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Research Article

Sequential estimation of the time-dependent heat transfer coefficient using the method of fundamental solutions and particle filters

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Pages 3322-3341 | Received 21 Nov 2019, Accepted 17 Oct 2021, Published online: 07 Nov 2021

References

  • Karageorghis A, Lesnic D, Marin L. A survey of applications of the MFS to inverse problems. Inverse Probl Sci Eng. 2011;19:309–336.
  • Karageorghis A, Fairweather G. The method of fundamental solutions for the numerical solution of the biharmonic equation. J Comput Phys. 1987;69:434–459.
  • Bogomolny A. Fundamental solutions method for elliptic boundary value problems. SIAM J Numer Anal. 1985;22:644–669.
  • Alves CJS, Chen CS. A new method of fundamental solutions applied to nonhomogeneous elliptic problems. Adv Comput Math. 2005;23:125–142.
  • Kupradze VD, Aleksidze MA. The method of functional equations for the approximate solution of certain boundary value problems. USSR Comput Math Math Phys. 1964;4:82–126.
  • Johansson BT, Lesnic D. A method of fundamental solutions for transient heat conduction. Eng Anal Bound Elem. 2008;32:697–703.
  • Johansson BT, Lesnic D, Reeve T. A comparative study on applying the method of fundamental solutions to the backward heat conduction problem. Math Comput Model. 2011;54(1-2):403–416.
  • Johansson BT, Lesnic D, Reeve T. The method of fundamental solutions for the two-dimensional inverse Stefan problem. Inverse Probl Sci Eng. 2014;22(1):112–129.
  • Dawson M, Borman D, Hammond RB, et al. A meshless method for solving a two-dimensional transient inverse geometric problem. Int J Numer Methods Heat Fluid Flow. 2013;23(5):790–817.
  • Masson PL, Loulou T, Artioukhine E. Estimation of a 2D convection heat transfer coefficient during a test: comparison between two methods and experimental validation. Inverse Probl Sci Eng. 2004;12:594–617.
  • Yang F, Yan L, Wei T. The identification of a Robin coefficient by a conjugate gradient method. Int J Numer Methods Eng. 2009;78:800–816.
  • Kaipio J, Somersalo E. Statistical and computational inverse problems. Berlin: Springer-Verlag; 2004.
  • Winkler R. An introduction to Bayesian inference and decision. Gainsville (FL): Probabilistic Publishing; 2003.
  • Doucet A, Godsill S, Andrieu C. On sequential Monte Carlo sampling methods for Bayesian filtering. Stat Comput. 2000;10:197–208.
  • Kalman R. A new approach to linear filtering and prediction problems. ASME J Basic Eng. 1960;82:35–45.
  • Arulampalam S, Maskell S, Gordon N, et al. A tutorial on particle filters for on-line non-linear/non-Gaussian Bayesian tracking. IEEE Trans Signal Process. 2001;50:174–188.
  • Kaipio J, Duncan S, Seppanen A, et al. Handbook of process imaging for automatic control, state estimation for process imaging. Boca Raton (FL): CRC Press; 2005.
  • Andrieu C, Doucet A, Sumeetpal S, et al. Particle methods for charge detection, system identification and control. Proc IEEE. 2004;92:423–438.
  • Hammersley JM, Hanscomb DC. Monte Carlo methods. New York: Chapman and Hall; 1964.
  • Gordon N, Salmond D, Smith AFM. Novel approach to nonlinear and non-Gaussian Bayesian state estimation. Inst Electr Eng. 1993;140:107–113.
  • Orlande HRB, Colaço MJ, Dulikravich GS, et al. State estimation problems in heat transfer. Int J Uncertain Quantif. 2012;2:239–258.
  • Silva WB, Dutra JCS, Costa JMJ, et al. A hybrid estimation scheme based on the sequential importance resampling particle filter and the particle swarm optimization (PSO-SIR). In: Computational intelligence, optimization and inverse problems with applications in engineering. New York: Springer International Publishing; 2019. p. 247–261.
  • Louahlia-Gualous H, Panday PK, Artioukhine EA. Inverse determination of the local heat transfer coefficients for nucleate boiling on a horizontal cylinder. J Heat Transf. 2003;125:1087–1095.
  • Osman AM, Beck JV. Investigation of transient heat transfer coefficients in quenching experiments. J Heat Transf. 1990;112:843–848.
  • Slodicka M, Van Keer R. Determination of a Robin coefficient in semilinear parabolic problems by means of boundary measurements. Inverse Probl. 2002;18:139–152.
  • Slodička M, Lesnic D, Onyango TTM. Determination of a time-dependent heat transfer coefficient in a nonlinear inverse heat conduction problem. Inverse Probl Sci Eng. 2010;18:65–81.
  • Johansson BT, Lesnic D, Reeve T. A method of fundamental solutions for two-dimensional heat conduction. Int J Comput Math. 2011;88(8):1697–1713.
  • da Silva WB, Dutra JCS, Kepperschimidt CEP, et al. Sequential particle filter estimation of a time-dependent heat transfer coefficient in a multidimensional nonlinear inverse heat conduction problem. Appl Math Model. 2021;89:654–668.
  • Lesnic D, Elliott L, Ingham DB. A boundary element method for the determination of the transmissivity of a heterogeneous aquifer in groundwater flow systems. Eng Anal Bound Elem. 1998;21(3):223–234.
  • Johansson BT, Lesnic D. A method of fundamental solutions for transient heat conduction in layered materials. Eng Anal Bound Elem. 2009;33(12):1362–1367.
  • Friedman A. Partial differential equations of parabolic type. Englewood Cliffs (NJ): Prentice Hall; 1964.
  • Yan L, Yang F, Fu C. Bayesian inference approach to identify a Robin coefficient in one-dimensional parabolic problems. J Comput Appl Math. 2009;231:840–850.
  • Onyango TTM, Ingham DB, Lesnic D, et al. Determination of a time-dependent heat transfer coefficient non-standard boundary measurements. Math Comput Simul. 2009;79:1577–1584.
  • Su J, Hewitt GF. Inverse heat conduction problem of estimating time-varying heat transfer coefficient. Numer Heat Transf Part A. 2004;45:777–789.
  • Nho Hao Dinh, Viet Huong Bui, Xuan Thanh Phan, et al. Identification of nonlinear heat transfer laws from boundary observations. Appl Anal. 2015;94:1784–1799.
  • Aykroyd RG, Lesnic D, Karageorghis A. A fully Bayesian approach to shape estimation of objects from tomography data using MFS forward solutions. Int J Tomogr Simul. 2015;28:1–21.
  • Grabski JK. On the sources placement in the method of fundamental solutions for time-dependent heat conduction problems. Comput Math Appl. 2021;88:33–51.
  • Johansson BT. Properties of a method of fundamental solutions for the parabolic heat equation. Appl Math Lett. 2017;65:83–89.
  • Campillo F, Rossi V. Convolution particle filter for parameter estimation in general state-space models. IEEE Trans Aerosp Electron Syst. 2009;45:1073–1072.
  • Doucet A, Freitas N, Gordon N. Sequential Monte Carlo methods in practice. Berlin: Springer; 2001.
  • Doucet A, Tadic VB. Parameter estimation in general state–space models using particle methods. Ann Inst Stat Math. 2003;55:409–422.
  • Liu J, West M. Combined parameter and state estimation in simulation-based filtering. In: Sequential Monte Carlo methods in practice. Statistics for Engineering and Information Science. New York: Springer; 2001. p. 197–223.
  • Silva WB, Rochoux MC, Orlande HRB, et al. Application of particle filters to regional-scale wildfire spread. High Temperatures High Pressures. 2014;43:415–440.
  • Salardani LSF, Albuquerque LP, Costa JMJ, et al. Particle filter-based monitoring scheme for simulated bio-ethylene production process. Inverse Probl Sci Eng. 2018;27:648–668.
  • Ristic B, Arulampalam S, Gordon N. Beyond the Kalman filter. Boston: Artech House; 2004.
  • Dias ACSR, Da Silva WB, Dutra JCS. Propylene polymerization reactor control and estimation using a particle filter and neural network. Macromol React Eng. 2017;11:1–20.
  • Marques R, Silva WB, Hoffmann R, et al. Sequential state inference of engineering systems through the particle move-reweighting algorithm. Comput Appl Math. 2017;37:220–236.
  • Liu J, Chen R. Sequential Monte Carlo methods for dynamical systems. J Amer Statist Assoc. 1998;93:1032–1044.
  • Onyango TTM, Ingham DB, Lesnic D. Reconstruction of heat transfer coefficients using the boundary element method. Comput Math Appl. 2008;56(1):114–126.

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