## 4 Based on the Random Forest Algorithm for Irregular Wellbore Diameter Weight Analysis
### The Maximum/Minimum ECD Multifactor Weight Analysis During Cementing Operations  
The control variables include the injection displacement rate, drilling fluid density, spacer density, cement slurry density, eccentricity, consideration of expanding diameter, and consideration of physical property changes in high-temperature and high-pressure fluids. The data labels and classification are shown in Table 5. A total of 90 groups of four-factor three-level and three-factor two-level experimental schemes were constructed to perform simulation calculations for the maximum/minimum ECD in cementing operations.  
According to the comprehensive weight analysis of the factors influencing the maximum ECD of the annulus using the random forest method, the model parameters were set with estimators at 200, a random state at 42, and a test set proportion at 0.3 with an R\({}^{2}\) of 0.8922 and an MSE of 2.84 \(\times\) 10\({}^{-4}\). The predictive results of the test set compared with the actual values are shown in Figure 9, indicating a good fit for the model. The significance of the factors is presented  
In addition, the positive and negative impacts of factors on ECD need to be analyzed. SHAP (SHapley Additive exPlanations) is an interpretable model inspired by the Shapley value and represents additive explanations. It quantifies the impact of each factor on the prediction outcome. By utilizing the SHAP model for in-depth data analysis, the output value for an individual sample is 0.0793, and the influence of sample factors is shown in Figure 11. This figure shows the impact of each sample's features on the model's prediction results. The horizontal axis is the SHAP value, and the vertical axis is the actual value of the feature. The redder the color, the higher the positive impact the feature has on the prediction results, and the bluer the color, the higher the negative impact. Meanwhile, the wider the color area on the horizontal axis, the greater the impact of the feature value on the result. The figure reveals that the flow rate, density of the drilling fluid, spacer, cement slurry, and consideration of wellbore enlargement are positively correlated with the maximum ECD result, while eccentricity and the consideration of high-temperature high-pressure fluid properties are negatively correlated with the outcome.  
We suggest the readers to refer to the previous analysis path to quantitatively analyze the factors affecting the minimum ECD. The R\({}^{2}\) for the minimum ECD model is 0.9982,  
Figure 11: Weight analysis of the influencing factors for the maximum ECD in the annulus.  
Figure 10: ECD of the weight analysis of annular influencing factors.  
By utilizing the SHAP model for in-depth data analysis, the output value for an individual sample is 0.1297. The influence of sample factors on the result is shown in Figure 14. This figure reveals that the density of the drilling fluid and the flow rate are positively correlated with the minimum ECD result, while high-temperature and high-pressure properties and wellbore enlargement are negatively correlated with the result. The influence of other factors is not significant. This understanding is consistent with the engineering experience, further demonstrating the model's good interpretability.