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

Abstract

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.

Adaptive regularisation for ensemble Kalman inversion

“…which, from (15), yields constraint (12). Noting that the selection of α −1 n in (14) is determined by the data misfit of the particles, we refer to our regularisation strategy as the data misfit controller (DMC).…”

“…For further details we refer the reader to [16], where the selection of α n according to (23) was implemented in a batch-sequential EKI framework to sequentially solve an inverse problem that arises in resin transfer moulding. The same EKI methodology was applied in [15] for parameter identification of the heat equation, including identification of thermal conductivity and heat capacitance given boundary measurement of heat flux. Both time-dependent applications tackled in [15,16] involved the inversion of small number of measurements (e.g.…”

“…The same EKI methodology was applied in [15] for parameter identification of the heat equation, including identification of thermal conductivity and heat capacitance given boundary measurement of heat flux. Both time-dependent applications tackled in [15,16] involved the inversion of small number of measurements (e.g. <30) at each observation time, and with relatively large noise informed by measurement protocols.…”

Estimation of depth-resolved profiles of soil thermal diffusivity from temperature time series and uncertainty quantification

“…Huang et al (2017) have derived the heat conductivity in the layer between the atmosphere and the soil surface, Choi et al (2018) have inferred soil thermal conductivity from a thermal response test, and Tran et al (2016) have inferred organic matter content from soil temperature, liquid water, and apparent resistivity data. Bayesian inference has been more widely applied in engineering (Kaipio and Fox, 2011) to estimate thermal properties of fins (Gnanasekaran and Balaji, 2013;Somasundharam and Reddy, 2017) and walls (De Simon et al, 2018;Rodler et al, 2019). While the above studies have shown promise in estimating thermal properties from time series of temperature, several challenges still remain, including the need for an approach that can assess the conditions under which such estimates are reliable.…”

Estimation of the thermal resistance of a building wall with inverse techniques based on rapid active in situ measurements and white-box or ARX black-box models

“…Biddulph et al [49] proposed a method using Bayesian inference to estimate the parameters and this method was improved by Gori et al [50] [51]. De Simon et al [52] also applied Bayesian inference to quantify the estimation uncertainty of thermophysical properties of walls. Bienvenido et al [53] developed a multilayer perceptron to estimate the U -value with the correction for storage effects.…”