STATEMENT OF THE PROBLEM OPTIMAL CONTROL THE HARDNESS OF THE STEEL PRODUCED BASED ON THE MODEL OF TAKAGI-SUGENO-KANG
Abstract
This study discusses the problem of mathematical modeling of complex technological systems under uncertainty to obtain the most optimal parameters in the management of the production process in the applied field – metallurgy. In the offered approach one of the most important tasks of management of technological process of steel smelting is considered: maintenance of the set hardness (calcification) of the steel distributed on depth of the smelted product. To minimize the inevitable errors associated with the expert choice of chemical composition, improve the management efficiency and the quality of the produced steel, it is proposed to apply the system of fuzzy production rules Takagi-Sugeno-Kanga (model TSK), based on the modeling of the dependence "composition-hardness". Application of this model will also allow to optimize the choice of the chemical composition of the steel in the conditions of stochasticity of the parameters of the regression models. In addition, in the study of the steel production process there is a need to solve the inverse problem – the determination of the chemical composition of the steel produced at a given hardness value. The proposed model of TSK based on fuzzy production rules for steel smelting prediction and control is presented in matrix form, so one of the possible ways to solve the control problem is to solve the corresponding matrix equation. At the same time, on the basis of experimental data, a significant shift in the estimates of the values of chemical elements was revealed. Therefore, governance must be based on an optimization approach. The proposed formulation of the optimization problem will develop an algorithm for solving the problem of optimal hardness control on the basis of the TSK model, characterized by the ability to automatically determine the required chemical composition of steel by a given distribution of its hardness. In addition, the developed model TSK using the optimal control problem will eliminate errors in determining the calculation model, as well as to determine the hardness of steel for the chemical composition does not fully correspond to a certain set of allowable intervals of changing the mass fractions of chemical elements.
References
[2] Zhang J. Optimal Control Problem of Converter Steelmaking Production Process Based on Operation Optimization Method. Discrete Dynamics in Nature and Society. 2015; 2015:483674, 13 pages. DOI: 10.1155/2015/483674
[3] Alrabghi A., Tiwari A. State of the art in simulation-based optimisation for maintenance systems. Computers & Industrial Engineering. 2015; 82:167-182. DOI: 10.1016/j.cie.2014.12.022
[4] Bondarchuk A.A., Matveev M.G. The Analysis of Control Models of Steel Hardness During its Melting. Mekhatronika, avtomatizatsiya, upravlenie. 2008; 3:37-40. Available at: http://www.novtex.ru/mech/mech08/Mh308.pdf (accessed 17.04.2018). (In Russian)
[5] Hamdaoui M., Oujebbour F-Z., Habbal A., Breitkopf P., Villon P. Kriging surrogates for evolutionary multi-objective optimization of CPU intensive sheet metal forming applications. International Journal of Material Forming. 2015; 8(3):469–480. DOI: 10.1007/s12289-014-1190-y
[6] Agronik A.Ju., Talalaev A.A., Fralenko V.P., Khachumov V.M., Shishkin O.G. Analysis of systems for technological chains and processes designing. Ontology of Designing. 2016; 6(3):255-269. DOI: 10.18287/2223-9537-2016-6-3-255-269 (In Russian)
[7] Mesarovich M., Mako D., Takahara I. Teorija ierarhicheskih mnogourovnevyh sistem [Theory of hierarchical multilevel systems]. M.: Izdatel'stvo «Mir», 1973. 344 p. (In Russian)
[8] Buslenko N.P. Modelirovanie slozhnyh system [Modeling of complex systems]. M.: Nauka, 1968. 356 p. (In Russian)
[9] Kabulova E.G. Matematicheskoe modelirovanie proizvodstvennyh processov v metallurgii [Mathematical modeling of production processes in metallurgy]. Staryj Oskol: Izd-vo «TNT», 2014. 131 p. (In Russian)
[10] Tang L., Zhao Y., Liu J. An improved differential evolution algorithm for practical dynamic scheduling in steelmaking-continuous casting production. IEEE Transactions on Evolutionary Computation. 2014; 18(2):209-225. DOI: 10.1109/TEVC.2013.2250977
[11] Gao J., Dai G., Zhao J., Li H., Xu L., Zhu Z. Influence of Indentation on the Fatigue Strength of Carbonitrided Plain Steel. Advances in Materials Science and Engineering. 2015; 2015:492693, 9 pages. DOI: 10.1155/2015/492693
[12] Sugeno M., Kang G.T. Structure identification of Fuzzy Model. Fuzzy Sets and Systems. 1988; 28(1):15–33. DOI: 10.1016/0165-0114(88)90113-3
[13] Takagi T. Fuzzy Identification of Systems and Its Applications to Modeling and Control. IEEE Transactions on Systems, Man and Cybernetics. 1985; SMC-15(1):116-132. DOI: 10.1109/TSMC.1985.6313399
[14] Rahmani A., Hosseinzadeh Lotfi F., Rostamy-Malkhalifeh M., Allahviranloo T. A New Method for Defuzzification and Ranking of Fuzzy Numbers Based on the Statistical Beta Distribution. Advances in Fuzzy Systems. 2016; 2016:6945184, 8 pages. DOI: 10.1155/2016/6945184
[15] Cheng Ch-H. A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems. 1998; 95(3):307-317. DOI: 10.1016/S0165-0114(96)00272-2
[16] Saati T.L. Prinyatie reshenii. Metod analiza ierarkhii [Decision making. Method of Analysis of Hierarchies]. Moscow, Radio and Communication Publ., 1993. 278 p.
[17] Golden B., Wasil E., Harker P. The analytic hierarchy process: applications and studies. Springer-Verlag Berlin Heidelberg, 1989. 265 p. DOI: 10.1007/978-3-642-50244-6
[18] Su L., Li Ch. Local Prediction of Chaotic Time Series Based on Polynomial Coefficient Autoregressive Model. Mathematical Problems in Engineering. 2015; 2015:901807, 14 pages. DOI: 10.1155/2015/901807
[19] Jiang Y., Yang Ch., Ma H. A Review of Fuzzy Logic and Neural Network Based Intelligent Control Design for Discrete-Time Systems. Discrete Dynamics in Nature and Society. 2016; 2016:7217364, 11 pages. DOI: 10.1155/2016/7217364
[20] Zadeh L.A. Fuzzy sets and systems. Proc. Symp. on Systems Theory, Polytechnic Institute of Brooklyn, New York, 1965. pp. 29-37.
[21] Jäntschi L., Pruteanu L.L., Cozma A.C., Bolboacă S.D. Inside of the Linear Relation between Dependent and Independent Variables. Computational and Mathematical Methods in Medicine. 2015; 2015:360752, 11 pages. DOI: 10.1155/2015/360752
[22] Deng Y., Liu Y., Zhou D. An Improved Genetic Algorithm with Initial Population Strategy for Symmetric TSP. Mathematical Problems in Engineering. 2015; 2015:212794, 6 pages. DOI: 10.1155/2015/212794
[23] Courvoisier D.S., Combescure C., Agoritsas T., Gayet-Ageron A., Perneger T.V. Performance of logistic regression modeling: beyond the number of events per variable, the role of data structure. Journal of Clinical Epidemiology. 2011; 64(9):993-1000. DOI: 10.1016/j.jclinepi.2010.11.012
[24] Žlender B., Jelušič P. Predicting Geotechnical Investigation Using the Knowledge Based System. Advances in Fuzzy Systems. 2016; 2016:4867498, 10 pages. DOI: 10.1155/2016/4867498
[25] Abbasov A.M., Shahbazova S.N. Functional Solution of the Knowledge Level Control Problem: The Principles of Fuzzy Logic Rules and Linguistic Variables. In: Tamir D., Rishe N., Kandel A., editors. Fifty Years of Fuzzy Logic and its Applications. Studies in Fuzziness and Soft Computing. Vol 326. Springer, Cham, 2015. pp. 25-38. DOI: 10.1007/978-3-319-19683-1_2
[26] Michalska H., Ellis J.E., Roberts P.D. Joint coordination method for the steady state control of large-scale systems. International Journal of Systems Science. 1985; 16(5):605 - 618. DOI: 10.1080/00207728508926697
[27] Sathiyamoorthy V., Sekar T., Elango N. Optimization of Processing Parameters in ECM of Die Tool Steel Using Nanofluid by Multiobjective Genetic Algorithm. The Scientific World Journal. 2015; 2015:895696, 6 pages. DOI: 10.1155/2015/895696
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication policy of the journal is based on traditional ethical principles of the Russian scientific periodicals and is built in terms of ethical norms of editors and publishers work stated in Code of Conduct and Best Practice Guidelines for Journal Editors and Code of Conduct for Journal Publishers, developed by the Committee on Publication Ethics (COPE). In the course of publishing editorial board of the journal is led by international rules for copyright protection, statutory regulations of the Russian Federation as well as international standards of publishing.
Authors publishing articles in this journal agree to the following: They retain copyright and grant the journal right of first publication of the work, which is automatically licensed under the Creative Commons Attribution License (CC BY license). Users can use, reuse and build upon the material published in this journal provided that such uses are fully attributed.
