Multivariate linear regression of LIBS spectra
Typ
Examensarbete för masterexamen
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2020
Författare
Ekström, Krister
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Laser induced breakdown spectroscopy (LIBS) is a spectroscopic technique for chemical analysis. LIBS can be used in rough environments and measurements can often
be made without any sample preparation. These properties make LIBS interesting
for in-situ measurements in industrial settings. However this physical robustness
and flexibility come at a cost: There are processes involved in a LIBS measurement
that are difficult to model. Therefore statistical methods constitute the best choice
for analysis of LIBS spectra. The accuracy and robustness obtained with current
methods have not been sufficient for widespread industrial adoption of LIBS. Careful
statistical analysis is required to further develop LIBS analysis and reach a level of
robustness and accuracy that enables widespread industrial adoption. This thesis
aims at contributing to that development by developing a method for multivariate
linear regression of LIBS spectra. The first part uses multivariate linear regression
on a calibration set to estimate the spectra of the elements in the sample, referred to
as the pure spectra. These pure spectra are then used to predict the concentrations
of new samples. The second part is a Bayesian continuation, utilizing a model from
CF-LIBS to create a constraining prior for the regression. The method constitutes a
change in perspective from previous multivariate attempts where the concentrations
are inferred from the spectrum using methods such as partial least squares, principle
component regression or multiple linear regression. The method presented in this
thesis builds on the view of the spectrum as a multivariate response to the concentrations. A relatively simple model is suggested for this response. This model builds
on common assumptions made when analyzing LIBS spectra using the conventional
univariate approach. As a result of this model-based approach, the method is not
only more interpretable and easier to develop but perhaps more importantly the degrees of freedom are decoupled from the number of pixels in the spectrum. Instead
the degrees of freedom are determined by the number of elements in the analysis
with two orders of magnitude improvement.
Beskrivning
Ämne/nyckelord
Laser induced breakdown spectroscopy, chemometrics, forward modeling, Bayesian inference, Markov chain Monte Carlo