Maximum likelihood estimation of a low-order building model

The aim of this paper is to investigate the accuracy of the estimates learned with an open loop model of a building whereas the data is actually collected in closed loop, which corresponds to the true exploitation of buildings. We propose a simple model based on an equivalent RC network whose parameters are physically interpretable. We also describe the maximum likelihood estimation of these parameters by the EM algorithm, and derive their statistical properties. The numerical experiments clearly show the potential of the method, in terms of accuracy and robustness. We emphasize the fact that the estimations are linked to the generating process for the observations, which includes the command system. For instance, the features of the building are correctly estimated if there is a significant gap between the heating and cooling setpoint.