Energy and Buildings 76 (2014) 81–91 Contents lists available at ScienceDirect Energy and Buildings j ourna l ho me page: www.elsevier.com/locate/enbuild Calibration of building thermal models using an optimal control approach Alexandre Nassiopoulos a,∗ , Raphaël Kuate b , Frédéric Bourquin b a LUNAM Université, IFSTTAR, COSYS, F-44344 Bouguenais, France b Université Paris-Est, IFSTTAR, COSYS, F-77447 Marne la Vallée, France a r t i c l e i n f o Article history: Received 30 September 2013 Received in revised form 20 December 2013 Accepted 19 February 2014 Available online 4 March 2014 Keywords: Energy performance monitoring Model identification Optimization Optimal control a b s t r a c t The prediction of a building’s thermal behaviour within a short time horizon is necessary in many energy management applications. A numerical model can serve this purpose provided a good accuracy is obtained through a suitable calibration procedure. The paper deals with a model calibration procedure based on short-time on-site and weather measurements. It builds upon optimal control theory: an adjoint model is introduced to derive the gradient of a least squares cost function at a low computational cost. Two problems are solved. The first one is a non-linear model training problem. It consists in identifying the main influencing parameters of the system of partial differential equations that form the tendency model. The second problem is a linear identification problem that consists in identifying the unknown internal gains. This second problem can be solved in real-time in a continuous monitoring process. Both problems are solved within the same framework and same tools, illustrating the efficiency of the optimal control tools in this context. We give simulation results that show the performance of the calibration procedure under uncertainties on input parameters. © 2014 Elsevier B.V. All rights reserved. 1. Introduction The accurate prediction of the evolution of the thermal state of a building within a time horizon of a few hours is of great importance in energy management applications [1,2]. Examples of such techniques include a wide range of approaches such as artifi- cial intelligence-based techniques [3], model predictive control or demand-response applications. Model predictive control consists in computing optimal heating or cooling strategies by taking into account the future evolution of the state of the building under fore- cast weather or use conditions [4,5]. Demand response strategies in smart grids consist in adjusting energy demand at the end-user level to reduce the overall demand thus resulting in end-user cus- tomer bill savings, increase of electricity market stability and of electricity supply reliability [6]. Such a prediction can be obtained using a numerical model that implement the most predominant phenomena explaining the evo- lution of the thermal state. However, modelling simplifications and uncertainties concerning building characteristics such as geome- try or material properties usually lead to discrepancies between ∗ Corresponding author. Tel.: +33 240845919. E-mail addresses: alexandre.nassiopoulos@ifsttar.fr (A. Nassiopoulos), raphael.kuate@ifsttar.fr (R. Kuate), frederic.bourquin@ifsttar.fr (F. Bourquin). the model predictions and the real performance. The desired model response can be obtained if the internal parameters of the model are calibrated using on-site measurements and model identification methods [7,8]. This paper deals with an identification methodology used for the calibration of a building energy model based on short-term mea- surements of indoors and outdoors temperature, heat consumption and total solar radiation. In order to be compatible with a large scale deployment the model described here was designed to rely on very simple end-user provided data such as floor area, envelope surface, windows surface, orientation and composition of the wall. The cal- ibrated model performance was assessed under large uncertainties on these data. There exists a wide literature dealing with the identification of building models. Regression techniques like ARX or ARMAX have been used with success for the prediction of temperature evolu- tion in buildings [9]. Several works report on the use of neural networks for model training (see [10–12] for instance). This kind of approaches is often referred to as black-box modelling approaches, even if some attempts to introduce physical knowledge blur the frontiers of the classification, like in [13] for instance. Their main disadvantage is the long measurement periods needed to derive the desired model. The so-called “grey-box” modelling approaches combine phys- ical considerations and experimental data. Madsen and Holtst [14] http://dx.doi.org/10.1016/j.enbuild.2014.02.052 0378-7788/© 2014 Elsevier B.V. All rights reserved.