### Calorific Value Analysis  
Since coal is used as the main fuel in coal-fired power generation, the calorific value of coal is a very important factor. Water vapor, which is a by-product of coal combustion, has latent heat. Therefore, a higher heating value (HHV) including the latent heat of steam is appropriate for the estimation of the calorific value of coal. The PLSR model was used to estimate the concentration of each element. The predicted calorific value can be obtained  
\begin{table}
\begin{tabular}{c c c c} \hline
**Element** & **Data Pre-Processing** & **RMSEC(avg.) (\%)** & **RMSECV(avg.) (\%)** \\ \hline \multirow{3}{*}{Carbon} & Original data & 0.7570 & 0.9538 \\  & SG smoothing & 0.7089 & 0.9080 \\  & SG derivative & 0.6792 & 0.9082 \\ \hline \multirow{3}{*}{Hydrogen} & Original data & 0.8652 & 1.3489 \\  & SG smoothing & 0.8461 & 1.3914 \\  & SG derivative & 0.6258 & 1.0519 \\ \hline \multirow{3}{*}{Oxygen} & Original data & 6.7308 & 9.0414 \\  & SG smoothing & 6.7563 & 9.0984 \\  & SG derivative & 5.8870 & 9.3883 \\ \hline \multirow{3}{*}{Sulfur} & Original data & 7.6019 & 9.1453 \\  & SG smoothing & 7.5098 & 9.0301 \\ \cline{1-1}  & SG derivative & 5.8513 & 8.6710 \\ \hline \end{tabular}
\end{table}
Table 1: Comparison of RMSE average (%) of mixed coal elements between original data and pre-processed data.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Element** & **Data Pre-Processing** & **SD** & **RMSECV** & **RPD** \\ \hline Carbon & SG derivative & 2.16 & 0.69847 & 3.10 \\ Hydrogen & SG derivative & 0.14 & 0.05312 & 2.63 \\ Oxygen & SG derivative & 2.38 & 1.4031 & 1.70 \\ Sulfur & SG derivative & 0.27 & 0.07727 & 3.53 \\ \hline \end{tabular}
\end{table}
Table 2: RPD of mixed coal.  
by substituting the predicted concentration of elements such as carbon, hydrogen, oxygen, and sulfur into [PERSON]'s equation, which is a higher heating value equation [21]:  
\[\text{HHV}\left(\text{kcal/kg}\right)=8080\text{C}+34460\text{H}-4308\text{O}+22 50\text{S}, \tag{5}\]  
where, C, H, O, and S are the concentrations (%) of carbon, hydrogen, oxygen, and sulfur, respectively. The calorific value obtained from the Daedeok Analytical Research Institute via industrial analysis was compared with the calorific value estimated from the PLSR models of each element shown above.  
Figure 16 shows the relative errors between the measured and predicted values for the PLSR model using the original data and the PLSR model pre-processed by the SG derivative method [22]. The predicted calorific value was obtained by substituting the concentration of the elements from the PLSR model into Equation (5), i.e., the higher heating value equation. The relative error of the original data ranged from 0.09 to 6.45% and the average relative error was 2.22%. The relative errors of the PLSR model pre-processed by the SG derivative varied from 0.02 to 5.54% and the average relative error was 2.18%. They are slightly improved when they are compared with the relative errors of the original data in the range from 0.09 to 6.45%, as shown in Figure 16. The mean relative error of 2.18% was smaller than that of 2.22% obtained from the result of Figure 16. Therefore, the prediction of calorific value via the SG derivative method provides more reliable values.