# Detection of Pneumatic Conveying by Acoustic Emissions
## 5 Results and Discussion
### Relationship Between Particle Mass Flow Rate/Size and The Ae Signal  
In this section, the influences of particle mass flow rate and size were investigated. As discussed, the AE signals obtained by the wire-mesh probe are more reliable and representative than the signals obtained by the T-type probe. Therefore, the data used in this section results from the wire-mesh probe sensor. First, the AE signals under a particle mass flow rate of 14 g/s and a particle size of 150 \(\upmu\)m were analyzed. It can be seen from Figure 9 that nine IMF components, together with a residual r9, were generated from the AE signal. In the time domain, the amplitude of all IMF components decreases by several orders of magnitude from the highest value in IMF1 to the lowest in IMF9. In the frequency domain, the same trend was observed, displayed in Figure 10, i.e., IMF1 has the highest instantaneous frequency and IMF9 has the lowest. Figure 8: The RMS average values of the AE signals with respect to particle mass flow rate at four different particle sizes. Figure 7: (**a**) The root mean square (RMS) distribution and (**b**) the relative error for each probe type. To reduce the influence of random error, five random AE signal samples were selected and decomposed. In order to select useful features from the IMF components, the correlation coefficients between different IMF components and the raw AE signal were computed, given in Figure 11 showing that the correlation coefficients for IMF1 to IMF4 are above 0.1. This means that all these four components have the potential to represent the raw sample signals to show a relationship between the AE signal and pneumatic conveying parameters. The relationship between the energies magnitudes for different IMFs, corresponding to the wire-mesh probe and the particle mass flow rate, is presented in Figure 12.  
Figure 10: Raw signal and a portion of the intrinsic mode functions (IMFs) in the frequency domain. Figure 9: The raw signal and the ensemble empirical mode decomposition (EEMD) signal results in time domain. It can be concluded that given the same particle size, with an increasing particle mass flow rate, the energy of IMFs will gradually increase. This can be explained, under certain conditions, since the increase in particle mass flow rate boosts the number of effective interactions, it causes an energy increase in the IMFs. Additionally, under the same airflow and particle mass flow rate, an increase in particle size results in rising IMF energy as well. This phenomenon is due to the high kinetic energy of single particles. To analyze the relationship between the features and particle flow rate, a linear-fitted line for the energies of the IMFs under given particle size is computed, and a parameter termed as the average relative deviation from linearity, \(\delta\), is introduced and defined as:  
\[\delta=\frac{1}{M}\sum_{1}^{M}\frac{|Y_{e}-Y_{s}|}{Y_{e}}*100\% \tag{9}\]  
where \(Y_{e}\) is the experimental energy under different mass flow rates; \(Y_{s}\) is the corresponding value for the fitted line, given the same condition represented by \(Y_{e}\); and \(M\) is the number of particle mass flow rate conditions. \(\delta\) can illustrate the performance of the line fitting, and Figure 13 shows the average relative deviation for different IMF components. Apparently, all \(\delta\)-values are under 0.1 (10%),  
Figure 11: Correlation coefficients between the IMF components and the raw AE signal. Figure 12: Relationship between IMF energy and particle mass flow rate for different particle sizes. meaning that they are all acceptable for an industrial process. Considering the four particle sizes, IMF3 or IMF4 may be best suited to develop the relationship for particle mass flow rate measurement in industrial processes.