## 2 Methodology
### Feature Selection  
Feature selection is a crucial step in machine learning and data analysis, aiming to identify the most influential features while eliminating redundant ones to enhance model efficiency and accuracy. To achieve this, we conducted a correlation analysis to remove variables with minimal impact. [PERSON]'s rank correlation coefficient is a nonparametric statistical method used to measure the monotonic relationship between two variables [23]. It is particularly suitable for data that are nonnormally distributed, contain outliers, or exhibit nonlinear correlations. The calculation formula is as follows:  
\[\rho=1-\frac{6\sum d_{i}^{2}}{n(n^{2}-1)} \tag{2}\]  
where \(d_{i}=R(X_{i})-R(Y_{i})\), which represents the rank difference between the two variables for each observation. \(R(X_{i})\) and \(R(Y_{i})\), respectively, represent the ranks of variable \(X_{i}\) and variable \(Y_{i}\). \(n\) is the number of data samples. The value of \(\rho\) ranges from \(-1\) to \(1\). \(\rho=1\): perfect positive correlation, meaning that as one variable increases, the other also increases. \(\rho=-1\): perfect negative correlation, meaning that as one variable increases, the other decreases. \(\rho=0\): no correlation, indicating no monotonic relationship between the variables. The Spearman correlation coefficient matrices between various influencing factors and the casing-cement interface and cement-formation interface are shown in Figures 1(a) and 1(b), respectively. In the Spearman correlation coefficient matrix heatmap, different colors represent the strength of the correlation between variables: Red (close to 1.0, strong positive correlation): Indicates a strong positive relationship between variables, meaning that as one variable increases, the other also tends to increase. Blue (close to \(-1.0\), strong negative correlation): Indicates a strong negative relationship, meaning that as one variable increases, the other tends to decrease. Near-white or light-colored areas (close to 0.0): Suggest little to no correlation between the variables. Among these variables, x1 to x19 correspond to those listed in Table 1, while y1 and y2 represent the casing-cement interface and cement-formation interface quality, respectively. x1 (well depth) and x8 (wellbore temperature) show a strong correlation (\(\rho=0.97\)), indicating that they provide highly redundant information. To reduce redundancy, this study discards wellbore temperature (x8), as it is less essential. x6 and x10 exhibit a strong negative correlation (\(\rho=-0.97\)), suggesting that one of them should be removed to optimize variable selection. This study chooses to discard Wellbore Pressure (x10) for better feature selection. Strongly correlated influencing factors include x16 (cement slurry flow rate) and x17 (preflush flow rate), with correlation coefficients of \(-0.71\) and \(0.61\), respectively. These variables should be given special attention during the cementing process to optimize cementing quality. The correlation coefficient between x5 (Azimuth) and the casing-cement interface quality is low (\(-0.07\)). Therefore, it is not considered in the analysis. A similar trend is observed in Figure 1(b), indicating that different variables also exhibit comparable effects on the cement-formation interface quality (y2). Figure 2: Spearman correlation coefficient matrix: (**a**) Casing-cement sheath interface; (**b**) Cement sheath-formation interface. Since the centralizer position data are discontinuous and represented as a binary sequence (0 and 1), it is not suitable for direct calculation using the Spearman correlation coefficient. Instead, Cramer's \(V\) correlation coefficient is used for analyzing the correlation coefficients among discrete variables [24]. The Cramer's \(V\) coefficient also lies within the range of 0 to 1. \(V=0\) indicates no association between two categorical variables. \(V=1\), indicates a perfect association.