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Parameter identification of a Round-Robin test box model using a
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deterministic and probabilistic methodology
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Authors
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Marta Fernández * a, Borja Conde b, Pablo Eguía a, Enrique Granada a
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a
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b
University of Vigo, School of Industrial Engineering, Department of Mechanical Engineering, Heat Engines and Fluid Mechanics, 36310 Vigo (Spain).
University of Vigo, School of Industrial Engineering, Department of Engineering Materials, Applied Mechanics and Construction, 36310 Vigo (Spain).
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E-mails:
[email protected],
[email protected]
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Tel: +34986818624
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* Corresponding Author
[email protected],
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[email protected],
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Abstract
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In this paper, two different methodologies are applied to the parameter estimation
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problem of a computational model of a Round-Robin test box. The numerical
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model is developed using TRNSYS. A global sensitivity analysis is carried out to
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determine the most important parameters that should be considered in the
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subsequent calibration procedure. Using the Bayesian (probabilistic) approach, the
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posterior distribution of the unknown input parameters is estimated via simulation
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techniques. Using the deterministic approach, executed in GenOpt, the calibration
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is performed by the minimization of an objective function that measures the
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differences between model predictions and real measured data. Parameter
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estimation results obtained with both methodologies are then compared and
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discussed. A reduction of the Coefficient of Variation of the Root Mean Square
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Error (CV (RMSE)) after calibration over 40% with both methods has been
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obtained, being the CV (RMSE) for calibration and validation periods on average
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3.21% and 2.40%, respectively.
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Keywords: Model calibration, Bayesian inference, Optimization, Round-Robin test box.
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Nomenclature:
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GSA: Global Sensitivity Analysis
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GPS: Generalized Pattern Search
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IEA: International Energy Agency
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EBC: Energy in Buildings and Communities’ program
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RMSE: Root Mean Square Error
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CV (RMSE): Coefficient of Variation of the Root Mean Square Error
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LHS: Latin Hypercube Sampling
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MCMC: Markov Chain Monte Carlo
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CoV: Coefficient of Variation
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PDF: Probability Density Function
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BEPS: Building Energy Performance Simulation
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BACCO: Bayesian Analysis of Computer Code Outputs
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MAE: Mean Absolute Error index
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R2: Coefficient of determination
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1. Introduction
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The European Union (EU) has as an overriding goal to reduce energy consumption by
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2020. The building sector is being put through restrictive regulations because this sector
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accounts for 40% of the EU’s total energy consumption and furthermore implies a
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significant potential for reducing CO2 emissions ("Directive 2010/31/EU of the European
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Parliament and of the Council of 19 May 2010 on the energy performance of buildings").
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Therefore, it has become necessary to be able to faithfully determine and control, as far
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as possible, the energy consumption in buildings, both in the design phase and under
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occupancy conditions.
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In this context, currently, Building Energy Performance Simulation (BEPS) tools are
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gaining more and more importance. Several authors have used different available BEPS
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software such as TRNSYS, Energy Plus, DOE-2 or ESP-r. (Dutta, Samanta, and Neogi
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2017; Martínez-Ibernón et al. 2016; Ciulla, Lo Brano, and D'Amico 2016; Barbaresi et
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al. 2017; Loonen et al. 2017; Delcroix, Kummert, and Daoud 2017). Thus, it has been
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proven that the abovementioned software yields satisfactory results. Using these tools, a
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model of the building is obtained, with both constructive features and internal loads due
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to normal operation. That model is simulated in a transitory regime, acquiring a highly
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reliable evaluation of the dynamic behaviour of the building.
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However, simulation is not always a true reflection of reality because the modeller has to
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rely on his own experience and knowledge to make several assumptions while developing
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the simulation model, what is not a negligible effect as previous studies indicate
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(Berkeley, Haves, and Kolderup 2014; Guyon 1997). This includes, among others, the
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need of dealing with unknown model inputs (parameter uncertainty) and the need of
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performing unavoidable modelling simplifications when approximating the complex real
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system behaviour (model inadequacy). Hence, building simulations need to be adjusted
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so that the observed data (energy consumption, inside air conditions, etc.) match with the
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prediction of the simulation tool (Kim and Park 2016; Reddy, Maor, and Panjapornpon
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2007; Clarke, Strachan, and Pernot 1993; Jiménez, Porcar, and Heras 2009). This is
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commonly known as model calibration, model updating or also parameter identification
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problem since usually, the main objective is related to obtaining suitable estimates for the
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unknown parameters so that differences between the model predictions and the field
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observations are as low as possible.
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Nonetheless, there is a lack of agreement when it comes to calibration methodologies. In
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general, it is possible to distinguish three major approaches (Kim and Park 2016): manual,
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deterministic (based on mathematical optimization), and probabilistic (based on the
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Bayes’ theorem); which, indeed, may even be grouped in two main categories: manual
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and automated methods (Coakley, Raftery, and Keane 2014). In the manual approach, the
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modeller tries to estimate, mainly through an iterative search, a set of parameter values
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that results in a reasonable agreement of the model output with the real observed data
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(Pan, Huang, and Wu 2007; Raftery, Keane, and O’Donnell 2011; Mustafaraj et al. 2014;
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Royapoor and Roskilly 2015). However, the main drawbacks associated with this
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approach reside in the fact that a considerable experience, as well as specific training, are
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required to successfully achieve such match (Li et al. 2015). Furthermore, the calibration
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exercise is usually a very cumbersome and time-demanding process, which may easily
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become unfeasible when there is a great number of unknown variable inputs to be
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calibrated or estimated (Kim and Park 2016). Thus, automated calibration methods, either
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adopting optimization or statistical techniques, constitute a more suitable approach. In
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regard the deterministic methodology, the unknown model inputs are generally estimated
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by coupling the building energy simulation model with an optimization algorithm aimed
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to minimize a specific error function that quantifies the differences between the numerical
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predictions and the measured data. Some applications of this calibration approach can be
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found, among others, in (Cacabelos et al. 2015; Ramos Ruiz et al. 2016; Yang et al. 2016;
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Chaudhary et al. 2016). As for the probabilistic methodology, a Bayesian inference
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procedure is employed to obtain the posterior probability distributions of the unknown
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parameters given field measurements. Application of the Bayesian framework has
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received increasing attention in the last years within the building energy model calibration
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context. Thus, several studies can be found in the recent literature; see among others (Heo,
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Choudhary, and Augenbroe 2012; Kang and Krarti 2016; Heo et al. 2015; Tian et al.
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2016).
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The International Energy Agency (IEA), in the framework of the Energy in Buildings and
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Communities’ program (EBC), launched in October 2016 the IEA EBC Annex 71 project
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(IEA-EBC_Annex71 2016), which aims to assess the monitoring of in-use buildings to
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guarantee its accuracy and reliability. The work presented in this paper was undertaken
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as part of a validation experiment conducted within that project, using the characteristics
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and registered data of a Round-Robin test box.
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Accordingly, in this paper, we present two calibration methodologies for in-use buildings,
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applied to the case study of a scale model of a dwelling. The TRNSYS (Solar-Energy-
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Laboratory 2012) software is employed as the calculation engine to model and simulate
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the building. A sensitivity analysis is carried out to determine the parameters that affect
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the model performance the most. The calibration process is undertaken in the next step,
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using a deterministic and probabilistic approach. This way, the major aim of this work is
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to assess the main characteristics and capabilities of both methodologies for the parameter
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estimation goal, indicating their possible pros and cons. Moreover, the goodness of both
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calibration methodologies is also evaluated by taking into account the real recorded data
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of the calibration and validation (prediction) periods and employing ASHRAE Guideline
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14 performance metrics (American Society of Heating 2002).
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Therefore, this paper is organized as follows. Section 1 is the introduction. Section 2
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provides the necessary details about the Round-Robin test box. In Section 3, the overall
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methodology employed in the work is exposed. Section 4 presents the results obtained
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and their subsequent discussion. Finally, Section 5 constitutes the conclusions.
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2. Case Study
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The selected experimental installation for carrying out this work is a test box built to
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perform a Round-Robin Experiment within the framework of the IEA EBC Annex 58
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(IEA-EBC_Annex58 2016; Roels et al. 2015; M.J. Jimenez 2016; Roels and Jiménez
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2014; Monari and Strachan 2014). It is located in the LECE laboratory at the Solar
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Platform of Almería, in Spain, where the CIEMAT has performed the measurement
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campaign. The test box is a scale model of a simplified building and was chosen as the
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case study because it allows one to perform the sensitivity analysis and calibration of a
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building in laboratory conditions. Because the monitoring data were registered within a
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short interval, i.e., 1 minute, the results of the simulation can be assessed with great
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accuracy. This also implied a bigger complexity than when simulating with the usual time
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step employed to calibrate a building model, which is one hour or even higher.
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2.1. Experimental system
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The studied building is a cubic space with external dimensions of 1.2×1.2×1.2 m3 and an
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inner volume of 0.96×0.96×0.96 m3. On the surface facing south, one wooden window is
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located. The test box was built to perform measurement experiments to assess its different
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properties. Hence, it was built with a surrounding structure, which allows for considering
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the building as isolated from the ground. Figure 1 shows the test box and the model
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employed in this study.
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Figure 1. Round-Robin Test Box (a) real box, (b) geometrical model render by SketchUp.
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The constructive characteristics of the building are summarized in Table 1. As it can be
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seen, the box has an identical composition for walls, floor and ceiling. The building
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geometry and properties, as well as the monitored data of the experiment, have been
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provided as part of the Round-Robin Test Box case study, from the IEA EBC Annex 71
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(IEA-EBC_Annex71 2016). A detailed explanation of the performed experiments can be
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found in that document.
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Table 1. Constructive characteristics of the test box Wall/ceiling/floor Layers Fibre cement boards XPS insulation Fibre cement boards Fibre cement cladding Total
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Thickness [m] 0.016 0.080 0.016 0.008 Thickness [m] 0.120
Conductivity [W/m·K] 0.35 0.034 0.35 0.60 U-value [W/m2·K] 0.381
Window glass Layers U-Value: g-value
4/15/4 1.13 0.606
mm W/m2·K -
2.10 2.16 0.35
W/m2·K -
Window frame U-Value: Window to frame ratio: Window to wall ratio: 1 2
Because it is not a real building but a test box of reduced dimensions, there is a lack of
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internal loads derived from the standard use of the building such as occupancy or lighting.
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A 100-W incandescent lamp was installed inside the box, to produce the effect of a
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heating device. The on/off setting of the lamp was made through two different control
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strategies. For a 12-days period, an external signal controlled the activation of the lamp,
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while, during the last 9 days of the experiment, a thermostatic control was implemented
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to set to 35°C the indoor air temperature of the test box.
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It needs to be mentioned that, when performing the parameter identification of the model,
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some of the parameters that would be considered in a real in-use building could not be
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studied here. Those are, for instance, the occupancy load or the thermal generation or
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distribution equipment, which do not exist in the test box. Furthermore, due to the level
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of tightness of the box, it was assumed that there are no infiltrations.
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2.2. Numerical model
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In the diagram of Figure 2, the principal components used to model the test box in the
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TRNSYS simulation tool are shown. Type 56 (TestBox) characterizes the geometry and
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constructive description of the building. It is also necessary to provide the simulation with
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meteorological registered data (type 99 is used, named Meteo in the figure) as well as the
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internal gains (HeatingGain) to calculate the temperature inside the test box during the
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calibration and validation periods. On the right side of the diagram, the components used
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to calculate the simulation error can be seen.
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Figure 2. Diagram of the simulation in the TRNSYS Simulation Studio
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2.3. Data
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Registered data for three weeks, from 6 to 26 December 2013, are provided to carry out
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the work presented in this article. The sampling frequency of all data is 1 minute, and
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therefore, it is the simulation time step.
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Because the objective of this study is to calibrate the model and then validate this
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calibration, the period from the 6th to the 19th was used in the calibration process, and the
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period from the 20th to the 26th was used to contrast the simulation results of the calibrated
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model with the actual data of this period.
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The different data that have been used can be summarized as follows:
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Meteorological data: dry bulb temperature, relative humidity, atmospheric
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pressure, velocity and direction of the wind near the box, global and diffuse solar
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radiation.
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Building thermal data: indoor temperature, exterior and interior surface
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temperature of the six surfaces constituting the box. Two sensors were located at
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1/3 and 2/3 of the total height of the box, along its vertical symmetry axis, to
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measure the indoor temperature. The interior surface temperature was obtained as
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the average of nine sensors distributed in the internal face of each surface.
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Internal gains: the power of a 100-W incandescent lamp installed inside the box with a thermostatic controller.
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The equipment employed to register the abovementioned data is detailed in Table 2 with
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the accuracy and operation range of each type of sensor.
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Table 2. Specifications of data acquisition sensors Sensor
Model
Norm
Air temperature PT100, 1/10 (indoor & outdoor) DIN
--
Outdoor Humidity
HMP45A/D
EN61326-1
Global solar radiation Wind speed & direction Average Surface temperature
Pyranometers CM11
ISO 9060:1990 EN 61326: 1998 IEC-5841982
Heating power
WindSonic Thermocouples Type T class 1 SINEAX DME 440
EN 60 688
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Operation range –50 to +250 °C
Accuracy ±0.05 °C
±2 %RH (0...90 %RH) 310 – 2800 nm 4 – 6 (50% points) µV/W·m-2 0-60 m/s 0.01 m/s 0-359º 1º - 40 ≤t ≤125 ±0.5 ºC ºC 1–6A 0.2 % 57 – 400 V 0.8...100 %RH
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3. Methodology
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Figure 3 depicts the steps that have been followed to carry out the calibration of the
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numerical model of the Round-Robin test box. The details are outlined in the following
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sections. Briefly, once the test box has been modelled, the first step undertaken was a
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sensitivity analysis of the model parameters involved. Afterwards, and taking into
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account the obtained results, the model of the test box is calibrated. The last step is to re-
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run the simulation using the calibrated values of unknown input parameters. Accordingly,
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the results obtained with both methodologies during the calibration and validation periods
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are then presented and discussed.
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Figure 3. Methodology adopted for the Round-Robin test box model calibration.
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3.1. Sensitivity Analysis
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First, a global sensitivity analysis (GSA) was performed to detect the parameters with the
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most influence on the target response of the model. The numerical study was conducted
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adopting thirteen input parameters, which are detailed in Table 3. In general, the studied
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parameters were those whose exact value was unknown or with poor accuracy. It is noted
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as well that the sensitivity study was performed following an iterative procedure, initially
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including additional parameters (e.g. surface emissivity and solar absorptance of walls),
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which were finally not studied and which are not detailed in the manuscript to shorten the
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explanation. For all parameters, prior uniform distributions were assumed because it is
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suitable for this case when there is not much information about the prior distribution, and
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it is assumed that between the bounds, the values are equally probable. The lower and
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upper bounds of the parameters were chosen based on the authors' experience and a proper
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engineering judgement, so as to drive the subsequent calibration procedure. The
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corresponding lower and upper limits are indicated in Table 3.
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The studied parameters were classified into five groups. Those corresponding to the wall
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properties were the thickness of two layers of the walls, and the external convective heat
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transfer coefficient, to which a multiplier was applied to modify the value calculated as a
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function of the instantaneous wind speed. Five parameters of the window were considered
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for the GSA: U-value, solar absorptance and emissivity of the frame; a shading factor to
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adjust the solar radiation entering through the glass and a multiplier applied to the external
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convective heat transfer coefficient. Two parameters affect the heating device: the load
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percentage corresponding to the power radiative part and a multiplier which scales the
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power of the lamp. The building indoor air capacitance was also assessed, since TRNSYS
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initial model only considers the volume of the indoor air, ignoring internal masses - in
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this case the lamp- which affect the effective capacitance. Finally, two external factors
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were studied both representing the reflectivity of the ground below the test box, that were
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calculated from the outdoor data registered during the experiment. As the ground
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reflectivity is used by two types of TRNSYS it was necessary to define two different
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parameters for the GSA in order to assess their influence independently: parameter x12,
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ground reflectance, is one of the inputs of Type 99, which calculates the weather
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parameters for the period of the simulation, while parameter x13, ground reflection, is
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used by Type 56, which represents the multi-zone Building. The weather parameters are
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controllable variables which were used as data, not as modifiable parameters in the
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calibration process, and hence, were not considered in the GSA.
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Table 3. Model input parameters. Parameter x1 x2
Units
Wall
Thickness of insulation layer Thickness of Fibre-cement board Wall convective heat transfer coeff. x3 multiplier x4 Window Frame U-value x5 Frame solar absorptance x6 Frame emissivity x7 External shading factor Glass convective heat transfer coeff. x8 multiplier x9 Internal Radiative percent of load x10 load Load power multiplier x11 Building Air Capacitance x12 Exterior Ground reflectance multiplier x13 Ground reflection
m m
Lower bound 0.079 0.014
-
0.800 W/m ·K 1.111 0.680 0.820 0.000 2
kJ/K -
0.800 0.800 0.800 1.000 0.900 0.351
Upper Bound 0.081 0.018 1.700 2.222 0.830 1.000 0.100 1.200 0.950 1.000 1.300 1.100 0.429
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The target response under investigation was the indoor air temperature of the Round-
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Robin test box. However, due to the dynamic nature of the output variable, an indirect
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measure was adopted instead, represented by the analysis of the Root Mean Square Error
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(RMSE) between the predicted and the actual measured temperature. See equation (1),
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where the temperature inside the box 𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠 , as predicted by the simulation, is compared 14
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with the actual indoor temperature, 𝑇𝑇𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 , through a number of points 𝑛𝑛, which is the time interval parameter adopted in the simulation (1 min). �∑𝑛𝑛𝑖𝑖=1(𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠 − 𝑇𝑇𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 )2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑛𝑛
(1)
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The Bayesian Analysis of Computer Code Output (BACCO) methodology (O’Hagan
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2006) was adopted in this work as an efficient and reliable tool from which to quantify
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the influence of each model parameter through the determination of appropriate
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sensitivity measures, namely the main and the total effect index of each input factor
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(Saltelli et al. 2008). The key aspect and major advantage of the BACCO method over
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traditional variance-based GSA methods relies on the fact that a Gaussian process
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emulator is adopted instead of exercising the actual numerical model, hence gaining
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considerable computational efficiency in the procedure (O’Hagan 2006). Some details
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about the Gaussian process emulation are given in the following section, but the interested
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reader may refer to (Oakley and O'Hagan 2004) for a thorough discussion of the topic
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and its application to GSA.
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In this work, to perform the sensitivity analysis, we have resorted to the use of the GEM-
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SA package (Kennedy 2005) (Gaussian Emulation Machine for Sensitivity Analysis). A
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brief description of the sensitivity indices used is given next. Let us denote by 𝑌𝑌 the output
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certain probability density functions (PDFs). If the model inputs are non-correlated, then
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of the numerical model at a set of input parameters 𝑋𝑋 = 𝑋𝑋1 … 𝑋𝑋𝑛𝑛 described through
the variance of 𝑌𝑌 can be decomposed as follows (Petropoulos, Griffiths, and Tarantola 2013):
𝑛𝑛
𝑉𝑉(𝑌𝑌) = � 𝐷𝐷𝑖𝑖 + � 𝐷𝐷𝑖𝑖,𝑗𝑗 + ⋯ + 𝐷𝐷1,2,…𝑛𝑛 , 𝑖𝑖=1
𝑖𝑖
