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Article information
2019 , Volume 24, ¹ 3, p.4-32
Berger J., Dutykh D.
Evaluation of the reliability of building energy performance models for parameter estimation
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.
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Keywords: mathematical model reliability, parameter estimation problem, building thermal performance, heat transfer, Du Fort - Frankel numerical model, thermal circuit model
doi: 10.25743/ICT.2019.24.3.002
Author(s):
Berger Julien
PhD.
Position: Research Scientist
Office: University Grenoble Alpes, University Savoie Mont Blanc, Centre National de Recherche, LOCIE CNRS
Address: 73370, France, Chambery, batiment Helios, 60 rue du lac Leman, Savoie Technolac
Dutykh Denys
Office: University Grenoble Alpes, University Savoie Mont Blanc, CNRS LAMA
Address: 73376, France, Chambery, batiment Helios, 60 rue du lac Leman, Savoie Technolac
Phone Office: (330) 4 79 75 94 38
E-mail: Denys.Dutykh@univ-smb.fr
References:
[1] Fourier, J. Theorie Analytique de la Chaleur. France, Sceaux: J. Gabay; 1988: 639.
[2] Kirkpatrick, S., Lee, J., Olive, T. S., Batters, H., Callaham, J., Farquhar, N., Pope, L. Complex heat transfer solved by electrical analogy. Chemical and Metallurgical Engineering. 1943; 50(12):111113.
[3] Lawson, D.I., McGuire, J.H. The solution of transient heat-flow problems by analogous electrical networks. Proceedings of the Institution of Mechanical Engineers. 1953; 167(1):275290. DOI: 10.1243/PIME PROC 1953 167 034 02.
[4] Robertson, A.F., Gross, D. An electrical-analog method for transient heat-flow analysis. Journal of Research of the National Bureau of Standards. 1958; 61(2):105115. Available at: http: //dx.doi.org/10.6028/jres.061.016
[5] Mendes, N., Chhay, M., Berger, J., Dutykh, D. Numerical methods for diffusion phenomena in building physics. Curitiba, Brazil: PUCPress; 2016: 224. DOI:10.7213/978-8568324-45-5.
[6] Fraisse, G., Viardot, C., Lafabrie, O., Achard, G. Development of a simplified and accurate building model based on electrical analogy. Energy and Buildings. 2002; 34(10):10171031. Available at: https://doi.org/10.1016/S0378-7788(02)00019-1
[7] Kampf, J.H., Robinson, D. A simplified thermal model to support analysis of urban resource flows. Energy and Buildings. 2007; 39(4):445453. Available at: https://doi.org/10.1016/j.enbuild.2006.09.002
[8] Naveros, I., Ghiaus, C. Order selection of thermal models by frequency analysis of measurements for building energy efficiency estimation. Applied Energy. 2015; 139(Supplement C):230244. Available at: https://doi.org/10.1016/j.apenergy.2014.11.033
[9] Roels, S., Bacher, P., Bauwens, G., Castaño, S., Jiménez, Madsen, H. On site characterisation of the overall heat loss coefficient: comparison of different assessment methods by a blind validation exercise on a round robin test box. Energy and Buildings. 2017; (153):179189. DOI: 10.1016/j.enbuild.2017.08.006.
[10] Jimenez, M.J., Porcar, B., Heras, M.R. Application of different dynamic analysis approaches to the estimation of the building component U value. Building and Environment. 2009; 44( 2):361367. DOI:10.1016/j.buildenv.2008.03.010.
[11] Berger, J., Orlande, H.R.B., Mendes, N., Guernouti, S. Bayesian inference for estimating thermal properties of a historic building wall. Building and Environment. 2016; 106(Supplement C):327339. Available at: https://doi.org/10.1016/j.buildenv.2016.06.037
[12] Berger, J., Gasparin, S., Dutykh, D., Mendes, N. On the comparison of three numerical methods applied to building simulation: Finite-differences, RC circuit approximation and a spectral method. Building Simulation: An International Journal. 2019. (Accept). DOI:10.1007/s12273-019-0555-z.
[13] Kabanikhin, S.I. Definitions and examples of inverse ill-posed problems. Journal of Inverse Problems and Ill -posed problems. 2008; (16):317357. DOI:10.1515/JIIP.2008.069.
[14] Kabanikhin, S.I. Inverse and ill-posed problems: theory and applications. Berlin: Walter De Gruyter; 2011: 459. ISBN: 9783110124009.
[15] Berger, J., Gasparin, S., Dutykh, D., Mendes, N. On the solution of coupled heat and moisture transport in porous material. Transport in Porous Media. 2018; 121(3):665702. DOI: 10.1007/s11242-017-0980-3.
[16] Nayfeh A. Perturbation Methods. New York: Wiley-Intersci; 1973: 425.
[17] Kahan, W., Palmer, J. On a proposed floating-point standard. ACM SIGNUM Newsletter. 1979; (14):1321. Available at: http://dx.doi.org/10.1145/1057520.1057522
[18] Du Fort, E.C., Frankel, S.P. Stability conditions in the numerical treatment of parabolic differential equations. Mathematical Tables and Other Aids to Computation. 1953; 7(43):135152.
[19] Taylor, P.J. The stability of the Dufort-Frankel method for the diffusion equation with boundary conditions involving space derivatives. The Computer Journal. 1970; 13(1):192. DOI:10.1093/comjnl/13.1.92.
[20] Gasparin, S., Berger, J., Dutykh, D., Mendes, N. Stable explicit schemes for simulation of nonlinear moisture transfer in porous materials. Journal of Building Performance Simulation. 2018; 11(2):129144. DOI:10.1080/19401493.2017.1298669.
[21] Gasparin, S., Berger, J., Dutykh, D., Mendes, N. An improved explicit scheme for whole-building hygrothermal simulation. Building Simulation. 2018; 11(3):465481. DOI:10.1007/s12273-017-0419-3.
[22] Davies, M.G. Building heat transfer. West Sussex: John Wiley & Sons; 2004: 524.
[23] Deconinck, A.H., Roels, S. Comparison of characterisation methods determining the thermal resistance of building components from onsite measurements. Energy and Buildings. 2016; 130(Supplement C):309320. DOI:10.1016/j.enbuild.2016.08.061.
[24] Reynders, G., Diriken, J., Saelens, D. Quality of grey-box models and identified parameters as function of the accuracy of input and observation signals. Energy and Buildings. 2014; 82(Supplement C):263274. DOI:10.1016/j.enbuild.2014.07.025.
[25] Walter, E., Lecourtier, Y. Global approaches to identifiability testing for linear and onlinear state space models. Mathematics and Computers in Simulation. 1982; 24(6):472482. DOI: 10.1016/0378-4754(82)90645-0.
[26] Driscoll, T.A., Hale, N., Trefethen, L.N. Chebfun guide. Oxford: Pafnuty Publications; 2014: 212.
[27] Beck, J.V., Arnold, K.J. Parameter estimation in engineering and science. New York: John Wiley and Sons; 1977: 501.
[28] Necati Ozisik, M. Inverse heat transfer: Fundamentals and applications. New York: CRC Press; 2000: 352.
[29] Kabanikhin, S.I., Hasanov, A., Penenko, A.V. A gradient descent method for solving an inverse coefficient heat conduction problem. Numerical Analysis and Applications. 2008; 1(1):3445. DOI:10.1134/S1995423908010047.
Bibliography link:
Berger J., Dutykh D. Evaluation of the reliability of building energy performance models for parameter estimation // Computational technologies. 2019. V. 24. ¹ 3. P. 4-32
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