Estimation of Boundary Conditions in Conduction Heat Transfer by Neural Networks

Authors

  • E.H. SHIGUEMORI
  • F.P. HARTER
  • H.F. CAMPOS VELHO
  • J.D.S. da SILVA

DOI:

https://doi.org/10.5540/tema.2002.03.02.0189

Abstract

Two different artificial neural networks (NN) are used for estimating a time dependent boundary condition (x = 0) in a slab: multilayer perceptron (MP) and radial base function (RBF). The input for the NN is the temperature time-series obtained from a probe next to boundary of interest. Our numerical experiments follow the work of Krejsa et al. [4]. The NNs were trainned considering 5 per cent of noise in the experimental data. The training was performed considering 500 similar test-functions and 500 different test-functions. Inversions with trained NNs with different test-functions were better. The RBF-NN presented a slightly better results than MP-NN.

References

[1] J. V. Beck, B. Blackwell, C. R. St. Clair, “Inverse Heat Conduction: Ill-Posed Problems”, John Wiley & Sons, 1985.

S. Haykin, “Neural Networks: A Comprehensive Foundation”, Mcmillan, 1994.

J. D. Hoffman, “Numerical Methods for Engineers and Scientists”, McGraw- Hill, Inc., New York, USA, 1993.

J. Krejsa, K.A. Woodbury, J.D. Ratliff, M. Raudensky, Assessment of strategies and potential for neural networks in the inverse heat conduction problem, Inverse Problems in Engineering, 7 (1999), 197-213.

N.J. McCormick, Inverse problems: methods and applications, em “Seleta do XXIII CNMAC” (E.X.L. Andrade et al., eds), Tendências em Matemática Aplicada e Computacional, Vol. 2, pp.1-12, SBMAC, 2001.

W.B. Muniz, F.M. Ramos, H.F. Campos Velho, Entropy- and Tikhonov- based regularization techniques applied to the backwards heat equation, Computers & Mathematics with Applications, 40 (2000), 1071-1084.

W.B. Muniz, H.F. Campos Velho, F.M. Ramos, A Comparison of some inverse methods for estimating the initial condition of the heat equation, Journal of Computational and Applied Mathematics, 101 (1999), 153-171.

M.N. Ozisik, “Heat Conduction”, John Wiley & Sons, 1980.

M.N. Ozisik, “Finite Difference Methods in Heat Transfer”, CRC Press, 1994.

M.N. Ozisik, H.R.B. Orlande, “Inverse Heat Transfer: Fundamentals and Applications”, Taylor & Francis, 2000.

J.D.S. Silva, E.H. Shiguemori, H.F. Campos Velho, Neural network systems for estimating the initial condition in a heat conduction problem, em “International Joint Conference on Neural Networks — World Conference on Computational Intelligence”, 2002, Honolulu, USA (Proceedings in CD Rom).

A.N. Tikhonov, V.Y. Arsenin, “Solutions of Ill-Posed Problems”, Winston and Sons, 1977.

K.A. Woodbury, Neural networks and genetic algorithms in the solution of inverse Pproblems, Bulletim of Brazilian Society for Computing and Applied Mathematics, available in the site: http://www.sbmac.org.br/a_sbmac/publicacoes/frames.htm .

Published

2002-06-01

How to Cite

SHIGUEMORI, E., HARTER, F., CAMPOS VELHO, H., & da SILVA, J. (2002). Estimation of Boundary Conditions in Conduction Heat Transfer by Neural Networks. Trends in Computational and Applied Mathematics, 3(2), 189–195. https://doi.org/10.5540/tema.2002.03.02.0189

Issue

Section

Original Article