Nonlinear system identification of thermal dynamics in buildings

Abstract

Abstract —Standard (black-box) linear regression modelsmay not necessarily sufce for accurate identication of thermaldynamics in buildings. This is particularly apparent when eithera radiant-heating (RH) system or a heating-ventilation-air-conditioning (HVAC) system is used for temperature controland the ow rate of the thermal medium varies signicantly.For this reason, this paper analytically derives, using physicalinsight, and investigates nonlinear regression models for systemidentication of thermal dynamics in buildings. The perfor-mance of these models is compared with standard (black-box)linear regression models through simulations. I. I NTRODUCTION Currently the increased demand for efcient use of elec-tricity in residential buildings requires efcient control designfor heating/cooling. Recently, there have been signicantefforts on designing efcient control strategies, usually basedon model-predictive control approaches [1], [2], [3], [4].However, an efcient control design requires rst an accuratesystem identication/prediction.In the optimal supervisory control formulation introducedin [1] for controlling residential buildings with an HVACsystem, a linear model is considered for modeling the over-all system dynamics. As pointed out in [1], including theactual dynamics might be complicated for the derivation ofoptimal control strategies. Similar is the assumption in thedynamic game formulation of HVAC thermally controlledbuildings in [5], where again a linear model is assumed forthe overall system. Keeping a balance between an accuratemodel description and the computational efcienc y in thederivation of optimal control strategies seems to be a greatchallenge.Most system identication schemes for buildings usuallyadopt linear transfer functions, such as standard ARX andARMAX black-box model structures (cf., [6]). Examplesof such implementations include, for example, the MIMOARMAX model in [7] and the nonlinear neural networkapproach in [8]. In reference [9], a comparison is performedbetween standard linear ARX models with two time-scaletransfer models, which according to the authors better rep-resent thermal models. Indeed, the operation of either anRH system or an HVAC system usually takes place in afaster time-scale than the room dynamics, an observationthat was also utilized for the derivation of a nonlinear modelpredictive controller in [4].