## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Coal Name**} & \multicolumn{3}{c}{**Concentration (\%)**} & \multicolumn{3}{c}{**Calorific Value**} & \multicolumn{2}{c}{**Chemical Analysis**} & \multirow{2}{*}{**Error**} \\  & **C** & **H** & **O** & **S** & **(kcal/kg)** & **(kcal/kg)** & **(kcal/kg)** \\ \hline GUNVOR & 75.03 & 5.27 & 12.55 & 0.46 & 7348.22 & 7360 & 0.16 \\ MSJ-1 & 68.7 & 5.21 & 13.88 & 0.52 & 6760.15 & 6915 & 2.24 \\ MSJ-2 & 68.1 & 5.15 & 17.96 & 0.84 & 6522.44 & 6852 & 4.81 \\ LANNA HARITA & 67.55 & 5.01 & 18.23 & 0.72 & 6415.43 & 6619 & 3.08 \\ MACQUARIE & 67.32 & 4.48 & 17.43 & 0.64 & 6246.87 & 6705 & 6.83 \\ PEABODY & 66.3 & 4.77 & 18.03 & 0.58 & 6237.19 & 6630 & 5.92 \\ KPU & 64.18 & 4.08 & 10.46 & 0.67 & 6156.22 & 6619 & 6.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Predicted caloric value of various coal samples by correlation analysis. In Figure 6, the correlation between the intensity of the LIBS signal at 247.7 nm and the concentration of carbon in coal samples was analyzed with delay times of 1.4 \(\upmu\)s for the CA and PLS methods and 1.0 \(\upmu\)s for the SNR method. The signal intensity at a wavelength of 247 nm, which is a representative spectrum of the atomic carbon from the LIBS spectra data, was selected for estimating the carbon concentration in the samples. Because the used coal samples were composed of over 60% carbon, the intensity of the carbon signal was larger than those of the other remaining elements. The carbon signal could be easily distinguished from the other elements. Depending on the coal sample, the carbon concentration varied from about 65 to 75% and the signal intensities were proportional to the carbon concentration. The \(R^{2}\) for the CA, PLS, and SNR methods was 0.98, 0.92, and 0.65, respectively. The magnitude of the error bars in the carbon samples were relatively small compared to that of the other elements, with a maximum of 4.3, 5.1, and 5.7% from the mean value for the CA, PLS, and SNR methods, respectively. This was caused by the large quantity of carbon in the coal samples. In Figure 7, the correlation between the LIBS signal intensity and the hydrogen concentration in coal was analyzed at the wavelength of 656.2 nm in the LIBS spectrum. The \(R^{2}\) for the CA, PLS, and SNR methods was 0.13, 0.14, and 0.06, respectively. The error bars represent the standard deviation of the signal intensity from the average intensity of 100 points. The standard deviation of the hydrogen peak was larger than that of carbon peak, as shown in Figure 6, which showed 7.7, 13.9, and 14.2% of maximum errors from the mean values for the CA, PLS, and SNR methods, respectively. The hydrogen concentrations in the coal samples ranged between 4.8 and 5.2%. The low concentration gave a low signal intensity and a small variation of less than 0.5% in hydrogen between the samples produced difficulty in distinguishing the intensity variation to identify the hydrogen concentration. In Figure 8, the LIBS signal intensity at the 844.6 nm wavelength was calibrated with the oxygen concentration in the coal samples. The oxygen concentration in the coal samples was found to be between 12 and 20% from Table 1. Oxygen is the second most abundant element in coal. The difference between the oxygen concentrations of different samples, which was relatively large compared to that of hydrogen, gave a better \(R^{2}\) value for the CA, PLS, and SNR methods, with values of 0.15, 0.18, and 0.16, respectively. In addition, as the LIBS signal was collected under atmospheric conditions, the oxygen in the atmosphere affected the measurement accuracy of the oxygen in coal. This resulted in a larger maximum errors compared to that of hydrogen, with values of 15.7, 26.8, and 27.4% for the CA, PLS, and SNR methods, respectively. Figure 6: Correlation between the intensity and C concentration with maximum \(R^{2}\) for CA, PLS, and SNR methods.