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Articles

Application of an adaptive MCMC method for the heat flux estimation

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Pages 859-876 | Received 29 Aug 2018, Accepted 13 Oct 2019, Published online: 30 Oct 2019

References

  • Beck JV, Blackwell B, Clair CR. Inverse heat conduction: ill-posed problems. New York (NY): Wiley Interscience; 1985.
  • Raynaud M, Beck J V. Methodology for comparison of inverse heat conduction methods. J Heat Transfer. 1988;110:30–37.
  • Alifanov OM. Inverse heat transfer problems. Berlin: Springer-Verlag; 1994.
  • Taler J, Duda P. Experimental verification of space marching methods for solving inverse heat conduction problems. Heat Mass Transfer. 2000;36(4):325–331.
  • Battaglia JL, Cois O, Puigsegur L, et al. Solving an inverse heat conduction problem using a non-integer identified model. Int J Heat Mass Transf. 2001;44:2671–2680.
  • Monde M. Analytical method in inverse heat transfer problem using Laplace transform technique. Int J Heat Mass Transf. 2000;43:3965–3975.
  • Qian WQ, He KF, Zhou Y. Estimation of surface heat flux for ablation and charring of thermal protection material. Heat Mass Transfer. 2016;52(7):1275–1281.
  • Schmidt DM, George JS, Wood CC. Bayesian inference applied to the electromagnetic inverse problem. Hum Brain Mapp. 1999;7(3):195–212.
  • Martin J, Wilcox LC, Burstedde C, et al. A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion. SIAM J Sci Comput. 2012;34(3):A1460–A1487.
  • Beaumount MA, Balding DJ. Identifying adaptive genetic divergence among populations from genome scans. Mol Ecol. 2004;13(4):969–980.
  • Mao SS. Bayesian statistic. Beijing: China Statistics Press; 1999;. Chinese.
  • Battaglia JL, Fudym O, Orlande HRB, et al. Estimation of thermal parameters from picoseconds thermo reflectance. Paper presented at: IPDO2013; 2013 June 26–28; Albi, France.
  • Orlande HRB, Dulikravich GS, Neumayer M, et al. Accelerated Bayesian inference for the estimation of spatially varying heat flux in a heat conduction problem. Numer Heat Transfer Part A: Appl. 2014;65(1):1–25.
  • Wang JB, Zabaras N. A Bayesian inference approach to the inverse heat conduction problem. Int J Heat Mass Transf. 2004;47:3927–3941.
  • Wang JB, Zabaras N. Hierarchical Bayesian models for inverse problems in heat conduction. Inverse Probl. 2005;21:183–206.
  • Balaji C, Padhi T. A new ANN driven MCMC method for multi-parameter estimation in two-dimension conduction with heat generation. Int J Heat Mass Transf. 2010;53:5440–5455.
  • Qian WQ, Cai JS. Parameter estimation of heat conduction coefficient and heat flux by sensitivity method. Acta Aerodynam Sin. 1998;16(2):226–231. Chinese.
  • Haario H, Saksman E, Tamminen J. Componentwise adaptation for high dimensional MCMC. Comput Stat. 2005;20:265–273.
  • Qian WQ, Zhou Y, Shao YP, et al. A preliminary analysis of identifiability of surface heat flux. J Exp Fluid Mech. 2013;27(4):17–22. Chinese.
  • Elden L, Berntsson F, Reginska T. Wavelet and Fourier method for solving the sideways heat equation. Siam J Sci Comput. 2000;21(6):2187–2205.
  • Cattani L, Maillet D, Bozzoli F, et al. Estimation of the local convective heat transfer coefficient in pipe flow using a 2D thermal quadrupole model and truncated singular value decomposition. Int J Heat Mass Transf. 2015;91:1034–1045.
  • Roberts GO, Gelman A, Gilks WR. Weak convergence and optimal scaling of random walk Metropolis algorithms. Ann Appl Probab. 1997;7(1):110–120.
  • Roberts GO, Rosenthal JS. Examples of adaptive MCMC. J Comput Graph Stat. 2009;18(2):349–367.
  • Bozzoli F, Cattani F, Mocerino A, et al. A novel method for estimating the distribution of convective heat flux in ducts: Gaussian filtered singular value decomposition. Inverse Problem Sci Eng. 2019;27(11):1595–1607.
  • Bozzoli F, Rainieri S. Comparative application of CGM and Wiener filtering techniques for the estimation of heat flux distribution. Inverse Probl Sci Eng. 2011;19(4):551–573.
  • Qian WQ, Wu SJ, Bu HT, et al. Preliminary investigation of principle experiment for aerothermodynamic parameter estimation. J Exp Fluid Mech. 2009;23(3):59–62. Chinese.

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