## 3 Results and Discussion
### Combination of Variable Selection Algorithms
Compared with the monitoring performance using the whole range of spectra (no selection of spectral variable), the prediction of the model with MWPLS-GA-RF was less noisy and closer to the reference value. In summary, the combination of two variable selection algorithms performed similarly to single variable selection algorithms, failing to further improve model accuracy or reduce the number of selected variables. In contrast, the combination of three variable selection algorithms was able to select fewer variables for modeling, and the selected variables were reasonable. The variables selected by MWPLS-GA-RF were used to construct the model, and the model's performance was satisfactory. When the model was used for real-time monitoring of the cell culture process, the concentration changes in components in the bioreactor were accurately depicted. In previous work [35], the optimal RMSEP values for glucose, lactate, and viable cell density were 0.22 g/L, 0.08 g/L, and 0.31 \(\times\) 10\({}^{6}\) cells/mL, respectively, and the number of spectral variables for each component was over 1000. In this study, the RMSEP was significantly reduced by selecting spectral variables based on MWPLS-GA. Using the variable selection method MWPLS-GA-RF with the number of variables < 100, the RMSEP values obtained for glucose, lactate, and viable cell density were 0.16 g/L, 0.05 g/L, and 0.40 \(\times\) 10\({}^{6}\) cells/mL, respectively, which is an improvement over the results from previous work. Figure 6: Spectral variables selected by MWPLS-GA-RF. (**A**) Glucose, (B) lactate, (**C**) viable cell density, and (**D**) ammonium ion. A mean spectrum after preprocessing was used to show the selected variables. It is important to note that researchers may have different objectives, such as improving model performance or simplifying the model, which can lead to variations in the definition of the optimal variable selection strategy. The combination method of MWPLS-GA-RF has been shown to enhance model performance, while effectively simplifying the model. However, if dimensionality reduction is not required, simpler approaches, such as spectral region selection (e.g., 600-1800 cm\({}^{-1}\) plus 2800-3000 cm\({}^{-1}\)) or single variable selection algorithms (e.g., GA and RF), can also effectively improve the model's performance. Model robustness is a key issue that needs to be addressed during the variable selection process, especially when fewer variables are chosen. In this study, the calibration set was used for cross-validation, and the external validation set was then used to assess the model's performance, which provided some assurance of model robustness. However, if the model is to be used in real production, more detailed robustness studies are required. For example, more external validation sets should be used to test the model further. In addition, the data in this study were collected from the fed-batch culture of CHO-S cells. To ensure broader applicability, it would be beneficial to include more cases, such as the culture of CHO-K1 cells and perfusion culture, to confirm the applicability of MWPLS-GA-RF.