Optimizing fitting parameters in thermogravimetry
This study presents an alternative to simple estimation of parametric fitting models used in thermal analysis. The addressed problem consists in performing an alternative optimization method to fit thermal analysis curves, specifically TG curves and their first derivatives. This proposal consists in estimating the optimal parameters corresponding to fitting kinetic models applied to thermogravimetric (TG) curves, using evolutionary algorithms: differential evolution (DE), simulated annealing and covariance matrix adapting evolutionary strategy. This procedure does not need to include a vector with the initial values of the parameters, as is currently required. Despite their potential benefits, the application of these methods is by no means usual in the context of thermal analysis curve’s estimation. Simulated TG curves are obtained and fitted using a generalized logistic mixture model, where each logistic component represents a thermal degradation process. The simulation of TG curves in four different scenarios taking into account the extent of processes overlapping allows us to evaluate the final results and thus to validate the proposed procedure: two degradation processes non-overlapped simulated using two generalized logistics, two processes overlapped, four processes non-overlapped and four processes overlapped two by two. The mean square error function is chosen as objective function and the above algorithms have been applied separately and together, i.e., taking the final solution of the DE algorithm is the initial solution of the remaining. The results show that the evolutionary algorithms provide a good solution for adjusting simulated TG curves, better than that provided by traditional methods.
KeywordsTG DTG Model-fitting Overlapping Global optimization Evolutionary algorithms
This research has been partially supported by the Spanish Ministry of Science and Innovation, Grant MTM2011-22392 (ERDF included).
- 1.Bicerano J. Prediction of polymer properties, 3rd ed., rev. and expanded. New York: Marcel Dekker; 2002.Google Scholar
- 6.R Development Core Team. R: A language and environment for statistical computing. Viena: R Foundation for statistical computing; 2009. http://www.R-project.org. Accessed 05 Oct 2013.
- 9.Price KV. Differential evolution: a practical approach to global optimization. Berlin: Springer; 2005.Google Scholar
- 11.Storn R. Differential Evolution Homepage. International Computer Science Institute, University of California, Berkeley. 2013. http://www1.icsi.berkeley.edu/~storn/code.html. Accessed 05 Oct 2013.
- 14.Gubian S, Xiang Y, Suomela B, Hoeng J. R functions for generalized simulated annealing. R Package ‘GenSA’; 2013. http://cran.r-project.org/web/packages/GenSA/. Accessed 05 Oct 2013.
- 17.Ghalanos A. Parma: portfolio allocation and risk management. R package version 1.03. 2013. http://cran.r-project.org/web/packages/parma/. Accessed 05 Oct 2013.
- 20.Levenberg K. A method for the solution of certain problems in least squares. Quart Appl Math. 1944;2:164–8.Google Scholar
- 23.Chambers JM, Hastie. Statistical models in S. Boca Raton, Fla.: Chapman & Hall/CRC; 1992.Google Scholar
- 25.Kingsland SE. Modeling nature: episodes in the history of population ecology. 2nd ed. Chicago: University of Chicago Press; 1995.Google Scholar
- 32.Artiaga R, Cao R, Naya S, González-Martín B, Mier JL, García A. Separation of overlapping processes from TGA data and verification by EGA. In: Pan WP, Judovits L, editors. Techniques in thermal analysis: hyphenated techniques, thermal analysis of the surface, and fast rate analysis. West Conshohocken, PA: ASTM Special Technical Publications; 2007. p. 60–71.Google Scholar