## 3 Results and Discussion  
### Predicted Results of \(Plsr\)  
The principle of PLSR is to build a linear regression model between the input and output data by injecting the input data into a new space, which takes advantage of the multiple linear regression analysis, principal component analysis, and typical correlation analysis. Generally, full spectrum data or partial spectral band data can be used as the input variables of the PLSR model. Full spectrum data contain a great mass of information, but there are also a lot of noise data, leading to the increased iteration time. In order to reduce the interference of irrelevant information and improve the iteration efficiency, the band spectral data containing the main characteristic spectral lines of the index-related elements are chosen as the input variables of the PLSR model shown in Table 2. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Industrial Index** & **Elements** & **Input Variables** \\ \hline \multirow{4}{*}{\begin{tabular}{l} Ash content \\ \end{tabular} } & Si, Al, Mg, K & 287.917–288.505; 308.055–308.615; 308.845–309.827; 394.060–394.714; \\  & Si, Al, Mg, K & 395.448–396.508; 279.268–279.683; 765.247–766.938; 768.723–770.204; \\  & Ti, Fe, Na, Ca, & 335.712–336.326; 438.056–438.580; 588.252–590.309; 392.915–393.815; \\  & Li & 396.508–397.483; 422.186–423.116; 669.629–671.148 \\ \hline \multirow{4}{*}{\
\begin{tabular}{l} Volatile matter \\ \end{tabular} } & C, CN, H, O, & 247.332–248.302; 380.918–390.123; 648.881–661.868; 773.839–779.961; \\  & Al, Mg, Ca, Fe & 394.060–394.714; 395.448–396.508; 279.268–279.683; 392.915–393.815; \\  & & 396.508–397.483; 438.056–438.580 \\ \hline \multirow{4}{*}{
\begin{tabular}{l} Calorific value \\ \end{tabular} } & C, C\({}_{2}\), CN, H, & 247.332–248.302; 470.288–473.889; 380.918–390.123; 432.433–432.850; \\  & O, Al, Mg, Ca, & 648.881–661.868; 406.911–408.268; 441.046–441.939; 773.839–779.961; \\ \cline{1-1}  & Fe, Si & 394.060–394.714; 395.48–396.508; 279.268–279.683; 392.915–393.815; \\ \cline{1-1}  & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\ \end{tabular}
\end{table} 
Table 2: Input variables of PLSR. The number of principal components of the PLSR model was determined by the remaining one cross-validation. The fitting prediction results of the ash content model are shown in Figure 2 and Table 3.  
Figure 2: _Cont._  
It can be seen from Figure 3 and Table 3 that the prediction results of the PLSR model with KS and SPXY partitioning methods are better than that with the RS method. It is easy to understand that the data set samples selected by the random method make it difficult to have a good overall representation, while the KS method and the SPXY method select the samples with large spectral differences as the training set based on Euclidean distance and leave the samples with small spectral differences as the test set, which is in essence to perform like cluster analysis. In addition, the KS method is better than the SPXY method in terms of volatile matter and calorific value prediction. The \(R^{2}\) of \(PLSR\) based on the KS data set partitioning method of volatile matter is 0.9990, the \(RMSEP\) of the volatile matter is 1.4518, the \(MRE\) is 3.90%, the \(R^{2}\) for calorific value regression is 0.9904, the \(RMSEP\) of the heating value is 0.9514, and the \(MRE\) is 3.77%. However, for the ash content, the model performs relatively poorly: the \(R^{2}\) is 0.9763, \(RMSEP\) is 2.5834 and \(MRE\) is 12.95%.