Solución numérica de un problema inverso aplicando un algoritmo genético continuo

• Autores: Stefan Berres, Aníbal Coronel, Richard Lagos
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 36, Nº. 2, 2018, págs. 67-81
• Idioma: español
• DOI: 10.18273/revint.v36n2-2018001
• Títulos paralelos:
  • Numerical solution of an inverse problem by applying a continuous genetic algorithm
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• Resumen
  • español

    En este artículo se considera el problema de la determinación de la función de flujo en una ley de conservación escalar que modela el fenómeno de sedimentación. Los datos de la observación experimental utilizada para la calibración corresponden a un perfil de la concentración de sólidos en un tiempo fijo. El problema de identificación se formula como uno de optimización, donde la función objetivo es la de mínimos cuadrados que minimiza la distancia entre los perfiles solución del modelo y la observación. La solución del problema directo es aproximada por un esquema de volúmenes finitos monótono. La solución numérica del problema de calibración se obtiene mediante un algoritmo genético continuo. Se presentan resultados numéricos para validar la eficiencia del algoritmo propuesto.

  • English

    In this paper we consider the problem of flux determination in a scalar conservation law modeling the phenomenon of sedimentation. The experimental observation data used for the calibration consist of a solid concentration profile at a fixed time. The identification problem is formulated as an optimization one, where the distance between the profiles of the model simulation and observation data is minimized by a least squares cost function. The direct problem is approximated by a monotone finite volume scheme. The numerical solution of the calibration problem is obtained by a continuous genetic algorithm. Numerical results are presented in order to validate the efficiency of the proposed algorithm.

     

• Referencias bibliográficas
  • Citas [1] Berres S., Bürger R., Coronel A. and Sepúlveda M., “Numerical identification of parameters for a strongly degenerate convection-diffusion...
  • [2] Bürger R., Coronel A. and Sepúlveda M., “A numerical descent method for an inverse problem of a scalar conservation law modelling sedimentation”,...
  • [3] Bürger R., Coronel A. and Sepúlveda M., “Numerical solution of an inverse problem for a scalar conservation law modelling sedimentation”,...
  • [4] Bürger R. andWendlandW. L., “Sedimentation and suspension flows: historical perspective and some recent developments”, J. Engrg. Math....
  • [5] Bustos M. C., Concha F., Bürger R. and Tory E. M., Sedimentation and thickening, vol 8 of Mathematical Modelling: Theory and Applications,...
  • [6] Concha F. and Bürger R., “Thickening in the 20th century: a historical perspective”, Minerals & Metallurgical Process 20 (2003), No....
  • [7] Engquist B. and Osher S., “One-sided difference approximations for nonlinear conservation laws”, Math. Comput. 36 (1981), 321–351.
  • [8] Eymard R., Gallouët T. and Herbin R., “Finite volume methods”, in Handbook of numerical analysis, Volume VII: Handb. Numer. Anal. North-Holland,...
  • [9] Fogel L.J., Owens A.J. and Walsh M.J., Artificial intelligence through simulated evolution, Wiley, Chichester, WS, UK, 1966.
  • [10] Gaffney J., Pearce C. and Green D., “Binary versus real coding for genetic algorithms: A false dichotomy?”, ANZIAM J. 51 (EMAC2009),...
  • [11] Goldberg D.E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Longman Publishing Co., Inc., Boston,...
  • [12] Hansen N., Auger A., Ros R., Finck S. and Pošík P., “Comparing results of 31 algorithms from the black-box optimization benchmarking...
  • [13] Haupt R.L. and Haupt S.E., Practical genetic algorithms, Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, second edition, 2004.
  • [14] Holland J.H., Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, MI, USA, 1975.
  • [15] Koza J.R., Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press, Cambridge, MA, USA, 1992.
  • [16] Kynch G.J., “A theory of sedimentation”, Trans. Faraday Soc 48 (1952), 166–176.
  • [17] LeVeque R.J., Numerical methods for conservation laws, Lectures in Mathematics ETH Zürich, Second edition, Basel: Birkhäuser Verlag,...
  • [18] Michalewicz Z., Genetic algorithms + data structures = evolution programs, Artificial Intelligence, Springer-Verlag, Berlin,...
  • [19] Rechenberg I., Evolutionstrategie: Optimierung Technisher Systeme nach Prinzipien des Biologischen Evolution, Fromman-Hozlboog Verlag,...
  • [20] Sweeney M.W. and Kabouris J.C., “Modeling, Instrumentation, Automation, and Optimization of Water Resource Recovery Facilities”, Water...
  • [21] Sivanandam S. N. and Deepa S. N., Introduction to genetic algorithms, Springer, Berlin, 2008.
  • [22] Tan Ch. K., Bao J. and Bickert G., “A study on model predictive control in paste thickeners with rake torque constraint´”, Mineral Engineering...
  • [23] Toro E.F., Riemann solvers and and numerical methods for fluid dynamics: A practical introduction, Third edition, Springer-Verlag, Berlin,...
  • [24] Xu N., Wang X., Zhou J., Wang Q., Feng W. and Peng X., “An intelligent control strategy for thickening process”, International Journal...