## 6 ATT-BiLSTM and SVR Repair Accuracy Evaluation
### Evaluation of ATT-BiLSTM Error Metrics  
In order to further validate the repair accuracy of the model, three evaluation metrics--MSE (mean square error), RMSE (root mean square error), and R\({}^{2}\) (coefficient of determination)--were introduced. Error evaluation metrics, global performance analysis, and local performance analysis were used for specific description [33]. 1. Mean Square Error (MSE): A statistical measure of the discrepancy between the restoration value and the true value. A low MSE indicates a high degree of accuracy in the restoration, with smaller values approaching 0. The formula for calculating MSE is shown in Formula (10). Where \(n\) denotes the sample size, \(y_{i}\) denotes the actual observations, and \(\hat{y}_{i}\) denotes the model predictions. 2. Root Mean Square Error (RMSE): The square root of the mean square error (MSE), which is a metric used to quantify the discrepancy between the values predicted by a model and the actual values [34]. \[RMSE=\sqrt{\frac{1}{n}{\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}}}\] (13)
3. Coefficient of Determination (R\({}^{2}\)): A statistical measure of how well a model aligns with observed data. A value of R\({}^{2}\) close to 1 indicates a stronger match between the model and the data, suggesting a higher degree of model fit. \[R^{2}=1-\frac{\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}}{\sum_{i=1}^{n}(y_{i}- \overline{y_{i}})^{2}}\] (14)
4. Global performance analysis The repair performance of the ATT-BiLSTM model for the global deflection dataset (including the repaired data as well as the normal data) is analyzed as follows: 1. The MSE is calculated to be 0.0226, indicating that the mean squared error between the predicted and true values of the model in the entire dataset is minimal. This finding reflects the model's strong predictive ability in the global range and its ability to accurately fit the overall distribution of the data. 2. The RMSE is 0.1505, which further confirms that the absolute value of the model's prediction error is small, indicating that the model's prediction accuracy in the whole dataset is high. 3. R\({}^{2}\) is 0.9943, which is close to 1. This indicates that the model has a good fit to the global dataset and that it is also predictive. Based on the aforementioned calculations, the ATT-BiLSTM model demonstrates remarkably high levels of prediction accuracy and goodness of fit on the global dataset. Furthermore, the model is capable of effectively capturing the overall trend and characteristics of the data. A comparison plot of the original data with all the data following ATT-BiLSTM repair is shown in Figure 11. In this figure, the vertical coordinate is the deflection data (mm), and the horizontal coordinates are the deflection data points. 2. Local performance analysis The repair performance of the ATT-BiLSTM model for the anomalous deflection dataset is analyzed as follows: 1. The MSE was calculated to be 0.5576, which is high relative to the global MSE value. However, the error value is still in the acceptable range due to the fact that anomalous data usually has higher uncertainty and complexity [35]. 2. The RMSE is 0.7467, which is marginally higher than the global RMSE due to the nature of the anomalous data. However, the accuracy generally meets the requirements. 3. The R\({}^{2}\) value of 0.9388 indicates a slight decrease compared to the global R\({}^{2}\) value, yet it remains close to 1, suggesting that the model continues to adequately fit the anomalous data and effectively identify and repair most anomalous data while maintaining high prediction accuracy. The comparison graph of the original anomalous data and the repaired anomalous data is shown in Figure 12.  
The ATT-BiLSTM model demonstrates a high degree of prediction accuracy and goodness of fit on the global deflection dataset, as evidenced by its ability to accurately fit the overall distribution and trend of the data.