TO THE QUESTION ABOUT REMOVING ERRORS IN THE PROCESS OF MATHEMATICAL MODELING OF METALLURGICAL PROCESSES WITHIN THE REGRESSION DATA ANALYSIS USING THE MATHCAD PACKAGE

M. I. Alkatsev, V. M. Alkatsev, Z. K. Abaev, A. E. Dzgoev

Abstract


This article presents frequently used methods for assessing the quality of regression models and their application in the study of certain metallurgical processes. These models are: R2 coefficient, correlation coefficient, multicollinearity, extrapolation, time systems, engineering prediction, full factorial experiment.Until now, a significant part of researchers have indicated that coefficient is used not only by economists, but also by graduate students of technical specialties as a diagnostic value, while the correction of this coefficient does little. The correlation coefficient is a numerical characteristic of the joint distribution of two random variables, independent of the dimension of the units. This rule applies equally to the correlation coefficient obtained by multiplying two matrixcolumns. The method of data processing in the presence of collinearity (intercorrelation) in them and its elimination is shown. The drawbacks of using the extrapolation method in the process of mathematical modeling are shown. A new forecasting method has been developed, based on finite time series, called the sliding matrix method and consisting in the continuous updating of the coefficients of the regression equation by removing the line with obsolete data from the matrix and entering new lines with data at the predicted point. The method allows you to continuously get rid of the old information “burden”, which allows you to make the forecast more correct. All calculations of the mathematical model were made using the Mathcad software product.

Keywords


mathematical modeling of non-ferrous metals; sliding matrix method

References


Alkatsev M.I., Alkatsev V.M., Voloshin S.B., Dzgoev A.E., Abaev Z.K. Simulation Modeling of Zinc Concentrates Roasting in the Fluidized Bed Furnaces. Bulletin of the South Ural State University. Ser. Metallurgy, 2018, vol. 18, no 3, pp. 26–32. (in Russ.) DOI: 10.14529/met180303

Kremer N.Sh. Teoriya veroyatnostey i matematicheskaya statistika: ucheb. dlya vuzov [Probability Theory and Mathematical Statistics: A textbook for universities]. Moscow, Unity-Dana Publ., 2004, 514 p.

Dougerti C. Introduction to econometrics. 3rd ed. Oxford: University Press, 2010.

Johnson N.L., Leone F.C. Statistics and experimental design in engineering and the physical science. N.Y., John Wiley and Sons Publ., 1977.

Kobzar A.I. Prikladnaya matematicheskaya statistika. Dlya inzhenerov i nauchnykh rabotnikov [Applied mathematical statistics. For engineers and scientists]. Moscow, Fizmatlit Publ., 2006, 816 p.

Bolt G.J. Marketing and sales forecasting: a total approach. 2nd rev. ed. London, Kogan Page Limited Publ., 1971.

Gmoshinskiy V.G. Inzhenernoye prognozirovaniye [Engineering forecasting]. Moscow, Energoizdat Publ., 1982, 208 p.

Orlova I.V., Polovnikov V.A. Ekonomiko-matematicheskiye metody i modeli: komp’yuternoye modelirovaniye [Economic-mathematical methods and models: computer simulated]. Moscow, University textbook Publ., Infra-M Publ., 2013.

Anderson T. Statisticheskiy analiz vremennykh ryadov [Statistical analysis of time series]. Translation from English by I.G. Zhurbenko and V.P. Sock. Edited by Yu.K. Belyaev. Moscow, Mir Publ., 1976.

Voskoboynikov Yu.E. Regressionnyy analiz dannykh v pakete Mathcad: ucheb. posobiye [Regression analysis of data in the Mathcad package: Tutorial]. St. Petersburg, Lan’ Publ., 2011, 224 p. (Textbooks for universities. Special literature).

Novik F.S, Arsov Ya.B. Optimizatsiya protsessov tekhnologii metallov metodami planirovaniya eksperimenta [Optimization of metal technology processes using experimental design methods]. Moscow, Bauman MSTU Publ., 2011.

Lebedev A.N. Моделирование в научно-технических исследованиях [Modeling in scientific and technical research]. Moscow, Radio and communication Publ., 1989. 224 p.

Sidnyaev N.I., Vilisova N.T. Vvedeniye v teoriyu planirovaniya eksperimenta [Introduction to the Experiments Planning Theory]. Moscow, Bauman MSTU Publ., 2011, 464 p.

Zarubin V.S. Matematicheskoye modelirovaniye v tekhnike: ucheb. dlya vuzov [Mathematical Modeling in Technique]. 3rd ed. Moscow, Bauman MSTU Publ., 2010. 495 p. (Ser. “Mathematic in Technical University”. Vol. XXI).

Alkatsev M.I., Dzgoev A.E., Betrozov M.S. [Sliding matrix method as a forecasting instrument for dynamic processes]. Proceeding of the International Scientific and Practical Conference “Theory and Practice of Modern Science”. Moscow, Institute of Strategic Researches Publ., 544 p. (in Russ.)

Kumaritov A.M., Alkatsev M.I., Dzgoev A.E., Betrozov M.S., Huzmiev I.M., Dobaev A.Z. Skol’zyashchaya matritsa kak metod statisticheskogo analiza dinamicheskikh ryadov [Sliding matrix as a method of statistical analysis of time series]. Certificate of state registration of computer programs (RU), no. 2013614024, 2013.

Alkatsev M.I., Voloshin S.B., Mamontov D.V. Programmnyy emulyator protsessa obzhiga sul’fidnykh tsinkovykh kontsentratov v pechi kipyashchego sloya 1.0 [Software emulator of the process of roasting sulphide zinc concentrates in a fluidized bed furnace 1.0]. Certificate of state registration of computer programs (RU), no. 2011311745, 2011.




DOI: http://dx.doi.org/10.14529/met200302

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