## Materials and Methods
### Generation of a Model for Predicting the Service Life of Sleeves from the Historical Data Collected  
To develop the digital twin of the cyclone bag filter, first, the digital model was generated based on simulation results and historical experimental data measured by the sensors installed on the plant. Thanks to the data collected, it was possible to model the behavior of the filter at different flow rates, including the variations in the system pressure drop and tangential velocity as the clogging level increased. The connection between the digital and the physical twin was performed using the LabView software connected to a data acquisition (DAQ) module. The sensor data (pressure drop and tangential velocity) were recorded every 30 s, and then a moving average was performed every 60-time steps, in accordance with the typical time scales of these plants. Therefore, one measurement period i corresponds to 30 min. As described above, currently, sleeve replacement is carried out when the pressure drop generated by the sleeves exceeds a certain threshold value. As a first step, therefore, it is possible to develop a Residual Useful Life (RUL) prediction model based on the trend of pressure drop monitored in real time. The method used to develop such a model is based  
Figure 5: Detail of the pattern of alternation between areas covered with the film and free areas. on the calculation of the sleeve clogging rate per unit of time at time t (\(C_{r,t}\)) to estimate the residual remaining time to reach the maximum admissible clogging (expressed as maximum allowable pressure drop, \(\Delta p_{max}\) and equal to 15 mbar). The sleeve clogging rate was estimated by measuring the pressure drop increase per measurement period. To have a prediction as stable as possible, since the air filtration process is susceptible to fluctuations in air flow rate values and consequently in pressure drops, and since the clogging rate is very low (usually sleeves are replaced every year or every year and a half approximately), it was decided to use the moving average method. The pressure drop value at the time t (\(\Delta p_{t}\)) was calculated as the average of the values of the previous \(n\) measurement periods, where \(n\) must be sufficiently high to smooth pressure drop fluctuations but not too large, to average between measurement periods in which sleeve permeability has not changed too much. \[RUL_{t}=\frac{\Delta p_{max}-\Delta p_{t}}{C_{r,t}} \tag{3}\]  
\[\Delta p_{t}=\frac{\sum_{i=t-n}^{t}\Delta p_{t}}{n} \tag{4}\]  
\[C_{r,t}=\frac{\Delta p_{t}}{\Delta t_{t-n,t}} \tag{5}\]  
In addition, especially at the beginning of the sleeve life, since the clogging rate is very slow, there would be a very overestimated prediction of the RUL. For this reason, the value of RUL calculated with the Equations (3)-(5) is always compared with the value of RUL calculated with reference to a planned replacement operation one and a half years after sleeve replacement. The lowest RUL value between the two is always considered. The pressure value alone, however, can make an accurate prediction only when the operating conditions remain in the standard range. When, for example, the breakage of a sleeve occurs, due to the abrasive effect on it of flour and bran dust, or due to repeated impact with other sleeves, there would be a reduction in pressure drop at the ends of the filter. This reduction in pressure drops, according to Equations (3)-(5) would lead to the calculation of a higher RUL value, when in fact replacement should be planned as soon as possible. Therefore, additional monitoring needs to be combined with pressure drop monitoring for a more accurate assessment of RUL. In this study, we focused on the measured tangential velocity value at the point identified through fluid dynamic simulations. Under standard operating conditions, there is an increasing velocity trend at this point. In the event of a sleeve rupture, a discontinuity in the velocity trend would be recorded at this point, which would then allow the anomaly to be identified.