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We introduce a computational framework to statistically infer thermophysicalproperties of any given wall from in-situ measurements of air temperature andsurface heat fluxes. The proposed framework uses these measurements, within aBayesian calibration approach, to sequentially infer input parameters of aone-dimensional heat diffusion model that describes the thermal performance ofthe wall. These inputs include spatially-variable functions that characterisethe thermal conductivity and the volumetric heat capacity of the wall. Weencode our computational framework in an algorithm that sequentially updatesour probabilistic knowledge of the thermophysical properties as newmeasurements become available, and thus enables an on-the-fly uncertaintyquantification of these properties. In addition, the proposed algorithm enablesus to investigate the effect of the discretisation of the underlying heatdiffusion model on the accuracy of estimates of thermophysical properties andthe corresponding predictive distributions of heat flux. By means ofvirtual/synthetic and real experiments we show the capabilities of the proposedapproach to (i) characterise heterogenous thermophysical properties associatedwith, for example, unknown cavities and insulators; (ii) obtain rapid andaccurate uncertainty estimates of effective thermal properties (e.g. thermaltransmittance); and (iii) accurately compute an statistical description of thethermal performance of the wall which is, in turn, crucial in evaluatingpossible retrofit measures.

Quantifying uncertainty in thermal properties of walls by means of Bayesian inversion