## 3 Results
### Feature Wavelength Selection
#### 3.2.1 Methodology for Feature Wavelength Interval Screening  
(1) Feature interval selection based on SiPLS  
The SiPLS algorithm was applied to the preprocessed standard sample dataset for feature wavelength selection. The joint interval numbers were set to 2, 3, and 4, and for each joint interval, optimal PLS models were established using a subset of subinterval principal component numbers that ranged from 6 to 30. The results of this analysis are consolidated in Table 4, and the optimal feature interval combinations selected by the SiPLS method are visualized in Figure 4.  
The modeling outcomes indicate that the optimal model performance is attained with a joint interval number of 4, a partition interval number of 21, a modeling interval combination of [1; 13; 16; 19], and nine principal components. The model displays an R\({}^{2}\)c value of 0.6003, a Root Mean Square Error of Cross-Validation (RMSECV) of 9.21%, an R\({}^{2}\)p of 0.7465, and an RMSEP of 9.13%. The selected feature wavelength intervals are 11,617 cm\({}^{-1}\) to 12,000 cm\({}^{-1}\), 7035 cm\({}^{-1}\) to 7413 cm\({}^{-1}\), 5889 cm\({}^{-1}\) to 6267 cm\({}^{-1}\), and 4755 cm\({}^{-1}\) to 5129 cm\({}^{-1}\).  
(2) Feature interval selection based on BiPLS  
Feature interval selection using the BiPLS algorithm divided the preprocessed standard sample dataset into intervals that ranged from 3 to 30, with models compared accordingly. The optimal model performance was realized with a partition interval number of 415 and a modeling interval combination of [1; 3; 4; 5]. The selected spectral regions are depicted in Figure 5a, and the variation of RMSECV with the number of principal components is  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \begin{tabular}{c} **Number of** \\ **Joint** \\ **Intervals** \\ \end{tabular} & \begin{tabular}{c} **Number of** \\ **Inervals** \\ \end{tabular} & \begin{tabular}{c} **Interval** \\ **Combinations** \\ \end{tabular} & \begin{tabular}{c} **Spectral** \\ **Range/(cm\({}^{-1}\))** \\ \end{tabular} & **n** & \begin{tabular}{c} **R\({}^{2}\)c** \\ **R\({}^{2}\)c** \\ \end{tabular} & \begin{tabular}{c} **RMSECV/(\%)** \\ \end{tabular} & \
\begin{tabular}{c} **R\({}^{2}\)p** \\ \end{tabular} &
\begin{tabular}{c} **RMSEP/(\%)** \\ \end{tabular} \\ \hline
2 & 28 & 14 28 &
\begin{tabular}{c} 8280–7990 \\ 4280–4000 \\ 12,000–11,270 \\ 6170–4725 \\ 12,000–11,617 \\ 7413–7035 \\ 6267–5889 \\ 5129–4755 \\ \end{tabular} & 6 & 0.4490 & 10.76 & 0.6495 & 11.19 \\
3 & 10.15 & 0.7329 & 9.27 \\
4 & 21 & 1 13 16 19 &
\begin{tabular}{c} 12,000–11,617 \\ 7413–7035 \\ 6267–5889 \\ 5129–4755 \\ \end{tabular} & 8 & 0.5185 & 10.15 & 0.7329 & 9.27 \\
5 & 0.6003 & 9.21 & 0.7465 & 9.13 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Optimal SiPLS model results with different joint interval numbers.  
Figure 4: Feature wavelength selection using SiPLS algorithm with joint intervals 4.  
demonstrated in Figure 5b. The model displays an R2c value of 0.5769, an RMSECV of 9.43%, an R2p of 0.7280, and an RMSEP of 9.48%. The selected feature wavelength intervals are 4000 cm\({}^{-1}\) to 5600 cm\({}^{-1}\) and 7200 cm\({}^{-1}\) to 12,000 cm\({}^{-1}\).