A Particle Swarm Optimization Algorithm and its Application in Hydrodynamic Equations

Abstract:

In fluid mechanics, how to solve multiple solutions in ordinary differential equations is always a concerned and difficult problem. A particle swarm optimization algorithm combining with the direct search method (DSPO) is proposed for solving the parameter estimation problems of the multiple solutions in fluid mechanics. This algorithm has improved greatly in precision and the success rate. In this paper, multiple solutions can be found through changing accuracy and search coverage and multi-iterations of computer. Parameter estimation problems of the multiple solutions of ordinary differential equations are calculated, and the result has great accuracy and this method is practical.

• Periodical: Advanced Materials Research (Volume 510)
• Pages: 472-477
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.510.472
• Online since: April 2012
• Authors: Jian Hui Zhou, Shu Zhong Zhao, Li Xi Yue, Yan Nan Lu, Xin Yi Si
• Keywords: Direct Search Method, Ordinary Differential Equations, Parameter Estimation, Particle Swarm Optimization Algorithm (PSO)

References

[1] W.A. Robinson. Journal of Engineering Mathematics. 10, 23 (1976).

[2] S.J. Liao. Applied Mathematics and Computation. 147, 499 (2004).

[3] S.J. Liao. Commun Nonlinear Sci Numer Simul. 14, 983 (2009).

[4] S. Abbasbandy, E. Shivanian. Commun Nonlinear Sci Numer Simulat. 15, 3830 (2010).

[5] S. Abbasbandy, E. Shivanian. Commun Nonlinear Sci Numer Simulat. 14, 3530 (2009).

[6] S.J. Liao. International Journal of Heat and Mass Transfer. 48, 2529 (2005).

[7] Y. Liu, X. He. in: Proc. of American Control Conf., Portland, OR, USA, 4484–4489(2005).

[8] M. Clerc, J. Kennedy. IEEE Transactions on Evolutionary Computation. 6, 58 (2002).

[9] H. Zhenya, W. Chen gjian, Y. Luxi, G. Xiqi, S. Susu, R.C. Eberhart, Y. Shi. on Evolutionary Computation, Anchorage, AK, USA. 74(1998).

[10] M.V.V. Amarnath, D.K. Pratihar. Journal of Engineering Manufacture. 223, 1575(2009).

[11] R. Storn, K. Price. Journal of Global Optimization 11(4) 341 (1997).

[12] J.J. Liang, A.K. Qin, P.N. Suganthan, S. Baskar. IEEE Transactions on Evolutionary Computation 10 (3) , 281 (2006).

[13] Gorla RSR, Takhar HS, Slaouti A, Pop I, Kumari M. Int. J. Heat Fluid Flow. 16, 62(1995).

DOI: 10.1016/0142-727x(94)00010-a

[14] Pop I, Lee JK, Gorla RSR. Int. J. Heat Mass Transfer. 36, 593 (1993).

[15] Zheng LC, Zhang XX, He JC. Chin. Phys. Lett. 20, 858 (2003).

[16] Zheng LC, Zhang XX, He JC. J. Therm. Sci. 13, 150(2004).

[17] Li BT, Zheng LC, Zhang XX. Energy Conversion and Management. 52, 355(2011).

[18] Nor Azizah Yacob, Anuar Ishak, Roslinda Nazar, Ioan Pop. International Communications in Heat and Mass Transfer. 38, 149 (2011).