## 4 Results and Discussion
Unlike the other elements under consideration, more than half of the marks located on the upper side of the diagonal line represent the tendency for overestimating the oxygen content. The KPU sample from Table 1 consisted of 20.97% oxygen, which is similar to the oxygen content in the air and shows a low estimation accuracy. The CA performed on the other samples showed estimated concentrations of oxygen that were close to the diagonal dotted line. Figure 11: Estimated hydrogen concentration with CA, PLS, and SNR. Table 1.0 Estimated oxygen concentrations with CA, PLS, and SNR. In Figure 13, the sulfur concentrations in the coal sample as estimated from the LIBS intensity were compared with the known concentration of sulfur in the sample. The sulfur concentration was approximately 1% in the coal sample. The sulfur peak from the LIBS spectrum could be identified in spite of the small concentration. The intensity of the peak was quite similar to that of the baseline noise. This could lead to the peak intensity fluctuations being affected by the baseline noise intensity fluctuations. In this study, LIBS was performed in the air. Errors due to the gas components in the air may affect the measurement of elements, especially O and H. However, the CA method showed an improved accuracy with a coefficient of determination of 0.971 compared to the PLS and SNR methods with the \(R^{2}\)s of 0.914 and 0.777, respectively. The CA method showed the negligible measurement error in the air. In Table 2, the estimated concentrations of the target elements in the coal sample to calculate the calorific value of coal are presented. The calorific values were calculated with [PERSON]'s equation based on the estimated concentrations of the elements in coal using the LIBS signal intensity with the CA method. The calculated calorific value was compared to the calorific value obtained from a bomb calorimeter presented as a chemical analysis. The error between the calculated calorific value and the calorific value from the chemical analysis was from 0.16 to 6.99%. By comparing Tables 1 and 2, the percent difference between the estimated concentrations of the elements in the coal samples and the known concentrations could be determined. From Equation (1), the accuracy of the calorific value calculation of coal is most affected by the percent difference in the estimated concentration of hydrogen, because hydrogen has the biggest coefficient value. With a similar magnitude of the percent difference in the estimated concentration, hydrogen brought about a bigger error in the calorific value estimation than carbon. In Table 3, the estimated concentrations of the elements in coal using the LIBS signal intensity with the PLS method is shown. The error between the calorific values calculated using [PERSON]'s equation and the chemical analysis was found to be from 8.72 to 17.71%. The estimated carbon concentration had around a 2% difference from the sample's carbon concentration, which is a similar level of accuracy as with the CA. As shown in Figure 11, the PLS method had a low accuracy in predicting the hydrogen concentration in coal compared to the CA method. It showed a maximum error of a 3% difference from the sample. The underestimated hydrogen concentration made the percent error bigger in the calorific value calculation. Table 1.1 Estimated sulfur concentration with CA, PLS, and SNR. In Table 4, the estimated concentration of the elements in coal using the LIBS signal intensity with the SNR method is presented. The estimated calorific value based on the SNR method showed an error range from 10.70 to 22.90% with the calorific value from the chemical analysis. This was quite a large error compared to those of the other methods. In some samples, the carbon and hydrogen concentrations were both underestimated by a maximum of 3%, which made the error larger. Because the SNR method considers the baseline noise in Equation (5), a smoothing method to reduce the effect of random fluctuations may be needed.