Roof components models simplification via statistical linearisation and model reduction techniques

This paper addresses the simplification of detailed models for predicting the thermal behaviour and the cooling performance of buildings roof components designed on the basis of evaporative and radiative cooling principles. Detailed models usually consist in a large set of non-linear ordinary differential equations whose integration requires a lot of time compared with the one needed for thermal analysis of conventional buildings. For natural roof cooling techniques to be taken into account in the building design process, simplifying such models is hence required. This paper presents a rigorous and systematic procedure for simplifying detailed roof models: in a first phase, statistical linearisation techniques are applied for going from an original model including N non-linear ordinary differential equations to one equivalent linear model formed by N linear ordinary differential equations; in a second one, model reduction techniques are applied for replacing the equivalent linear model before by a set of nmuch less-thanN linear ordinary differential equations. The proposed methodology has been applied to a detailed roof planted model.