Second-order statistical regression and conditioning of replicate transient kinetic data

Abstract

A new method has been developed to estimate physico-chemical parameters from transient kinetic data: second-order statistical regression (SOSR). It allows to account for heteroskedasticity and nonwhiteness of the noise in the time series measured. SOSR makes use of replicates to estimate the second-order statistics, i.e. the autocovariance pattern of the noise. A sample principal noise component analysis of the experimental time series allows nonlinear least-squares (NLSQ) regression of the latter. The method has been validated by regression of artificially generated experimental data and the results have been compared with those obtained with direct NLSQ regression. The SOSR has also been applied to the irreversible adsorption of oxygen on a reduced vanadia/silica catalyst and the interaction of propane with a copper/ceria catalyst, as studied with a Temporal Analysis of Products (TAP) setup. In general, compared with those obtained with direct NLSQ regression, the parameter estimates and their confidence intervals are more accurate.

A shortcut method for faster determination of permeability coefficient from time lag experiments

“…Roelanta et al [18] suggested a nonlinear least square method of preconditioning transient experiments containing time-series replicates based on systems of partial differential equations such as the one presented in this paper. Alternatively, the time series replicates may be averaged and regressed; this follows important assumptions that the noise is normally distributed amongst the replicates and that the independent time variable has no experimental error associated with it (automated data acquisition is thus recommended).…”

“…The mathematical expression of J AVG is obtained by combining the expressions for J in and J out given by Eqs. (18) and (10), respectively:…”

“…7). Despite this problem, with preconditioning of the transient data suggested by Roelanta et al [18], one can get an excellent approximation of the slope, which is used for the determination of the diffusivity (Eq. (13)).…”

Forty years of temporal analysis of products

“…31,148,149 Analytical advances specific to the TAP methodology have also been reported. 146,[150][151][152][153][154] Since 2001 a step-by-step advancement of the mathematical theory of the TAP "reaction-diffusion" systems has been constructed, including:…”

Superposition of artificial experimental error onto calculated time series: Construction of in-silico data sets

“…Section 2.1 gives the detailed mathematical background and Section 2.2 gives some examples of this directly-implementable theory. The interested reader can find another application in Roelant et al [2] , [3] .…”