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.

Automated summary

This paper proposes non-linear autoregressive models with exogenous inputs to model the air temperature in each room of a Danish school building. It introduces methods to estimate the solar radiation effect and the valve position of the radiator thermostats. The models are able to accurately predict the temperature 24 hours ahead and capture the variations in solar radiation and heat inputs.