## 4 Results and Discussion
### Machine Learning Identification  
In Section 4.2, the time domain characteristics and EMD energy spectrum of differential pressure signals are calculated. After analyzing these characteristics, it can be found that it is difficult to classify and identify all working conditions with a single parameter, and there is often overlap between parameters. The complex characteristics make it difficult for researchers to accurately identify flow patterns through subjective judgment. The development of machine learning technology, especially support vector machine (SVM) technology and neural network technology, provides new ideas and tools for solving these problems. Through SVM technology and neural network technology, the recognition model can be trained by using multi-dimensional feature vectors based on certain mathematical rules. Compared with manual recognition, these mathematical models can quickly and accurately judge the flow pattern according to the input feature vector, which greatly reduces the impact of subjectivity on the results and improves the recognition efficiency. Therefore, this section uses SVM technology and neural network technology to train \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Particle Diameter**} & \multirow{2}{*}{**Quartile**} & \multicolumn{4}{c}{**Bubbly Flow**} & \multicolumn{4}{c}{**Slug Flow**} & \multicolumn{4}{c}{**Annular Flow**} \\ \cline{3-11}  & & **Level 4** & **Level 5** & **Level 6** & **Level 4** & **Level 5** & **Level 6** & **Level 4** & **Level 5** & **Level 6** \\ \hline \multirow{3}{*}{1.5 mm} & min & & & & 12.89\% & 5.62\% & 4.17\% & 14.67\% & 8.20\% & 3.18\% \\  & median & & & & 41.20\% & 15.76\% & 8.70\% & 49.53\% & 19.06\% & 6.34\% \\  & max & & & & 54.80\% & 28.95\% & 15.18\% & 63.68\% & 32.43\% & 15.24\% \\ \hline \multirow{3}{*}{3 mm} & min & 4.20\% & 7.78\% & 6.28\% & 18.91\% & 8.80\% & 3.56\% & 17.22\% & 9.26\% & 2.95\% \\  & median & 27.93\% & 23.54\% & 15.71\% & 38.60\% & 16.42\% & 9.37\% & 47.36\% & 25.62\% & 5.35\% \\  & max & 41.96\% & 36.65\% & 30.57\% & 54.29\% & 31.79\% & 23.24\% & 53.11\% & 36.10\% & 9.27\% \\ \hline \multirow{3}{*}{6 mm} & min & 15.70\% & 11.03\% & 6.56\% & 8.97\% & 10.90\% & 5.52\% & & & \\  & median & 32.78\% & 22.00\% & 13.26\% & 22.36\% & 20.97\% & 15.36\% & & & \\  & max & 46.04\% & 37.71\% & 27.43\% & 39.97\% & 33.70\% & 31.20\% & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Distributions of EMD energy spectrum on levels 4-6. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Particle Diameter**} & \multirow{2}{*}{**Quartile**} & \multicolumn{4}{c}{**Bubbly Flow**} & \multicolumn{4}{c}{**Slug Flow**} & \multicolumn{4}{c}{**Annular Flow**} \\ \cline{3-11}  & & **Level 1** & **Level 2** & **Level 3** & **Level 1** & **Level 2** & **Level 3** & **Level 1** & **Level 2** & **Level 3** \\ \hline \multirow{3}{*}{1.5 mm} & min & & & & 2.38\% & 1.15\% & 0.35\% & 1.46\% & 0.74\% & 0.29\% \\  & median & & & & 5.50\% & 2.55\% & 0.86\% & 3.83\% & 1.81\% & 3.23\% \\  & max & & & & 9.06\% & 4.37\% & 8.97\% & 7.61\% & 3.58\% & 30.81\% \\ \hline \multirow{3}{*}{3 mm} & min & 3.05\% & 1.53\% & 0.48\% & 1.05\% & 0.54\% & 0.21\% & 3.07\% & 1.47\% & 0.40\% \\  & median & 7.55\% & 3.53\% & 0.97\% & 2.48\% & 1.23\% & 1.94\% & 8.84\% & 4.15\% & 1.53\% \\  & max & 16.77\% & 7.71\% & 7.02\% & 5.01\% & 2.31\% & 12.42\% & 12.24\% & 5.88\% & 5.96\% \\ \hline \multirow{3}{*}{6 mm} & min & 4.41\% & 2.34\% & 0.78\% & 2.81\% & 1.51\% & 0.56\% & & & \\  & median & 10.36\% & 5.25\% & 1.46\% & 5.24\% & 2.86\% & 0.90\% & & & \\  & max & 26.74\% & 12.76\% & 3.55\% & 7.50\% & 4.04\% & 2.29\% & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Distributions of EMD energy spectrum on levels 1–3.