# Detection of Pneumatic Conveying by Acoustic Emissions
## 5 Results and Discussion
### Relationship Between Particle Mass Flow Rate/Size and The Ae Signal
After determining a fitting process, additional experimental conditions sought to validate the approach, and the results are presented in Table 2. After analysis by the EEMD method, all of the results were compared with the described fitting function, and the resulting relative deviations are displayed in Table 3. One can note that all of the relative deviations are under 10%. In view of these additional data points, it is clear that the energies for IMF3 and IMF4 have the best linear relationship with particle mass flow rates for different particle sizes, which is useful in characterizing flow rate change. In Figure 12a, there are two magenta ovals to specify two data points that, while representing different conditions, nearly share the same energy value. To consider this further, Table 4 presents the IMF energies for the two different conditions. The first row represents a particle mass flow rate of 6 g/s and a particle size of 180 \(\upmu\)m; the second row corresponds to 14 g/s and 150 \(\upmu\)m, respectively. This side-by-side comparison validates the value similarity between the two IMF components, which shows a case where distinguishing the two could result in an incorrect judgment. Therefore, at least two parameters are required to avoid incorrect judgment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Conveying Velocity (m/s)** & **Particle Mass Flow Rate (g/s)** & **Particle Loading (\%)** & **Particle Size (\(\upmu\)m)** \\ \hline
21 & 18/20 & 0.018/0.02 & 550/250/180/150 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Additional experiment conditions for validation. Figure 13: Average relative deviation from linearity for the IMF features given different particle sizes. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Particle Mass Flow Rate (g/s)** & **IMF Number** & **550 \(\upmu\)m** & **250 \(\upmu\)m** & **180 \(\upmu\)m** & **150 \(\upmu\)m** \\ \hline \multirow{4}{*}{18} & IMF1 & 2.041 & 0.424 & 4.300 & 3.399 \\  & IMF2 & 2.677 & 0.392 & 5.895 & 4.483 \\  & IMF3 & 2.161 & 1.726 & 4.063 & 3.176 \\  & IMF4 & 2.704 & 0.387 & 3.839 & 2.256 \\ \hline \multirow{4}{*}{20} & IMF1 & 0.580 & 5.874 & 3.784 & 4.522 \\  & IMF2 & 2.474 & 6.552 & 4.852 & 4.405 \\ \cline{1-1}  & IMF3 & 3.439 & 3.587 & 1.909 & 3.802 \\ \cline{1-1}  & IMF4 & 1.454 & 5.532 & 4.051 & 3.620 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relative deviation for the validation experiments. In this paper, the mean-squared error contribution fraction (MSECF) for different IMFs is defined as:  
\[p_{i}=\frac{\frac{1}{N}\sum_{1}^{N}\left(c_{i}(n)-\overline{c_{i}(n)}\right)^{2 }}{\sum_{1}^{m}\left(\frac{1}{N}\sum_{1}^{N}\left(c_{i}(n)-\overline{c_{i}(n)} \right)^{2}\right)} \tag{10}\]  
which indicates the importance of the IMF components to the raw AE signal. \(N\) is the sampling number (set as \(N=16384\)); \(\frac{1}{N}\sum\limits_{1}^{N}\left(c_{i}(n)-\overline{c_{i}(n)}\right)^{2}\) is the mean-squared error; and \(m\) is the number of the IMF component. Figure 14 presents the MSECF for different IMF components. As the particle size increases, according to the formula 1, the dominant frequency of the AE signal gradually decrease, which result in a gradual decrease in the MSECF of the high frequency components. This can explain why the MSECF of the IMF1 would have a reversely performance compared with other IMF components, and the curves for IMF4 indicate the four particle sizes clearly. Therefore, the MSECF may perform better when distinguishing particle size. The linear fit for the average MSECF respective of particle size is presented in Figure 15, with the fitting equation:  
\[y=0.55858+0.00144*x \tag{11}\]  
In this fitting function, \(y\) is the MSECF value, and \(x\) represent the particle flow rate. The adjusted R-Squared of the curve is 0.98745, which indicates a good fit.