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Vol: 60(74) No: 1 / March 2015 GPU Based Implementation of Inverse Heat Conduction Problem Solver Sándor Szénási Óbuda University, Faculty of Informatics, Bécsi út 96/b, 1034 Budapest, Hungary, phone: +36 (1) 666-5551, e-mail: szenasi.sandor@nik.uni-obuda.hu Imre Felde Óbuda University, Faculty of Informatics, Bécsi út 96/b, 1034 Budapest, Hungary, phone: +36 (1) 666-5528, e-mail: felde.imre@nik.uni-obuda.hu István Kovács Óbuda University, Faculty of Informatics, Bécsi út 96/b, 1034 Budapest, Hungary, e-mail: kovacs.istvan.perez@outlook.com Keywords: IHCP, HTC, GPU, PSO, Parallel Algorithm Abstract Inverse Heat Conduction Problem means that the surface Heat Transfer Coefficient (HTC)/Heat Flux (HF) must be determined from transient temperature measurements at given interior points. This is a typical ill-posed problem, because the solution’s behaviour does not change continuously with the initial conditions; therefore, there are no already known direct solutions. There are several heuristic methods to solve the IHCP, and one of the most promising methods is Particle Swarm Optimization (PSO) developed by Eberhart and Kennedy in 1995. It has the ability to find the optimal solution in very large parameter spaces; however, it has some limitations. The main weaknesses are the high computational demand (and consequently a large runtime), and the unpredictable chance to find only a local but not the global optimum. This paper presents the implementation and the evaluation of a graphics accelerator-based parallel approach, which has significantly lower runtime (this GPU implementation is about three times faster than the original CPU-based sequential method). Furthermore, the authors examined the relationship between the size of the initial swarms and the final fitness values. The results indicate that it is worth it to generate a larger initial swarm and continue the processing using smaller further swarms. This technique combines the advantages of the large (better accuracy) and small (lower runtime) particle counts. References [1] I. Felde and W. Shi, “Hybrid approach for solution of inverse heat conduction problems,” in Systems, Man and Cybernetics (SMC), 2014 IEEE International Conference on, 2014, pp. 3896–3899. [2] O. M. Alifanov, Inverse Heat Transfer Problems. Springer, 1994. [3] M. N. Özisik and H. R. B. Orlande, Inverse Heat Transfer: Fundamentals and Applications. Taylor & Francis, 2000. [4] J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the nelder--mead simplex method in low dimensions,” SIAM J. Optim., vol. 9, no. 1, pp. 112–147, 1998. [5] R. Das, “A simplex search method for a conductive–convective fin with variable conductivity,” Int. J. Heat Mass Transf., vol. 54, pp. 5001–5009, 2011. [6] O. Nelles, Nonlinear System Identification. Springer-Verlag, 2001. [7] J. Kennedy and R. Eberhart, “Particle swarm optimization,” Neural Networks, 1995. Proceedings., IEEE Int. Conf., vol. 4, pp. 1942–1948, 1995. [8] R. C. David, R. E. Precup, E. M. Petriu, M. B. Rǎdac, and S. Preitl, “Gravitational search algorithm-based design of fuzzy control systems with a reduced parametric sensitivity,” Inform. Sci., vol. 247, pp. 154–173, 2013. [9] N. A. El-Hefnawy, “Solving bi-level problems using modified particle swarm optimization algorithm,” International Journal of Artificial Intelligence, vol. 12, no. 2. pp. 88–101, 2014. [10] E. Toth-Laufer, M. Takacs, and I. J. Rudas, “Real-time fuzzy logic-based sport activity risk calculation model optimization,” in IEEE 14th International Symposium on Computational Intelligence and Informatics (CINTI), 2013, pp. 291–295. [11] S. Szénási and Z. Vámossy, “Evolutionary algorithm for optimizing parameters of GPGPU-based image segmentation,” Acta Polytech. Hungarica, vol. 10, no. 5, pp. 7–28, 2013. [12] F. Valdez, P. Melin, and O. Castillo, “An improved evolutionary method with fuzzy logic for combining particle swarm optimization and genetic algorithms,” Applied Soft Computing, vol. 11, no. 2, pp. 2625–2632, 2011. [13] A.-C. Zăvoianu, G. Bramerdorfer, E. Lughofer, S. Silber, W. Amrhein, and E. Peter Klement, “Hybridization of multi-objective evolutionary algorithms and artificial neural networks for optimizing the performance of electrical drives,” Eng. Appl. Artif. Intell., vol. 26, no. 8, pp. 1781–1794, 2013. [14] S. Szénási, I. Felde, and I. Kovács, “Solving one-dimensional IHCP with particle swarm optimization using graphics accelerators,” in 10th Jubilee IEEE International Symposium on Applied Computational Intelligence and Informatics, 2015, pp. 365–369. [15] D. B. Kirk and W. W. Hwu, Programming Massively Parallel Processors: A Hands-on Approach, 1st ed. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc., 2010. [16] NVIDIA, “CUDA C Programming Guide.” 2014. [17] G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods. Clarendon Press, 1985. [18] E. Campana and G. Fasano, “Dynamic system analysis and initial particles position in particle swarm optimization,” IEEE Swarm Intell., no. 1, 2006. [19] D. Palupi Rini, S. Mariyam Shamsuddin, and S. Sophiyati Yuhaniz, “Particle swarm optimization: Technique, system and challenges,” Int. J. Comput. Appl., vol. 14, no. 1, pp. 19–27, 2011. [20] Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J. C. Hernandez, and R. G. Harley, “Particle swarm optimization: Basic concepts, variants and applications in power systems,” IEEE Trans. Evol. Comput., vol. 12, no. 2, pp. 171–195, 2008. [21] A. Bogárdi-Mészöly, A. Rövid, H. Ishikawa, S. Yokoyama, and Z. Vámossy, “Tag and topic recommendation systems,” Acta Polytech. Hungarica, vol. 10, no. 6, pp. 171–191, 2013. [22] S. Sergyán and L. Csink, “Automatic Parametrization of Region Finding Algorithms in Gray Images,” in 4th International Symposium on Applied Computational Intelligence and Informatics (SACI), 2007, pp. 199–202. |