Method for Automatic Generation of Indirect Hard Models using Crossvalidation (MAGIC) for the Spectral Analysis of Mixture Spectra

Indirect Hard Modeling (IHM) is a physics-based method for the quantitative analysis of fluids' compositions using Raman, IR or NMR spectroscopy. IHM models mixture spectra with a superposition of their corresponding pure component models consisting of a sum of parametrized peak functions. By specifically adjusting parameters of the peak functions, IHM allows to properly handle non-linear effects in the mixture spectra, like peak shifts. However, the accuracy of the predicted compositions using IHM strongly depends on user-decisions regarding the number of peak functions and the chosen peak parameter adjustments. Existing algorithms to overcome this user-dependency choose number of peak functions and peak parameter adjustments independently from each other, based on the error of the spectral fit. As the error of the spectral fit steadily decreases with increasing model complexity, user-defined stopping criteria are still required. We present a Method for Automatic Generation of Indirect Hard Models using Crossvalidation (MAGIC) that jointly chooses number of peak functions and peak parameter adjustments by minimizing the error of the crossvalidated compositions of the calibration spectra. This requires no stopping criterion and leads to models with higher accuracy regarding the predicted compositions, while keeping the model complexity low. We present the advantages of MAGIC in comparison to the existing algorithms for the quantitative analysis of Raman spectra by applying it to exemplary spectra of three different mixtures.