## 3 Case Analysis
### Comparative Experimental Analysis and Data Reconstruction Effectiveness  
To evaluate the effectiveness of the proposed outlier detection, identification, and imputation-correction method in seepage pressure data reconstruction, we conducted a comparative experimental validation using four different method combinations based on actual engineering operational datasets. Details are provided in Table 2.  
In order to better evaluate the accuracy of data reconstruction, the coefficient of determination (\(R^{2}\)), root mean square error (_RMSE_), and mean absolute error (_MAE_) were used as evaluation indexes to comprehensively judge the accuracy of seepage pressure data reconstruction. \(R^{2}\) is an indicator for measuring the fit of a method; the closer it is to 1, the better the result. _RMSE_ directly reflects the error in data reconstruction; the smaller its value, the closer the detected values are to the actual measured values. _MAE_ is unaffected by the scale of the data; the smaller its value, the higher the data reconstruction accuracy of the method. The calculation equation of each evaluation index is in Equations (20)-(22):  
\[R^{2}\ =\ 1-\ \sum_{i\ =\ 1}^{n}{(\hat{y}_{i}-y_{i})^{2}}/\sum_{i\ =\ 1}^{n}{(\overline{y}_{i}-y_{i})^{2}} \tag{20}\]  
\[RMSE\ =\ \sqrt{\frac{1}{n}\sum_{i\ =\ 1}^{n}{(y_{i}-\hat{y}_{i})^{2}}} \tag{21}\]  
\[MAE\ =\ \frac{1}{n}\sum_{i\ =\ 1}^{n}{|y_{i}-\hat{y}_{i}|} \tag{22}\]  
where \(y_{i}\) is the true value; \(\hat{y}_{i}\) is the detection value; \(n\) is the number of samples; \(\overline{y}_{i}\) is the average of the true value. The experiment evaluates the reconstruction accuracy and stability of each method by comparing the differences in data reconstruction effect among four combination methods (traditional particle filter + mean filling, traditional particle filter + MissForest filling, improved particle filter + mean filling, and improved particle filter + MissForest filling). From Figure 9, it can be seen that the particle scatter distribution under filtering indicates the effectiveness of methods in the following order: method 4 > method 3 > method 2 > method 1. The improved particle filter combined method can to some extent determine the concentration of particle distribution, as shown by the particle distributions under method 3 and method 4. Moreover, the particle distribution based on the MissForest filling method is superior to that of the mean filling method and more stable. The combined method based on method 4 in Figure 9 demonstrates better data reconstruction capability, indicating its method is more reliable and effective. \begin{table}
\begin{tabular}{c c c} \hline \hline Experiment & **Abnormal Value Identification** & **Refine the Correction** \\ Method & **Method** \\ \hline method one & Traditional particle filter algorithm & Mean filling method \\ method two & Traditional particle filter algorithm & MissForest filling method \\ method three & Improve the particle filter algorithm & Mean filling method \\ method four & Improve the particle filter algorithm & MissForest filling method \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental comparison and verification design. From the distribution chart in Figure 10, method 4 (improved particle filter + MissForest Imputation) demonstrates concentrated and stable particle distribution with the smallest error range, indicating superior data filtering performance. In contrast, the filter particles of method 1 (traditional particle filter + mean filling method) have a larger and more fluctuating error range, indicating poor method effectiveness and significant data fluctuations. Compared to method 1, the error distribution of the filter particles in method 2 is more concentrated, suggesting that the MissForest filling method effectively reduces data fluctuations and provides higher precision reconstruction results.