Ways of compensationof incomplete formal axiomatics in identification ofcomplex objects

Authors

  • V. M. Volchuk Department of Materials Science and Material Processing, State Higher Education Institution“Prydniprovska State Academy of Civil Engineering and Architecture”, 24-a, Chernyshevskoho St., 49600, Dnipro, Ukraine https://orcid.org/0000-0001-7199-192X
  • Yu. I. Dubrov Department of Materials Science and Material Processing, State Higher Education Institution“Prydniprovska State Academy of Civil Engineering and Architecture”, 24-a, Chernyshevskoho St., 49600, Dnipro, Ukraine https://orcid.org/0000-0002-3213-4893

DOI:

https://doi.org/10.30838/J.PMHTM.2413.261218.31.562

Keywords:

incompleteness of formal axiomatic, complex object, fractal geometry, the principle “external additions”, cast iron,

Abstract

Abstract. Introduction.The discrepancies between the results of modeling and the data obtained after direct experiments on a real object indicate incompleteness of the formal axiomatics of the existing methods of research in various fields of science and technology. To assess the incompleteness of the formal axiomatics of the object, the theorem of K. Godel and the principle of “external  complementing  of  S.  Bir” are  used.  In  purpose  to  compensate  for  the  incompleteness  of  formal  axiomatics,  it  is proposed to perform modeling of the microstructure of an object with the use of a language of a higher level. Theoretical basis and results.As an example, the cast iron structure represented by the fractal model is considered. Comparison of the analysis results of the structure and mechanical properties of cast iron with the use of fractal and traditional methods with field testing data is carried out. The correlation coefficients between the topological characteristics of the structure of cast-iron rolls of the brand SPHN (percentage content of perlite and carbides) and mechanical properties are 0,53and 0,52, respectively. Between the fractal dimensions of perlite and carbides and the mechanical properties of these rolls, the coefficients of correlation make up 0,94 and 0,93, respectively. The obtained results indicate the prospects of using fractal geometry for the identification of complex objects in  comparison  with  the  Euclidean  geometry. Originality.  In  order  to  partially  eliminate  the  incompleteness  of  the  formal axiomatics that arises when identifying the structure and properties of complex objects, according to the principle of “external addition”S. Bier, it is shown that it is possible to apply a higher level language fractal geometry. Conclusion. An algorithm is proposed for partial compensation of the incompleteness of the formal axiomatics of the structure of complex objects using fractal modeling.  The  results  obtained  highlight  the  prospects  of  using  the  fractal  geometry  to  partially  compensate  for  the incompleteness of the formal axiomatics in the model under consideration.

Author Biographies

V. M. Volchuk, Department of Materials Science and Material Processing, State Higher Education Institution“Prydniprovska State Academy of Civil Engineering and Architecture”, 24-a, Chernyshevskoho St., 49600, Dnipro

Dr. Sc. (Tech.), As. Prof.

Yu. I. Dubrov, Department of Materials Science and Material Processing, State Higher Education Institution“Prydniprovska State Academy of Civil Engineering and Architecture”, 24-a, Chernyshevskoho St., 49600, Dnipro

Dr. Sc. (Tech.), Prof.

References

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Published

2018-12-26

Issue

No. 4 (2018): Metal Science and Heat Treatment of Metals

Section

Technical science

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