The Use of Trapezoidal Fuzzy Numbers in the Model to Optimize the Batch of Electric Arc Furnace

Abstract:

The classical models to optimize the batch of electric arc furnace require precise and predetermined numerical values. In order to determine the scrap steel properties (eg. chemical composition), we are not able to define these values precisely and accurately. This situation is due to the heterogeneity and specificity of this material, which is related to its origin and way of obtaining. Therefore the usefulness of classical models to optimize the batch of electric arc furnace is limited. The fuzzy numbers with trapezoidal membership function were applied as a model in order to describe the technological process of steelmaking, which is neither accurate nor of ambiguous nature of the parameters. The advantage of trapezoidal numbers is a simple algorithm of arithmetic operations as well as easy and intuitive interpretation. The structure of optimization model with fuzzy parameters is similar to the classical linear optimization model of the mixtures composition. The optimization model, that is formulated on the fuzzy ranges arithmetic principles, allows to ensure that the quality parameters of the batch mix for the electric arc furnace are as precise as the ones described by electro-steel works, even though the quality parameters of scrap steel as well as some of the parameters of steel melting technological process are described ambiguously.

• Periodical: Solid State Phenomena (Volume 226)
• Pages: 199-204
• DOI: https://doi.org/10.4028/www.scientific.net/SSP.226.199
• Online since: January 2015
• Authors: Bolesław Machulec*, Andrzej Kuźnik
• Keywords: Batch Optimization, Electric Arc Furnace Process, Fuzzy Numbers, Scrap Steel

References

[1] E. Ziółkowski, Modelowanie namiarowania wsadu dla pieców odlewniczych z uwzględnieniem materiałów wsadowych o rozmytych parametrach (in Polish), Ed. AGH, Rozprawy i Monografie 169, Kraków (2007).

[2] L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338-353.

[3] D. Rutkowska, M. Piliński, L. Rutkowski, Sieci neuronowe, algorytmy genetyczne i systemy rozmyte (in Polish), Ed. PWN, Warszawa-Łódź (1997).

[4] S. Banerjee, T.R. Kumar, Arithmetic Operations on Generalized Trapezoidal Fuzzy Number and its Applications, Turkish Journal of Fuzzy Systems 3 (1) (2012) 16-44.

[5] A. Kuźnik, Modelowanie namiarowania wsadu dla celów optymalizacji procesu wytopu stali w piecach elektrycznych (in Polish), Doctor thesis, Silesian University of Technology, Faculty of Material Science and Metallurgy, Katowice (2014).

[6] B. Kolman, R.E. Beck, Elementary Linear Programming with Applications, Elsevier Science & Technology Books, (1995).