## 3 ROP Prediction Based on the Random Forest Machine Learning Model
### Factor Analysis  
Parameter correlation analysis and feature importance ranking are important tools for optimizing the prediction performance of random forest models. They can improve model performance, reduce feature dimensions, enhance model execution speed, and increase prediction accuracy. Additionally, they help in understanding the causal relationships behind the mechanism-based theoretical model. This study involved a total of 5 training wells (Fu4, Fu9, Fu10, Fu48, Fu49, and Kangtan1) and 2 test wells (Fu39 and Kangtan2). A total of 50,000 data sets were selected for the training set, and 10,000 data sets for the test set. Among these wells, Fu4, Fu9, Fu10, Fu48, and Fu49 belong to the same block, while Kangtan1 and Kangtan2 are located at a greater distance from the other 5 wells and belong to adjacent blocks. Choosing Kangtan2 well as a test well also served, to some extent, as a test of the generalization ability of the random forest drilling speed prediction model. The dataset established for this study comprises a total of 10 feature parameters and has undergone fundamental statistical description, as illustrated in Table 1.  
First, the relationships between the engineering parameters, such as annular pressure, torque, drilling pressure, rotation speed, equivalent density, viscosity, inlet flow rate, outlet flow rate, total pump speed, and ROP, were analyzed. Pearson's correlation coefficients were used to assess the strength of linear relationships between the parameters, as shown \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Count** & **Mean** & **Std** & **Min** & **Max** \\ \hline SPP/MPa & 50,000 & 22.5680 & 2.9507 & 11.18 & 25.64 \\ Torque/KN\(\cdot\)m & 50,000 & 7.2473 & 2.7384 & 4.18 & 20.51 \\ WOB/KN & 50,000 & 50.7053 & 26.3114 & 10 & 201 \\ RPM & 50,000 & 109.6535 & 37.3567 & 46 & 185 \\ ECD/g\(\cdot\)cm\({}^{-3}\) & 50,000 & 1.4658 & 0.1457 & 1.03 & 1.82 \\ Viscosity/s & 50,000 & 88.3048 & 22.3630 & 12 & 152 \\ INF/L\(\cdot\)s\({}^{-1}\) & 50,000 & 47.2738 & 4.7340 & 24.74 & 58.26 \\ OUTF/L\(\cdot\)s\({}^{-1}\) & 50,000 & 39.4409 & 5.9599 & 22.79 & 56.45 \\ Pump Speed & 50,000 & 133.8123 & 36.3426 & 68 & 192 \\ ROP/m\(\cdot\)s\({}^{-1}\) & 50,000 & 19.1330 & 16.2476 & 0.37 & 130.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Fundamental statistical description for the dataset. in Figure 4. The results indicate that the drilling fluid equivalent density and viscosity are negatively correlated with ROP, while torque, rotation speed, drilling fluid flow rate, and pump speed are positively correlated with ROP. This is consistent with our understanding based on the traditional mechanistic models. However, there is a negative correlation between the drilling pressure and ROP, which is inconsistent with the mechanistic model's understanding. The main reason for this discrepancy is the occurrence of complex situations, such as mud packs or drilling tool vibrations in difficult drilling sections. This also explains the opposite trend between the ROP predicted by the mechanical-specific energy model in Fu39 well, as shown in Figure 2.  
Feature importance ranking is of great significance in data analysis and machine learning. It helps us to understand data and models and make more informed decisions. Importance ranking explains the prediction results of a model, providing information about which features have a greater impact on the model's output. This is crucial for understanding the decision-making process of the model and why it makes specific predictions. In some cases, feature importance ranking can be used to identify potential issues or anomalies. In this study, feature importance rankings and their impact percentages on the drilling speed for two test wells provided by the random forest model were combined with mechanistic models to explain the degree of coupling between model predictions and actual results.