## 3 Results and Discussion
### Calorific Value Analysis  
#### 3.2.1 Partial Least Square Regression (PLSR)  
From [PERSON]'s equation, it can be found that carbon, hydrogen, oxygen, and sulfur are the main elements contributing to the higher heating value of coal. Higher heating value, HHV can be theoretically estimated by the following equation [24]:  
\[\mathrm{HHV(kcal/kg)}=8080\mathrm{C}+34,460\mathrm{H}-4308\mathrm{O}+2250 \mathrm{S}. \tag{4}\]  
The elemental concentration is by weight percent on a dry basis. The PLSR is a linear combination of spectral data and can be used in regression equations. Thus, redundant variables can be removed from data with numerous variables and only the most relevant variants of the spectrum are used in regression analysis. The effect of each variable on the PLSR model can be presented in the form of a regression coefficient plot. The regression coefficient summarizes the relationship between all predictors and the given response. In the LIBS analysis, spectral data is summarized as variables, mainly seven factors. The regression coefficients for these seven factors condense the relationship between the predictors and the response, as a model with seven components approximates it. The information at the wavelength corresponding to the element that greatly influences the property estimation plays an important role. In this study, calorific value will be predicted only using the reference calorific value by PLSR instead of predicting the value for each element and substituting it into Equation (4). Although the use of segments within the full range of the spectrum has been proposed for a better elemental analysis [25], the full range of spectra data was used to preserve informative data when creating the PLSR model. This is because the wavelengths of the elements that significantly affect the calorific value lie in the entire spectral range. The data processing method is essential for a robust calibration model. In the case of sulfur concentration measurements, the third-order polynomial with seven points in the SG smoothing method was used to eliminate noise.  
Figure 9a,b represents the PLSR results obtained from the original data for calorific values and the PLSR results of the data processed by SG smoothing, respectively. When compared with the PLSR obtained from the original data, the PLSR of the data processed by the SG smoothing produced better results in terms of the \(R^{2}\) and the RMSE values in the calorific value estimation. A better result can be found in Figure 9b compared to Figure 9a. The \(R^{2}\)s for calibration and cross-validation in Figure 9a were 0.9359 and 0.9000, respectively. The RMSEC and RMSECV in Figure 9a were 52.6233 and 66.8441, respectively. In the case of Figure 9b, the \(R^{2}\)s for calibration and cross-validation were improved to 0.9472 and 0.9182, respectively. The RMSEC and RMSECV values were decreased to 47.8026 and 60.4917, respectively.  
To compare the degree of improvement, the predicted error of the calorific value between the PLSR for original data and the SG smoothing-processed data are shown in Figures 10 and 11, respectively. The relative error was calculated individually from the reference value and predicted value. There was no dramatic improvement as shown in the case of sulfur concentration estimation, but the error was reduced. The maximum relative error value for PLSR of the original data was 2.3525%. This value is relatively small compared to the error in sulfur concentration analysis. In the case of the processed data with SG smoothing, the largest relative error value was 2.1265%. If the concentration of elements in coal can be accurately predicted in real-time, it can contribute to complete combustion and reduce unburned carbon content by estimating the appropriate amount of combustion air.  
Figure 10: Relative error of calorific value between measured and predicted value for the PLSR of original data.  
Figure 9: PLSR model results (**a**) original data (**b**) the third-order polynomial with seven points SG smoothing method applied.