A multivariate dominant factor based non-linearized PLS model is proposed. The intensities of different lines were taken to construct a multivariate dominant factor model, which describes the dominant concentration information of the measured species. In constructing such a multivariate model, non-linear transformation of multi characteristic line intensities according to the physical mechanisms of laser induced plasma spectrum were made, combined with linear-correlation-based PLS method, to model the nonlinear self-absorption and inter-element interference effects. This enables the linear PLS method to describe the non-linear relationship more accurately and provides the statistics-based PLS method with physical backgrounds. Moreover, a secondary PLS is applied utilizing the whole spectra information to further correct the model results. Experiments were conducted using standard brass samples. Taylor expansion was applied to make the nonlinear transformation describe the self-absorption effect of Cu. Then, line intensities of another two elements, Pb and Zn, were taken into account for inter-element interference. The proposed method shows a significant improvement when compared with conventional PLS model. Results also show that, even compared with the already-improved baseline dominant-factor-based PLS model, the present PLS model based on the multivariate dominant factor yields the same calibration quality (R2 = 0.999) while decreasing the RMSEP from 2.33% to 1.97%. The overall RMSE was also improved to 1.05% from 1.27%.
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