## Materials and Methods
### Generation of a Model for Predicting the Service Life of Sleeves from the Historical Data Collected
The presence of simulation and historical data under different conditions lays the foundation for the continuous estimation of the filter clogging level based on the sensor measurements. Furthermore, it allows estimating an expected range of values for the measured data, making it possible to generate immediate alarms if the deviation from the estimates is higher than a limit value. Thanks to continuous data acquisition, it is possible to monitor the trends in the measured values, correlating them to the possible failures potentially affecting the plant [2; 55; 56]. In particular, the filter condition is estimated based on the difference in the values measured at consecutive measurement periods (see Table 8). To allow for a better comprehension of the monitored conditions, the trends in the measurements are schematically represented by arrows, in particular: \(\uparrow\) represents an increase in a measured value compared to previous data; \(\uparrow\uparrow\) represents a strong increase; \(\rightarrow\) represents a slight variation, lying within the accuracy range of the sensor, that may be traced back to measurement inaccuracies; \(\downarrow\) and \(\downarrow\downarrow\) represent a decrease in the measured value and a strong decrease, respectively. This deviation can be compared to defined reference values (\(\delta_{\rm p}\), \(\Delta_{\rm p}\), \(\delta_{\rm v}\), \(\Delta_{\rm v}\)) to detect fault conditions. In particular, \(\delta_{\rm p}\) and \(\delta_{\rm v}\) account for the sensor accuracy: the clogging rate, as well as possible minor malfunctions, can be monitored according to the variation between the pressure drop and velocity measurements of two consecutive time periods and their comparison with \(\delta_{\rm p}\) and \(\delta_{\rm v}\), respectively. \(\Delta_{\rm p}\) and \(\Delta_{\rm v}\), on the other hand, represent maximum allowable variations in standard operating conditions, and a variation between consecutive measurements higher than these critical values is likely to indicate severe failures. In this way, it is possible to automatically schedule alarms, and eventually plant arrests, whenever a severe failure is detected. Furthermore, by performing an adequate moving averaging of the data, it is possible to perform a continuous estimation of the RUL (Figure 6). Thanks to the digital twin, the system monitoring and the detection of failures can be automatically and constantly performed, minimizing human decision making and possible human errors (Figure 7). In particular, the method was used to report the occurrence of sleeve breakage and, consequently, generate an alarm and a request for a replacement intervention when the velocity variation between two consecutive time periods exceeded the value of \(\Delta_{\rm v}\) and, at the same time, a pressure drop reduction greater than a threshold value \(\delta_{\rm p}\) was recorded. Obviously, the values of \(\Delta_{\rm v}\) and \(\delta_{\rm p}\) must be defined and calibrated according to the filter geometry, sensors' characteristics, and operating conditions. In this study, they were set to 0.2 m/s and 0.1 mbar, respectively. Generation of a Model for the Real-Time Adjustment of the Sequence and Frequency of Compressed Air Jets  
From the simulations conducted under different sleeve clogging conditions, the air flow rate through each sleeve was derived. In particular, the focus was on the upper part of the sleeve (sector 1), as this is where the compressed air jet is most effective in removing the particles trapped in the fabric. The basic hypothesis, supported by experimental evidence reported by both the filter manufacturer and the end users, is that the greater the air flow through the sleeve, the greater the clogging rate. Based on this, it would therefore be