## 1 Introduction
The digital twin functioning is based on Industry 4.0 technologies, such as simulation, Internet of Things, artificial intelligence and machine learning, cloud computing and blockchain technology [15]. The digital models developed can replicate multiscale physical systems, from single components and devices to entire plants and even cities. Furthermore, digital twins can be leveraged in human-robot systems for a plethora of different applications [16]. By creating digital twins of their systems, the companies can gain several benefits, including data collection and analysis, constant monitoring of the system functioning, identification of trends and patterns, problem detection and optimization of maintenance activities, as well as process enhancement and minimization of human decision making [17]. An important application of industrial digital twins, indeed, is in the maintenance sector [18; 19; 20; 21; 22]. In particular, the application of the digital twin to preventive maintenance has received much interest in recent years. Predictive maintenance has been applied in various sectors, such as intelligent manufacturing, the power industry, construction industry, aerospace industry, and shipbuilding industry. The manufacturing sector is where the largest number of applications of the digital twins oriented to preventive maintenance can be found; in particular, the digital twins have been implemented in several areas, such as process equipment, automobile manufacturing, cyber-physical systems, product life cycle management and fault diagnosis [21]. In general, most of the applications of predictive maintenance based on digital twin technology are developed from a physics-based model representation type; a few works can still be found in the literature in which the digital twins were developed based on a hybrid-approach model representation type, integrating real data with the results obtained from numerical simulations [19]. Indeed, digital twins can be developed based on historical data measured by sensors, simulation results, or as an integration of both [23; 24; 25; 26; 27; 28]. The available data can be analyzed by means of non-deep learning methods, such as regression models, or deep-learning methods, such as deep neural networks. Among these latter, mass customization system and Social Internet of Things emerged as a valid application of interconnecting deep learning technology and digital twin technology to keep the system in good working condition [29]. With reference to industrial equipment, the simulations are often performed with Computational Fluid Dynamics (CFD) techniques, that allow the characterization of the system and its functioning in-depth under different operating conditions. The simulations can be performed to test what-if scenarios and alternative configurations without having to carry out experimental tests, thus minimizing the use and the waste of resources. In addition, the simulations allow monitoring of the values of the parameters of interest at each point of the device, resulting in a series of \"virtual sensors\" [30; 31]. This allows monitoring of the system functioning, even at locations where physical sensors could not be installed. An example of a simulation applied to milling operations is presented in [32] where a multiscale DEM-PBM approach was used to model the breakage behavior in a co-milling process. The use of discrete element modeling for the interactions and the collisions between the particles, combined with population balance modeling, utilized to describe the breakage events and the evolution of the particle size distribution, allowed the authors to gain insights into the mechanism of kernel breakage and thus optimize its performance. CFD simulation has been extensively applied to all kinds of industrial plants and devices in the last decades [33; 34], including food industry applications [35; 36; 37; 38; 39].