## 3 Signal Processing Methods  
This paper ignores the influence of gas compression and considers the gas flow rate at any cross section of the conical cylinder to be the same. The superficial gas velocity at any section is calculated using the following equations:  
\[U_{\text{h}}=\overline{x}_{\text{f}}/S_{\text{h}} \tag{4}\]  
\[U_{0}=\overline{x}_{\text{f}}/S_{0} \tag{5}\]  
where \(\overline{x}_{\text{f}}\) is the average value of the flow rate time-series signal (\(x_{\text{f}}\)) and \(S_{\text{h}}\) is the sectional area of the conical cylinder at the height of \(h\). The number of the empty bed experiment is 00, and the relationships among the fan opening, \(U_{0}\), and \(\Delta P_{\text{P}}\) are shown in Figure 3. As shown in Figure 3, with an increase in the fan opening, \(U_{0}\) and \(\Delta P_{\text{P}}\) continue to increase. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Material Number**} & \multicolumn{5}{c}{**Experimental Number**} \\ \cline{2-6}  & **Material Mass** & **Material Mass** & **Material Mass** & **Material Mass** & **Material Mass** \\  & **2 kg** & **2.5 kg** & **3 kg** & **3.5 kg** & **4 kg** \\ \hline \#1 & 01 & 02 & 03 & 04 & 05 \\ \#2 & 06 & 07 & 08 & 09 & 10 \\ \#3 & 11 & 12 & 13 & 14 & 15 \\ \#4 & 16 & 17 & 18 & 19 & 20 \\ \#5 & 21 & 22 & 23 & 24 & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental number correspondence table. As shown in Equation (6), by subtracting the average values of \(x_{\rm P1}\) and \(x_{\rm P2}\) in the empty bed experiment (material mass \(W=0\)), the pressure drop generated by the gas distribution plate (\(\Delta P_{\rm P}\)) can be calculated. For each fan opening, \(\Delta P_{\rm P}\) and \(U_{0}\) were recorded so that the mapping relationship between a series of \(\Delta P_{\rm P}\) and a series of \(U_{0}\) can be established. Therefore, for a given \(U_{0}\), the value of \(\Delta P_{\rm P}\) can be determined by this mapping relationship. As shown in Equation (7), for experiments 01-25, by subtracting the average values of \(x_{\rm P1}\) and \(x_{\rm P2}\) and then subtracting \(\Delta P_{\rm P}\) (under the current \(U_{0}\)), \(\Delta P\) can be obtained. \[\Delta P_{\rm P}=(\overline{x}_{\rm P1}-\overline{x}_{\rm P2})|_{W=0}\ \ \mbox{(empty bed experiment, number 0)} \tag{6}\]  
\[\Delta P=\overline{x}_{\rm P1}-\overline{x}_{\rm P2}-\Delta P_{\rm P}|_{U_{0 }}\ \ \mbox{(experiment 01--25)} \tag{7}\]  
The intersection method is used to determine \(U_{\rm 0 mf}\) and \(\Delta P_{\rm mf}\). The specific determination process is as follows. first determine an inflection point, and from the second point before the inflection point, take as many points as possible near a straight line to fit the first straight line; then, from the second point after the inflection point, take 4-6 continuous points, then plot a horizontal straight line as the second line, whose height is the average of the taken points' ordinate values; the intersection point of the two straight lines is considered to be the point (\(U_{\rm 0 mf}\), \(\Delta P_{\rm mf}\)). Take experiment 06 shown in Figure 4 as an example. The two black lines in Figure 4 are the two straight lines, and \(U_{\rm 0 mf}\) and \(\Delta P_{\rm mf}\) are the abscissa and ordinate of the intersection point, respectively. In this paper, the root mean square error (RMSE) and R\({}^{2}\) are used to describe the fitting accuracy quantitatively. RMSE means the root mean square error; the smaller the value, the closer the fitting  
Figure 4: Schematic diagram of the \(U_{\rm 0 mf}\) and \(\Delta P_{\rm mf}\) measurement method. Figure 3: \(U_{0}\) and \(\Delta P_{\rm P}\) at different fan openings in the empty bed experiment (number 00). value is to the actual value. R\({}^{2}\) is the determination coefficient, and its value is between 0 and 1. The higher the value is, the higher the fitting accuracy.