## 3 Results and Discussion
### Combination of Variable Selection Algorithms  
To further explore the impact of variable selection on model simplification and performance, we consider combining different variable selection algorithms. According to Tables 4 and 5, MWPLS tends to select a larger number of variables, and RF tends to \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multirow{2}{*}{**Algorithm**} & \multirow{2}{*}{**N**} & \multirow{2}{*}{**LV**} & \multicolumn{3}{c}{**Calibration**} & \multicolumn{3}{c}{**Prediction**} & \multirow{2}{*}{**PI (\%)**} \\ \cline{5-6} \cline{8-9}  & & & & **RMSEC** & & **R\({}_{\text{C}}\)** & **RMSEP** & **R\({}_{\text{P}}\)** \\ \hline \multirow{4}{*}{Gluc} & MWPLS & 800 & 15 & 0.10 & 0.98 & 0.15 & 0.98 & 27 \\  & GA & 100 & 8 & 0.16 & 0.97 & 0.18 & 0.97 & 16 \\  & RF & 80 & 9 & 0.09 & 0.99 & 0.23 & 0.95 & \(-8\) \\  & MWPLS & 2900 & 14 & 0.05 & 0.99 & 0.11 & 0.88 & 41 \\  & GA & 200 & 9 & 0.06 & 0.98 & 0.06 & 0.96 & 66 \\  & RF & 200 & 15 & 0.02 & 0.99 & 0.08 & 0.93 & 54 \\  & MWPLS & 800 & 10 & 0.36 & 0.97 & 0.44 & 0.96 & 8 \\  & GA & 300 & 13 & 0.28 & 0.98 & 0.34 & 0.98 & 29 \\  & RF & 60 & 10 & 0.21 & 0.99 & 0.57 & 0.95 & \(-21\) \\  & MWPLS & 100 & 7 & 0.77 & 0.98 & 1.17 & 0.98 & \(-36\) \\ \(\text{NH}_{4}{}^{+}\) & GA & 90 & 13 & 0.56 & 0.99 & 0.69 & 0.99 & 20 \\  & RF & 100 & 10 & 0.29 & 0.99 & 0.70 & 0.99 & 19 \\ \hline \hline \end{tabular} N represents the number of selected variables.  
\end{table} 
Table 4: Calibration and prediction results of models with three variable selection algorithms. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multirow{2}{*}{**Algorithm**} & \multirow{2}{*}{**N**} & \multirow{2}{*}{**LV**} & \multicolumn{3}{c}{**Calibration**} & \multicolumn{3}{c}{**Prediction**} & \multirow{2}{*}{**PI(\%)**} \\ \cline{5-6} \cline{8-9}  & & & & **RMSEC** & & **R\({}_{\text{C}}\)** & **RMSEP** & **R\({}_{\text{P}}\)** \\ \hline \multirow{4}{*}{Gluc} & MWPLS & 600 & 8 & 0.12 & 0.98 & 0.12 & 0.99 & 42 \\  & GA & 200 & 7 & 0.13 & 0.98 & 0.16 & 0.97 & 25 \\  & RF & 200 & 12 & 0.06 & 0.99 & 0.19 & 0.95 & 12 \\  & MWPLS & 1300 & 5 & 0.08 & 0.98 & 0.07 & 0.93 & 60 \\  & GA & 100 & 7 & 0.06 & 0.98 & 0.05 & 0.97 & 73 \\  & RF & 300 & 12 & 0.03 & 0.99 & 0.06 & 0.95 & 65 \\  & MWPLS & 1100 & 8 & 0.29 & 0.98 & 0.28 & 0.99 & 41 \\ VCD & GA & 400 & 7 & 0.30 & 0.98 & 0.33 & 0.99 & 31 \\  & RF & 100 & 10 & 0.18 & 0.99 & 0.36 & 0.98 & 25 \\  & MWPLS & 1300 & 7 & 0.51 & 0.99 & 0.54 & 0.99 & 37 \\ \(\text{NH}_{4}{}^{+}\) & GA & 400 & 7 & 0.52 & 0.99 & 0.49 & 0.99 & 43 \\  & RF & 100 & 14 & 0.29 & 0.99 & 0.62 & 0.99 & 29 \\ \hline \hline \end{tabular} N represents the number of selected variables.  
\end{table} 
Table 5: Calibration and prediction result of models with three variable selection algorithms after spectral region selection. select a smaller number of variables. Therefore, three combination methods, MWPLS-GA, MWPLS-RF, and MWPLS-GA-RF, were proposed. Such combinations were used to reduce the number of variables and improve the model's performance, and the results are listed in Table 6. It should be noted that all variable selection algorithms were used after spectral regions 600-1800 cm\({}^{-1}\) and 2800-3000 cm\({}^{-1}\) were selected. MWPLS-GA improved the model performance by 10-66% by selecting 100-200 variables. MWPLS-RF improved the model performance by 7-47% by selecting 70-200 variables. MWPLS-GA-RF improved the model performance by 16-70% by selecting 30-60 variables. The combination of variable selection algorithms can effectively reduce the number of selected variables, while ensuring the performance of the model. MWPLS-GA-RF especially improved the model performance by selecting less than 100 variables, which could promote the application of Raman spectroscopy in the cell culture process. For MWPLS-GA and MWPLS-RF, the number of selected variables was relatively large, and the model performance improvement was limited.