On the Application of Fractal Formalism for Ranging Criteria of Quality of Multiparametric Technologies

Abstract

Ключевые слова: чугунные валки, механические свойства, микрострук-тура, область самоподобия, фрактальный формализм.У роботі проведено оцінку критеріїв якости багатопараметричних техно-логій. Запропонований підхід уможливлює, залежно від величини облас-ти самоподібности визначального параметра, оцінювати ступінь значу-щости критеріїв на прикладі визначення їх для сортопрокатних чавунних валків.Ключові слова: чавунні валки, механічні властивості, мікроструктура, область самоподібности, фрактальний формалізм.In the article, the quality criteria of multiparametric technologies are analysed. An approach allowing estimating a significance of the criteria depending on the size of the area of key parameters' self-similarity is proposed. As an illustrative example, this approach for the case of cast-iron rolls is used.

Regularization of One Conditionally Ill-Posed Problem of Extractive Metallurgy

“…In order to determine the working area of stable indicators for quality criteria of the multiparameter technologies, their ranking by importance was carried out. The criteria ranking methodology is more particularly described in the paper [6]. The criteria ranking procedure was carried out on the basis of the analysis concerning their area of selfsimilarity.…”

“…Such stipulations may include the definition of the ways to optimize the multicriteria and multiparameter technologies in the working area by finding areas with the best combination of partial indicators (criteria). From this point of view, the problem of ranking quality criteria of the multiparameter technologies, examined earlier [6], taking into account the fractal formalism [7][8][9], seems to be incomplete and can be transformed as the conditionally ill-posed one, whose solution, depending on various initial conditions, can vary. According to J. Hadamard [10], the problem is deemed to be ill-posed, if: it has no solution (in our concerned class), it has many solutions (from two or more), and the procedure for finding the solution is unstable (i.e.…”

“…The second item cannot be fulfilled subject to possible changes in the customer's requirements as for the significance of partial criteria. In this regard, the ranking of criteria can be carried out according to the customer's requirements, by the degree of influence of the chemical composition elements, and by the detectable value of the area of self-similarity for each of partial criteria [6] determining the stability of the technology operation. The third item of ill-posedness stipulations cannot be fulfilled as well, since the procedure for finding one or another solution of this conditionally ill-posed problem can vary depending on periodically changing parameters in the working area (chemical composition, cooling conditions, etc.…”

Fractal Model of Estimating Quality of Cold Worked Fuel Cladding Tubes

“…The use of fractal (fractional) dimensions in materials science has made it possible to determine average grain size in metals [10], predict mechanical properties of low-carbon steel after heat treatment [11], estimate residual life of aircraft structures [12], develop a fractal accelerator based on a corrugated plasma waveguide [13], etc. Application of the fractal theory confirms a more accurate estimation of quality characteristics of various materials (cast iron rolls of cold rolling mills [14], metals [15], concretes [16]) due to their ranking which contributes to stabilization of the multi-parameter technology of their production.…”

Method of material quality estimation with usage of multifractal formalism

“…Fractal approach is these days successfully used for the structure analysis [6][7][8][9]. Particularly, multifractal theory is used for estimation of heterogeneous structures of metals, concretes, polymers and other materials.…”