## 4 Results and Discussion
### Machine Learning Identification
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Vector Type**} & \multicolumn{6}{c}{**Parameters**} & \multirow{2}{*}{**Label**} & \multirow{2}{*}{**Flow Pattern**} \\ \cline{2-2} \cline{6-9}  & **m** & **S** & **R** & **Level 4** & **Level 5** & **Level 6** & \(d_{p}\) \\ \hline \multirow{3}{*}{Vector-1} & 4.86 & 0.22 & 1.64 & 12.41\% & 16.73\% & 30.57\% & 3 & 1 & Bubbly \\  & 3.96 & 0.39 & 2.69 & 22.55\% & 24.26\% & 15.26\% & 6 & 2 & Slug \\  & 8.74 & 0.34 & 2.71 & 55.92\% & 12.33\% & 9.04\% & 1.5 & 3 & Annular \\ \hline \multirow{3}{*}{Vector-2} & **m** & **S** & **R** & **Level 1** & **Level 2** & **Level 7** & \(d_{p}\) \\ \cline{2-9}  & 4.86 & 0.22 & 1.64 & 16.24\% & 7.14\% & 12.95\% & 3 & 1 & Bubbly \\ \cline{1-1}  & 3.96 & 0.39 & 2.69 & 3.60\% & 1.95\% & 13.84\% & 6 & 2 & Slug \\ \cline{1-1}  & 9.08 & 0.34 & 2.72 & 6.23\% & 2.85\% & 2.90\% & 1.5 & 3 & Annular \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Examples of vectors with different features. As shown in Table 9, the identification ability of different BP network models varies greatly. The BP-1 model has the best identification ability, which is not only better than the BP-2 model but also better than SVM-1 and SVM-2 models. The identification ability of the BP-2 model is the worst of the four models. Moreover, the models containing one, two, and seven levels of EMD energy perform worse than the models containing four, five, and six levels of EMD energy. Next, consider further improving the identification ability of flow patterns. The idea of bagging technology in integrated learning technology is introduced. That is, train multiple models at the same time, let these models vote on the results, and determine the final results according to the voting results. In this study, four models are trained. If all the models participate in the voting, there may be a tie vote. Due to the poor performance of BP-2, its results may mislead the correct results. Therefore, SVM-1, SVM-2, and BP-1 were selected to form an integrated model. The identification process is shown in Figure 8, moreover, considering the special situation (bubble flow: annular flow: slug flow, 1:1:1). Since the BP-1 model performed best among the three models, it is considered that the final result of BP-1 model will prevail when the conflict occurs. Table 10 shows the identification results of an integrated model. It can be seen that the integrated model further improves identification ability based on the original models. The test data of bubbly flow and annular flow have been correctly identified, and only two groups of slug flow data have not been correctly identified. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Flow Pattern** & **Correct Identification** & **Total Number** & **Accuracy** \\ \hline \multirow{4}{*}{Integrated model} & Bubbly & 63 & 63 & 100.00\% \\  & Slug & 63 & 65 & 96.92\% \\ \cline{1-1}  & Annular & 25 & 25 & 100.00\% \\ \cline{1-1}  & Overall & 151 & 153 & 98.69\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Identification results of integrated model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**SVM Model** & **Flow Pattern** & **Correct Identification** & **Total Number** & **Accuracy** \\ \hline \multirow{4}{*}{SVM-1} & Bubbly & 60 & 63 & 95.24\% \\  & Slug & 62 & 65 & 95.38\% \\  & Annular & 23 & 25 & 92.00\% \\  & Overall & 145 & 153 & 94.77\% \\ \hline \multirow{4}{*}{SVM-2} & Bubbly & 61 & 63 & 96.83\% \\  & Slug & 60 & 65 & 92.31\% \\ \cline{1-1}  & Annular & 22 & 25 & 88.00\% \\ \cline{1-1}  & Overall & 143 & 153 & 93.46\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The identification results of SVM models.