# Dam Deformation Monitoring Model Based on Deep Learning and Split Conformal Quantile Prediction
## 3 Case Study
### Comparative Analysis of Different Interval Prediction Models  
#### 3.3.1 Interval Prediction Performance of SCQP  
This comparative experiment primarily validates the superiority and effectiveness of SCQP over other interval prediction methods for dam deformation prediction. In addition to the proposed Bi-SCQLSTM, the baseline models involved in the experiment include SCP, QR, Confidence Interval Estimation (CIE), and GPR. For the SCP, QR, and CIE methods, the base regressor is set to Bi-LSTM. Figure 10 illustrates the prediction results of different interval methods on L5H291R. The evaluation results of the deformation PIs constructed by these models are presented in Table 1.  
Figure 10: _Cont._  
It can be observed in Figure 10 that the PIs constructed by the Bi-SCQLSTM and the Bi-QLSTM are significantly different from other models. The coverage widths of these PIs show dynamic changes according to the actual dam deformation process. In practice monitoring experience, the peaks and troughs often imply sudden deformation due to changes in external environmental factors. Consequently, deformation uncertainty is more pronounced in these periods. The prediction results of the Bi-SCQLSTM indeed conform to this feature (the width of the interval coverage at the peaks and troughs is significantly larger than in other periods), which illustrates that the proposed model can adequately accommodate the non-homogeneous uncertainties of deformation and construct the corresponding PIs. As can be seen in Table 1, the deformation PIs constructed by the Bi-SCQLSTM are more consistent with the criteria of high-quality PIs than those constructed by other interval prediction methods. The _PICP_ of the Bi-SCQLSTM model is 0.951, while the MPIW is only 5.815 mm The Bi-SCQLSTM achieves the smallest _CWC_ among five models, namely 5.815 mm. These results demonstrate that our proposed Bi-SCQLSTM strikes a delicate balance between effective coverage and interval coverage width and applies to the dam deformation data of different distribution types. Thanks to the quantile pinball loss, the proposed model can generate high-confidence PIs that satisfy the PINC and reflect the heterogeneous uncertainties of dam deformation processes under the influence of combined factors through the adaptive change of the width of PIs. On the other hand, the SCP algorithm enables the Bi-SCQLSTM to further reduce the coverage width of the dam deformation PI by identifying abrupt changes within the samples while still ensuring that the effective coverage rate meets the standard. This allows the generated deformation PIs to more closely adhere to high-quality standards. It is worth noting that although the PIs constructed by GPR satisfy the _PINC_ in terms of PICP as high as 0.986, the consequence of over-pursuing the effective coverage is reflected in having the high _MPIW_, which are 18.429. The PIs that are too wide are not conducive to \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Deformation Interval**} & \multicolumn{3}{c}{**LSH291R**} \\ \cline{2-4}  & **PICP** & **MPIW (mm)** & **CWC (mm)** \\ \hline Bi-SCQLSTM & 0.951 & 5.815 & 5.815 \\ Bi-QLSTM & 0.957 & 7.853 & 7.853 \\ Bi-SCLSTM & 0.821 & 8.577 & 39.735 \\ CIE & 0.713 & 39.735 & 100.329 \\ GPR & 0.986 & 18.429 & 18.429 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Quantitative evaluation of different interval prediction results. Figure 10: 95% PIs obtained from different interval methods on L5H291R: (**a**) Bi-SCLSTM, (**b**) Bi-QLSTM, (**c**) CIE, (**d**) GPR, (**e**) Bi-SCQLSTM. quantifying the uncertainties in dam deformation, and therefore the confidence in these deformation PIs is not satisfactory. Table 2 presents the computation times for different interval prediction models. Among them, GPR exhibits the lowest computational complexity and the shortest runtime, taking only 20.932 s. This is followed by the CIE and Bi-SCLSTM models, which are based on point prediction, with computation times of 28.024 s and 28.513 s, respectively.