  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 lased 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 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 to 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%.
