Rapid estimation of rate constants using on-line SW-NIR and trilinear models

In this paper, two algorithms are presented to estimate reaction rate constants from on-line short-wavelength near-infrared (SW-NIR) measurements. These can be applied in cases where the contribution of the different species in the mixture spectra is of exponentially decaying character. From a single two-dimensional dataset two two-way datasets are formed by splitting the original dataset such that there is a constant time lag between the two two-way datasets. Next, a trilinear structure is formed by stacking these two two-way datasets into a three-way array. In the first algorithm, based on the generalized rank annihilation method (GRAM), the trilinear structure is decomposed by solving a generalized eigenvalue problem (GEP). Because GRAM is sensitive to noise it leads to rough estimations of reaction rate constants. The second algorithm (LM-PAR) is an iterative algorithm, which consists of a combination of the Levenberg-Marquardt algorithm and alternating least squares steps of the parallel factor analysis (PARAFAC) model using the CRAM results as initial values. Simulations and an application to a real dataset showed that both algorithms can be applied to estimate reaction rate constants in case of extreme spectral overlap of different species involved in the reacting system. (C) 1998 Elsevier Science B.V. All rights reserved.