Multivariate linear regression of LIBS spectra
Examensarbete för masterexamen
Engineering mathematics and computational science (MPENM), MSc
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.
Laser induced breakdown spectroscopy, chemometrics, forward modeling, Bayesian inference, Markov chain Monte Carlo