Parameter estimation for externally simulated thermal network models

• Published in: Energy and buildings 2019-05, Vol.191, p.200-210
• Main Authors: Brastein, O.M., Lie, B., Sharma, R., Skeie, N.-O.
• Format: Article
• Language: English
• Subjects: Circuits; Computer simulation; Dynamic models; Electric filters; Ensemble Kalman filter; Extended Kalman filter; Grey-box models; Jacobians; Kalman filters; Parameter estimation; Parameter identification; Profile likelihood; Statistical analysis; Stochastic differential equations; Stochastic models; Stochasticity; Thermal network models; Thermal simulation; Thermodynamic properties; Topology; Unscented Kalman filter
• ISSN: 0378-7788; 1872-6178
• DOI: 10.1016/j.enbuild.2019.03.018

•Building thermal behaviour is modelled as a thermal network RC-circuit equivalent.•The model is implemented as a component list and simulated in an external simulator.•Parameters are estimated by maximising the likelihood function based on residuals computed in a Kalman Filters.•The externally simulated model requires a Kalman filter implementation that can handle non-differentiable models.•Unscented and Ensemble Kalman filters are tested and compared.•Identifiability of parameters is analysed using the Profile Likelihood method.•Profile likelihood is extended to analyse 2D profiles which allows for identification of parameter interdependence. Obtaining accurate dynamic models of building thermal behaviour requires a statistically solid foundation for estimating unknown parameters. This is especially important for thermal network grey-box models, since all their parameters normally need to be estimated from data. One attractive solution is to maximise the likelihood function, under the assumption of Gaussian distributed residuals. This technique was developed previously and implemented in the Continuous Time Stochastic Modelling framework, where an Extended Kalman Filter is used to compute residuals and their covariances. The main result of this paper is a similar method applied to a thermal network grey-box model of a building, simulated as an electric circuit in an external tool. The model is described as a list of interconnected components without deriving explicit equations. Since this model implementation is not differentiable, an alternative Kalman filter formulation is needed. The Unscented and Ensemble Kalman Filters are designed to handle non-linear models without using Jacobians, and can therefore also be used with models in a non-differentiable form. Both Kalman filter implementations are tested and compared with respect to estimation accuracy and computation time. The Profile Likelihood method is used to analyse structural and practical parameter identifiability. This method is extended to compute two-dimensional profiles, which can also be used to analyse parameter interdependence by providing insight into the parameter space topology.