PROBLEMS CONSTRUCTION REGRESSIAN MODEL OF CUTING PROCESS

Authors

  • С. М. Лапач National Technical University of Ukraine «Kyiv Polytechnic Institute», Kyiv, Ukraine

DOI:

https://doi.org/10.20535/2305-9001.2014.72.36838

Keywords:

linear regression analysis, cutting process modeling, model specification, model adequacy, transformation of background factors, Chebyshev polynomial

Abstract

The comparison of different approaches to cutting operations model specification and their feasibility from statistical and substantial viewpoints was made. It is shown that the linearization to be used for solving the problem for the multiplicative model leads to a change in the correlation coefficients between the covariates and the response. The result is a distortion of the model structure (composition and relative importance of the covariates). When using Chebyshev polynomials distortion does not occur. Demonstrated a conflict between the various statistical indicators, which also ceteris paribus leads to different structure models. The solutions of specific tasks show the disadvantages of traditional multiplicative model (from statistical and physical viewpoints), also discrepancy between statistical estimate of adequacy in regression analysis and requirements to the model in object region. It is suggested not to use multiplicative models due to absence of their feasibility and as leading to changes of original problem. The adequacy of model is suggested to be estimated coming from the requirements of object region

References

1. Kolesov I.M. Osnovy tehnologi mashinostroenija: Ucheb. dlja mashinostroit. spec. vuzov (Bases of technology of engineer: Studies. for mashinostroit. special. institutes of higher). Moskow: Vyssh. shk., 2001.591p.

2. Kacev P.G. Statisticheskie metody issledovanija rezhushhego instrumenta. Izd. 2-e, pererab. i dop.(Statistical methods of research of cutting tool. 2-nd ed.). Moskow: Mashinostroenie, 1974. 231p.

3. Lapach S.N., Radchenko S.G., Babich P.N. Planirovanie, regressija i analiz modelej PRIAM (PRIAM). Katalog programmnye produkty Ukrainy. [Design, regression and analysis of models of PRIAM: Catalogue software products of Ukraine]. Kyiv.: 1993. pp. 24-27.

4. S.N. Lapach Problemy postroenija matematicheskih modelej jeksperimental'no-statisticheskimi metodami. Progresivna tehnіka і tehnologіja mashinobuduvannja, priladobuduvannja і zvarjuval'nogo virobnictva. Pracі NTUU “KPІ”, T. 2, [Problems of construction of mathematical models statistical methods: A progressive technique and technology of engineer, instrument-making and welding production]. Kyiv: NTUU “KPІ”, 1998. pp.25-29.

5. S.N. Lapach, A.V. Chubenko, Babich P.N. Statisticheskie metody v mediko-biologicheskih issledovanijah s ispol'zovaniem Excel –2 izd. pererab. i dop.( Statistical methods in medics and biology researches with the use of Excel – 2nd Ed.).Kyiv: 2001, Morion. 408p.

6. Radchenko S.G. Metodologija regressionnogo analiza (Regression analysis methodology).Kyiv.: «Kornіjchuk», 2011. 376p.

7. Ivanov G.A. Turban A.F. Statisticheskie metody vosstanovlenija istinnoj zavisimosti po jeksperimental'nym dannym (Statistical methods of reducing of true dependence on experimental data). Kyiv: Znanie. 1986. 22 p.

Published

2015-02-02

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