Constrained least squares methods for estimating reaction rate constants from spectroscopic data

Abstract

Model errors, experimental errors and instrumental noise influence the accuracy of reaction rate constant estimates obtained from spectral data recorded in time during a chemical reaction. In order to improve the accuracy, which can be divided into the precision and bias of reaction rate constant estimates, constraints can be used within the estimation procedure. The impact of different constraints on the accuracy of reaction rate constant estimates has been investigated using classical curve resolution (CCR). Different types of constraints can be used in CCR. For example, if pure spectra of reacting absorbing species are known in advance, this knowledge can be used explicitly. Also, the fact that pure spectra of reacting absorbing species are non‐negative is a constraint that can be used in CCR. Experimental data have been obtained from UV‐vis spectra taken in time of a biochemical reaction. From the experimental data, reaction rate constants and pure spectra were estimated with and without implementation of constraints in CCR. Because only the precision of reaction rate constant estimates could be investigated using the experimental data, simulations were set up that were similar to the experimental data in order to additionally investigate the bias of reaction rate constant estimates. From the results of the simulated data it is concluded that the use of constraints does not result self‐evidently in an improvement in the accuracy of rate constant estimates. Guidelines for using constraints are given. Copyright © 2002 John Wiley & Sons, Ltd.

Analysis of video images from a gas–liquid transfer experiment: a comparison of PCA and PARAFAC for multivariate image analysis

“…The multivariate modeling of movies has been successfully used to identify features with different dynamic profiles. It can easily be envisaged that by fitting kinetic models to the profiles found, as has already been done within standard spectrometry [44,45], imaging could be used as a means of identifying chemical constants such as diffusion rates. Application of this methodology is not limited to video imaging, but is relevant to any form of chemical imaging in which measurement at regular time intervals is possible.…”

“…the CO 2 layer and the 'hole') between the two score images. One possible solution to this problem is to employ a bilinear decomposition which uses alternative parameter constraints to identify the model [42][43][44][45].…”

Grey component analysis

“…Therefore, nonnegativity and unimodality constraints are often used [3]. Even the incorporation of hard kinetic models has been shown useful [4][5][6][7].…”

Uncertainties and error propagation in kinetic hard-modelling of spectroscopic data

“…However, this calculation systematically underestimates this uncertainty when compared to the one resulting from multiple repetitions of the experiment under the same conditions. Some other contributions to the uncertainty in the rate constants, such as baseline shifts [26,27], spectral constraints in the least squares [28] and preceding calibration procedures [29] have been studied. Also, bootstrapping has been compared to variance-covariance based uncertainty calculations [30].…”