# A Comprehensive Hybrid Deep Learning Approach for Accurate Status Predicting of Hydropower Units
## 5 Experimental Results and Discussion
### Comparative Experiments Results  
To demonstrate the superiority of the proposed hybrid deep learning model, experiments were conducted using real-time data collected from hydroelectric power units, specifically focusing on unit flow rate, guide vane opening, and maximum water guide tile temperature. The experimental results of the hybrid model were compared with four sets of experiments: LSTM, GRU, LSTM-GRU, and a variation of the hybrid model in which the TSO algorithm was substituted with a random search method. For the LSTM, GRU, and LSTM-GRU models, we utilized random search for hyperparameter optimization. The number of iterations was set to 50, and the Root Mean Squared Error (RMSE) was used as the evaluation metric. The hyperparameter combination yielding the minimum RMSE was selected as the optimal set for each model. The hyperparameter optimization results for the comparative models are presented in Tables 1-3. The proposed model was benchmarked against the LSTM, GRU, and LSTM-GRU hybrid models, and a version of the hybrid model where TSO was replaced with a random search optimization algorithm (referred to as RS) to validate its predictive accuracy. The prediction error curves are displayed in Figures 6-8. Figure 6: Comparison results of unit flow rate prediction models. Figure 7: Comparison results of guide vane opening prediction models. To quantitatively compare the performance of the different models in predicting unit flow rate, guide vane opening, and maximum water guide tile temperature, several key indicators were computed and are presented in Table 4.  
Scatter plots visually demonstrate the relationship between predicted and actual values by the distribution of points. In these graphs, the \(x\)-axis corresponds to the actual values, while the \(y\)-axis denotes the predicted values. Each point corresponds to an observation, with its coordinates representing the actual and predicted values, respectively. The line of best fit drawn through the points in the scatter plots offers a more intuitive view of the relationship between the predicted and actual values. The Pearson correlation coefficient, \(r\), provides a quantitative measure of the strength and direction of this linear relationship, indicating how closely the predictions align with the actual outcomes. Scatter plots for the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Prediction Status** & **Model** & **MSE** & **MAE** & \(\mathbf{R^{2}}\) \\ \hline \multirow{4}{*}{Unit Flow Rate (m\({}^{3}\)/s)} & GRU & 395.735 & 4.247 & 0.853 \\  & LSTM & 402.180 & 4.411 & 0.851 \\  & LSTM-GRU & 389.763 & 6.007 & 0.855 \\  & RS & 331.760 & 6.957 & 0.877 \\  & Proposed & 294.481 & 3.508 & 0.891 \\ \hline \multirow{4}{*}{Guide Vane Opening (degrees)} & GRU & 10.831 & 1.146 & 0.895 \\  & LSTM & 11.783 & 0.913 & 0.886 \\ \cline{1-1}  & LSTM-GRU & 11.476 & 0.941 & 0.889 \\ \cline{1-1}  & RS & 9.962 & 0.946 & 0.903 \\ \cline{1-1}  & Proposed & 8.943 & 0.553 & 0.913 \\ \hline \multirow{4}{*}{Maximum Water  Guide Tile Temperature (\({}^{\circ}\)C)} & GRU & 0.109 & 0.123 & 0.989 \\ \cline{1-1}  & LSTM & 0.107 & 0.117 & 0.989 \\ \cline{1-1}  & LSTM-GRU & 0.099 & 0.125 & 0.990 \\ \cline{1-1}  & RS & 0.084 & 0.134 & 0.992 \\ \cline{1-1}  & Proposed & 0.058 & 0.097 & 0.994 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of different models under three prediction states. Figure 8: Comparison results of maximum water guide tile temperature prediction models. unit flow rate, guide vane opening, and maximum water guide tile temperature are shown in Figures 9-11. Figure 10: Guide vane opening scatter plot: (**a**) GRU model predicted vs. actual guide vane opening (degrees). (**b**) LSTM model predicted vs. actual guide vane opening (degrees). (**c**) LSTM-GRU model predicted vs. actual guide vane opening (degrees). (**d**) RS model predicted vs. actual guide vane opening (degrees). (**e**) Proposed model predicted vs. actual guide vane opening (degrees).