# A Comprehensive Hybrid Deep Learning Approach for Accurate Status Predicting of Hydropower Units
## 5 Experimental Results and Discussion
### Comparative Experiment Analysis  
This section evaluates the performance of five different neural network architectures in predicting unit flow rate, guide vane opening, and maximum water guide tile temperature. The predictive accuracy of each model was assessed using MSE, MAE, and \(R^{2}\). Scatter plots, fitted curves, and the Pearson correlation coefficient were used to evaluate the consistency of the predicted trends. In the comparative analysis of predictive models for hydropower unit status as detailed in Figure 6, the hybrid deep learning model shows closer alignment with the actual data curves than the other models tested: GRU, LSTM, LSTM-GRU, and RS. This alignment is quantitatively supported by the performance metrics presented in Table 5. Specifically, the hybrid model achieves the lowest MSE and MAE at 294.481 and 3.508, respectively, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Prediction Status** & **Optimized Method** & **MSE** & **MAE** & \(R^{2}\) \\ \hline \multirow{4}{*}{Unit Flow Rate (m\({}^{3}\)/s)} & GS & 350.592 & 3.557 & 0.870 \\  & GA & 339.178 & 3.138 & 0.874 \\  & RS & 331.760 & 6.957 & 0.877 \\  & Proposed & 294.481 & 3.508 & 0.891 \\ \hline \multirow{4}{*}{Guide Vane Opening (degrees)} & GS & 10.351 & 1.036 & 0.899 \\  & GA & 12.265 & 1.734 & 0.881 \\  & RS & 9.962 & 0.946 & 0.903 \\  & Proposed & 8.943 & 0.553 & 0.913 \\ \hline \multirow{2}{*}{Maximum Water  Guide Tile Temperature (C)} & GS & 0.110 & 0.113 & 0.989 \\  & GA & 0.118 & 0.156 & 0.988 \\ \multirow{2}{*}{Temperature (C)} & RS & 0.084 & 0.134 & 0.992 \\  & Proposed & 0.058 & 0.097 & 0.994 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of hyperparameter optimization methods. indicative of its superior accuracy in forecasting unit flow rates. In comparison, the GRU model recorded an MSE of 395.735 and an MAE of 4.247, the LSTM model recorded values of 402.180 and 4.411, and the LSTM-GRU model had an MSE of 389.763 and an MAE of 6.007, while the RS model showed an MSE of 331.760 and an MAE of 6.957. The lower error values for the hybrid model suggest fewer large errors and a more reliable average prediction error. This is significant because the MSE metric, which squares errors, disproportionately impacts the score with larger error values, whereas the MAE provides an average level of predictive errors, offering a direct measure of average error magnitude. Furthermore, the hybrid model not only outperforms in error metrics but also achieves the highest coefficient of determination (\(R^{2}\)) among the models at 0.891, compared with 0.853 for GRU, 0.851 for LSTM, 0.855 for LSTM-GRU, and 0.877 for RS. This high \(R^{2}\) value indicates a better fit to the actual data trends, signifying the hybrid model's effectiveness in capturing the underlying patterns in the data. The scatter plots in Figure 9 further illustrate these findings by depicting the alignment of the predicted values with the actual values through fitted lines. Ideally, perfect predictions would result in a Pearson correlation coefficient of one. The hybrid model's fitted line shows a Pearson coefficient of 0.944, which is closer to the ideal than those achieved by GRU (0.925), LSTM (0.924), LSTM-GRU (0.929), and RS (0.940). This indicates that the hybrid model's predictions are not only more accurate in numerical terms but also more reflective of the true data trends in the hydropower unit flow rates. In the context of predicting the guide vane opening for hydropower units, the comparative analysis highlighted in Figure 7 clearly demonstrates that the hybrid deep learning model more accurately aligns with the actual values than the alternative models (GRU, LSTM, LSTM-GRU, and RS). This superior alignment is quantitatively supported by the performance metrics in Table 5, where the hybrid model records the lowest MSE and MAE at 8.943 and 0.553, respectively. In contrast, the MSE and MAE for GRU are 10.831 and 1.146; for LSTM, 11.783 and 0.913; for LSTM-GRU, 11.476 and 0.941; and for RS, 9.962 and 0.946.