Application of non-linear regression methods for the estimation of common kinetic parameters from several thermoanalytical curves

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Abstract

Novel methods of unified evaluation of two (or more) thermogravimetric curves have been worked out on the basis of known non-linear parameter estimating procedures (Gauss-Newton-Marquardt-type regression and the direct integral method of Valkó and Vajda were adapted). Their ability to provide estimate for common kinetic parameters of several TG (m-T) or DTG (d m/d t-T) curves were tested for pairs of curves of different heating rates, and for repeated curves of the same heating rate, obtained for the decomposition of CaCO3 in open crucible. In these cases the Arrhenius terms and the n-th order model functions were assumed. The fitting ability of estimations made for single curves and for pairs of curves sharing different number of parameters, was judged on the base of residual deviations (S res ) and compared to the standard deviation of the measurements. In the case of different heating rates, the two curves could not be described with the assumption of three common parameters, because of the minimum residual deviation was very high. However, sharing of activation energy and preexponential term only, and applying different exponents for the two curves, provided a satisfactory fit by our methods. Whilst in the case of repeated curves, we could find such a common three-parameter set, which has a residual deviation comparable with the standard deviation of the measurements. Because of their flexibility (taking into account the variable number of common parameters and the versatile forms of model equations), these methods seem to be promising means for unified evaluation of several related thermoanalytical curves.

Original languageEnglish
Pages (from-to)539-550
Number of pages12
JournalJournal of Thermal Analysis
Volume42
Issue number2-3
DOIs
Publication statusPublished - Aug 1994

Fingerprint

Heating rate
Kinetic parameters
regression analysis
kinetics
curves
Crucibles
Activation energy
Decomposition
deviation
heating
standard deviation
evaluation
crucibles
newton
flexibility
estimating
exponents
activation energy
decomposition
estimates

Keywords

  • multiple scans
  • non-linear regression methods
  • residual deviation

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Engineering(all)

Cite this

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title = "Application of non-linear regression methods for the estimation of common kinetic parameters from several thermoanalytical curves",
abstract = "Novel methods of unified evaluation of two (or more) thermogravimetric curves have been worked out on the basis of known non-linear parameter estimating procedures (Gauss-Newton-Marquardt-type regression and the direct integral method of Valk{\'o} and Vajda were adapted). Their ability to provide estimate for common kinetic parameters of several TG (m-T) or DTG (d m/d t-T) curves were tested for pairs of curves of different heating rates, and for repeated curves of the same heating rate, obtained for the decomposition of CaCO3 in open crucible. In these cases the Arrhenius terms and the n-th order model functions were assumed. The fitting ability of estimations made for single curves and for pairs of curves sharing different number of parameters, was judged on the base of residual deviations (S res ) and compared to the standard deviation of the measurements. In the case of different heating rates, the two curves could not be described with the assumption of three common parameters, because of the minimum residual deviation was very high. However, sharing of activation energy and preexponential term only, and applying different exponents for the two curves, provided a satisfactory fit by our methods. Whilst in the case of repeated curves, we could find such a common three-parameter set, which has a residual deviation comparable with the standard deviation of the measurements. Because of their flexibility (taking into account the variable number of common parameters and the versatile forms of model equations), these methods seem to be promising means for unified evaluation of several related thermoanalytical curves.",
keywords = "multiple scans, non-linear regression methods, residual deviation",
author = "J. Madar{\'a}sz and G. Pokol and S. G{\'a}l",
year = "1994",
month = "8",
doi = "10.1007/BF02548534",
language = "English",
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pages = "539--550",
journal = "Journal of Thermal Analysis and Calorimetry",
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AU - Madarász, J.

AU - Pokol, G.

AU - Gál, S.

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N2 - Novel methods of unified evaluation of two (or more) thermogravimetric curves have been worked out on the basis of known non-linear parameter estimating procedures (Gauss-Newton-Marquardt-type regression and the direct integral method of Valkó and Vajda were adapted). Their ability to provide estimate for common kinetic parameters of several TG (m-T) or DTG (d m/d t-T) curves were tested for pairs of curves of different heating rates, and for repeated curves of the same heating rate, obtained for the decomposition of CaCO3 in open crucible. In these cases the Arrhenius terms and the n-th order model functions were assumed. The fitting ability of estimations made for single curves and for pairs of curves sharing different number of parameters, was judged on the base of residual deviations (S res ) and compared to the standard deviation of the measurements. In the case of different heating rates, the two curves could not be described with the assumption of three common parameters, because of the minimum residual deviation was very high. However, sharing of activation energy and preexponential term only, and applying different exponents for the two curves, provided a satisfactory fit by our methods. Whilst in the case of repeated curves, we could find such a common three-parameter set, which has a residual deviation comparable with the standard deviation of the measurements. Because of their flexibility (taking into account the variable number of common parameters and the versatile forms of model equations), these methods seem to be promising means for unified evaluation of several related thermoanalytical curves.

AB - Novel methods of unified evaluation of two (or more) thermogravimetric curves have been worked out on the basis of known non-linear parameter estimating procedures (Gauss-Newton-Marquardt-type regression and the direct integral method of Valkó and Vajda were adapted). Their ability to provide estimate for common kinetic parameters of several TG (m-T) or DTG (d m/d t-T) curves were tested for pairs of curves of different heating rates, and for repeated curves of the same heating rate, obtained for the decomposition of CaCO3 in open crucible. In these cases the Arrhenius terms and the n-th order model functions were assumed. The fitting ability of estimations made for single curves and for pairs of curves sharing different number of parameters, was judged on the base of residual deviations (S res ) and compared to the standard deviation of the measurements. In the case of different heating rates, the two curves could not be described with the assumption of three common parameters, because of the minimum residual deviation was very high. However, sharing of activation energy and preexponential term only, and applying different exponents for the two curves, provided a satisfactory fit by our methods. Whilst in the case of repeated curves, we could find such a common three-parameter set, which has a residual deviation comparable with the standard deviation of the measurements. Because of their flexibility (taking into account the variable number of common parameters and the versatile forms of model equations), these methods seem to be promising means for unified evaluation of several related thermoanalytical curves.

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KW - residual deviation

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