Estimation of thermal impulse response of a multi-layer building wall through in-situ experimental measurements in a dynamic regime with applications

Abstract

The dynamic thermal characteristics of the components of a building have a primary influence on the energy performance of the building's envelope under real environmental conditions. In this study, a novel approach for estimation of the thermal impulse response (TIR) functions and determination of the dynamic thermal characteristics of a multilayer facade wall with unknown thermal properties, structure, and dimensions is proposed. Unlike existing approaches, such as those presented by Luo et al. (2010) and Fernandes et al. (2015), which are based on the use of known physical parameters and dimensions of the considered structure for determination of the transfer function, the proposed framework is based solely on data from in-situ experimental measurements of surface temperatures and thermal fluxes through the inner and outer wall surfaces in a dynamic regime. Consequently, the estimated TIR functions and dynamic thermal characteristics reflect the actual physical conditions of the considered building wall. The building wall is modelled as a two-input, two-output linear time invariant (LTI) dynamic system where the surface temperatures and fluxes from both sides are used as system inputs and outputs, respectively. The input and output quantities are related by the convolution integrals and TIR functions. The TIR functions are obtained using the measured data and the least square estimator. As the corresponding system of linear equations is ill-posed, the Tikhonov regularization technique with a single parameter is implemented to overcome the numerical difficulties. The optimal regularization parameter is obtained using the L-curve approach. The estimated TIR functions are validated by comparison with the analytical solutions. The dynamic thermal characteristics of the considered building wall with unknown parameters are determined using the Fourier transform (FT) of the estimated TIR functions. The practical applications of the estimated TIR functions related to the energy performance of buildings (EPB) and energy efficiency, along with additional validation, are demonstrated by the evaluation of the dynamic thermal characteristics, cumulative heat losses, heat accumulation, conductive part of thermal transmittance (U-value), and surface heat fluxes, using only the estimated TIR functions and a control set of the experimental data.