Optimization Methods in Modeling the Mechanical Properties of Heavy Steel Plates / Metody Optymalizacyjne W Modelowaniu Własności Mechanicznych Blach Grubych

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The paper is devoted to an optimization approach to a problem of statistical modeling of mechanical properties of heavy steel plates during a real industrial manufacturing process. The approach enables the manufacturer to attain a specific set of the final product properties by optimizing the alloying composition within the grade specifications. Because this composition has to stay in the agreement with earlier indicated specifications, it leads to the large system of linear constraints, and the problem itself can be expressed in the form of linear programming (LP) task. It turns out however, that certain of the constraints contain the coefficients which have to be estimated on the base of the data gathered in the production process and as such they are uncertain. Consequently, the initial optimization task should be modeled as so-called Chance Constrained Programming problem (CCP), which is a special class within the stochastic programming problems. The paper presents mathematical models of the optimization problem that result from both approaches and indicates differences which are important for the decision makers in the production practice. Some examples illustrating the differences in solutions resulting from LP and CCP models are presented as well. Although the statistical analysis presented in this paper is based on the data gathered in the ISD Czestochowa Steelworks, the proposed approach can be adopted in any other process of steel production.

[1] G.S. Dulikravich, I.N. Egorov, Robust optimization of concentrations of alloying ele­ments in steel for maximum temperature, strength, time-to-rupture and minimum cost and weight, Conference on Computational Methods for Coupled Problems in Science and Engineering - Coupled Problems 2005, Greece, 2005. available version: http://www.iosotech.com/files/alication/Alloys-properties-optimization.pdf

[2] J. Kusiak, A. Żmudzki, A. Danielewska-Tulecka, Optimization of material processing using a hybrid technique based on artificial neural net­works, Archives of Metallurgy and Materials 3, 50, 609-620 (2005).

[3] S. Natschlager, S. Dimitrov, K. Stohl, EAF process optimization: theory and real results, Archives of Metallurgy and Materials 2, 53, 373-378 (2008).

[4] P.K. Ray, R.I. Ganguly, A.K. Panda, Optimiza­tion of mechanical properties of an HSLA-100 steel through control of heat treatment variables, Materials Science and Engineering A346, 122-131 (2003).

[5] A.P. Paiva, E.J. Paiva, J.R. Ferreira, P.P. Balestrassi, S.C. Costa, A multivariate mean square error optimization of AISI 52100 hardened steel turning, International Journal of Advanced Manufactur­ing Technology 43, 631-643 (2009).

[6] T.N. Sidorina, I.V. Kabanov, Optimization of carburizing steels for drilling tools within grade chemi­cal composition, Metal Science and Heat Treatment 49, 9-10 (2007).

[7] Liu XiangHua, Lan HuiFang, Du LinXiu, Liu WeiJie, High performance low cost steels with ultrafine grained and multi-phased microstructure, Science China Technological Sciences 52, 8, 2245-2254 (2009).

[8] J. Talar, Data mining methods - application in met­allurgy, Archives of Metallurgy and Materials 2, 52, 239-250 (2007).

[9] J. Moravka, K. Michalek, B. Chmiel, Statis­tical analysis of heats with targeted overheating realized in the EAF at Trinec Steelworks, Archives of Metallurgy and Materials 2, 53, 1-8 (2008).

[10] H.B. Xie, Z.Y. Jiang, X.H. Liu, G.D. Wang, A.K. Tieu, Prediction of coiling temperature on run-out table of hot strip mill using data mining, Jour­nal of Materials Processing Technology 177, 121-125 (2006).

[11] P. Palanisamy, I. Rajendran, S. Shanmugasundaram, Prediction of tool wear using regres­sion and ANN models in end-milling operation, Interna­tional Journal of Advanced Manufacturing Technology 37, 29-41 (2008).

[12] V.K. Potemkin, O.S. Khlybov, V.A. Peshkov, Complex mathematical model for predicting mechanical properties and structure of steel sheets, Metal Science and Heat Treatment 42, 11-12 (2000).

[13] P.C.M. Rodrigues, E.V. Pereloma, D.B. Santos, Mechanical properties of an HSLA bainitic steel subjected to controlled rolling with accelerated cool­ing, Materials Science and Engineering A283, 136-143 (2000).

[14] A.Z. Grzybowski, Z. Urbanowicz, Statysty­czne modelowanie własności mechanicznych blach grubych przy regulowanym walcowaniu, Materiały Konferencji Zastosowania Komputerów w Zakładach Przetwórstwa Metali, Bukowina Tatrzańska, 25-33 (1998).

[15] A. Charnes, W.W. Cooper, Chance-constrained programming, Management Sciences 6, 73-80 (1959).

[16] N.V. Sahinidis, Optimization under uncertainty: state-of-the-art and opportunities, Computers and Chem­ical Engineering 28, 971-983 (2004).

[17] A. Ruszczynski, A. Shapiro, Stochastic pro­gramming. Handbooks in operations research and man­agement science, Elsevier, Amsterdam 2003.

[18] D.A. Guryanov, B.N. Zamotaev, I.V. Rubezhanskaya, Influence of the rolling parame­ters in high-temperature thermomechanical treatment on the structure and mechanical properties of steel, Steel in Translation 37, 9, 730-732 (2007).

[19] D.A. Belsley, Conditioning diagnostics: collinearity and weak data in regression, J. Wiley & Sons, New York 1991.

[20] A.Z. Grzybowski, Z. Urbanowicz, Alterna­tive methods of regression in modeling properties of steel plate - a comparative studies, [in:] Proceedings of 3d International Conference on Parallel Processing & Alied Mathematics, Kazimierz Dolny, 533-542 (1999).

[21] I.C. Dima, A.Z. Grzybowski, J.K. Grabara, G.R. Goldbach, O.R. Popescu, Utilizing of mathematics-statistics methods concerning mechanic properties of heavy steel plates - dealing with the ill conditioned data - [in:] Proceedings of International Conference on Mathematical Models for Engineering Science (MMES ’10) (ed. V. Mladenov, K. Psarris, N. Mastorakis, A. Caballero, G. Vachtsevanos ), WSEAS Press, 277-284 (2010).

[22] E.W. Frees, Data Analysis Using Regression Models, Prentice Hall, New Jersey 1996.

[23] A.Z. Grzybowski, Monte Carlo optimization pro­cedure for chance constrained programming - simula­tion study results, Scientific Research of the Institute of Mathematics and Computer Science 1, 8, 39-46 (2009).

[24] T.D. Kelly, G.R. Matos, Historical Statistics for Mineral and Material Commodities in the Unit­ed States, Open-File Report 01-006, U.S. Geologi­cal Survey Data Series 140, (2010) available on-line: http://minerals.usgs.gov/ds/2005/140/ (July 30, 2011).

[25] P. Kall, J. Mayer, Stochastic linear programming - models, theory, and computation, Springer, 2011.

Archives of Metallurgy and Materials

The Journal of Institute of Metallurgy and Materials Science and Commitee on Metallurgy of Polish Academy of Sciences

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