TY - JOUR
T1 - Evaluation of the reliability of building energy performance models for parameter estimation
AU - Berger, J.
AU - Dutykh, D.
N1 - Funding Information:
The authors acknowledge the Junior Chair Research program “Building performance assessment, evaluation and enhancement” from the University of Savoie Mont Blanc in collaboration with The French Atomic and Alternative Energy Center (CEA) and Scientific and Technical Center for Buildings (CSTB). The authors also would like to acknowledge Dr. Celine Labart (LAMA UMR 5127, University Savoie Mont Blanc, France) for her precious discussions on numerical matters.
Publisher Copyright:
© ICT SB RAS, 2019
PY - 2019
Y1 - 2019
N2 - The fidelity of a model relies both on its accuracy to predict the physical phenomena and its capability to estimate unknown parameters using observations. This article focuses on this second aspect by analyzing the reliability of two mathematical models proposed in the literature for the simulation of heat losses through building walls. The first one, named DF, is the classical heat diffusion equation combined with the Du Fort-Frankel numerical scheme. The second is the so-called RC lumped approach, based on a simple ordinary differential equation to compute the temperature within the wall. The reliability is evaluated following a two stages method. First, samples of observations are generated using a pseudo-spectral numerical model for the heat diffusion equation with known input parameters. The results are then modified by adding a noise to simulate experimental measurements. Then, for each sample of observation, the parameter estimation problem is solved using one of the two mathematical models. The reliability is assessed based on the accuracy of the approach to recover the unknown parameter. Three case studies are considered for the estimation of (i) the heat capacity, (ii) the thermal conductivity or (iii) the heat transfer coefficient at the interface between the wall and the ambient air. For all cases, the DF mathematical model has a very satisfactory reliability to estimate the unknown parameters without any bias. However, the RC model lacks of fidelity and reliability. The error on the estimated parameter can reach 40 % for the heat capacity, 80 % for the thermal conductivity and 450 % for the heat transfer coefficient.
AB - The fidelity of a model relies both on its accuracy to predict the physical phenomena and its capability to estimate unknown parameters using observations. This article focuses on this second aspect by analyzing the reliability of two mathematical models proposed in the literature for the simulation of heat losses through building walls. The first one, named DF, is the classical heat diffusion equation combined with the Du Fort-Frankel numerical scheme. The second is the so-called RC lumped approach, based on a simple ordinary differential equation to compute the temperature within the wall. The reliability is evaluated following a two stages method. First, samples of observations are generated using a pseudo-spectral numerical model for the heat diffusion equation with known input parameters. The results are then modified by adding a noise to simulate experimental measurements. Then, for each sample of observation, the parameter estimation problem is solved using one of the two mathematical models. The reliability is assessed based on the accuracy of the approach to recover the unknown parameter. Three case studies are considered for the estimation of (i) the heat capacity, (ii) the thermal conductivity or (iii) the heat transfer coefficient at the interface between the wall and the ambient air. For all cases, the DF mathematical model has a very satisfactory reliability to estimate the unknown parameters without any bias. However, the RC model lacks of fidelity and reliability. The error on the estimated parameter can reach 40 % for the heat capacity, 80 % for the thermal conductivity and 450 % for the heat transfer coefficient.
KW - Building thermal performance
KW - Du fort-frankel numerical model
KW - Heat transfer
KW - Mathematical model reliability
KW - Parameter estimation problem
KW - Thermal circuit model
UR - http://www.scopus.com/inward/record.url?scp=85117891191&partnerID=8YFLogxK
U2 - 10.25743/ICT.2019.24.3.002
DO - 10.25743/ICT.2019.24.3.002
M3 - Article
AN - SCOPUS:85117891191
SN - 1560-7534
VL - 24
SP - 4
EP - 32
JO - Journal of Computational Technologies
JF - Journal of Computational Technologies
IS - 3
ER -