Ebrahimi, M., Vakilipour, S., Inanlou Shahverdi, M. (2017). A novel computational procedure based on league championship algorithm for solving an inverse heat conduction problem. Journal of Computational Applied Mechanics, 48(2), 285-296. doi: 10.22059/jcamech.2017.238583.168

Morteza Ebrahimi; Shidvash Vakilipour; Mohammad Ebrahim Inanlou Shahverdi. "A novel computational procedure based on league championship algorithm for solving an inverse heat conduction problem". Journal of Computational Applied Mechanics, 48, 2, 2017, 285-296. doi: 10.22059/jcamech.2017.238583.168

Ebrahimi, M., Vakilipour, S., Inanlou Shahverdi, M. (2017). 'A novel computational procedure based on league championship algorithm for solving an inverse heat conduction problem', Journal of Computational Applied Mechanics, 48(2), pp. 285-296. doi: 10.22059/jcamech.2017.238583.168

Ebrahimi, M., Vakilipour, S., Inanlou Shahverdi, M. A novel computational procedure based on league championship algorithm for solving an inverse heat conduction problem. Journal of Computational Applied Mechanics, 2017; 48(2): 285-296. doi: 10.22059/jcamech.2017.238583.168

A novel computational procedure based on league championship algorithm for solving an inverse heat conduction problem

^{1}Department of Network Sciences and Technology, Faculty of New Science and Technologies, University of Tehran, Tehran, Iran

^{2}Department of Aerospace Engineering, Faculty of New Science and Technologies, University of Tehran, Tehran, Iran

Receive Date: 26 July 2017,
Revise Date: 12 September 2017,
Accept Date: 12 September 2017

Abstract

Inverse heat conduction problems, which are one of the most important groups of problems, are often ill-posed and complicated problems, and their optimization process has lots of local extrema. This paper provides a novel computational procedure based on finite differences method and league championship algorithm to solve a one-dimensional inverse heat conduction problem. At the beginning, we use the Crank-Nicolson semi-implicit finite difference scheme to discretize the problem domain and solve the direct problem which is a second-order method in time and unconditionally stable. The consistency, stability and convergence of the method are investigated. Then we employ a new optimization method known as league championship algorithm to estimate the unknown boundary condition from some measured temperature on the line. League championship algorithm is a recently proposed probabilistic algorithm for optimization in continuous environments, which tries to simulate a championship environment wherein several teams with different abilities play in an artificial league for several weeks or iterations. To confirm the efficiency and accuracy of the proposed approach, we give some examples for the engineering applications. Results show an excellent agreement between the solution of the proposed numerical algorithm and the exact solution.

[1] M. Ebrahimi, R. Farnoosh, and S. Ebrahimi, "Biological applications and numerical solution based on Monte Carlo method for a two-dimensional parabolic inverse problem,"Applied Mathematics and Computation,vol. 204, no. 1, pp. 1-9, 2008/10/01/ 2008.

[2] R. Farnoosh and M. Ebrahimi, "Monte Carlo simulation via a numerical algorithm for solving a nonlinear inverse problem,"Communications in Nonlinear Science and Numerical Simulation,vol. 15, no. 9, pp. 2436-2444, 2010/09/01/ 2010.

[3] X. Luo and Z. Yang, "A new approach for estimation of total heat exchange factor in reheating furnace by solving an inverse heat conduction problem,"International Journal of Heat and Mass Transfer,vol. 112, pp. 1062-1071, 2017/09/01/ 2017.

[4] A. Shidfar, M. Fakhraie, R. Pourgholi, and M. Ebrahimi, "A numerical solution technique for a one-dimensional inverse nonlinear parabolic problem,"Applied Mathematics and Computation,vol. 184, no. 2, pp. 308-315, 2007/01/15/ 2007.

[5] A. Shidfar, R. Pourgholi, and M. Ebrahimi, "A Numerical Method for Solving of a Nonlinear Inverse Diffusion Problem,"Computers & Mathematics with Applications,vol. 52, no. 6, pp. 1021-1030, 2006/09/01/ 2006.

[6] R. Li, Z. Huang, G. Li, X. Wu, and P. Yan, "Study of the conductive heat flux from concrete to liquid nitrogen by solving an inverse heat conduction problem,"Journal of Loss Prevention in the Process Industries,vol. 48, pp. 48-54, 2017/07/01/ 2017.

[7] R. Li, Z. Huang, G. Li, X. Wu, and P. Yan, "A modified space marching method using future temperature measurements for transient nonlinear inverse heat conduction problem,"International Journal of Heat and Mass Transfer,vol. 106, pp. 1157-1163, 2017/03/01/ 2017.

[8] J. Crank and P. Nicolson, "A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,"Mathematical Proceedings of the Cambridge Philosophical Society,vol. 43, no. 1, pp. 50-67, 2008.

[9] J. W. Thomas,Numerical Partial Differential Equations: Finite Difference Methods. Springer New York, 2013.

[10] A. Husseinzadeh Kashan, "League Championship Algorithm (LCA): An algorithm for global optimization inspired by sport championships,"Applied Soft Computing,vol. 16, pp. 171-200, 2014/03/01/ 2014.

[11] J. V. Beck and K. A. Woodbury, "Inverse heat conduction problem: Sensitivity coefficient insights, filter coefficients, and intrinsic verification,"International Journal of Heat and Mass Transfer,vol. 97, pp. 578-588, 2016.

[12] P. Duda, "Numerical and experimental verification of two methods for solving an inverse heat conduction problem,"International Journal of Heat and Mass Transfer,vol. 84, pp. 1101-1112, 2015.

[13] J.-C. Jolly and L. Autrique, "Semi-analytic Conjugate Gradient Method applied to a simple Inverse Heat Conduction Problem,"IFAC-PapersOnLine,vol. 49, no. 8, pp. 156-161, 2016.

[14] T. Lu, W. Han, P. Jiang, Y. Zhu, J. Wu, and C. Liu, "A two-dimensional inverse heat conduction problem for simultaneous estimation of heat convection coefficient, fluid temperature and wall temperature on the inner wall of a pipeline,"Progress in Nuclear Energy,vol. 81, pp. 161-168, 2015.

[15] E. Shivanian and H. R. Khodabandehlo, "Application of meshless local radial point interpolation (MLRPI) on a one-dimensional inverse heat conduction problem,"Ain Shams Engineering Journal,vol. 7, no. 3, pp. 993-1000, 2016.

[16] M. Cui, W.-w. Duan, and X.-w. Gao, "A new inverse analysis method based on a relaxation factor optimization technique for solving transient nonlinear inverse heat conduction problems,"International Journal of Heat and Mass Transfer,vol. 90, pp. 491-498, 2015/11/01/ 2015.

[17] A. P. Fernandes, M. B. dos Santos, and G. Guimarães, "An analytical transfer function method to solve inverse heat conduction problems,"Applied Mathematical Modelling,vol. 39, no. 22, pp. 6897-6914, 2015/11/15/ 2015.

[18] H.-L. Lee, T.-H. Lai, W.-L. Chen, and Y.-C. Yang, "An inverse hyperbolic heat conduction problem in estimating surface heat flux of a living skin tissue,"Applied Mathematical Modelling,vol. 37, no. 5, pp. 2630-2643, 2013/03/01/ 2013.

[19] B. Movahedian and B. Boroomand, "The solution of direct and inverse transient heat conduction problems with layered materials using exponential basis functions,"International Journal of Thermal Sciences,vol. 77, pp. 186-198, 2014/03/01/ 2014.

[20] R. Pourgholi, H. Dana, and S. H. Tabasi, "Solving an inverse heat conduction problem using genetic algorithm: Sequential and multi-core parallelization approach,"Applied Mathematical Modelling,vol. 38, no. 7, pp. 1948-1958, 2014/04/01/ 2014.

[21] K. A. Woodbury and J. V. Beck, "Estimation metrics and optimal regularization in a Tikhonov digital filter for the inverse heat conduction problem,"International Journal of Heat and Mass Transfer,vol. 62, pp. 31-39, 2013/07/01/ 2013.

[22] T.-S. Wu, H.-L. Lee, W.-J. Chang, and Y.-C. Yang, "An inverse hyperbolic heat conduction problem in estimating pulse heat flux with a dual-phase-lag model,"International Communications in Heat and Mass Transfer,vol. 60, pp. 1-8, 2015/01/01/ 2015.

[23] A. Friedman,Partial differential equations of parabolic type. Prentice-Hall, 1964.

[24] P. D. Lax and R. D. Richtmyer, "Survey of the stability of linear finite difference equations,"Communications on Pure and Applied Mathematics,vol. 9, no. 2, pp. 267-293, 1956.

[25] J. Dréo,Metaheuristics for Hard Optimization: Methods and Case Studies. Springer, 2006.

[26] J. M. Gutiérrez Cabeza, J. A. Martín García, and A. Corz Rodríguez, "A sequential algorithm of inverse heat conduction problems using singular value decomposition,"International Journal of Thermal Sciences,vol. 44, no. 3, pp. 235-244, 2005/03/01/ 2005.