## 5 Results and Discussion
### Discussion  
In order to more objectively and comprehensively evaluate the eight ROP prediction models established in this paper, we calculated their evaluation indicators and obtained Table 4 and Figure 12.  
Among the three evaluation indicators, the smaller the RMSE and MRE, the higher the prediction accuracy of the model; the smaller the PEV, the better the stability, robustness, and generalization of the model. The hybrid model outperformed the two single models that compose it, with average reductions of 33% in the RMSE, 45% in the MRE, and 41% in the PEV. Compared with the Motahhari model, the Mota-ANN model reduced the three indicators by 21.47%, 32.00%, and 29.80%, respectively, and decreased them by 28.27%, 41.38%, and 41.27%, respectively, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Evaluating** **Indicators** & **Hareland** & **Motahhari** & **ANN** & **SVM** & **RF** & **Mota-ANN** & **Mota-SVM** & **Mota-RF** \\ \hline Runtime(s) & 44.14 & 20.97 & 27.24 & 65.67 & 14.63 & 48.21 & 86.64 & 35.60 \\ RMSE & 7.25 & 5.59 & 6.12 & 5.71 & 5.14 & 4.39 & 4.22 & 2.65 \\ MRE & 0.40 & 0.25 & 0.29 & 0.24 & 0.21 & 0.17 & 0.15 & 0.09 \\ PEV & 4.73 & 3.02 & 3.61 & 3.32 & 3.16 & 2.12 & 2.01 & 1.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation indicators of different prediction models. Figure 11: ROP prediction results of Mota-RF hybrid model and single models: (**a**) ROP prediction results of RF model; (**b**) ROP prediction results of Motahhari model; (**c**) ROP prediction results of Mota-RF hybrid model. compared with the ANN model. Secondly, compared with the Motahhari model, the three indicators of the Mota-SVM model were reduced by 24.51%, 40.00%, and 33.44%, respectively, and compared with the SVM model, they were reduced by 26.09%, 37.50%, and 39.46%, respectively. The best-performing model was the Mota-RF hybrid model, which reduced the indicators by 52.59%, 64.00%, and 50.00%, respectively, compared with the Motahhari model, and reduced them by 48.44%, 57.14%, and 52.22%, respectively, compared with the RF model. A fair comparison should not ignore the model runtime, at which point the performance of the hybrid model becomes mediocre. Because the hybrid model is a combination of the physical model and empirical model, it takes longer to run than the two single models that compose it. This is an unavoidable problem. By comparing the evaluation indicators and through further analysis, it can be seen that the three indicators of the hybrid model have obvious advantages, especially the smaller PEV, which was reduced by up to 41% compared with the single model. This demonstrates that the hybrid model is more stable and has the robustness and generalization that the machine learning model lacks. In addition, compared with the empirical model, the RMSE and MRE of the hybrid model were reduced by 33% and 45%, respectively, which proves that the hybrid model has higher accuracy than the empirical model. Further analysis shows that both the empirical model and machine learning model play very important roles in the hybrid model. Based on the data similarity analysis, the data with high data similarity are input into the machine learning model for processing, giving full play to its high prediction accuracy. At the same time, the data with low data similarity are input into the optimized empirical model to ensure the robustness and prediction stability while improving the accuracy as much as possible, as the main function of the empirical model is to make up for the loss of stability of the machine learning model. Therefore, we can conclude that the hybrid model combines the high prediction accuracy of the machine learning method with the good robustness and generalization of the empirical method, overcoming the shortcomings of any single model. Among the three hybrid models, the Mota-RF hybrid model performs better and has the shortest runtime, which has obvious advantages compared to the other two hybrid models.