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 -