## 4 Experimental Process and Analysis
### Prediction of Dye Formulas and Ultrasonic Pretreatment Power
#### 4.4.3 Comparative Analysis of Experimental Results
Figure 12: Performance comparison between the proposed model and other machine learning models according to \(R^{2}\), _RPIQ_, _RPD_, _RMSE_, and _MAE_. (**a**) presents a comparison of \(R^{2}\), _RPIQ_, and _RPD_ metrics, (**b**) presents a comparison of _RMSE_ and _MAE_ metrics. Figure 13: Running time comparison between the proposed model and other machine learning models. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Model** & \(\mathbf{R^{2}}\) & _RMSE_ & _RPIQ_ & _RPD_ & _MAE_ \\ \hline SAT Fusion-Gated BiLSTM & 0.8999 & 0.0547 & 4.8005 & 4.3340 & 0.0280 \\ WOA-SAT Fusion-Gated BiLSTM & 0.9217 & 0.0501 & 5.2440 & 4.7344 & 0.0244 \\ DBO-SAT Fusion-Gated BiLSTM & 0.9173 & 0.0511 & 5.1414 & 4.6417 & 0.0245 \\ IDBO-SAT Fusion-Gated BiLSTM & **0.9274** & **0.0470** & **5.5825** & **5.0400** & **0.0229** \\ \hline \end{tabular}
\end{table} 
Table 4: Comparison of the performance of the proposed model optimized with different optimization algorithms (adding spectral characteristic parameters and spectral similarity metric parameters) according to \(R^{2}\), _RPIQ_, _RPD_, _RMSE_, and _MAE_. Figure 14: Comparison of the performance of the proposed model optimized with different optimization algorithms (adding spectral characteristic parameters and spectral similarity metric parameters) according to \(R^{2}\), \(RPIQ\), \(RPD\), \(RMSE\), and \(MAE\). (**a**) presents a comparison of \(R^{2}\), \(RPIQ\), and \(RPD\) metrics, (**b**) presents a comparison of \(RMSE\) and \(MAE\) metrics. Figure 15: Scatter plots of true versus predicted values for the testing dataset. (**a**) Predicted versus true concentrations of reactive red dye. (**b**) Predicted versus true concentrations of reactive yellow dye. (**c**) Predicted versus true concentrations of reactive blue dye. (**d**) Predicted versus true values for ultrasonic pretreatment power. As shown in Table 2, the inclusion of spectral characteristic parameters and spectral similarity metric parameters led to a performance improvement in most models, although the enhancement was not substantial. The SVR model exhibited the poorest performance, with an \(R^{2}\) value of 0.5885, an \(RMSE\) value of 0.1314, an \(RPIQ\) value of 1.9973, an \(RPD\) value of 1.8032, and a \(MAE\) value of 0.0782. Notably, while the inclusion of these parameters allowed the BiLSTM and LSTM models to achieve an optimal performance--with BiLSTM attaining an \(R^{2}\) of 0.7733 and \(RMSE\), \(RPIQ\), \(RPD\), and \(MAE\) values of 0.0944, 2.7801, 2.5099, and 0.0481, respectively, and LSTM achieving an \(R^{2}\) of 0.7350, with \(RMSE\), \(RPIQ\), \(RPD\), and \(MAE\) values of 0.0919, 2.8574, 2.5797, and 0.0519, respectively--the BiLSTM demonstrated a superior performance in terms of \(R^{2}\) and \(MAE\), whereas the LSTM achieved the best \(RMSE\), \(RPIQ\), and \(RPD\) metrics, slightly outperforming the BiLSTM in these areas. However, the improvements seen in sequence models such as LSTM, GRU, ConvLSTM, and BiLSTM were relatively minor compared to those of the CNN and RF models. This limited enhancement may be attributed to the nature of the added spectral characteristic parameters and spectral similarity metric parameters, which differ from spectral reflectance data types and are non-aligned sequences. Simply concatenating these distinct spectral data lacks an understanding and utilization of the intrinsic relationships between features, hindering deep interactions among the data. This approach can lead to overlooked correlations between features, reduced efficiency in information utilization, and the potential introduction of redundancy, ultimately constraining the modeling performance of sequence models and resulting in only a limited performance gain.