## 4 Experimental Process and Analysis
### Prediction of Dye Formulas and Ultrasonic Pretreatment Power
#### 4.4.3 Comparative Analysis of Experimental Results  
To assess the performance of the proposed model, it was compared with several commonly used models, including LSTM, Convolutional Long Short-Term Memory (ConvLSTM), Gated Recurrent Unit (GRU), BiLSTM, CNNs, Support Vector Regression (SVR), Random Forest (RF), and Attention Feature Fusion-Gated Bidirectional Long Short-Term Memory (AT Fusion-Gated BiLSTM). The primary distinction between the AT Fusion-Gated BiLSTM model and the proposed model lies in the feature fusion module. While the former uses traditional cross-attention to construct the Discrepancy Information Injection Module (DIIM) and the Common Information Injection Module (CIIM), the proposed model employs a separable cross-attention mechanism for feature fusion. The comparison was conducted using five evaluation metrics: \(R^{2}\), \(RMSE\), \(RPIQ\), \(RPD\), and \(MAE\). The corresponding prediction performance evaluations are shown in Tables 2-4. The comparison results of \(R^{2}\), \(RMSE\), \(RPIQ\), \(RPD\), \(MAE\), and running time are shown in Figures 12-14, respectively. Table 2 shows a comparison between the performance of several models without the spectral characteristic parameters and spectral similarity metric parameters and the performance of several models with these parameters. Figures 12 and 13 compare the performance of the proposed model with several traditional machine learning models after adding spectral characteristic parameters and spectral similarity metric parameters. Table 3 shows the experimental effects of removing or adding each module in the overall SAT Fusion-Gated BiLSTM. Table 4 shows the performance comparison among the models after adding spectral characteristic parameters and spectral similarity metric parameters and after optimizing the proposed models with different optimization algorithms. Figure 15 presents scatter plots comparing the predicted and actual values for the concentrations of reactive red, reactive yellow, and reactive blue dyes, as well as for the ultrasonic pretreatment power. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & \(\mathbf{R^{2}}\) & \(\mathbf{RMSE}\) & \(\mathbf{RPIQ}\) & \(\mathbf{RPD}\) & \(\mathbf{MAE}\) \\ \hline LSTM (without parameters) & 0.7098 & 0.1181 & 2.2230 & 2.0069 & 0.0593 \\ LSTM & 0.7350 & **0.0919** & **2.8574** & **2.5797** & 0.0519 \\ ConvLSTM (without parameters) & 0.6377 & 0.1270 & 2.0667 & 1.8658 & 0.0719 \\ ConvLSTM & 0.6535 & 0.1112 & 2.3604 & 2.132. & 0.0683 \\ GRU (without parameters) & 0.6328 & 0.1213 & 2.1634 & 1.9532 & 0.0665 \\ GRU & 0.6466 & 0.1138 & 2.3069 & 2.0827 & 0.0686 \\ BiLSTM (without parameters) & 0.7408 & 0.1049 & 2.5026 & 2.2594 & 0.0529 \\ BiLSTM & **0.7733** & 0.0944 & 2.7801 & 2.5099 & **0.0481** \\ CNNs (without parameters) & 0.6191 & 0.1329 & 1.9754 & 1.7835 & 0.0727 \\ CNNs & 0.7313 & 0.1040 & 2.5246 & 2.2793 & 0.0598 \\ SVR (without parameters) & 0.5734 & 0.1342 & 1.9566 & 1.7664 & 0.0783 \\ SVR & 0.5885 & 0.1314 & 1.9973 & 1.8032 & 0.0782 \\ RF (without parameters) & 0.6926 & 0.1279 & 2.0525 & 1.8531 & 0.0566 \\ RF & 0.7591 & 0.1138 & 2.3068 & 2.0826 & 0.0486 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparison of several models with and without the spectral characteristic parameters and spectral similarity metric parameters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & \(\mathbf{R^{2}}\) & \(\mathbf{RMSE}\) & \(\mathbf{RPIQ}\) & \(\mathbf{RPD}\) & \(\mathbf{MAE}\) \\ \hline Gated BiLSTM & 0.7396 & 0.1038 & 2.5299 & 2.2840 & 0.0518 \\ Gated linear BiLSTM & 0.8282 & 0.0789 & 3.3277 & 3.0044 & 0.0412 \\ SAT Fusion-Gated BiLSTM & **0.8999** & **0.0547** & **4.8005** & **4.3340** & **0.0280** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Model ablation experiments for SAT Fusion-Gated BiLSTM include the gated BiLSTM with the gated linear unit and the SAT Fusion module removed, the gated linear BiLSTM with the SAT Fusion module removed, and the SAT Fusion-Gated BiLSTM.