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

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 GRAM 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.