# Article

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Keywords:
heat radiation; heat conduction; optimization; differential evolution algorithm; mathematical model; parallel programming
Summary:
This article focuses on heat radiation intensity optimization on the surface of a shell metal mould. Such moulds are used in the automotive industry in the artificial leather production (the artificial leather is used, e.g., on car dashboards). The mould is heated by infrared heaters. After the required temperature is attained, the inner mould surface is sprinkled with special PVC powder. The powder melts and after cooling down it forms the artificial leather. A homogeneous temperature field of the mould is a necessary prerequisite for obtaining a uniform colour shade and material structure of the artificial leather. The article includes a description of a mathematical model that allows to calculate the heat radiation intensity on the outer mould surface for each fixed positioning of the infrared heaters. Next, we use this mathematical model to optimize the locations of the heaters to provide approximately the same heat radiation intensity on the whole outer mould surface during the heating process. The heat radiation intensity optimization is a complex task, because the cost function may have many local minima. Therefore, using gradient methods to solve this problem is not suitable. A differential evolution algorithm is applied during the optimization process. Asymptotic convergence of the algorithm is shown. The article contains a practical example including graphical outputs. The calculations were performed by means of Matlab code written by the authors.
References:
[1] Affenzeller, M., Winkler, S., Wagner, S., Beham, A.: Genetic Algorithms and Genetic Programming. Modern Concepts and Practical Applications. Numerical Insights 6, CRC Press, Boca Raton (2009). DOI 10.1201/9781420011326 | MR 2535244 | Zbl 1231.90003
[2] Antia, H. M.: Numerical Methods for Scientists and Engineers. Birkhäuser, Basel (2002). MR 1911995 | Zbl 1014.65001
[3] Budinský, B.: Analytic and Differential Geometry. Matematika pro vysoké školy technické, SNTL, Praha (1983), Czech. Zbl 0539.51017
[4] Cengel, Y. A., Ghajar, A. J.: Heat and Mass Transfer: Fundamentals and Applications. McGraw-Hill Education, New York (2015).
[5] Hu, Z., Xiong, S., Su, Q., Zhang, X.: Sufficient conditions for global convergence of differential evolution algorithm. J. Appl. Math. 2013 (2013), Article ID 193196, 14 pages. DOI 10.1155/2013/193196 | MR 3122108
[6] Knobloch, R., Mlýnek, J., Srb, R.: The classic differential evolution algorithm and its convergence properties. Appl. Math., Praha 62 (2017), 197-208. DOI 10.21136/AM.2017.0274-16 | MR 3647040 | Zbl 06738488
[7] Mlýnek, J., Knobloch, R., Srb, R.: Temperature field optimization on the mould surface. Advanced Mechatronics Solutions R. Jablonski, T. Brezina Advances in Intelligent Systems and Computing 393, Springer, Cham (2015), 225-230. DOI 10.1007/978-3-319-23923-1_34
[8] Mlýnek, J., Martinec, T., Srb, R.: Heating of mould in manufacture of artificial leathers in automotive industry. Mechatronics 2013. Recent Technological and Scientific Advances T. Březina, R. Jabloński Springer, Cham (2014), 119-126. DOI 10.1007/978-3-319-02294-9_16
[9] Mlýnek, J., Srb, R.: The process of an optimized heat radiation intensity calculation on a mould surface. Proceedings 26th European Conference on Modelling and Simulation, ECMS 2012 K. G. Troitzsch, M. Möhring, U. Lotzmann European Council for Modelling and Simulation, Dudweiler (2012), 461-467. DOI 10.7148/2012-0461-0467
[10] Mlýnek, J., Srb, R., Knobloch, R.: The use of graphics card and nVidia CUDA architecture in the optimization of the heat radiation intensity. Programs and Algorithms of Numerical Mathematics 17 Proceedings of Seminar, Dolní Maxov, 2014, Institute of Mathematics, Academy of Sciences of the Czech Republic, Praha J. Chleboun et al. (2014), 150-155. MR 3587746 | Zbl 1374.65114
[11] Price, K. V., Storn, R. M., Lampien, J. A.: Differential Evolution. A Practical Approach to Global Optimization. Natural Computing Series, Springer, Berlin (2005). DOI 10.1007/3-540-31306-0 | MR 2191377 | Zbl 1186.90004
[12] Simon, D.: Evolutionary Optimization Algorithms. Biologically Inspired and Population-Based Approaches to Computer Intelligence. John Wiley & Sons, Hoboken (2013). MR 3362741 | Zbl 1280.68008
[13] Stoker, J. J.: Differential Geometry. Wiley Classics Library, John Wiley & Sons, New York (1989). MR 1013365 | Zbl 0718.53001
[14] Zhang, J., Sanderson, A. C.: Adaptive Differential Evolution. A Robust Approach to Multimodal Problem Optimization. Adaptation, Learning, and Optimization 1, Springer, Berlin (2009). DOI 10.1007/978-3-642-01527-4 | MR 2549074

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