Sensor placement and parameter identi?ability in grey-box models of building thermal behaviour

Building Energy Management systems can reduce energy consumption for space heating in existing buildings, by utilising Model Predictive Control. In such applications, good models of building thermal behaviour is important. A popular method for creating such models is creating Thermal networks, based cognitively on naive physical information about the building thermal behaviour. Such models have lumped parameters which must be calibrated from measured temperatures and weather conditions. Since the parameters are calibrated, it is important to study the identifiability of the parameters, prior to analysing them as physical constants derived from the building structure. By utilising a statistically founded parameter estimation method based on maximising the likelihood function, identifiability analysis can be performed using the Profile Likelihood method. In this paper, the effect of different sensor locations with respect to the buildings physical properties is studied by utilising likelihood profiles for identifiability analysis. The extended 2D profile likelihood method is used to compute two-dimensional profiles which allows diagnosing parameter inter-dependence, in addition to analysing the identifiability. The 2D profiles are compared with confidence regions computed based on the Hessian.