## 4 Results and Discussion
### Feature Extraction  
#### 4.2.1 Time Domain Feature Extraction  
According to Equations (1)-(3), three time domain parameters (average value, standard deviation, and range) corresponding to each group of data are obtained. The average reflects the concentration trend of the differential pressure signal, the standard deviation reflects the dispersion degree of the differential pressure signal, and the range quantifies the fluctuation range of the differential pressure signal. After sorting out the calculation results, the time domain characteristic distributions of different flow patterns in porous beds with different particle diameters are obtained, as shown in Figure 6.  
Figure 6: Diagram of time domain characteristic parameter distribution. (**a**). Time domain characteristic parameter distribution in porous bed with a particle diameter of 1.5 mm. (**b**). Time domain characteristic parameter distribution in porous bed with a particle diameter of 3 mm. (**c**). Time domain characteristic parameter distribution in porous bed with a particle diameter of 6 mm. (**d**). Time domain characteristic parameter distribution in all porous beds. It can be seen from Figure 6a that there is an obvious boundary between the slug flow and annular flow in a porous bed with a particle diameter of 1.5 mm. Figure 6b shows that in a porous bed with a particle diameter of 3 mm, a few data points of slug flow and bubble flow overlap in the time domain distribution. In Figure 6c, it can be seen that in the porous bed with a particle diameter of 6 mm, there is also an obvious boundary between the distribution of bubble flow and slug flow data in the time domain. Nevertheless, it can be found from Figure 6d that when the influence of particle diameter of porous media bed is not considered, there will be a lot of overlap in the distribution of time domain characteristics of different flow patterns, which indicates that particle diameter is also one of the important parameters affecting classification, and the influence of particle diameter cannot be ignored. In order to better analyze the distribution of time domain characteristics, the distribution range and median of time domain characteristic parameters of different flow patterns are counted, and the calculation results are shown in Table 2.  
It can be seen from the Table 2 that for the porous bed with a particle diameter of 1.5 mm, the average value of the differential pressure signal of the slug flow is 5.74-7.05 kPa, and that of the annular flow is greater than 8.02 kPa. Therefore, the data with the average value of the differential pressure signal falling within these ranges can be directly distinguished between the slug flow and the annular flow in the porous bed with a particle diameter of 1.5 mm. Similarly, in the porous media bed with a particle diameter of 6 mm, the average value of the differential pressure signal can also be directly used to distinguish bubbly flow and slug flow (bubbly flow is 4.11-4.76 kPa, slug flow is 3.38-3.97 kPa). However, it should be considered that the average value of differential pressure signal alone cannot distinguish all the flow patterns. Firstly, in a porous media bed with a particle diameter of 3 mm, there is a range of overlap between the characteristic parameters of different flow patterns. Secondly, for porous media beds with particle diameters of 1.5 and 6 mm, it is also difficult to distinguish data that are between two ranges (for example, the average value of differential pressure signal is within 7.05-8.02 kPa) through the judgment of researchers. This is why multiple parameters rather than a single parameter are selected to judge the flow pattern. To solve the above problems, new features (EMD energy spectrum) are introduced to provide a more judgment basis. At the same time, machine learning technology is employed to identify and classify different flow patterns from a mathematical point of view.