## 3 Case Study
### Synchronous Prediction with Multiple Inputs and Multiple Outputs Model  
Following the determination of the unified factor set, the trained MIMO-PSO-LSSVM model can be utilized to achieve the synchronous prediction of the displacement of the same dam block. In this paper, three prediction models, SVM, BPNN, and PSO-LSSVM, are selected as comparison models for the MIMO-PSO-LSSVM model. The computational parameters of the BPNN model are set as follows: the maximum number of training iterations is set to 1000, the learning rate is 0.1, and a default sigmoid function is employed between the input and hidden layers. The computational parameters of the SVM model are set as follows: the radial basis kernel function \(g\) takes the value of 0.8, and the penalty factor \(c\) takes the value of 4.0. The computational parameters of the PSO-LSSVM model are set as follows: the SVM adopts the least squares learning algorithm and uses the radial basis kernel function, the PSO optimization algorithm is chosen to determine the penalty parameters and the radial basis kernel function parameters, the initial population size of  
Figure 13: Comparison of model prediction performance before and after feature selection. the PSO algorithm is set to 20, the maximum number of iterations is 300, the inertia factor \(\omega\) is set to 0.8, and the learning factors \(c_{1}\) and \(c_{2}\) are set to 2. The computational parameters of the MIMO-PSO-LSSVM model are set as follows: the penalty parameter, the regularisation parameter, and the radial basis kernel function parameter take values ranging from 0.01 to 15, and the PSO optimization algorithm is chosen to determine these parameters; the initial population size of the PSO algorithm is taken to be 20, the maximum number of iterations is 300, the inertia factor \(\omega\) takes the value of 0.8, and the learning factors \(c_{1}\) and \(c_{2}\) take the value of 2. As illustrated in Figure 14, the performance of the four prediction models, SVM, BPNN, PSO-LSSVM, and MIMO-PSO-LSSVM, is evaluated through eight measurement points. These eight measurement points comprise the non-overflow dam block measurement points YZ15-1, YZ16-1, and YZ17-1, the overflow dam block measurement points YZ20-1, YZ21-1, and YZ22-1, and the different elevation measurement points DC23-1 and DC23-2. It can be observed that all the models capture the main trends of the displacement changes of the dam block, with the MIMO-PSO-LSSVM model predicting the closest to the true value of the displacement, while the PSO-LSSVM model is the next closest, and the BPNN and SVM models predicting the worst. Figure 14: _Cont._  
Figure 14: Comparison of predicted dam displacements using different prediction models. The comparison of the comprehensive performance evaluation metrics under different prediction models is shown in Table 5. Each model is benchmarked against the proposed MIMO-PSO-LSSVM model. The analysis is conducted based on the average data obtained from eight measurement points. Compared with the SVM model, the MIMO-PSO-LSSVM model achieves an improvement of 3.56%, 60.18%, and 58.92%, in terms of R\({}^{2}\), MAE, and RMSE, respectively. Compared with the BPNN model, the MIMO-PSO-LSSVM model achieves an improvement of 2.54%, 56.13%, and 51.22%, in terms of R\({}^{2}\), MAE, and RMSE, respectively. Compared with the PSO-LSSVM model, the MIMO-PSO- LSSVM model achieves an improvement of 0.27%, 12.72%, and 9.74%, in terms of R\({}^{2}\), MAE, and RMSE, respectively. The enhancement effect is illustrated in Figure 15. This result demonstrates that when predicting multiple datasets with high correlation, the prediction accuracy of the traditional single-output model is inferior to that of the proposed MIMO-PSO-LSSVM model. This is due to the fact that the MIMO-PSO-LSSVM model takes into account the potential spatial correlation between the displacement data, thus enhancing the prediction accuracy.