## Materials and Methods
### Generation of a Model for Predicting the Service Life of Sleeves from the Historical Data Collected
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Estimated Failure** & & & & & & \\
**Based on the Pressure Drop** & & & & & & \\ \hline \multirow{4}{*}{Clogging} & dp(i) \(-\) dp(i \(-\) 1) \(>\)\(\delta_{\rm p}\) & \(\uparrow\) & v(i) \(-\) v(i \(-\) 1) \(>\)\(\delta_{\rm v}\) & \(\uparrow\) & \multicolumn{2}{c}{CASE 1: Standard clogging.} \\  & dp(i) \(-\) dp(i \(-\) 1) \(>\)\(\Delta_{\rm p}\) & \(\uparrow\)\(\uparrow\) & & & & \\  & & & & & & \\  & dp(i) \(-\) dp(i \(-\) 1) \(>\)\(\delta_{\rm p}\) & \(\uparrow\) & \(\mid\) v(i) \(-\) v(i \(-\) 1) \(<\)\(\delta_{\rm v}\) & \(\rightarrow\) & & \\  & dp(i) \(-\) dp(i \(-\) 1) \(>\)\(\delta_{\rm p}\) & \(\uparrow\) & v(i) \(-\) v(i \(-\) 1)\(<\)\(\delta_{\rm v}\) & \(\downarrow\) & & \\  & dp(i) \(-\) dp(i \(-\) 1) \(>\)\(\delta_{\rm p}\) & \(\uparrow\) & v(i) \(-\) v(i \(-\) 1)\(<\)\(\delta_{\rm v}\) & \(\downarrow\) & & \\  & & & & & & \\ \hline \multirow{4}{*}{Breakage of a filtering sleeve} & \(\) dp(i) \(-\) dp(i \(-\) 1) \(<\)\(\delta_{\rm p}\) & \(\rightarrow\) & v(i) \(-\) v(i \(-\) 1) \(>\)\(\delta_{\rm v}\) & \(\uparrow\) & \multicolumn{2}{c}{CASE 5: Anomaly, possibly concurrent failures.} \\  & dp(i) \(-\) dp(i \(-\) 1) \(<\)\(\delta_{\rm p}\) & \(\rightarrow\) & \(\mid\) v(i) \(-\) v(i \(-\) 1) \(<\)\(\delta_{\rm v}\) & \(\rightarrow\) & \multicolumn{2}{c}{CASE 6: Standard functioning with weak clogging} \\  & \(\mid\) dp(i) \(-\) dp(i \(-\) 1) \(<\)\(\delta_{\rm p}\) & \(\rightarrow\) & v(i) \(-\) v(i \(-\) 1)\(<\)\(\delta_{\rm v}\) & \(\downarrow\) & \multicolumn{2}{c}{CASE 7: Atypical, possibility of concurrent minor failures} \\ \cline{1-1} \cline{2-5}  & dp(i) \(-\) dp(i \(-\) 1) \(<\)\(\delta_{\rm p}\) & \(\downarrow\) & v(i) \(-\) v(i \(-\) 1) \(>\)\(\Delta_{\rm v}\) & \(\uparrow\uparrow\) & \multicolumn{2}{c}{CASE 8: Bag breakage occurring at the bottom sectors} \\ \cline{1-1}  & dp(i) \(-\) dp(i \(-\) 1) \(<\)\(\delta_{\rm p}\) & \(\downarrow\) & \(\mid\) v(i) \(-\) v(i \(-\) 1) \(<\)\(\delta_{\rm v}\) & \(\rightarrow\) & \multicolumn{2}{c}{CASE 9: Possible coexistence of minor failures} \\ \cline{1-1}  & dp(i) \(-\) dp(i \(-\) 1) \(<\)\(\delta_{\rm p}\) & \(\downarrow\) & v(i) \(-\) v(i \(-\) 1)\(<\)\(-\Delta_{\rm v}\) & \(\downarrow\downarrow\) & \multicolumn{2}{c}{CASE 10: Bag breakage in the top sectors} \\ \hline \end{tabular}
\end{table} 
Table 8: Logics of condition monitoring for real-time anomaly detection, based on the comparison of the values measured in consecutive time periods i.  
recommended to associate the frequency with which compressed air is injected through the sleeve with the air flow rate through it. Based on the framework described in the previous paragraph, the digital twin can detect whether the system is operating under standard clogging conditions or not. In the first case, the measured pressure drop value allows the identification of the actual clogging condition. From there, thanks to the simulation performed under those specific clogging conditions, the model is able to trace the air flow rate through each sleeve, and based on that, it can define the optimal sequence and frequency of cleaning operations.