Estimation of a Location- and Time-Dependent High-Magnitude Heat Flux in a Heat Conduction Problem Using the Kalman Filter and the Approximation Error Model

REFERENCES

• H. R. B. Orlande, G. S. Dulikravich, M. Neumayer, D. Watzenig, and M. J. Colaço Accelerated Bayesian Inference for the Estimation of Spatially Varying Heat Flux in a Heat Conduction Problem, Numer. Heat Transf. Part A, vol. 65, pp. 1–25, 2013.
   Web of Science ®Google Scholar
• B. H. Dennis and G. S. Dulikravich Simultaneous Determination of Steady Temperatures and Heat Fluxes on Surfaces of Three Dimensional Objects Using FEM, ASME IMECE2001/HTD-24310, New York, November 11–16, 2001.
   Google Scholar
• B. H. Dennis and G. S. Dulikravich Inverse Determination of Unsteady Temperatures and Heat Fluxes on Inaccessible Boundaries, Inverse Ill-Posed Probl., vol. 20, no. 5–6, pp. 791–803, 2012.
   Web of Science ®Google Scholar
• Z. C. Feng, J. K. Chen, Y. Zhang, and J. L. Griggs Jr., Estimation of Front Surface Temperature and Heat Flux of a Locally Heated Plate from Distributed Sensor Data on the Back Surface, Int. J. Heat Mass Transf., vol. 54, pp. 3431–3439, 2011.
   Web of Science ®Google Scholar
• N. Afrin, Z. C. Feng, Y. Zhang, and J. K. Chen Inverse Estimation of Front Surface Temperature of a Locally Heated Plate with Temperature-dependent Conductivity via Kirchhoff Transformation, Int. J. Therm. Sci., vol. 69, pp. 53–60, 2013.
   Web of Science ®Google Scholar
• S. K. Kim Prameterized Gradient Integration Method For Inverse Heat Conduction Problems, Numer. Heat Transf. Part B Fundam., vol. 61, no. 2, pp. 116–128, 2012.
   Web of Science ®Google Scholar
• F. Berntsson An Inverse Heat Conduction Problem and Improving Shielded Thermocouple Accuracy, Numer. Heat Transf. Part A Appl., vol. 61, no. 10, pp. 754–763, 2012.
   Web of Science ®Google Scholar
• M. R. Golbahar Haghighi, P. Malekzadeh, H. Rahideh, and M. Vaghefi Inverse Transient Heat Conduction Problems of a Multilayered Functionally Graded Cylinder, Numer. Heat Transf. Part A Appl., vol. 61, no. 9, pp. 717–733, 2012.
   Web of Science ®Google Scholar
• A. Azimi, K. Bamdad, and H. Ahmadikia Inverse Hyperbolic Heat Conduction in Fins with Arbitrary Profiles, Numer. Heat Transf. Part A Appl., vol. 61, no. 3, pp. 220–240, 2012.
   Web of Science ®Google Scholar
• E. Hetmaniok, I. Nowak, D. Słota, and A. Zielonka Determination of Optimal Parameters for the Immune Algorithm used for Solving Inverse Heat Conduction Problems with and Without a Phase Change, Numer. Heat Transf. Part B Fundam., vol. 62, no. 6, pp. 462–478, 2012.
   Web of Science ®Google Scholar
• H. Rahideh, P. Malekzadeh, M. R. Golbahar Haghighi, and M. Vaghefi Two-Dimensional Inverse Transient Heat Conduction Analysis of Laminated Functionally Graded Circular Plates, Numer. Heat Transf. Part A Appl., vol. 62, no. 12, pp. 992–1014, 2012.
   Web of Science ®Google Scholar
• S. Vakili and M. S. Gadala A Modified Sequential Particle Swarm Optimization Algorithm with Future Time Data for Solving Transient Inverse Heat Conduction Problems, Numer. Heat Transf. Part A Appl., vol. 59, no. 12, pp. 911–933, 2011.
   Web of Science ®Google Scholar
• K.-C. Liu and C.-T. Lin Solution of an Inverse Heat Conduction Problem in a Bi-Layered Spherical Tissue, Numer. Heat Transf. Part A Appl., vol. 58, no. 10, pp. 802–818, 2010.
   Web of Science ®Google Scholar
• S. K. Kim Resolving the Final Time Singularity in Gradient Methods for Inverse Heat Conduction Problems, Numer. Heat Transf. Part B Fundam., vol. 57, no. 1, pp. 74–88, 2010.
   Web of Science ®Google Scholar
• Z. Chen Bayesian Filtering: from Kalman Filters to Particle Filters, and Beyond, Statistics (Ber), vol. 182, no. 1, pp. 1–69, 2003.
   Google Scholar
• D. Gamerman Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Taylor & Francis, Boca Raton, FL, 1997.
   Google Scholar
• M. S. Grewal and A. P. Andrews Kalman Filtering: Theory and Practice Using MATLAB, Wiley, Hoboken, 2008.
   Google Scholar
• R. E. Kalman A New Approach to Linear Filtering and Prediction Problems, Trans. ASME-Journal Basic Eng., vol. 82, no. Series D, pp. 35–45, 1960.
   Google Scholar
• H. R. B. Orlande, M. J. Colaço, G. S. Dulikravich, F. L. V. Vianna, W. B. da Silva, H. M. Fonseca, and O. Fudym State Estimation Problems in Heat Transfer, Int. J. Uncertain. Quantif., vol. 2, no. 3, pp. 239–258, 2012.
   Google Scholar
• R. M. Cotta and M. D. Mikhailov Heat Conduction: Lumped Analysis, Integral Transforms, Symbolic Computation, Wiley Ed., Chichester, 1997.
   Google Scholar
• J. P. Kaipio and E. Somersalo Statistical and Computational Inverse Problems. Springer Science+Business Media, Inc, New York, NY, 2004.
   Google Scholar
• J. Huttunen and J. P. Kaipio Approximation and Modelling Errors in Nonstationary Inverse Problems, University of Kuopio, Kuopio University Library, Kuopio, 2008.
   Google Scholar
• M. N. Ozisik Heat Conduction, 2nd ed., John Wiley & Sons, Inc., New York, NY, 1993.
   Google Scholar
• M. Neumayer, D. Watzenig, H. R. B. Orlande, M. J. Colaço, and G. S. Dulikravich Fast Bayesian Inference for an Inverse Heat Transfer Problem Using Approximations, Inst. Meas. Technol. Conf. (I2MTC), IEEE International, pp. 1923–1928, 2012.
   Google Scholar
• J. L. Griggs Albuquerque, NM, Private Communication, 14 December, 2011.
   Google Scholar
• S. V. Patankar Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Company, Washington, 1980.
   Google Scholar
• H. K. Versteeg and W. Malalasekera An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Longman Group Ltd, Harlow, 1995.
   Google Scholar
• J. H. Ferziger and M. Peric Computational Methods in Fluid Flow, Springer-Verlag, New York, NY, 2002.
   Google Scholar