## 4 Comparisons and Results
### Simulation Comparison of GWO-GRU Model and VMD-GWO-GRU Model  
To enhance the predictive performance of the water quality parametric model, this study employed the VMD method to decompose the DO dataset. This decomposition allowed for a more accurate representation of the variations in DO characteristics. After fully decomposing the DO dataset using the VMD method, eight components were obtained, and then GRU models were established for the eight obtained components. Each GRU model used the GWO algorithm to find the optimal hyperparameters to establish eight GWO-GRU models. The prediction results obtained by each component were superimposed to obtain the final prediction result. The population size and number of iterations of GWO remained the same as above and were also set to 5 and 20. The hyperparametric combinations of each GWO-GRU model after optimization by the GWO algorithm are shown in Table 6.  
The combined prediction results, as shown in Figure 14, highlight a significant improvement in the predictive accuracy of the water quality parameter model. The original  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Component** & **Number of Hidden Layer Units** & **Initial Learning Rate** & **Iterations** \\ \hline VMD-IMF 1 & 121 & 0.01645 & 313 \\ VMD-IMF 2 & 94 & 0.00723 & 365 \\ VMD-IMF 3 & 104 & 0.00649 & 378 \\ VMD-IMF 4 & 91 & 0.00775 & 432 \\ VMD-IMF 5 & 113 & 0.00622 & 500 \\ VMD-IMF 6 & 50 & 0.00576 & 474 \\ VMD-IMF 7 & 85 & 0.00365 & 447 \\ VMD-IMF 8 & 102 & 0.01032 & 442 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Hyperparameters for each component model.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **RMSE** & **MAPE** \\ \hline GRU & 0.40713 & 3.4169\% \\ GWO-LSTM & 0.41804 & 3.8265\% \\ GWO-GRU & 0.34507 & 2.8886\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Evaluation indicators for the GRU, GWO-GRU, and GWO-LSTM models.  
data are represented by the black curve, while the purple curve shows the predictions and absolute errors of the GWO-GRU model, and the orange curve displays the predictions and absolute errors of the VMD-GWO-GRU model. As can be seen in Figure 14a, the VMD-GWO-GRU model we proposed significantly improved the lag of the prediction results. The prediction results were closer to the real monitoring data. It was better at predicting some mutation values, but it was found that unfortunately, the predictive effect was not good at the 100 th to 125 th sampling points. This may have been caused by the VMD method's insufficient decomposition of the original data. However, the method we proposed has obvious advantages in overall prediction accuracy. It can be seen that the absolute error of the predicted value of the VMD-GWO-GRU model relative to the true value is smaller in Figure 14b.  
Table 7 displays the RMSE and MAPE outcomes for both the VMD-GWO-GRU model and the GWO-GRU model. In contrast to the GWO-GRU model, the VMD-GWO-GRU model demonstrated a reduction of 23.9% and 25.9% in its RMSE and MAPE, correspondingly. The experimental results show that the VMD method can be used to decompose original data into multiple components and effectively extract the change characteristics of a water quality parametric sequence. This helps the GWO-GRU model to fully learn the change characteristics of each component. The data in Table 7 support the effectiveness of the VMD method we introduced in the data processing stage, and more accurate prediction results for future data values of water quality parameters were obtained.