  We introduce a computational framework to statistically infer thermophysical
properties of any given wall from in-situ measurements of air temperature and
surface heat fluxes. The proposed framework uses these measurements, within a
Bayesian calibration approach, to sequentially infer input parameters of a
one-dimensional heat diffusion model that describes the thermal performance of
the wall. These inputs include spatially-variable functions that characterise
the thermal conductivity and the volumetric heat capacity of the wall. We
encode our computational framework in an algorithm that sequentially updates
our probabilistic knowledge of the thermophysical properties as new
measurements become available, and thus enables an on-the-fly uncertainty
quantification of these properties. In addition, the proposed algorithm enables
us to investigate the effect of the discretisation of the underlying heat
diffusion model on the accuracy of estimates of thermophysical properties and
the corresponding predictive distributions of heat flux. By means of
virtual/synthetic and real experiments we show the capabilities of the proposed
approach to (i) characterise heterogenous thermophysical properties associated
with, for example, unknown cavities and insulators; (ii) obtain rapid and
accurate uncertainty estimates of effective thermal properties (e.g. thermal
transmittance); and (iii) accurately compute an statistical description of the
thermal performance of the wall which is, in turn, crucial in evaluating
possible retrofit measures.
