## 3 Results
### Results of Feature Wavelengths Extracted in Coal Spectra  
The results of the characteristic wavelength extraction for coal quality indices are shown in Figure 6. The sensitive characteristic wavelengths for Ash, VM, MC, FC, and CV are 65, 26, 25, 14, and 48, accounting for 14.13%, 5.65%, 5.43%, 3.04%, and 10.43% of the total wavelengths, respectively. The characteristic wavelengths of Ash are particularly concentrated near 750-1050 nm and 2135-2235 nm, where the former can be explained by the absorption due to the transition metal electron jump of Fe\({}^{2+}\) and Fe\({}^{3+}\) in iron oxides [34], and the latter is primarily due to the absorption of Al-OH in kaolinite and clay minerals [35]. The characteristic wavelengths of VM are more uniformly distributed, mainly observed at 722 nm, 1035 nm, 1430 nm, 1740 nm, 1940 nm, 2160 nm, and 2240 nm, which are associated mainly with C-H stretching and C-C stretching in organics as well as CH\({}_{2}\) asymmetric stretching and symmetric bending [35; 36]. The characteristic wavelengths of MC are distributed in the range of 500-1000 nm, 1700 nm, 1900 nm, and 2300 nm, which is mainly consistent with the -OH frequency multiplication and H\({}_{2}\)O vibration [34; 35]. FC has only a relatively small number of characteristic wavelengths at 2160 nm, which are related to the combination of aromatic C-H stretching and C-C stretching [35]. The characteristic \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Coal Quality** **Indices**} & \multirow{2}{*}{**Spectra**} & \multirow{2}{*}{**PCs**} & \multicolumn{2}{c}{**Calibration Set**} & \multicolumn{2}{c}{**Prediction Set**} \\ \cline{3-6}  & & & \(R_{c}^{2}\) & \(RMSE_{c}\) & \(R_{p}^{2}\) & \(RMSE_{p}\) \\ \hline \multirow{4}{*}{Ash (\%)} & OR & 7 & 0.957 & 2.297 & 0.930 & 2.242 \\  & SG & 7 & 0.955 & 2.333 & 0.929 & 2.250 \\  & FD & 7 & 0.995 & 0.741 & 0.971 & 1.723 \\  & MSC & 7 & 0.985 & 1.387 & 0.972 & 1.342 \\  & OR & 7 & 0.964 & 1.255 & 0.930 & 1.378 \\  & SG & 7 & 0.963 & 1.272 & 0.928 & 1.399 \\  & FD & 7 & 0.996 & 0.436 & 0.948 & 1.030 \\  & MSC & 7 & 0.982 & 0.919 & 0.969 & 0.801 \\  & OR & 7 & 0.755 & 0.418 & 0.803 & 0.300 \\  & SG & 7 & 0.747 & 0.424 & 0.803 & 0.300 \\  & FD & 4 & 0.961 & 0.167 & 0.473 & 0.438 \\  & MSC & 6 & 0.806 & 0.384 & 0.581 & 0.366 \\  & OR & 7 & 0.895 & 1.678 & 0.812 & 1.618 \\ FC (\%) & SG & 7 & 0.890 & 1.724 & 0.828 & 1.550 \\  & FD & 7 & 0.982 & 0.699 & 0.850 & 1.534 \\  & MSC & 7 & 0.942 & 1.256 & 0.859 & 1.426 \\  & OR & 16 & 0.999 & 0.116 & 0.908 & 0.869 \\  & SG & 10 & 0.981 & 0.537 & 0.964 & 0.545 \\  & FD & 7 & 0.992 & 0.343 & 0.967 & 0.516 \\  & MSC & 13 & 0.995 & 0.283 & 0.973 & 0.440 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: PLSR modeling results based on the raw and different preprocessed spectra. wavelengths of CV are mainly clustered at 1035 nm, 1440 nm, 1680 nm, 1990 nm, 2200 nm, and 2300 nm. Table 4 shows the results of the machine learning models based on MSC spectra at different characteristic wavelengths. In terms of feature extraction methods, the number of extracted feature wavelengths among all coal quality indicators is ranked as iVISSA, CARS, Boruta, and SPA, which indicates that the wavelength compression ability of SPA and Boruta is better than that of CARS and iVISSA from the number of wavelengths, which can greatly reduce the pressure of modeling. However, excessive wavelength compression may lead to a loss of effective data information and cut down the model characterization ability. Appropriate wavelength selection can both specialize the feature wavelengths and best characterize the object information, with the characteristic wavelengths selected by CARS fulfilling this requirement effectively. Therefore, it can be found that the optimal models were constructed based on the wavelengths selected by CARS, except for FC, which may be due to the fact that FC is closely related to carbon content which does not have a  
Figure 6: Results of characteristic wavelength extraction (marked by red square).