DOI: https://doi.org/10.30838/J.PMHTM.2413.241219.47.600

Ways of regularization of materials science ill-posed problems

Yu. I. Dubrov, V. M. Volchuk

Abstract


Introduction. The ill-posedness of the problems is mainly caused by the incompleteness of their formal axiomatics, which is a consequence of the incompleteness of our knowledge of the object of identification. This fact demonstrates the formal axiomatic incompleteness, arising in description of the metal structure elements by means of traditional configurations of Euclidean geometry, which triggers the need to use other promising approaches to the structure assessment. The aim of the work is to establish solutions to some conditionally incorrect materials science problems. Statement of basic materials. On the basis of the analysis of quantitative and qualitative assessment of the real structures of many iron carbon alloys, there are observed some significant, for practical purposes, divergences between results of direct experiments and results of their prediction. Basic ways of regularization of identification problems of multi-parameter objects, criteria selection for multi-criteria technology optimization, ranging of multi-parameter technologies quality criteria, material quality estimation are considered. It is shown that regularization of materials science conditionally ill-posed problems is acceptable with application of specific algorithms for every specific case. Conclusions. It is shown that some of the conditionally incorrect problems are solved by applying a language of a higher level - the language of fractal geometry.

Keywords


ill-posed problems; multiparametric technology; the area of self-similarity; materials; the regularization

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References


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