Identifying building envelope thermal properties from the calibration of a lumped model raises identifiability issues. Not only needs the simplified model to be structurally identifiable, i.e. deliver unique estimates after calibration, but also the data used might not be informative enough to result in either or both accurate estimates and physically interpretable values. This could particularly be the case when data is extracted from non intrusive in situ measurements, in the sense not disturbing potential occupancy. In this frame, this paper develops a method to investigate the physical interpretation of the parameters of lumped models through a numerical tests procedure. Each test runs a simulation of a comprehensive thermal model of a building, with variations in thermal resistance properties of the envelope. Each simulation delivers data used to calibrate a lumped model. The parameters of the lumped model are then physically interpretable if their value vary according to the variations of the comprehensive model. The overall test procedure is applied to the study of a 2R2C model. Results show that the calibration of this model delivers robust calibration results for all parameters but one and also shows satisfactory robustness of the estimation of the overall thermal resistance. This paper concludes that the numerical test procedure does allow to evaluate practical identifiability of lumped models, and will in future work be used to examine more complex lumped model

Foucquier, Aurélie

Fraisse, Gilles

Juricic, Sarah

Rouchier, Simon

English

Syracuse University Research Facility and Collaborative Environment

Healthy, Intelligent and Resilient Buildings and Urban Environments7th International Building Physics ConferenceProceedingsibpc2018.org    #ibpc2018Evaluation of the physical interpretability of calibrated building model parametersSarah Juricic1,*, Simon Rouchier1, Aurélie Foucquier2 and Gilles Fraisse1 1Univ. Grenoble Alpes, Univ. Savoie Mont-Blanc,  CNRS, LOCIE, 73000 Chambéry France 2Univ Grenoble Alpes, CEA, LITEN, DTS, INES, F-38000 Grenoble, France*Corresponding email: sarah.juricic@univ-smb.frABSTRACTIdentifying building envelope thermal properties from the calibration of a lumped model raises identifiability issues. Not only needs the simplified model to be structurally identifiable, i.e. deliver unique estimates after calibration, but also the data used might not be informative enough to result in either or both accurate estimates and physically interpretable values. This could particularly be the case when data is extracted from non intrusive in situ measurements, in the sense not disturbing potential occupancy. In this frame, this paper develops a method to investigate the physical interpretation of the parameters of lumped models through a numerical tests procedure. Each test runs a simulation of a comprehensive thermal model of a building, with variations in  thermal resistance properties of the envelope. Each simulation delivers data used to calibrate a lumped model. The parameters of the lumped model are then physically interpretable if their value vary according to the variations of the comprehensive model. The overall test procedure is applied to the study of a 2R2C model. Results show that the calibration of this model delivers robust calibration results for all parameters but one and also shows satisfactory robustness of the estimation of the overall thermal resistance. This paper concludes that the numerical test procedure does allow to evaluate practical identifiability of lumped models, and will in future work be used to examine more complex lumped models.KEYWORDS Practical identifiability, Parameter estimation, Model calibration, Lumped models INTRODUCTIONA major lever for decreasing energy consumption in both newly built and existing buildings would be to accurately estimate, in situ, the building envelope thermal performance. Delivering valuable information on that performance relies then on an accurate, detailed  and robust analysis of the building’s envelope. Methods such as the coheating test, QUB or ISABELE methods  (Sonderegger 1978; Mangematin et al 2012; Schetelat and Bouchié 2014) deliver a satisfyingly accurate Heat Loss Coefficient of the envelope, but cannot identify weaker parts of the building’s envelope on which concentrate retrofit efforts. Furthermore, these methods are hardly applicable for in-use buildings as they rely on a lot of measurement equipment and require inoccupancy for a period from a few days to a few weeks. Recent literature (Reynders, Diriken, and Saelens 2014; Deconinck and Roels 2017; Menberg, Heo, and Choudhary 2017) has focused on calibrating dynamic simplified thermal models in the hope of physically interpreting calibrated parameters. It showed that the overall Heat Loss Coefficients may be robustly estimated, but that in the particular settings studied, thermal properties of each layer of the envelope could not. This paper presents a method that assesses how each parameter of a lumped model truly represents the building envelope. The method is first described and then applied to a 2R2C lumped model.11997th International Building Physics Conference, IBPC2018METHODS Overview of the numerical test procedureTo test different envelope settings, the method is based on an entirely numerical study. Givenknown weather boundary conditions, a comprehensive model defined in EnergyPlus (Figure 1:  I)  is  written  in  N versions  representing  as  many envelope settings  to  test.  Each settinggenerates  a  thermal  dynamic  simulation.  Each  simulation  returns  an  indoor  temperatureprofile (Figure 1 : II) from which 5 days data in January are extracted. Noise from a normaldistribution  N(0,0.2)  is  then  added to  the data.  The third step  is  to  calibrate  the  selectedlumped  model  ,  i.e.  fit  it  to  the  noisy data  (Figure  1  :  III).  The  objective  of  the  overallprocedure is then to study the variability of the calibrated parameters (Figure 1 : IV) : do theestimations of the parameters vary according to the changes made in the original completethermal  model?  In  other  words,  to  what  extent  are  the  parameters  of  an  RC  modelrepresentative of the physical thermal properties of the original comprehensive model?Figure 1: Numerical test procedureSpecific settings of this case studyThe comprehensive model used in this  work is based on a Bestest 600 case  (Judkoff andNeymark  1995) equipped  with  a  convective  electric  heater  and  no  air  infiltration  norventilation. Window area is 3 m2 to avoid the overheating from the original Bestest scenario.Indoor temperature setpoint schedules are set to reach 17°C at night and 20°C during the day.Table 1: Design of experiments used in this study. From left to right, the envelope is poorly tohighly insulatedExperiment number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Wall insulation (cm) 5 5 5 5 5 5 5 5 20 20 20 20 20 20 20 20Roof insulation (cm) 5 5 5 5 20 20 20 20 5 5 5 5 20 20 20 20Window air gap (mm) 4 4 20 20 4 4 20 20 4 4 20 20 4 4 20 20Floor insulation (K/W) 10 25 10 25 10 25 10 25 10 25 10 25 10 25 10 25We  choose  for  a  design  of  experiments,  as  suggested  in  (Iooss  2011).  The  thermal comprehensive model therefore undergoes four different changes in insulation thicknesses, ground floor thermal resistance and double pane glazing air gap thickness. This design of experiment is therefore intended to only assess the influence of thermal resistance properties. Each parameter takes two possible values as shown in Table 1 and a full factorial design is run, i.e. 16 different configurations.12007th International Building Physics Conference, IBPC2018In the present paper,  we apply the method to the calibration and study of a 2R2C model(Figure 2). As for any model calibration, the structural identifiability of the 2R2C model hasto be checked and it has been found structurally identifiable (Bellu et al. 2007). This meansthat, in theory, there exists only one set of parameter values towards which the calibrationalgorithm will converge.Figure  2: Model 2R2C. In  blue the model output, in orange the model inputs, in black theunknown parameters and state variablesEach model is calibrated by bayesian inference (Figure 1 III), where the parameters and the unknowns are considered to be probability distributions. Calibrating the model then means determining the parameters probability distributions given the available data, also known as posterior distributions. The literal expressions of the posterior distributions cannot be known and  are  therefore  sampled  by  an  adaptive  Metropolis  algorithm  (Haario,  Saksman,  and Tamminen 2001). Each parameter distributions can then be plotted with a boxplot as in Figure 1  IV,  showing  the  most  probable  value,  its  standard  deviation  and  its  95%  confidence intervals.RESULTSContribution of envelope properties to the calibrated parametersEstimations of all five parameters of the 2R2C model for each experiment setting are shown in Figure 3.Resistance parameters Rext and Rint in  Figure 3 (a) vary differently. Rext shows a significant correlation  with the  thermal  properties  variations  in  the  experiment,  whereas  Rint is  quite steady  and  takes  values  between  4.10-4 and  9.10-4  K/W.  From  this  experiment  could  be inferred that Rext actually represents the thermal resistance of the envelope itself. Rint might rather represent the resistive air layer at the indoor surface, which is theoretically in the range [8.10-4 K/W , 13.10-4 K/W].The solar  coefficient  Asol estimation  in  Figure 3 (b)  is  also significantly  correlated  to  the thermal resistance properties of the building envelope. The better the insulation, the lower the parameter estimation. Ground floor insulation or window air gap show however no significant influence on the value taken by the solar coefficient Asol. This result is not coherent with the expectation that this parameter should not vary with thermal properties. We indeed expect it to be physically related to window orientation and size, that are not changed in this design of experiments. We explain this unexpected result first by the fact that the 2R2C lumped model is quite simplistic and might not be entirely interpretable when fitted to data. Also, the solar irradiation and the indoor-outdoor temperature differences are probably partially correlated to begin with. A different indoor temperature setpoint schedule and/or adding a shading schedule might give better interpretability of the Asol parameter.Figure 3 (c) shows that the thermal capacity parameter Cext is not significantly varying with the different  experiment  settings,  which is  the expected  result.  Indeed,  the comprehensive model is one of the Bestest low thermal inertia scenarii  and has indoor insulation.  As the12017th International Building Physics Conference, IBPC2018experiments  only varied thermal  resistance properties,  the thermal  capacity  is  expected toremain steady. Compared to the values taken by the thermal capacity Cint in Figure 3 (d), Cextseems to represent the thermal capacity of the envelope itself. Noteworthy is that C int takesvalues indicating that it could represent the indoor air thermal capacity, but with extremelylarge confidence intervals. This shows that this parameter is poorly identifiable, meaning thatits exact value cannot be inferred from these results. Data with more frequent measurements,every 1 to 5 min instead of 10 min, might enhance its identifiability though.Robustness of overall thermal resistance of the envelopeAn equivalent resistance Req can be calculated from the estimation of both resistances of the 2R2C model : Req = Rext + Rint. The equivalent resistance Req may then be compared to a theoretical overall thermal resistance Rth of the comprehensive model envelope.From Figure 4 can be seen that fitting the 2R2C model gives a satisfactory estimation of Req (mean error up to 6,5 %). In the case of a highly insulated envelope (experiments 9 to 16), the error to the theoretical value is higher than with poorly insulated envelopes (experiments 1 to 8), especially when the ground floor is poorly insulated, for example in the experiments 13 orFigure 3: Variation of all 5 parameters of the lumped model with the experiments settings12027th International Building Physics Conference, IBPC201815. The 2R2C model  does not  include any term representing the  losses  to the  ground todifferentiate  them from the losses to the ambient  air.  So as soon as losses to the groundbecome significant compared to losses to the ambient air, the resistances of the model take thelosses to the ground into account. This needs to be considered when comparing the estimatedequivalent resistance of the building to a target value from a norm or a regulation, as in theorylosses to the ground are not taken into account in the theoretical calculations.DISCUSSIONFirst of all, the methodology applied to a 2R2C model showed that the parameter estimation converged towards unique estimates, except for parameter Cint. This stresses out that theoretical identifiability is necessary but not sufficient. The data here is not informative enough for  the parameter Cint. It is however sufficient to uniquely estimate values for the other parameters, which is promising for future work where data from occupied buildings are used. Indeed, this shows that major temperature differences, as seen in Schetelat and Bouchié (2014) or in Mangematin et al (2012) are not necessary to identify thermal properties of a building envelope. Additionnaly, it would be interesting to study the robustness of the results with fewer days data. In particular, one could study the influence of outdoor conditions which might particularly affect the results when the model is fitted on fewer days. We refer here to (Juricic et al. 2018).Secondly, the study showed that the estimates could be, to a certain extent, identified with true thermal properties of the envelope. Rext and Cext have been found representing the envelope thermal properties itself, whereas Rint and Cint were found rather related to properties of the indoor air.  It seems though that this model cannot identify thermal properties of layers inside the envelope. It would be interesting to study how parameters of more complex models can be identified  to  different  envelope  layers,  starting  with  3R3C  models.  At  the  same  time, estimating the overall thermal resistance in these conditions shows satisfactory robustness, unless ground floor insulation is much poorer than envelope insulation, which would rarely happen  in  existing  buildings  though.  This  result  is  promising  when  considering  testing existing buildings for regulatory purposes. Compared to Deconinck and Roels (2017) who found poor identifiability in all of the tested RC models for a cavity wall in winter, this case study studies the whole envelope has quite different boundary conditions which is probably why the parameters here were found to be identifiable even in winter. The work of Deconinck & Roels however suggests, by extrapolation, that estimations from the 3R3C model should be more trustworthy.Figure 4: Estimation of the overall thermal resistance : agreement to the theoretical value12037th International Building Physics Conference, IBPC2018Finally, if a design of experiments approach was coherent with the goal of this study, furtherwork should focus on variations of many more envelope properties of the reference building.A  preferable  approach  will  be  to  use  sensitivity  analysis  tools,  namely  the  RBD-FASTvariance  decomposition  approach,  allowing at  the same time an efficient  parameter  spaceexploration and a more detailed study of the parameters interactions.CONCLUSIONSThis  paper  shows  how  the  numerical  tests  procedure  allows  to  evaluate  practicalidentifiability, i.e. interpretability of model parameters. Future work will focus on differentcomprehensive models, starting with scenarii with heavier thermal mass, on more complexlumped models in the hope of distinguishing contributions of separate parts of the envelopeand  finally  on  combining  this  methodology  with  a  study  of  the  influence  of  boundaryconditions on identifiability.ACKNOWLEDGEMENTThe authors would like to thank the ANR-15-CE22-0003 BAYREB funding which has madethis work possible. All results of the project are online at locie.github.io/bayreb.REFERENCESBellu,  Giuseppina,  Maria  Pia  Saccomani,  Stefania  Audoly,  and  Leontina  D’Angiò.  2007.“DAISY:  A  New  Software  Tool  to  Test  Global  Identifiability  of  Biological  andPhysiological Systems.” Computer Methods and Programs in Biomedicine 88 (1):52–61Deconinck, An-Heleen, and Staf Roels. 2017. “Is Stochastic Grey-Box Modelling Suited forPhysical Properties Estimation of Building Components from on-Site Measurements?”Journal of Building Physics, FebruaryHaario,  Heikki,  Eero  Saksman,  and  Johanna  Tamminen.  2001.  “An Adaptive  MetropolisAlgorithm.” BernoulliIooss, Bertrand. 2011. “Revue Sur l’analyse de Sensibilité Globale de Modèles Numériques.”Journal de La Société Française de StatistiqueJudkoff,  Ron,  and  Joel  Neymark.  1995.  “International  Energy  Agency  Building  EnergySimulation Test (BESTEST) and Diagnostic Model.”Juricic, Sarah, Jeanne Goffart, Simon Rouchier, Aurélie Foucquier, and Gilles Fraisse. 2018.“Impact  de La Variabilité  Naturelle Des Conditions Météorologiques Sur l’estimationDes  Paramètres :  Application  Aux  Modèles  RC.”  In  Conférence  Francophone  del’International Building Performance Simulation Association, 1–8. Bordeaux.Mangematin,  Eric,  Guillaume Pandraud, and Didier Roux. 2012. “Quick Measurements ofEnergy Efficiency of Buildings.” Comptes Rendus Physique 13:383–90Menberg, Kathrin, Yeonsook Heo, and Ruchi Choudhary. 2017. “Efficiency and Reliability ofBayesian Calibration  of Energy Supply System Models.” In  Proceedings  of the 15thIBPSA Conference San Francisco, CA, USA, 1594–1603.Reynders,  Glenn,  J.  Diriken,  and Dirk  Saelens.  2014.  “Quality  of  Grey-Box Models  andIdentified Parameters as Function of the Accuracy of Input and Observation Signals.”Energy and Buildings 82 (0):263–74Schetelat,  Pascal,  and  Rémi  Bouchié.  2014.  “ISABELE :  A  Method  for  PerformanceAssessment  at  Acceptance  Stage  Using  Bayesian  Calibration.”  9th  InternationalConference on System Simulation in Buildings 1 (1):1–16.Sonderegger,  Robert.  1978.  “Diagnostic  Tests  Determining  the  Thermal  Response  of  aHouse.” In ASHRAE Meeting. Atlanta.12047th International Building Physics Conference, IBPC2018

Evaluation of the physical interpretability of calibrated building model parameters

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Evaluation of the physical interpretability of calibrated building model parameters

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