## 3 Case Study
### Synchronous Prediction with Multiple Inputs and Multiple Outputs Model
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Measurement Point** & **Prediction Model** & \(\mathbf{R^{2}}\) & _MAE/(mm)_ & _RMSE/(mm)_ \\ \hline \multirow{4}{*}{YZ15-1} & SVM & 0.9351 (\(-5.39\)\%) & 0.3027 (\(-56.29\)\%) & 0.4102 (\(-52.71\)\%) \\  & BPNN & 0.9450 (\(-4.29\)\%) & 0.2889 (\(-54.21\)\%) & 0.3777 (\(-48.64\)\%) \\  & PSO-LSSVM & 0.9826 (\(-0.29\)\%) & 0.1447 (\(-8.59\)\%) & 0.2122 (\(-8.57\)\%) \\  & MIMO-PSO-LSSVM & **0.9855 (0\%)** & **0.1323 (0\%)** & **0.1940 (0\%)** \\ \hline \multirow{4}{*}{YZ16-1} & SVM & 0.9492 (\(-4.15\)\%) & 0.3120 (\(-57.98\)\%) & 0.4356 (\(-52.50\)\%) \\  & BPNN & 0.9593 (\(-3.05\)\%) & 0.2833 (\(-53.72\)\%) & 0.3901 (\(-46.96\)\%) \\  & PSO-LSSVM & 0.9852 (\(-0.34\)\%) & 0.1534 (\(-14.51\)\%) & 0.2348 (\(-11.89\)\%) \\  & MIMO-PSO-LSSVM & **0.9886 (0\%)** & **0.1311 (0\%)** & **0.2069 (0\%)** \\ \hline \multirow{4}{*}{YZ17-1} & SVM & 0.9630 (\(-3.15\)\%) & 0.3481 (\(-64.23\)\%) & 0.4779 (\(-57.27\)\%) \\  & BPNN & 0.9732 (\(-2.07\)\%) & 0.3136 (\(-60.30\)\%) & 0.4068 (\(-49.80\)\%) \\  & PSO-LSSVM & 0.9921 (\(-0.12\)\%) & 0.1421 (\(-12.41\)\%) & 0.2204 (\(-7.34\)\%) \\  & MIMO-PSO-LSSVM & **0.9933 (0\%)** & **0.1245 (0\%)** & **0.2042 (0\%)** \\ \hline \multirow{4}{*}{YZ20-1} & SVM & 0.9760 (\(-2.11\)\%) & 0.4597 (\(-62.80\)\%) & 0.6691 (\(-62.64\)\%) \\  & BPNN & 0.9818 (\(-1.51\)\%) & 0.4320 (\(-60.42\)\%) & 0.5814 (\(-57.00\)\%) \\  & PSO-LSSVM & 0.9961 (\(-0.05\)\%) & 0.1881 (\(-9.08\)\%) & 0.2700 (\(-7.39\)\%) \\  & MIMO-PSO-LSSVM & **0.9966 (0\%)** & **0.1710 (0\%)** & **0.2500 (0\%)** \\ \hline \multirow{4}{*}{YZ21-1} & SVM & 0.9734 (\(-2.38\)\%) & 0.5535 (\(-62.73\)\%) & 0.8382 (\(-64.30\)\%) \\  & BPNN & 0.9857 (\(-1.11\)\%) & 0.4730 (\(-56.38\)\%) & 0.6149 (\(-54.17\)\%) \\ \cline{1-1}  & PSO-LSSVM & 0.9959 (\(-0.07\)\%) & 0.2301 (\(-10.35\)\%) & 0.3295 (\(-9.21\)\%) \\ \cline{1-1}  & MIMO-PSO-LSSVM & **0.9966 (0\%)** & **0.2063 (0\%)** & **0.2992 (0\%)** \\ \hline \multirow{4}{*}{YZ22-1} & SVM & 0.9731 (\(-2.39\)\%) & 0.5630 (\(-63.21\)\%) & 0.8681 (\(-63.32\)\%) \\  & BPNN & 0.9848 (\(-1.18\)\%) & 0.4784 (\(-56.71\)\%) & 0.6528 (\(-51.23\)\%) \\ \cline{1-1}  & PSO-LSSVM & 0.9956 (\(-0.08\)\%) & 0.2415 (\(-14.23\)\%) & 0.3519 (\(-9.52\)\%) \\ \cline{1-1}  & MIMO-PSO-LSSVM & **0.9964 (0\%)** & **0.2071 (0\%)** & **0.3184 (0\%)** \\ \hline \multirow{4}{*}{DC23-1} & SVM & 0.9476 (\(-4.78\)\%) & 0.3303 (\(-61.94\)\%) & 0.4807 (\(-63.22\)\%) \\ \cline{1-1}  & BPNN & 0.9599 (\(-3.44\)\%) & 0.3174 (\(-60.40\)\%) & 0.4206 (\(-57.96\)\%) \\ \cline{1-1}  & PSO-LSSVM & 0.9912 (\(-0.17\)\%) & 0.1457 (\(-13.75\)\%) & 0.1968 (\(-10.16\)\%) \\ \cline{1-1}  & MIMO-PSO-LSSVM & **0.9929 (0\%)** & **0.1257 (0\%)** & **0.1768 (0\%)** \\ \hline \multirow{4}{*}{DC23-2} & SVM & 0.9326 (\(-4.26\)\%) & 0.2231 (\(-40.21\)\%) & 0.2933 (\(-35.87\)\%) \\ \cline{1-1}  & BPNN & 0.9365 (\(-3.82\)\%) & 0.2201 (\(-39.39\)\%) & 0.2847 (\(-33.93\)\%) \\ \cline{1-1}  & PSO-LSSVM & 0.9620 (\(-1.07\)\%) & 0.1653 (\(-19.30\)\%) & 0.2202 (\(-14.59\)\%) \\ \cline{1-1}  & MIMO-PSO-LSSVM & **0.9723 (0\%)** & **0.1334 (0\%)** & **0.1881 (0\%)** \\ \hline \hline \end{tabular} Note: Values in parentheses refer to the reduction percentage in performance of the single-output model relative to the multi-output model, respectively. Bold values indicate the optimal value of the indicator.  
\end{table} 
Table 5: Comprehensive performance evaluation indicators under different prediction models. Figure 15: _Cont._  
Furthermore, the MIMO-PSO-LSSVM model has been shown to exhibit superiority over the single-output PSO-LSSVM model with regard to prediction efficiency. To illustrate this, consider the non-overflow dam section measurement points YZ15-1, YZ16-1, and YZ17-1. The MIMO-PSO-LSSVM model requires approximately 203 s to predict all the measurement points, whereas the single-output PSO-LSSVM model requires approximately 614 s, which is about three times higher in terms of speed.