## 2 Materials and Methods
### The Rolling Mill Architecture and Main Customer Needs  
The rolling mill performs either hot or cold material processing, exploiting different architectures [33; 34]. In the hot rolling of steel, the billet is heated approximately up to 900 \({}^{\circ}\)C, and then it passes through the rolls of the rolling path. This action allows reducing its thickness in every step of rolling, namely \"pass\", with a given surface finish of the rolled product. Moreover, heating and cooling of the rolled material even cause some geometrical imperfections in the final product. Their prediction allows for assessing the mill layout and choosing the most suitable manufacturing technology. In the hot rolling mill, the working roll in contact with the worked material undergoes a very high temperature, which requires an adequate cooling action, being provided by water injection, on the roll surface. Unfortunately, the roll is exposed to several thermal shocks per revolution, leading to surface cracking and spalling damages [35]. Those effects increase the severity of the wear process and sometimes excite the thermomechanical fatigue of materials [36], thus reducing the life of the working roll and even the mean time between failures, or MTBF [37]. If the mean temperature of the roll reaches a defined threshold value, some collateral risks increase, such as those of combustion of lubricant and of unsafe interaction with human operators. Those effects motivate thermal monitoring of the rolling mill elements. In contrast, the cold rolling process offers several advantages. It provides a more accurate shape of the final product and a smoother and better surface finish. Among several mill configurations, the Sendzimir mill (Figure 1a) is often exploited for fast material processing [38]. It includes slender working rolls in contact with rolled material, surrounded by several back rolls, used to prevent bending and vibration of the work roll to ensure precise processing and reduce surface defects. A more compact layout of the cluster mill characterizes the Z-Mill [39], where the crown of back rolls is limited to a few elements, actively controlled by hydraulic actuators, which allow applying the required forces to control the work roll deformation [2]. This layout leads to a reduced size of the rolling mill, but some dynamic problems may arise. During the cold rolling process, the strip is worked in several passes (up to over ten). In each pass, the work rolling speed changes because of the thickness reduction in the strip. Consequently, the rotational speed of rolls and back bearings increases up to five times. This leads to a wide range of frequency of dynamic phenomena associated. In this case, continuous monitoring of dynamic behavior helps the operators in controlling the process and ensures a safe service. In the cold rolling process, reaching the best surface finish possible is the main customer need. It requires that chatter marks and other defects are absent from the rolled product or at least reduced to a minimum size, negligible for the related application. To fulfill this requirement, the rolling mill must work regularly, with moderate mill cage vibration, small roughness of the working roll surface, and regular pressure distribution. Preferably, the temperature should not exceed 70 \({}^{\circ}\)C. Easy detection of any anomalous heating is therefore required, and this turns out into a need for a fast warning of operators provided by clear evidence of alert (sound, light, configuration change useful to trap the operators' attention). In the hot rolling process, the geometric tolerances of the final product are different, but the health of working rolls in operation is a critical issue. As the temperature and its gradient across the cross-section of roll during system operation are higher, surfaces and structures suffer thermal stress, which usually leads to severe wear damage and thermomechanical fatigue [36]. Vibration monitoring is even important since it affects the product thickness [40].