A key challenge for intelligent domestic heating systems is to obtain sufficient knowledge of the thermal dynamics of the home to build an adaptive thermal model. We present a study where stochastic grey-box modelling is used to develop thermal models and an extended Kalman filter is used for parameter estimation for a room in a family hom

Alam, Muddasser

Aris-Athanasios, Panagopoulos

Jennings, Nicholas R.

Rogers, A.

Scott, James

English

Southampton (e-Prints Soton)

Poster Abstract: Applying Extended Kalman Filters to AdaptiveThermal Modelling in HomesMuddasser Alam, Athanasios Aris Panagopoulos, Alex Rogers, Nicholas R. JenningsUniversity of Southampton, UK.fmoody,ap1e13,acr,nrjg@ecs.soton.ac.ukJames ScottMicrosoft Research Cambridge, Cambridge, UK.jws@microsoft.comAbstractA key challenge for intelligent domestic heating systemsis to obtain sufﬁcient knowledge of the thermal dynamics ofthe home to build an adaptive thermal model. We presenta study where stochastic grey-box modelling is used to de-velop thermal models and an extended Kalman ﬁlter is usedfor parameter estimation for a room in a family home.1 IntroductionA key challenge for intelligent domestic heating systems(IDHS) is to obtain sufﬁcient knowledge of the thermal dy-namics of the home to build an adaptive thermal model thatcan reliably predict the spatial and temporal effects of its ac-tions. This challenge has been studied extensively for largebuildings where thermal models are maintained via the off-line or on-line learning. In the former, the thermal model islearned either once or at infrequent intervals and assumedto be ﬁxed over an arbitrary horizon. For example, Gaoet al. applies linear regression to historical data to learn aﬁxed thermal model of a room in an ofﬁce [1]. Likewise,Rogers et al. conducted a ﬁeld-study of 750 UK homesand used non-linear regression to infer the thermal modelof each home [3]. However, the assumption of a ﬁxed modelis inadequate in highly dynamic environments, and insteadthe on-line (or adaptive) learning where models are updatedcontinuously has been shown to be more effective. In par-ticular, variants of the extended Kalman ﬁlter (EKF) havebeen used for adaptive thermal modelling in buildings [2].Although, such techniques are equally applicable to modernhomes, one must consider the challenges peculiar to homes(e.g., more diverse heating systems, less reliable occupancypatterns, lack of structural data) for their effective use.Against this background, we propose an adaptive mod-Permission to make digital or hard copies of part or all of this work for personal orclassroom use is granted without fee provided that copies are not made or distributedfor proﬁt or commercial advantage and that copies bear this notice and the full citationon the ﬁrst page. Copyrights for third-party components of this work must be honored.For all other uses, contact the Owner/Author.Copyright is held by the owner/author(s).BuildSys’14, November 5–6, 2014, Memphis, TN, USA.ACM 978-1-4503-3144-9/14/11.http://dx.doi.org/10.1145/2674061.2675041elling approach based on stochastic grey-box modelling andthe EKF to infer thermal properties of homes. We apply it toa room in a family home and show that our thermal modelpredicts the room temperature where the 95th percentile ofthe absolute prediction error is 0:95C and 1:37C for 2 and4 hours predictions, respectively; in contrast to the corre-sponding 2:09C and 3:11C errors of the existing historical-average based thermal model (called PreHeat, see [4]).2 Case StudyWe consider the living room of a family house in Cam-bridge, UK, that is equipped with the per-room based under-ﬂoor heating which is controlled via a room unit. The roomunit has temperature and occupancy detection sensors, and aradio module to communicate with a PC (see [4]). The use ofunderﬂoor heating involves multiple heat transfers processeswhereby heat is transferred from the source to an intermedi-ate thermal mass (ﬂoor) that slowly leaks to its surroundings- introducing thermal lags and additional leakages, thus mak-ing this room interesting from a control perspective.3 Thermal ModellingWe adapt the grey-box modelling approach which usesthe prior physical knowledge of the system and observeddata to derive a thermal model. In our case, the prior knowl-edge of the room includes the (i) use of underﬂoor heating(ii) binary status of heating (iii) indoor air temperature and(iv) presence of considerable process noise. We note thatthere is no knowledge of the (i) heater output (ii) ﬂoor andhouse envelope temperature (iii) thermal capacities and re-sistance of the walls and (iv) the room layout (e.g., dimen-sion of the walls). These system states are considered hiddenand therefore must be inferred indirectly. We now outline anumber of increasingly complex thermal models.Single-Box Model (Ta) is the simplest model where thetransfer of heat is assumed to be direct between the heaterand the indoor air which then leaks to the outside. Here,no thermal delay for the heat transfer exists, enabling us tomeasure the effect of thermal delays in other models.ˆ Ta = Ta+rhlh+fao(To Ta) (1)Underﬂoor Heating Model (TaTf) models the transfer ofheat from the heater to the indoor air via an intermediaryPreHeat Ta TaTf TaTfTe00.511.522.533.542.093.111.422.181.211.831.101.73ModelsAbs.PredictionErr.−95thPercentile(°C)2 hours   predictions4 hours predictions(a) Comparative analysis of models2 4 6 8 10 12 14 16 18 20 22 2400.511.522.533.54Hour of DayAbs.PredictionErr.−95thPercentile(°C)2 Hours − TfTaTe4 Hours − TfTaTe2 Hours − TfTaTeS4 Hours − TfTaTeS(b) Effect of solar radiance on pred. errorTaS TaTfS TaTfTeS00.511.522.533.541.211.781.071.500.951.32ModelsAbs.PredictionErr.−95thPercentile(°C)2 hours predictions4 hours predictions(c) Thermal models with solar irradiancethermal mass (ﬂoor), thus introducing a thermal lag. Theindoor air then leaks heat to the outside.ˆ Tf = Tf +rhlh+ffa(Ta Tf) (2)ˆ Ta = Ta+ffa(Tf  Ta)+fao(To Ta) (3)Underﬂoor and Envelope Model (TaTfTe) extends TfTasuch that the heat escapes to outside via the house envelope.ˆ Tf = Tf +rhlh+ffa(Ta Tf) (4)ˆ Ta = Ta+ffa(Tf  Ta)+fae(Te Ta) (5)ˆ Te = Te+fae(Ta Te)+feo(To Te) (6)Complete Model (TaTfTeS) extends TfTaTeto include the ef-fect solar irradiation on ˆ Ta and ˆ Te.ˆ Tf = Tf +rhlh+ffa(Ta Tf) (7)ˆ Ta = Ta+rals+ffa(Tf  Ta)+fae(Te Ta) (8)ˆ Te = Te+rels+fae(Ta Te)+feo(To Te) (9)4 Empirical EvaluationWe use data from November, 2011 to March, 2012 (150days) which is sufﬁcient to evaluate our models for infre-quent events (e.g., turning off the heating for holidays) andthe effect of seasonal changes. We use publicly availabledata for the external temperature and solar irradiance1.While the time and accuracy requirements of prediction varybased on the system and its objectives, we ﬁnd that in ourcase, predicting 2 and 4 hours ahead with the accuracy of1C and 1:5C, is sufﬁcient for the effective heating con-trol. Thus, we analyse the absolute errors for 2 and 4 hourspredictions within 95th percentile (roughly corresponding tothe conﬁdence interval of 2 SD) of all models, as in Fig-ure 1(a). We note that as modelling increasingly capturesthe physical properties of the building, the prediction accu-racy increases further. To drive our model selection further,we analyse the nature of the prediction error with TfTeTf.Figure 1(b) shows the absolute prediction errors (95th per-centile) of TfTeTf against the hour of day. The error is rel-atively large during the daytime hours, hinting on the im-portance of solar irradiance. This is indeed the case (Fig-ure 1(b)) where the prediction accuracy improves when thesolar irradiance is factored in TfTeTfS, however, it is notcompletely eliminated in TfTeTfS as our solar irradiance data1https://www.cl.cam.ac.uk/research/dtg/weather/http://re.jrc.ec.europa.eu/pvgis/apps4/pvest.phpTimek k+1 UnitsFloor temperature Tf ˆ TfCRoom air temperature Ta ˆ TaCEnvelope temperature Te ˆ TeCExternal temperature To - CHeater output lh ˆ lhC/hrGlobal Solar Irradiance ls - J/m2/hrSolar Irradiance (Air) la - J/m2/hrSolar Irradiance (Envelope) le - J/m2/hrHeating time ratio rh - 2 [0;1]Irradiance ratio (Air) ra ˆ raC:m2/JIrradiance ratio (Envelope) re ˆ reC:m2/JLeakage rate (Floor, Air) ffa ˆ ffa 1/hrLeakage rate (Air, Outside) fao ˆ fao 1/hrLeakage rate (Air, Envelope) fae ˆ fae 1/hrLeakage rate (Envelope, Outside) feo ˆ feo 1/hrTable 1. Notation used for thermal modelling.consists of monthly averages and thus, can only be used asan approximation to the actual irradiance. Figure 1(b) con-ﬁrms that solar irradiance can make predictions more accu-rate but it does not indicate which of our models will beneﬁtthe most by it. Therefore, we include solar irradiance in allmodels and calculate the 95th percentiles of prediction errorfor every model, as in Figure 1(c). It is evident that the pre-diction errors of TfTeTfS meet our requirements and hence,no further model extension is required.5 Conclusions and Future WorkAdaptive thermal modelling techniques such as EKFs thatpreviously has been used in large buildings can also be usedin homes with necessary modiﬁcation to tackle the chal-lenges unique to homes. We demonstrated this technique fora room and showed that the EKF-based models can be use-ful for the efﬁcient control of heating. Our future work is toextend our model to selected homes.6 References[1] P. X. Gao and S. Keshav. Optimal Personal Comfort Management Us-ing SPOT+. In Proceedings of the Fifth ACM Workshop on EmbeddedSystems For Energy-Efﬁcient Buildings, pages 1–8. ACM, 2013.[2] X. Li and J. Wen. Review of building energy modeling for control andoperation. Renewable and Sustainable Energy, pages 517 – 537, 2014.[3] A. Rogers, S. Ghosh, R. Wilcock, and N. R. Jennings. A scalable low-cost solution to provide personalised home heating advice to house-holds. In Proceedings of the Fifth ACM Workshop on Embedded Sys-tems For Energy-Efﬁcient Buildings, pages 1–8. ACM, 2013.[4] J. Scott, A. Bernheim Brush, J. Krumm, B. Meyers, M. Hazas,S. Hodges, and N. Villar. Preheat: Controlling home heating usingoccupancy prediction. In Proceedings of the Thirteenth ACM Interna-tional Conference on Ubiquitous computing. ACM, 2011.

A scalable lowcost solution to provide personalised home heating advice to households.

Optimal Personal Comfort Management Using SPOT+.

Preheat: Controlling home heating using occupancy prediction.

Review of building energy modeling for control and operation. Renewable and Sustainable Energy,

Poster abstract. Applying extended kalman filters to adaptive
thermal modelling in homes

Poster abstract. Applying extended kalman filters to adaptive thermal modelling in homes

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