Permissible Extrapolation Justification of the Multiplicative Multifactorial Model and Its Application to the White Soot Production Technology

Lyutsiya Karimova, Guldana Makasheva, Vitaliy Malyshev, Yelena Kharchenko, Yerlan Kairalapov

Abstract


The solution to a specific technological problem is combined with the methodological development of a nonlinear multifactorial relationship to justify the boundaries of its extrapolation beyond the experimental range used. White soot was produced through two-stage carbonization of a silicate solution (composition, g/l: Na2O = 126.5, SiO2 = 107.7, Al2O3 = 3.1), obtained after processing waste tailings with carbon dioxide in a recirculation system. The influence of the deposition duration, temperature, and final pH value of the pulp on the formation of the specific surface area (Ssp, m2/g) of white soot was studied. The specific surface area was calculated from the average diameter of the white soot particles measured using an electron microscope. A multifactorial experiment was designed, and the experimental results were processed using a probabilistic deterministic method for experiment design (PDED) to obtain a nonlinear multiplicative combined model. A new interpretation of the subordination of the nonlinear multiple correlation coefficient R and the R2 value was given as relating to the structural and adaptive components of complex self-organizing systems. This determines their use for assessing the ratio of the basic R and extrapolated R2ranges of variation for each factor and any combinations thereof and multifactorial dependence in general. The results are presented in the form of multifactor tabular nomograms measured by the number of multifactor cells in localized areas of optimal sets that allow isolation by one or another combination of factors. The technological object of extrapolation of the ‘white soot’ production is linked to the solution of emerging methodological problems and illustrates the accessibility of the engineering application of the proposed method for combining nonlinear and linear approaches to mathematical experimental design.

 

Doi: 10.28991/HIJ-2024-05-03-08

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Keywords


White Soot; Specific Area; Multifactor Model; Correlation; Permissible Extrapolation.

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DOI: 10.28991/HIJ-2024-05-03-08

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