Stochastic modelling of temperatures for a full-scale occupied building zone subject to natural random influences

Buildings are usually subject to a variety of stochastic influences. Though the deterministic approach to building thermal modelling is widespread, it cannot easily model the effects of such influences, and a different approach might be better. In this study, stochastic models are derived which describe the thermal behaviour of a full-scale room exposed to the naturally occurring disturbances of climate (temperature, solar irradiance, infiltration), occupancy and appliance usage. A Box-Jenkins time series analysis technique is employed, and univariate stochastic models are fitted to the internal and external air temperature series. The models are validated by comparing the observed temperature with values forecasted ahead (in steps of 1 h) by the models, over a 36-h period; agreement was found to be good. It is concluded that the stochastic modelling approach can be applied successfully to the thermal analysis of a building's behaviour, thereby affording a method which accounts for random influences in a compact model format. The technique has particular relevance to advanced model-based control implemented via [`]intelligent' digital controllers and building energy management systems, and its application in this respect is discussed.