# A Comprehensive Hybrid Deep Learning Approach for Accurate Status Predicting of Hydropower Units
## 5 Experimental Results and Discussion
### Comparative Experiment Analysis
These results indicate that the hybrid model not only presents fewer large errors but also maintains a lower average predictive error compared with the other models. Moreover, the hybrid model boasts the highest coefficient of determination (\(R^{2}\)) at 0.913, surpassing the \(R^{2}\) values of GRU (0.895), LSTM (0.886), LSTM-GRU (0.889), and RS (0.903). This suggests that the hybrid model provides a better fit compared with the other models analyzed. Further analysis from Figure 10 shows the Pearson correlation coefficients of the fitted lines for each model: GRU at 0.946, LSTM at 0.942, LSTM-GRU at 0.946, RS at 0.953, and the hybrid model at 0.956. The closer proximity of the hybrid model's Pearson coefficient to one, which would indicate perfect prediction alignment, underscores its superior trend prediction relative to the actual values of guide vane opening. This fitting proximity is a crucial indicator that the hybrid deep learning model not only provides higher accuracy in predictions but also more closely matches the actual trends observed in the data. These results suggest that the hybrid model, along with LSTM-GRU and RS, offers a significant improvement over single-prediction models (GRU and LSTM) in terms of the predictive accuracy and alignment with actual data trends. This further validates the efficacy of using a hybrid deep learning approach to achieve better predictive outcomes in the context of hydropower unit operations. The predictive outcomes for the maximum water guide tile temperature are visually presented in Figure 8. When evaluating the performance metrics summarized in Table 5, the hybrid deep learning model exhibits superior accuracy with the smallest maximum and average prediction errors compared with the GRU, LSTM, LSTM-GRU, and RS models. Specifically, the MSE and MAE for the hybrid model are 0.058 and 0.097, respectively. In contrast, GRU's MSE and MAE are 0.109 and 0.123; LSTM's are 0.107 and 0.117; LSTM-GRU's are 0.099 and 0.125; and RS's are 0.084 and 0.134. Moreover, the coefficient of determination (\(R^{2}\)) values further underline the fitting superiority of the hybrid model, which achieved an \(R^{2}\) of 0.994, compared with GRU (0.989), LSTM (0.989), LSTM-GRU (0.990), and RS (0.992). These values demonstrate that the hybrid model not only predicts with less error but also aligns more closely with the actual data trends. In terms of prediction trends, all four models exhibit strong predictive capabilities. The GRU model has a fitting coefficient of 0.995, the LSTM model also has a fitting coefficient of 0.995, the LSTM-GRU model shares the same fitting coefficient of 0.995, and the RS model has a slightly higher coefficient of 0.996. The proposed hybrid deep learning model achieves the highest fitting coefficient of 0.997 in Figure 11. While the GRU, LSTM, and LSTM-GRU models share the same fitting coefficient, their specific MSE, MAE, and R\({}^{2}\) values differ. The fitting coefficient reflects the model's ability to capture trends in data fluctuations, while the metrics indicate the model's precision in predicting exact values. The proposed hybrid deep learning model outperforms the others by achieving a balance between trend capture and prediction accuracy, making it more suitable for the operational conditions of hydropower units. Although the improvement in the Pearson correlation coefficient between the proposed model and the other models is relatively small at 0.002, its significance becomes more evident when considering the substantial reductions in the other key error metrics. Specifically, the MSE and MAE for the hybrid model are 0.058 and 0.097, respectively, compared with the MSE and MAE for GRU (0.109 and 0.123), LSTM (0.107 and 0.117), LSTM-GRU (0.099 and 0.125), and RS (0.084 and 0.134). The proposed model achieves a reduction in MSE of 46.79% compared with GRU, 45.79% compared with LSTM, 41.41% compared with LSTM-GRU, and 30.95% compared with RS.