing resources in the cloud, since it realizes the data computing on the edge node; second, it avoids unnecessary data transmission, resulting in low latency fault diagnosis; third, it also allows the simultaneous dynamic control of the machinery. In [23], a framework including both edge and cloud computing for equipment failure prediction is proposed. According to this framework, a machine learning prediction model is built based on historical data in the cloud, which has theoretically unlimited resources; then, the model is applied to new incoming data streams at the edge, which has fewer computation resources, to identify possible failures with increased responsiveness. A similar approach was adopted in [24], where a multi-sensor edge computing architecture was proposed for wind turbine generators. To the best of our knowledge, no edge-cloud PHM framework has been designed for facilitating the data exchange and analysis between a machine producer and a machine user. In this context, the edge-cloud-based framework should allow reducing the amount of data to transmit and store; also, it should allow hiding sensitive information to the producer (which corresponds to the maintenance provider). Indeed, machinery working conditions can be strategic for the production process, and thus, clients are not willing to share this kind of information with other companies.