## 3 Results and Discussion
### Combination of Variable Selection Algorithms
Compared with the results of GA and RF, the results of MWPLS-GA and MWPLS-RF were unsatisfactory. The spectral variables selected by MWPLS-GA-RF are plotted in Figure 6. For glucose, the selected spectral variables are mainly located at 850-1150 cm\({}^{-1}\), 1250-1500 cm\({}^{-1}\), and 2850-2950 cm\({}^{-1}\), which are related to \(\
u\)(C-O) and \(\
u\)(C-C) stretches (1000-1200 cm\({}^{-1}\)); \(\delta\)(CH\({}_{2}\)) and \(\delta\)(CH\({}_{2}\)OH) deformations (1300-1500 cm\({}^{-1}\)); \(\delta\)(C-OH), \(\delta\)(C-CH), and \(\delta\)(O-CH) side-group deformations (800-950 cm\({}^{-1}\)); \(\
u\)(C-O) and \(\
u\)(C-C) stretches (950-1200 cm\({}^{-1}\)); and \(\delta\)(CH\({}_{2}\)) and \(\delta\)(CH\({}_{2}\)OH) deformations (1250-1500 cm\({}^{-1}\)) [54]. For lactate, the selected spectral variables are mainly located at 600-900 cm\({}^{-1}\), 1000-1300 cm\({}^{-1}\), 1400-1500 cm\({}^{-1}\), and 2800-3000 cm\({}^{-1}\). According to the literature [55], the characteristic spectral regions of lactate were 640-660 cm\({}^{-1}\), 720-775 cm\({}^{-1}\), 855 cm\({}^{-1}\), 930 cm\({}^{-1}\), and 2900-2980 cm\({}^{-1}\), involving C-COH deformations, C-CO\({}_{2}\)- stretches, C-COO- stretching, CH\({}_{3}\) rocking, and CH\({}_{3}\) stretching vibrations. The spectral variables selected for viable cell density are mainly located between 800 cm\({}^{-1}\) and 1500 cm\({}^{-1}\), which are related to C-C stretch modes (926-975 cm\({}^{-1}\)), the C-N vibration mode of lipids and proteins (1076 cm\({}^{-1}\)), C-O vibration mode of carbohydrates (1125 cm\({}^{-1}\)), and the ring breathing mode of adenine and guanine nucleobases in DNA and RNA (1326-1475 cm\({}^{-1}\)) [21]. The spectral variables of ammonium ion are mainly located in 600-800 cm\({}^{-1}\), 1000-1100 cm\({}^{-1}\), 1300-1500 cm\({}^{-1}\), and 2800-3000 cm\({}^{-1}\), which are similar to the report [9]. Although Raman spectroscopy does not provide direct structural variation information about ammonium ion, it can still provide better prediction results through indirect relation. In addition, the selection of C-H stretching regions was consistent with the results in Section 3.1. Except for viable cell density, the addition of C-H stretching regions \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Component**} & \multirow{2}{*}{**Combination**} & \multirow{2}{*}{**N**} & \multirow{2}{*}{**LV**} & \multicolumn{3}{c}{**Calibration**} & \multicolumn{3}{c}{**Prediction**} \\ \cline{4-9}  & & & & **RMSEC** & **R\({}_{\text{C}}\)** & **RMSEP** & **R\({}_{\text{P}}\)** & **PI(\%)** \\ \hline \multirow{4}{*}{Gluc} & MWPLS-GA & 200 & 5 & 0.16 & 0.97 & 0.19 & 0.96 & 10 \\  & MWPLS-RF & 70 & 12 & 0.09 & 0.99 & 0.12 & 0.99 & 43 \\  & MWPLS-GA-RF & 50 & 6 & 0.13 & 0.98 & 0.16 & 0.98 & 26 \\  & MWPLS-GA & 100 & 5 & 0.07 & 0.98 & 0.06 & 0.95 & 66 \\ Lac & MWPLS-RF & 90 & 14 & 0.04 & 0.99 & 0.10 & 0.87 & 47 \\  & MWPLS-GA-RF & 60 & 5 & 0.07 & 0.98 & 0.05 & 0.96 & 70 \\  & MWPLS-GA & 100 & 6 & 0.34 & 0.98 & 0.26 & 0.99 & 46 \\ VCD & MWPLS-RF & 200 & 10 & 0.17 & 0.99 & 0.44 & 0.96 & 7 \\  & MWPLS-GA-RF & 30 & 9 & 0.30 & 0.98 & 0.40 & 0.97 & 16 \\  & MWPLS-GA & 200 & 7 & 0.52 & 0.99 & 0.52 & 0.99 & 40 \\ NH\({}_{4}\)\({}^{*}\) & MWPLS-RF & 200 & 12 & 0.25 & 0.99 & 0.79 & 0.99 & 8 \\  & MWPLS-GA-RF & 50 & 8 & 0.47 & 0.99 & 0.58 & 0.99 & 33 \\ \hline \end{tabular} N represents the number of selected variables.  
\end{table} 
Table 6: Calibration and prediction result of models with three combinations of variable selection algorithms after spectral region selection. could improve the model's performance. All of these indicate that the variables selected by MWPLS-GA-RF are reasonable. The cell culture process was monitored in real time using the model constructed with the spectral variables selected by MWPLS-GA-RF. As shown in Figure 7, the models effectively projected the concentrations of these four components and captured the perturbations induced by additional medium feeding.