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Appl Spectrosc. 2013 Mar;67(3):291-300. doi: 10.1366/11-06393.

A nonlinearized multivariate dominant factor-based partial least squares (PLS) model for coal analysis by using laser-induced breakdown spectroscopy.

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  • 1State Key Lab of Power Systems, Department of Thermal Engineering, Tsinghua-BP Clean Energy Center, Tsinghua University, Beijing 100084, China.


A nonlinearized multivariate dominant factor-based partial least-squares (PLS) model was applied to coal elemental concentration measurement. For C concentration determination in bituminous coal, the intensities of multiple characteristic lines of the main elements in coal were applied to construct a comprehensive dominant factor that would provide main concentration results. A secondary PLS thereafter applied would further correct the model results by using the entire spectral information. In the dominant factor extraction, nonlinear transformation of line intensities (based on physical mechanisms) was embedded in the linear PLS to describe nonlinear self-absorption and inter-element interference more effectively and accurately. According to the empirical expression of self-absorption and Taylor expansion, nonlinear transformations of atomic and ionic line intensities of C were utilized to model self-absorption. Then, the line intensities of other elements, O and N, were taken into account for inter-element interference, considering the possible recombination of C with O and N particles. The specialty of coal analysis by using laser-induced breakdown spectroscopy (LIBS) was also discussed and considered in the multivariate dominant factor construction. The proposed model achieved a much better prediction performance than conventional PLS. Compared with our previous, already improved dominant factor-based PLS model, the present PLS model obtained the same calibration quality while decreasing the root mean square error of prediction (RMSEP) from 4.47 to 3.77%. Furthermore, with the leave-one-out cross-validation and L-curve methods, which avoid the overfitting issue in determining the number of principal components instead of minimum RMSEP criteria, the present PLS model also showed better performance for different splits of calibration and prediction samples, proving the robustness of the present PLS model.

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