Optimization Method for Simultaneous Kinetic Analysis

Abstract

Kinetic analysis is often carried out for simultaneous determinations; thus, a theory to establish its optimal conditions is necessary. A very simple and fast model to find conditions for optimum analytical performance and to predict the quality of simultaneous kinetic analysis has been developed. It is general and applicable to any reaction order or rate constant. The model has been based on the angle between the kinetic vectors and on their norm ratio, which are readily calculated for any kinetic scheme. Evaluation of the proposed model has been carried out by detailed simulations of numerous experimental conditions and analysis by full PCR calculations (when applicable) or nonlinear least-squares fitting. An important conclusion is that analytical performance is determined to a large extent by the stability of the space spanned by the relevant component vectors (in addition to experimental noise and other factors). The quality of the analysis is governed by the angle between the kinetic vectors, while the norm ratio determines the error distribution between components. Optimum conditions for simultaneous kinetic analysis have been studied in several representative examples, regarding the timing of the kinetic monitoring and the effects of concentrations and of rate constant ratios, as well as several other factors of experimental relevance.

Optimization of Informative Spectral Regions in FT-NIR Spectroscopy for Measuring the Soluble Solids Content of Apple

“…Figure 3 shows the histogram of frequency of selection of each sub-region (or interval). In Figure 3, the frequency of selected interval Kleynen et al, 2003;Mendoza et al, 2012;Nicolaï et al, 2007;Nicolaï et al, 2008;Paz et al, 2009;Pierna et al, 2009;Spiegelman et al, 1998;Xu & Schechter, 1996;Zhu et al, 2007) were greater than or equal to 60% and these intervals were considered as informative regions, corresponding ranges of 4355 -4983, 5303 -5932, 8466 -9727 and 10047 -10676 cm 21 .…”

“…To overcome this disadvantage, partial least squares (PLS) regression has been widely used for NIR analytic resolution due to its ability in overcoming deviations from the real linear response caused by effects such as spectral bands overlapping and interactions between components. Furthermore, lots of advanced calculation methods have been developed for PLS to enhance its performance both at theoretical (Goicoechea & Olivieri, 2002;Xu & Schechter, 1996;Pierna, Abbas, Baeten, & Dardenne, 2009;Spiegelman et al, 1998) and experimental aspects (Kleynen, Leemans, & Destain, 2003;Liu, Jiang, & He, 2009;Xiaobo, Jiewen, Xingyi, & Yanxiao, 2007). For example, for region selection in multicomponent spectral analysis, typical algorithms include branch and bound (Yizeng, Yu-long, & Ru-Qin, 1989), stepwise selection (Brown, 1992), genetic algorithms (Lucasius & Kateman, 1991), iPLS and its evolution (Nørgaard et al, 2000), moving window PLS (Jiang, Berry, Siesler, & Ozaki, 2002) and its analogues (Du, Liang, Jiang, Berry, & Ozaki, 2004), genetic algorithms iPLS-based Ying & Liu, 2008), variable-bagging PLS (Pi, Shinzawa, Wang, Han, & Ozaki, 2009), backward variable selection PLS (Huang, He, & Yang, 2013;Pierna et al, 2009) and others (Xu & Schechter, 1996).…”

Wavelength selection-based nonlinear calibration for transcutaneous blood glucose sensing using Raman spectroscopy

“…Over the years, wavelength selection techniques have been demonstrated (theoretically 21,22 and experimentally 23 ) to improve calibration model accuracy and robustness. As noted in the literature, wavelength (variable) selection can be viewed as a subset of the more generic process of dimension reduction.…”

Wavelet packet transform and artificial neural network applied to simultaneous kinetic multicomponent determination

“…If the Hessian matrix is not definitely positive the minimum cannot be found. Inversion of the approximated Hessian matrix can be stabilized by using the LM algorithm [9,10]: (5) where I is the identity matrix, λ is the non-negative scalar and can be adjusted to maintain matrix H at the full rank.…”

“…Recently, multicomponent kinetic analyses have received much attention from chemists. Chemometric approaches [1,2] such as Kalman filtering [3,4], principal component regression [5] and partial least squares [6] are being used increasingly in multicomponent kinetic determination. However, these approaches are more often applicable to linear systems.…”