## 4 Experimental Process and Analysis
### Prediction of Dye Formulas and Ultrasonic Pretreatment Power
#### 4.4.3 Comparative Analysis of Experimental Results
Removing the SAT Fusion module and the gated linear unit resulted in a sequential decrease in model performance, indicating that the gated linear unit and the SDIIM- and SCIIM-based SAT Fusion modules are essential for optimizing network performance. The effectiveness of the gated linear unit and the SDIIM- and SCIIM-based SAT Fusion modules is thus verified. It can be seen that the \(R^{2}\), \(RPIQ\), \(RPD\), \(RMSE\), and \(MAE\) values of the entire SAT Fusion-Gated BiLSTM network reached the optimal performance level, proving the effectiveness of each module. As shown in Table 4 and Figure 14, the proposed IDBO-SAT Fusion-Gated BiLSTM model achieved the best performance among all evaluated models, with an \(R^{2}\) value of 0.9274 and \(RMSE\), \(RPIQ\), \(RPD\), and \(MAE\) values of 0.0470, 5.5825, 5.0400, and 0.0229, respectively. These values are the optimal results among the models tested. Compared to the SAT Fusion-Gated BiLSTM model without parameter optimization by the IDBO algorithm, the IDBO-SAT Fusion-Gated BiLSTM model demonstrated further enhanced predictive performance, with increases in \(R^{2}\), \(RPIQ\), and \(RPD\) values of 3.06%, 16.29%, and 16.29%, respectively, and decreases in \(RMSE\) and \(MAE\) values of 14.08% and 18.21%, respectively. The experimental results confirm that the proposed method outperforms other approaches in terms of evaluation metrics. The results demonstrate that even in the absence of the Improved Dung Beetle Optimization (IDBO) algorithm for parameter optimization, the proposed SAT Fusion-Gated BiLSTM model is capable of effectively handling multimodal and complex spectral data. Furthermore, the model performance is markedly superior to that of the commonly utilized models, including LSTM, ConvLSTM, GRU, BiLSTM, CNNs, SVR, and RF. This corroborates the assertion that the proposed SAT Fusion module is efficacious in integrating disparate spectral features, thereby reducing the incidence of prediction errors. The predictive efficacy of the model is further enhanced following the optimization of its parameters through the application of the IDBO algorithm. To sum up, the proposed IDBO-SAT Fusion-Gated BiLSTM model evinces a pronounced improvement across all evaluation metrics, particularly in the \(RPIQ\) metric and the \(RPD\) metric, which exhibits an increase of 100.80% in comparison to the BiLSTM, which is the best performing of the traditional deep learning models. As shown in Figure 15, the predicted values were very close to the true values. The scatter plots for reactive red, yellow, and blue dyes (Figure 15a, Figure 15b, and Figure 15c) exhibited strong linear relationships, with \(R^{2}\) values of 0.928, 0.876, and 0.925, respectively. These \(R^{2}\) values indicate that the model explains 92.8%, 87.6%, and 92.5% of the variance in the predicted dye concentrations, respectively. For the ultrasonic pretreatment power (Figure 15d), an even stronger linear correlation was observed, with an \(R^{2}\) value of 0.980, indicating that the model explains 98.0% of the variance in predicted power values. In summary, these results demonstrate the model's strong performance, achieving high accuracy in predicting both dye concentrations and ultrasonic pretreatment power. This highlights the model's effectiveness and reliability in these predictive tasks.