Identification of non-linear autoregressive models with exogenous inputs for room air temperature modelling

This paper proposes non-linear autoregressive models with exogenous inputs to model the air temperature in each room of a Danish school building connected to the local district heating network. To obtain satisfactory models, the authors find it necessary to estimate the solar radiation effect as a function of the time of the day using a B-spline basis expansion. Furthermore, this paper proposes a method for estimating the valve position of the radiator thermostats in each room using modified Hermite polynomials to ensure monotonicity of the estimated curve. The non-linearities require a modification in the estimation procedure: Some parameters are estimated in an outer optimisation, while the usual regression parameters are estimated in an inner optimisation. The models are able to simulate the temperature 24 h ahead with a root-mean-square-error of the predictions between 0.25 degrees C and 0.6 degrees C. The models seem to capture the solar radiation gain in a way aligned with expectations. The estimated thermostatic valve functions also seem to capture the important variations of the individual room heat inputs.