Quantifying uncertainty in thermal properties of walls by means of Bayesian inversion
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Quantifying the uncertainty from simulations of the energy performance in buildings is crucial for the development of effective policy making aimed at reducing carbon emissions from the built environment. One of the main sources of uncertainty in energy simulations of existing buildings arises from the lack of an accurate characterisation of thermal properties of walls. In this paper we introduce a methodology to infer, under the presence of uncertainty, thermal properties of walls from in-situ measurements of air temperature and surface heat fluxes. The proposed methodology uses a one-dimensional heat diffusion model that describes the thermal performance of any wall, given a set of input parameters which include functions that characterise the spatial variability of the thermal conductivity and the volumetric heat capacity. We use in-situ measurements to calibrate the heat diffusion model via a sequential Bayesian framework that infers input parameters. We encode this framework in a computational algorithm that sequentially updates the probabilistic knowledge of the thermal properties as new measurements are assimilated, and thus enables an on-the-fly uncertainty analysis of averaged/effective properties such as the wall's U-value and the C-value. By means of virtual/synthetic and real experiments we show the capabilities of the proposed approach to (i) characterise the internal variability of the wall that can reveal existence of cavities and insulators potentially overlooked during visual inspections; and (ii) obtain rapid and accurate uncertainty estimates of effective thermal properties. We further use the proposed framework to investigate the potential detrimental effect of using coarse-grid approximations of heat diffusion models which are, in turn, the basis of most existing approaches that characterise effective thermal properties of walls.
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