Genetic Algorithm and Variational Method to Identify Initial Conditions: Worked Example in Hyperbolic Heat Transfer
DOI:
https://doi.org/10.1590/S2179-84512013005000012Abstract
The identification of initial condition from measurements at a giventime is a hard inverse problem, and it can be applied to evaluate the robustnessof inversion strategies. Relevant scientific issues are related with estimation of initialcondition: cosmology and data assimilation are good examples. Two differentinversion methods are employed to identify initial condition for parabolic and hyperbolicdifferential equations: Genetic Algorithm and Variational Method. Theheat transfer process was selected to be used in our tests. A harder inversion isverified on hyperbolic case. Both inverse methods were effective: the numericaldifference between the inverse solution was not significant, although the variationalmethod presented a smoother inversion. The inversion obtained with the variationalmethod presented lower processing time.References
O.M. Alifanov (1974): Solution of an Inverse Problem of Heat Conduction by
Iteration Methods, Journal of Engineering Physics, 26(1974), 471-476.
H.F. Campos–Velho (2008): Problemas Inversos em Pesquisa Espacial, Minicurso
Congresso Nacional de Matemática Aplicada e Computacional (CNMAC),
Belém (PA), Brasil, 120 p.
L.D. Chiwiacowsky, “Método Variacional e Algoritmo Genético em Identificação
de Danos Estruturais”, Tese de Doutorado, CAP, INPE, São José dos Campos,
SP, 2005.
L.B.L. Santos, “Abordagem hierárquica ao método híbrido de identificação de
danos em estruturas aeroespaciais”, Dissertação de Mestrado, CAP, INPE, São
José dos Campos, SP, 2011.
L.D. Chiwiacowsky, “Uso da Função de Transferência em problemas de condução
do calor com a Lei de Fourier modificada”, Dissertação de Mestrado, EM,
UFRGS, Porto Alegre, RS, 2002.
L.D. Chiwiacowsky, H.F. de Campos Velho, Different Approaches for the Solution
of a Backward Heat Conduction Problem, Inverse Problems in Engineering,
, No. 3, 471–494.
L.D. Chiwiacowsky, P. Gasbarri, H.F. de Campos Velho, Damage Assessment of
Large Space Structures Through the Variational Approach, Acta Astronautica,
, No. 10 (2008), 592–604.
R. Das, S.C. Mishra, T.B.P. Kumar, R. Uppaluri, An Inverse Analysis for Parameter
Estimation Applied to a Non-Fourier Conduction-Radiation Problem,
Heat Transfer Engineering, 32, No. 6 (2011), 455–466.
U. Frisch, S. Matarrese, R. Mohayaee, A. Sobolevski, A reconstruction of the
initial conditions of the Universe by optimal mass transportation, Nature, 417,
No. 6886 (2002), 260–262.
C. Huang, W. Hsin–Hsien, An inverse hyperbolic heat conduction problem
in estimating surface heat flux by the conjugate gradient method, Journal of
Physics D: Applied Physics, 39, No. 18 (2006), 4087–4096.
C.H. Huang, C.Y. Lin, An iterative regularization method in estimating the
unknown energy source by laser pulses with a dual-phase-lag mode, International
Journal for Numerical Methods in Engineering, 76, No. 1 (2008), 108–126.
C.H. Huang, C.Y. Lin, Inverse Hyperbolic Conduction Problem in Estimating
Two Unknown Surface Heat Fluxes Simultaneously, Journal of Thermophysics
and Heat Transfer, 22, No. 4 (2008), 766-774.
E. Kalnay, Atmospheric Modeling, Data Assimilation and Predictability, 2. ed.,
New York: Cambridge University Press, 2003.
W. Kaminsk, Hyperbolic heat conduction equation for materials with a nonhomogeneous
inner structure, Journal of Heat Transfer, 112 (1990), 555–560.
J. M. Kozlowska, M. Kozlowski, Z. Mucha, Thermal waves in two-dimensional
heterogeneous materials, Lasers Engineering, 11, No. 3 (2001), 189–194.
F.L.L. Medeiros, “Algoritmo Genético Híbrido como um Método de Busca de
Estados Estacionários de Sistemas Dinâmicos”, Dissertação de Mestrado, CAP,
INPE, São José dos Campos, SP, 2003.
L.B.L. Santos, L.D. Chiwiacowsky, H.F. de Campos Velho, Análise de robustez
do método híbrido de estimação de dano estrutural, TEMA: Tendências em
Matemática Aplicada e Computacional, 12, No. 3 (2011), 245–252.
Downloads
Published
How to Cite
Issue
Section
License
Copyright
Authors of articles published in the journal Trends in Computational and Applied Mathematics retain the copyright of their work. The journal uses Creative Commons Attribution (CC-BY) in published articles. The authors grant the TCAM journal the right to first publish the article.
Intellectual Property and Terms of Use
The content of the articles is the exclusive responsibility of the authors. The journal uses Creative Commons Attribution (CC-BY) in published articles. This license allows published articles to be reused without permission for any purpose as long as the original work is correctly cited.
The journal encourages Authors to self-archive their accepted manuscripts, publishing them on personal blogs, institutional repositories, and social media, as long as the full citation is included in the journal's website version.
