A novel parametric spectral technique to solve inverse heat problems for the estimation of wall thermophysical properties

Determining the thermophysical properties of building walls, such as thermal conductivity and heat capacity, is critical for assessing energy performance and optimizing thermal efficiency. This work presents a novel approach for estimating these properties by combining a gradient-based method with a parametric spectral reduced order model. The solution of the direct problem is decomposed according to space, time and the diffusivity. Then, this parametric model is used to compute off-line the iso-lines of the cost function gradient. It enables a faster convergence of the inverse problem algorithm. To evaluate the proposed technique, a benchmark is considered using synthetic data, ensuring a controlled environment for testing accuracy and robustness. Then, a real case-study in a historical wall is considered to retrieve the thermal conductivity of each layer based on temperature measurement obtained during a one-year monitoring. The results indicate that this method offers substantial potential for applications in building diagnostics and energy efficiency evaluation, providing a reliable tool for characterizing wall thermophysical properties in various structural contexts.

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