The reduction of rotational ambiguity in soft-modeling by introducing hard models

Rotational ambiguity is a major problem in the application of soft-modeling analysis to a variety of multivariate mixture resolution problems and particularly important in the analysis of kinetic data. Soft-modeling analyses rely on constraints that restrict the concentration profiles and/or the spectral responses of all components. The main goal of this work is to demonstrate how a hard-modeling constraint on concentration profiles drastically decreases the extent of the rotational ambiguity. Therefore, in the present paper the discussion is focused on systems in which hard-modeling information is available. The results of simulated examples reveal that the utilized hard constraint decreases the rotational ambiguity in estimated concentration profile even components that do not take part in the explicit model. In addition, the rate constant of known reaction is determined in this method.

Range of feasible concentration profiles before (top) and after hard constraint (right); each concentration profile is normalised to a maximum of one.Figure optionsDownload as PowerPoint slideHighlights
► This is the first systematic study of effects of hard-model constraints on rotational ambiguity.
► The resulting reduction of the area of feasible solutions is substantial.
► This is demonstrated on a set of representative systems with three components.