Development of polynomial regression models for composite dynamic envelopes’ thermal performance forecasting

The building envelope’s insulating efficiency is always a key element regarding the energy consumption control of the whole building. This article aims to propose a simple method based on classic and fractional factorial simulation plans to obtain regression models in the form of polynomial functions that link the angle, the thermal conductivity and the thickness of each envelope’s component to the overall wall’s thermal resistance. Original software that combines classic and novel modeling techniques has been used in order to have a precise and validated numerical investigation that focuses in a variety of possible composite dynamic wall’s configurations. For the purposes of this study, the combined radiation/conduction heat transfer finite volume numerical model was updated complex enough to predict the temperature distribution and heat transfer in composite envelopes for a variety of inclination angles. The model takes into account the coupling between the solid conduction of both solid and fibrous systems and the gaseous conduction and radiation. The radiation heat transfer through each insulating layer has been modeled via the two flux approximation in order to take into account both optically thick and optically thin materials, as well as potential reflective surfaces currently used on composite wall’s applications. Different simulation scenarios have been conceived according to basic fractional factorial simulation plans in order to obtain valid empirical polynomial functions. To validate this statistical forecast system, many simulation scenarios were carried out and the statistical results are in compliance with the numerical simulations. The regression models’ results show that the error caused by simplification is acceptable in most conditions, and a lot of coupling calculation could be saved. Furthermore, the reduction of the complex numerical model to simple regression models in the form of polynomial equations aims to assist architects and engineers to directly obtain during the early design stages a high precision forecast of a composite envelope’s thermal performance without mobilizing an expert’s knowledge. Hence, having this knowledge they could optimize during the early design process the envelope’s performance in order to finally achieve an integrated building design.