Article

# Evaluation of the reliability of building energy performance models for parameter estimation

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## Abstract

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 DuFort-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 pseudospectral 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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... It represents interesting strategies since they intend to compute solutions with a lower computational cost while preserving the whole complexity of the physical phenomena. Lumped models, such as lumped capacitance ones do have a lower computational cost but the predictions' reliability are questionable as remarked in [10,11]. In recent years, several works have been published to propose reduced-order models for the computation of diffusion problems in building physics [12]. ...
... Before developing any numerical algorithm to compute the governing equations, a dimensionless model is formulated [10,11,41]. For each layer i, the dimensionless temperature is defined: ...
... due to the orthogonality of the basis vectors. Equations (10), (11) and (12) enable to compute the spatial coefficients b i n N n=1 for each layer i . With this approach, the problem to solve scale with N χ × N . ...
Article
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Within the environmental context, numerical modeling is a promising approach to assess the energy efficiency of building. Resilient buildings need to be designed, capable of adapting to future extreme heat. Simulations are required assuming a one-dimensional heat transfer problem through walls and a simulation horizon of several years (nearly 30). The computational cost associated with such modeling is quite significant and model reduction methods are worth investigating. The objective is to propose a reliable reduced-order model for such long-term simulations. For this, an alternative model reduction approach is investigated, assuming a known Proper Orthogonal Decomposition reduced basis for time, and not for space as usually. The model enables computing parametric solutions using basis interpolation on the tangent space of the Grassmann manifold. Three study cases are considered to verify the efficiency of the reduced-order model. Results highlight that the model has a satisfying accuracy of 10-3 compared to reference solutions. The last case study focuses on the wall energy efficiency design under climate change according to a four-dimensional parameter space. The latter is composed of the load material emissivity, heat capacity, thermal conductivity and thickness insulation layer. Simulations are carried over 30 years considering climate change. The solution minimizing the wall work rate is determined with a computational ratio of 0.1% compared to standard approaches.
... Lumped model such as RC approaches have been proposed due to their very small computational cost. However, their reliability to estimate accurately the thermal diffusivity is questioned in [13]. The model has to be based on detailed heat diffusion process. ...
... The final time is t f = 24 h and the wall of length L = 0.5 m . The points of interest are the same as defined in Eq. (13). The discretisation parameters is ∆t = 30 s for both models. ...
... The issue is to estimate the global thermal diffusivity α of the wall by assuming an equivalent homogenous model [14]. Note that the structural identifiability of this parameter has been demonstrated in [13]. For this aim, the wall are monitored using five intrusive calibrated sensors HOBO TMC-6-HA as shown in Figures 8(a) to 8(c). ...
Preprint
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... This may be very relevant within the context of determining materials properties using experimental observations of the field. In [33], the unknown parameters to estimate are reduced from four to two between the dimensionless and dimensional models. Then, from a numerical point of view, solving one dimensionless problem is equivalent to solving a whole class of dimensionless problems sharing the same scaling parameters. ...
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