## 3 Results
### Feature Wavelength Selection
#### 3.2.3 Joint-Feature Variable Screening Method  
Based on the test findings from Sections 3.2.1 and 3.2.2, it is apparent that different variable screening algorithms optimize the modeling of characteristic wavelengths, thereby enhancing detection performance. Notably, the SVR modeling performance of the SiPLS and CARS methods proves superior. In a bid to further enhance data quality and improve the model's detection performance, a refined approach incorporating SiPLS and CARS has been introduced. A comparative analysis was conducted on the SVR modeling results from diverse feature variable screening algorithms to identify sensitive variables, simplify model complexity, and bolster detection performance. The modeling outcomes are displayed in Table 6.  
Figure 10: CARS algorithm optimized feature variable SVR modeling detection results (**a**) Training set. (**b**) Testing set. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variable Selection Method**} & \multirow{2}{*}{**Number of Variables**} & \multicolumn{2}{c}{**SVR Modeling Parameters**} & \multicolumn{2}{c}{**Training Set**} & \multicolumn{2}{c}{**Test Set**} \\ \cline{3-7}  & & **c** & **g** & **RMSEC/(\%)** & **R\({}^{2}\)\({}_{\mathbf{c}}\)** & **RMSEP/(\%)** & **R\({}^{2}\)\({}_{\mathbf{p}}\)** \\ \hline There is no & 2074 & 128 & 0.0009765 & 27.88 & 0.6595 & 26.63 & 0.4196 \\ IRIV & 27 & 1024 & 0.0625 & 15.02 & 0.8144 & 26.44 & 0.6189 \\ VCPA & 12 & 181.02 & 0.1767766 & 15.38 & 0.8063 & 22.49 & 0.7320 \\ RF & 50 & 181.02 & 0.0027621 & 14.66 & 0.8275 & 21.35 & 0.7668 \\ CARS & 80 & 1024 & 0.0055242 & 14.57 & 0.8266 & 19.10 & 0.8149 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: SVR modeling outcomes of feature variables utilizing various wavelength point screening algorithms. The comparative results indicate that the combination of SiPLS with the RF algorithm (SIPLS-RF) for feature variable screening results in the most effective SVR modeling detection. The modeling incorporates 50 feature wavelength points, representing a compression of wavelengths to 2.41% of the full spectrum. The Root Mean Square Error (RMSEC) of the training set stands at 13.76%, with a determination coefficient (R\({}^{2}\)c) of 0.8559. The Root Mean Square Error (RMSEP) for the test set registers at 17.04%, with a determination coefficient (R\({}^{2}\)p) of 0.8386. When compared to full-spectrum data modeling, the Root Mean Square Error of the test set decreases by 36.01%, and the coefficient of determination increases by 99.86%. This marks a significant improvement in the model's detection performance. The SVR modeling results derived from the SiPLS-RF feature variable screening are illustrated in Figure 11.  
By examining the joint-variable screening process of the SIPLS-RF algorithm, we observed that RF optimization was performed on the 395 feature variables identified via SiPLS. The variation of the SIPLS-RF iteration error is depicted in Figure 12a, with the smallest error registered when the iteration count is at 545. The selection probabilities of different variables are displayed in Figure 12b, with the 395 variables ordered in descending sequence based on their likelihood of selection. A selection probability of 0.35 serves as the threshold, with variables surpassing this threshold retained as key variables for modeling. At this juncture, 50 characteristic wavelengths were chosen, their dispersion is depicted in Figure 13.