The paper gives a quantitative comparison of two methodological approaches to the solution of the inverse kinetic problem: the traditional approach and the nontraditional approach suggested by the authors. It is shown that the amount of information (in the sense of Shannon) obtained within the scope of the nontraditional approach is always greater than that obtained with the use of the traditional approach.
This review deals with the choice of a method of solving the inverse kinetic problem (IKP) which would provide the most definite description of the process under conditions of ambiguity. Two fundamentally different methodologies are possible for the IKP solution: one is based on the principle of unambiguous description (discrimination), while the other relies upon the complementarity principle (generalized descriptions). Specific IKP solution methods have been classified, the methodological differences being taken into account. In the first part of this review, general and special limitations in discrimination of formal models have been analysed.
As a numerical characteristic of the sensitivity of the kinetic parameter calculation method to the form of the kinetic function in non-isothermal kinetics, the value of the curvature of the line plotting residual dispersionvs. formal reaction order at the minimum point is suggested. The efficiency of this characteristic is exemplified.
Restrictions of the simplest use of correlation and regression analysis to obtain a single-valued solution to the inverse kinetic problem are considered. The Coats-Redfern method is suggested as a version of nonlinear regression analysis to increase the unambiguity of the solution.
Authors:S. V. Vyazovkin, I. S. Romanovsky, and A. I. Lesnikovich
A method is suggested for a generalized kinetic description of solid-phase processes on the basis of the complementarity principle. It enables one to obtain spectra as discrete distributions of the probability of describing a process in terms of kinetic functions according to their ordinal numbers. The spectra obtained make it possible to control changes in the behaviour of a solidphase process due to changing process conditions.
Authors:A. I. Lesnikovich, S. V. Vyazovkin, and I. S. Romanovsky
The possibility of describing complex processes by means of the KEKAM equation is demonstrated. The extensive descriptive ability of this equation can be explained within the nontraditional methodology of inverse kinetic problem solving.