# Multi-Point Deformation Prediction Model for Concrete Dams Based on Spatial Feature Vector
## 3 Case Study
### Validation of the Validity of a Multi-Point Model Incorporating Spatial Feature Vectors  
To more intuitively verify the validity of the multi-point model with fused spatial feature vectors, the final input factor \(X_{f^{\prime}}\) constructed in the 2D-1D-CNN model in Section 3.2 is extracted from the network, reconstructed as the input factor \(X_{f^{\prime\prime}}\in R^{n\times(k\times 10)}\) with fused spatial features according to the format of the input factor of the SVM model, input to the SVM model prediction and compared with the conventional multi-point SVM model with the introduction of spatial coordinates in Section 3.2 to analyze the variation of prediction accuracy of the SVM model with different input factors; the results are shown in Figure 7 and Table 3.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Monitoring** & **Statistical** & **2D-1D-CNN** & **SVM** & **BPNN** & **1D-CNN** & **HT\({}_{\text{A}}\)T** \\ \hline \multirow{4}{*}{EX3} & RMSE/mm & 0.121 & 0.5472 & 0.4162 & 0.4222 & 0.3426 \\  & MAE/mm & 0.0971 & 0.4782 & 0.3649 & 0.3826 & 0.2840 \\  & MAPE & 11.75\% & 46.82\% & 39.14\% & 51.27\% & 38.30\% \\  & \(R^{2}\) & 0.9658 & 0.8678 & 0.5957 & 0.5840 & 0.7261 \\ ine & RMSE/mm & 0.1635 & 0.4263 & 0.7347 & 0.4413 & 0.5345 \\ EX5 & MAE/mm & 0.1241 & 0.3245 & 0.6284 & 0.2713 & 0.4236 \\  & MAPE & 6.47\% & 21.04\% & 24.90\% & 13.82\% & 19.43\% \\  & \(R^{2}\) & 0.9694 & 0.8486 & 0.3833 & 0.7775 & 0.6736 \\ ine & RMSE/mm & 0.1296 & 0.5349 & 0.4781 & 0.5115 & 0.4134 \\ EX7 & MAE/mm & 0.1045 & 0.4501 & 0.3176 & 0.412 & 0.3437 \\  & MAPE & 4.95\% & 17.27\% & 14.53\% & 16.54\% & 15.94\% \\  & \(R^{2}\) & 0.9772 & 0.8817 & 0.6892 & 0.6442 & 0.7676 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Model prediction statistical indexes comparison table.  
Figure 7: Comparison of SVM prediction results with different input factors.  
Figure 7 and Table 3 show that the prediction results of the SVM model with spatial feature vectors can be more in line with the trend of measured values, and the prediction accuracy is more significantly improved at the moment when the deformation fluctuation is large. The RMSE index on the three measuring points decreased by 56.51%, 14.62% and 44.87%, respectively. This shows that the spatial feature vectors used in this paper can more accurately reflect the spatial correlation between the deformation sequences of each measuring point and have validity. At the same time, because the traditional multi-point model needs to combine the causal factor with the zeroth to third degree of the spatial coordinates, every time the one-dimensional coordinate increases, the number of input factors increases exponentially by four, which easily produces the problem of excessive input factors. The spatial feature factor constructed in this paper reflects the spatial characteristics in the form of vectors, and the complexity of the space increases linearly, so the overall computational efficiency is stronger than that of the traditional multi-point model; with the increase of the coordinate dimension, the advantages of the spatial feature factor proposed in this paper in computational efficiency will be more prominent.