## 5 Conclusions  
The existing methods for the detection of coal are labor intensive and time consuming. In this work, LIBS technology assisted with machine learning was introduced to support the current condition that the coal quality information lags in the real-time combustion status in the coal-fired boiler. The experimental optimization was conducted to reduce the \begin{table}
\begin{tabular}{c c c c} \hline \hline Clustering & Data source & Comprehensive silhouette coefficient & Prediction silhouette coefficient \\ \hline K-means & Section 4.1.1 & 0.621 & 0.663 \\ DBSCAN & Section 4.1.2 & 0.604 & 0.437 \\ \hline \multicolumn{4}{c}{**(b) The classification results by machine learning**} \\ \hline Classification & Data source & Accuracy CV & Accuracy P \\ \hline K-nearest neighbor & Section 4.2.1 & 0.957 & 0.933 \\ Naive Bayes & Section 4.2.2 & / & 0.967 \\ \hline \multicolumn{4}{c}{**(c) The quantification results by machine learning**} \\ \hline Regression & Item & R\({}^{2}\) CV & RMSECV & R\({}^{2}\) P & RMSEP \\ \hline \multirow{3}{*}{Partial least squares} & Ash & 0.942 & 1.349\% & 0.970 & 1.012\% \\  & Volatiles & 0.882 & 0.803\% & 0.934 & 0.878\% \\ \cline{1-1}  & Fixed carbon & 0.933 & 1.443\% & 0.956 & 1.409\% \\ \cline{1-1}  & Ash & 0.943 & 1.405\% & 0.967 & 1.063\% \\ \cline{1-1} LASSO & Volatiles & 0.840 & 0.923\% & 0.904 & 1.060\% \\ \cline{1-1}  & Fixed carbon & 0.942 & 1.310\% & 0.937 & 1.688\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The different performances of clustering, classification, and regression models. Figure 14: Cross-validation results of LASSO regression fixed carbon quantification (**a**), and prediction set regression results (**b**). spectral RSD, and the pretreatment of LIBS spectra was used for the removal of noise and laid a foundation for classification and qualification. Then, two clustering models, two classification models, and two regression models were established to show their application conditions and performances. Two clustering models could realize the clustering of coal samples according to the LIBS spectra with unknown labels, and the results showed that K-means clustering could effectively divide coal samples into four clusters that the spectra and coal quality information of samples within the same cluster were similar to each other. As for the two classification models, they could trace the source of coal samples with known labels, and the results indicated that the prediction performance of naive Bayesian classification was better than the K-nearest neighbor with a prediction accuracy of 0.967. Two regression models could give quantitative prediction results of various proximate analysis indicators, the PLSR showed better performance than the LASSO regression, and the RMSEP of ash, volatiles, and fixed carbon were 1.012%, 0.878%, and 1.409%, respectively. In this work, the performance of different results could provide a reference when applying LIBS to industry. In addition, attention should be paid to the improvement of LIBS spectral accuracy, repeatability, and the fitting degree of classification and regression model. In the future, if the mentioned three factors can be achieved at the same time, meanwhile, there is a similar prediction sample in the database, the prediction accuracy will be perfect, which is also an important development trend in LIBS technology. Writing--original draft, Y.Z. ; methodology, QL. ; software, A.C.; writing--review and editing, Y.L. ; supervision, X.R. All authors have read and agreed to the published version of the manuscript. This research was funded by the Hebei Administration for Market Regulation Science and Technology Program of China, grant number: 2022 ZD09. Not applicable. The authors declare no conflict of interest. Proximate analysis results of 100 coal samples.