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RESEARCH PAPERS

Bayesian Parameter Estimation of Convective Heat Transfer Coefficients of a Roof-Mounted Radiant Barrier System

[+] Author and Article Information
Philippe Lauret

 University of Reunion Island, Faculté des Sciences et Technologies, Laboratoire de Génie Industriel, Equipe Génie Civil et Thermique de l’habitat, BP 7151, 15 avenue René Cassin, 97 715 Saint-Denis, Francelauret@univ-reunion.fr

Frédéric Miranville

 University of Reunion Island, Faculté des Sciences et Technologies, Laboratoire de Génie Industriel, Equipe Génie Civil et Thermique de l’habitat, BP 7151, 15 avenue René Cassin, 97 715 Saint-Denis, Francefrederic.miranville@univ-reunion.fr

Harry Boyer

 University of Reunion Island, Faculté des Sciences et Technologies, Laboratoire de Génie Industriel, Equipe Génie Civil et Thermique de l’habitat, BP 7151, 15 avenue René Cassin, 97 715 Saint-Denis, Franceharry.boyer@univ-reunion.fr

François Garde

 University of Reunion Island, Faculté des Sciences et Technologies, Laboratoire de Génie Industriel, Equipe Génie Civil et Thermique de l’habitat, BP 7151, 15 avenue René Cassin, 97 715 Saint-Denis, Francegarde@univ-reunion.fr

Laetitia Adelard

 University of Reunion Island, Faculté des Sciences et Technologies, Laboratoire de Génie Industriel, Equipe Génie Civil et Thermique de l’habitat, BP 7151, 15 avenue René Cassin, 97 715 Saint-Denis, Franceadelard@univ-reunion.fr

J. Sol. Energy Eng 128(2), 213-225 (Sep 12, 2005) (13 pages) doi:10.1115/1.2188957 History: Received November 25, 2004; Revised September 12, 2005

This paper deals with the application of Bayesian methods to the estimation of two convective heat-transfer coefficients of a roof-mounted radiant barrier system. As part of an empirical validation of the thermal model of the roofing complex, a parametric sensitivity analysis highlighted the importance of convective coefficients in the thermal behavior of a roofing complex. A parameter estimation method is then used in order to find the values of the coefficients that lead to an improvement of the thermal model. However, instead of using a classical parameter estimation method, we used a Bayesian inference approach to parameter estimation. The aim of the paper is to introduce the basic concepts of this powerful method in this simple two-parameter case. We show that Bayesian methods introduce an explicit treatment of uncertainty in modeling and a corresponding measure of reliability for the conclusions reached.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Section view of the roofing complex

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Figure 3

Instrumentation of the roofing complex

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Figure 4

Some meteorological variables measured during the experiment

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Figure 5

Comparison between measurement and prediction of the indoor dry air temperature of the test cell Tai

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Figure 6

Comparison between measurement and prediction of the indoor dry air temperature of the lower air layer Tlo

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Figure 7

Sketch of the parametric sensitivity analysis

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Figure 8

Fourier transforms of ΔTlo (a) and effects of some important factors (b)

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Figure 9

Posterior pdf of h1 and h2 (a) and the corresponding Gaussian approximation (b). The contours correspond to 5%, 15%, …, 85%, and 95% of the maximum probability.

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Figure 10

Marginal posterior distributions of h1 (a) and h2 (b). The Gaussian approximation is shown with dashed lines.

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Figure 11

Gamma prior distributions for h1 (a) and h2 (b). The wide prior is shown with a solid line.

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Figure 12

Posterior pdf of h1 and h2 for the case of wide Gamma prior (a) and narrow Gamma prior (b)

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Figure 13

Marginal posterior distributions of h1 (a) and h2 (b). The solid lines correspond to a flat prior for the parameters; the dashed lines correspond to the wide prior Gamma distributions and the dotted lines correspond to the narrow prior Gamma distributions.

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Figure 14

Marginal posterior distribution of the noise σ

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Figure 15

Comparison between measurement and prediction of the indoor dry air temperature of the lower air layer Tlo. The old residual corresponds to the one depicted in Fig. 6.

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Figure 16

Comparison between measurement uncertainty intervals (continuous line) and prediction intervals (dotted line)

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