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Calibration of a building energy model considering parametric uncertainty.


The total energy consumption for US commercial buildings was 17.43 quads (CBECS, 2003), approximately 18% of the total U.S. energy consumption. The Department of Energy (DOE), the International Energy Agency (IEA), Intergovernmental Panel on Climate Change (IPCC) and other agencies have declared a need for commercial buildings to become 70-80% more energy efficient. Building energy modeling recently has received increased attention as a tool to reduce building energy consumption. Most of time, energy models provide hourly calculations of building energy consumption, HVAC (Heating, Ventilation and Air-conditioning), and lighting systems performance, taking into account the dynamic interactions among the building envelope, airflow, weather, internal loads, building usage, equipment, and controls. Energy models can be used for evaluations of different concepts during the building design stage and reference points for building real time performance monitoring and energy diagnostics during the operation stage. The performance generated by the energy model, which represents "design intent" or ideal performance, can be compared with real time measured data from the building. The performance deviation will indicate suboptimal operation or faults.

Model calibration and validation is essential to ensure that the building and HVAC systems are properly modeled and integrated together to predict the building energy performance. Model based assessment of different Energy Conservation Measures (ECM) has been widely applied in building energy community. Kaplan and Canner (1992) have made recommendations for the maximum allowable difference between predicted and monitored data. For instance, the prediction of energy use for interior loads such as lighting, receptacles, or domestic hot water is satisfactory when the difference is within 5% on a monthly basis and 15% on a daily basis. However, the acceptable difference may increase up to 15%-25% (monthly) and 25%-35% (daily) for the simulation of HVAC systems. The annual simulated energy use should be within 10% of collected information, while a difference of less than 25% is acceptable on a seasonal basis. These recommendations are well aligned with conclusions from a recent workshop at the ASHRAE existing building conference (Tuluca, 2010). In this paper, an EnergyPlus model for a historic office building was calibrated and validated with real time measured data by using sensitivity analysis and automated tuning of input parameters. The adequacy of this calibration was evaluated against the ASHRAE Guideline 14-2002. The purpose of this study is to provide a calibrated model as a reference point for model based performance monitoring and energy diagnostics.

The building used in this case study is Building 26, Fleet and Family Support Center (FFSC)/Navy Marine Corps Relief Society (NMCRS), at Naval Training Center, Great Lakes, IL. It is a two-storey office building with basement. The gross area of this building is approximately 37,000 [ft.sup.2] (3,437 [m.sup.2]).This building has special historical masonry construction and is one of the original barracks of Naval Station Great Lakes dating back to 1901. Since then, there were several major renovations including windows upgrades, exterior repairs and a HVAC system retrofit in 2006. Figure 1 shows the front view of this building.


The Building 26 HVAC system consists of two airside systems and two separate waterside systems. The office and administrative area on the first and second floors is served by two variable-air volume (VAV) Air Handling Units (AHU) with VAV terminal units (with hot water reheat). These AHUs have both heating and cooling capability. Operation of these units depends on the occupancy of the building. The chilled water system consists of one 54.5-ton air-cooled rotary-screw type chillers with fixed-speed primary pumping. Heating is supplied from the existing base-wide steam system through a steam-to-water heat exchanger. The hot water serves unit heaters, VAV box reheating coils, and air handling unit heating coils while electric unit heaters and baseboards are used to provide heating to stairwells and restrooms. The communication service room is served by one dedicated split system. Table 1 lists major HVAC equipment used in Building 26. A distributed Direct Digital Control (DDC) system is installed in this building which monitors all major environmental systems. In addition to this, building electric and water meters are being read by the DDC system. Operator workstations provide graphics with real-time status for all DDC input and output connections.
Table 1. Major Equipment Used in Building 26

Equipment                           Number

Duct free split system                   1

Air cooled screw chiller                 1

Variable volume air handler unit         2

Hydronic unit heater                     4

Electric unit heater                     2

Electric baseboard                       4

VAV box with hot water reheat coil      38

Pumps                                    6

Additional meters and sensors are required to calibrate models and accurately measure energy consumption to validate results. An on-site weather station, including a pyranometer, aspirated wet and dry bulb temperature sensors, and wind speed and direction sensors, is installed on the roof. BTU meters (a matched pair of supply and return water temperature sensors, water flow meters) are installed for the chiller and hot water loop. Lighting load power, plug load power and individual chiller power are also monitored through sub meters. These sensors and meters are integrated into the existing building Energy Management and Control System (EMCS).


A whole-building EnergyPlus simulation model representing the performance of the envelope, HVAC, lighting, water, and control systems was developed in EnergyPlus (EnergyPlus, 2011), which is a whole-building simulation program developed by the United States Department of Energy. An EnergyPlus model takes as input a description of the building (e.g., geometry, materials, roof type, window type, shading geometry, location, orientation etc.), its usage and internal heat loads (as a scheduled function of time), and the HVAC equipment and system description (e.g., chiller performance), and then computes the energy flows, zonal temperatures, airflows, and comfort levels on sub-hourly intervals for periods of days to years. There are 2063 input parameters (parameters with numerical values) for this EnergyPlus model.

The EnergyPlus interface used for this study is DesignBuilder (DesignBuilder, 2011), which allows for a graphical display of all the three-dimensional geometry. After the geometry is entered into DesignBuilder, an IDF file with all geometry information is exported, and then EnergyPlus IDF Editor is used to create the HVAC system model. The image in Figure 2a contains rendered geometry outline generated by DesignBuilder.


The version of EnergyPlus used in this study was 6.0 (build Annual real time weather data in for 2010, including outside dry bulb temperature, wet bulb temperature, wind direction and speed, direct normal solar radiation and diffuse horizontal radiation etc., were used as ambient conditions for the simulation. In order to keep the size of the model and computation time manageable, zoning simplifications were made when entering the building geometry. All the rooms served by the same VAV box were integrated into one thermal zone. The building model consists of 44 conditioned zones (5, 17, and 22 zones for the basement, first, and second floors respectively). Some zones represent a physical room in the building while other zones represent adjacent multiple rooms operating under similar energy usage/requirements. Each zone includes an "internal mass" that represents the thermal storage capacity of the room(s) (e.g., interior walls, furnishings, books, etc.). Figure 2b indicates the zoning used for the second floor in Building 26. This includes 4 unconditioned zones.

HVAC System Model

HVAC Zone Setup. For the zones served by VAV boxes with reheating coils, the EnergyPlus Object (AirTerminal:SingleDuct:VAV:Reheat) is used. EnergyPlus Objects (ZoneHVAC:Baseboard:Convective:Electric and ZoneHVAC:Baseboard:Convective:Water) are used to model the electric baseboard and hydronic unit heater. Thermostat schedules for all zones are as follows:

* Cooling set point: 76 [degrees]F (24.4[degrees]C) occupied, 86 [degrees]F (30[degrees]C) unoccupied

* Heating set point: 70 [degrees]F (21.1[degrees]C) occupied, 59 [degrees]F (15[degrees]C) unoccupied

Hot Water and Chilled Water Distribution Loops. The heating water distribution loop in the building is modeled as a variable flow system including variable speed drives on the pumps, which are modeled with premium efficiency motors. The chilled water distribution loop in the building is modeled as constant flow system including constant speed drive on the pump. The chilled water loop is modeled with a set-point temperature of 45 [degrees]F (7.2 [degrees]C). The heating-water loop is modeled with a set-point temperature of 180 [degrees]F (82.2[degrees]C). Pump power consumption is described by the following part load performance curve.

Fraction Full Load Power = [C.sub.1] +[C.sub.2]PLR+[C.sub.3]PL[R.sup.2]+ [C.sub.4]PL[R.sup.3] (1)

The coefficients [C.sub.1], [C.sub.2], [C.sub.3], and [C.sub.4] are constant parameters and PLR is the Part Load Ratio (i.e., PLR=water flow rate/design water flow rate).

Chiller Model. One 54.5-ton air cooled chiller (Carrier 30RAN055-61PK) is used in the chiller plant. This chiller model is an empirical model, which is commonly used in the EnergyPlus building energy simulation program (DOE, 2010). The model uses performance information at reference conditions along with three curve fits for cooling capacity and efficiency to determine chiller operation at off-reference conditions. Chiller performance curves are generated by fitting information from a manufacturer's catalog. Cooling is available from April 15th to October 15th, and whenever the outside air temperature is greater than 58 [degrees]F (14.4 [degrees]C), the chiller is turned on. Whenever the outside air temperature is less than 56 [degrees]F (13.3 [degrees]C), the chiller is turned off.


Originally, the EnergyPlus model for Building 26 was created and selection of its 2063 parameters was performed using the best information that was available at the time. For example, the plug and lighting load profiles were generated by using real time submetered data for two months (March and April) in 2010. HVAC system operation schedules and setpoints were taken from actual building EMCS data. During model calibration, a smaller subset of the 2063 parameters that are most critical was identified using sensitivity analysis and subsequently automatically tuned so that the model better matches measured data. Model calibration was performed using annual measured data from 2010, and the outputs of the model were then compared to measured data for a few months in 2011 in which the model was not specifically tuned to match (model verification).

Predominate historical data included monthly metering data for total building electricity, plug load electricity and steam usage. This data had been recorded for 2009, 2010, and part of 2011 at the time of this study. Since there were issues with condensate meter, the steam usage data was not selected for the calibration analysis.

Calibration Approach

The model calibration process relies heavily on characterizing parametric influences on the outputs of the model. This analysis is performed by sampling all parameters of the model around their nominal value to create a database of output data which is used to calculate the sensitivity of these outputs to parameter variation as well as to derive an analytic meta-model based on this model data (Eisenhower et al. 2011a). Once the most influential parameters (on the order of 10 to 20) of the model are identified, an optimization can be performed (using the meta-model) in order to identify parameter combinations that produce the best fit to measured data. Only 10-20 of the most influential input parameters instead of thousands were optimized during the optimization/calibration process to avoid the issue of over fitting the model.

This type of work has been performed in a manual way in a previous project (O'Neill et al., 2011). A schematic of the automated process used in this paper is presented in Figure 3. Although the case study presented in this paper is focusing on the calibration of an EnergyPlus model, the proposed calibration approach can be implemented for any other building simulation programs.


Uncertainty Analysis (UA) and Sensitivity Analysis (SA)

The purpose of the uncertainty and sensitivity analysis is to identify which of the entire list of parameters (i.e., 2063 parameters in this study) are best to use for calibration purposes. In order to do this, a list of the parameters and their nominal values is collected and a range is then created which spans +/- 25% of the nominal value using a uniform distribution if the nominal value is nonzero and an exponential distribution otherwise. 6500 samples are created in this range, which are concurrently perturbed using a deterministic sampling approach (Aimdyn, 2010). The EnergyPlus models associated with these samples are then simulated in parallel on a 184 CPU Linux cluster to generate output data for each of these instances.

Once the output data (e.g., monthly plug and total electricity consumption in this study) is generated, sensitivity analysis is performed to rank-order the parameters in terms of their influence on the output. An example of the sensitivity calculation for total electricity in March, 2010 is presented in Figure 4. In this figure, all 2063 sensitivity indices are plotted while the top 10 most influential parameters that influence total electricity in March are highlighted in the legend. The sensitivity index is the relative influence that each parameter has on a particular output. For months in the cooling season, different input parameters including chiller capacity and chiller reference COP are identified to be most influential parameters using the same approach.


Optimization (Calibration)

To perform the actual calibration, a mathematical optimization problem is defined in which parameters are varied in order to minimize the difference between the model output and measured data. Optimization using whole-building energy models is often challenging due to the computationally expensive nature of the simulation as well as discontinuities that are often found in the cost surface (Wetter and Wright, 2003). In order to circumvent these issues, an analytic model of the full EnergyPlus model (meta-model) is created using a machine learning regression technique (Eisenhower et al. 2011b).

With an analytic representation of the building dynamics, rapid optimization is performed on the meta-model using an interior point method (a gradient based optimizer) and confirmed using the full EnergyPlus model. Since the function evaluation is so rapid, optimization experiments can be performed with thousands or just a few key parameters of the model. In order to perform the optimization, a cost function is defined as the following:

[square root of ([summation][(model - data).sup.2])]

where the two variables under the radical are either monthly or annual energy consumption in this study.

An issue that arose during the calibration process was the significant disparity between the un-calibrated model and measured data. In the first subplot of Figure 5, the uncertainty distribution for January total electricity consumption is presented along with the prediction of the baseline un-calibrated model (red dot) as well as measured data (blue dot). It is evident in this plot that the measured data is significantly far from the baseline model such that changing the parameters by +/- 25% does not move the output into the range of the measured data. This is an issue for the calibration process because the meta-model that is used for calibration is most accurate where the uncertainty data was generated and becomes less accurate on the tails of the distribution (under the black curve in Figure 5a). To alleviate this concern, optimization was performed with constraints on the output variables. Optimal parameters were defined such that the output did not leave an ellipse (in black color) that encompasses the data (as illustrated in Figure 5b).


The optimization results for monthly energy consumption are presented in Figure 6 where it can be seen that there is significant improvement with respect to the ability of the model to represent measured data after the automated calibration. The total facility and plug electricity consumption predictions from the calibrated EnergyPlus model match the actual measured monthly data within [+ or -]5%. The calibrated model outputs and measured data are also compared in terms of Mean Bias Error (MBE) and coefficient of variation of Root Mean Squared Error (CV(RMSE)). Table 2 shows that both MBE and CV(RMSE) are far less than the limits defined by ASHRAE guideline 14-2002, respectively, [+ or -]5% and [+ or -]15% (ASHRAE 2002). In each case, only the top 10-20 significant parameters were used for the calibration. Table 3 shows final values for the top 10 input parameters (in March, 2010) identified by the optimization/calibration process. It should be noted that these results are from the optimization with output constraints and the error can be reduced if these constraints are lifted. These constraints can be lifted by moving the cloud of sampled data (with which the meta-model is derived) closer to the measured data. This can be done by either larger perturbations on the sampled inputs, or by moving the nominal value closer to the measured data. One recommended way to achieve this is to perform SA on the entire list of parameters with few samples to determine strong parameters, and then hand tune these strong parameters to get the model output mean closer to measured data. Another SA will be followed only for these strong parameters with larger ranges. The proposed automated calibration then will be performed.

Table 2. Calibration Results for Building 26
EnergyPlus Model

Error     Plug Electricity  Total Electricity

MBE                  0.02%             -2.31%

CV(RMSE)             0.47%              2.80%

* Equations to calculate MBE and CV(RMSE) are
from ASHRAE Guideline 14-2002 (ASHRAE 2002).

Table 3. Top 10 parameters values before and after

Parameters       Before        After
               Calibration  Calibration

FL2 Zone5               20       17.513
plug load
power density

FL2 Zone15              14       17.083
plug load
power density

Hot water             2238     2797.498
pump rated

FL2 Zone11              14       17.335
plug load
power density

FL1 Zone4             14.5       18.118
plug load
power density

FL1 Zone1             14.5       18.106
plug load
power density

FL0 Zone5              600      652.766
plug load
power density

Hot water              100       85.758
loop max

FL1 Zone11              14       17.500
plug load
power density

Office                0.26        0.250

* Top 10 parameters were selected based on the
sensitivity indices (see the Figure 4).


The above calibration process illustrates how well a model can be tuned to fit a pre-described measured data set. Once the model is calibrated, it is desirable for the model to have prediction capability for future data. This validation process was performed using three months of measured data from 2011 (recall that the model was calibrated for 2010 data) and presented in Figure 7. This Figure illustrates that the error in prediction using the calibrated model (Verification with 2011 weather in blue bar) is acceptable and better than the un-calibrated model (Nominal with 2011 weather in green bar). There is a significant error in the month of May which is due to a chiller failure (confirmed with facility team), which did not occur when the model was calibrated with 2010 data. In a sense, this verification test for May, 2011 illustrated an unexpected excursion in the data due to an equipment fault which is well predicted by the validated model. This demonstrates that a well calibrated energy model can be a means for fault detection and diagnostics.



We presented a systematic and automated way to calibrate building energy models with a large number of uncertain input parameters. A subset of these parameters was identified using sensitivity analysis and subsequently automatically tuned so that the model better matches measured data. Using the proposed approach, the total facility and plug electricity consumption predictions from the calibrated EnergyPlus model match the actual measured monthly data within [+ or -]5% for a historic office building. The calibrated model gives 2.80% of CV(RMSE) and -2.31% of MBE for the whole building electricity use, which is acceptable based on the ASHRAE Guideline 14.


This work was performed under the project EW09-29 administered by ESTCP (Environmental Security Technology Certification Program) technology program of the Department of Defense. We would like to thank ESTCP program manager, Dr. James Galvin and facility manager at Great Lakes, Mr. Peter Behrens, for their support. We would also like to thank Satish Narayanan (UTRC) and Professor Igor Mezic (UCSB) for insightful discussions on this topic. Views, opinions, and/or findings contained in this paper are those of the authors and should not be construed as an official Department of Defense position or decision unless so designated by other official documentation.


Aimdyn GoSUM Software, 2010. Global Optimization, Sensitivity and Uncertainty in Models (GoSUM) [online]. Santa Barbara, CA: Aimdyn Inc. Available from: [Accessed 11 August 2011].

ASHRAE. 2002. ASHRAE Guideline: Measurement of energy demand and savings. ASHRAE Guideline 14-2002.

CBECS. 2003.

DesignBuilder, 2011.

DoE. 2010. EnergyPlus documentation: engineering reference.

Eisenhower, B., O'Neill, Z., Fonoberov, V. A., and Mezic, I. 2011a. Uncertainty and sensitivity decomposition of building energy models. Journal of Building Performance Simulation, In Press. DOI: 10.1080/19401493.2010.549964

Eisenhower, B., O'Neill, Z., Narayanan, S., Fonoberov, V. A., and Mezic, I., 2011b. A methodology for meta-model based optimization in building energy models. Energy and Buildings. In Press doi:10.1016/j.enbuild.2011.12.001.

EnergyPlus. 2011.

Kaplan, M., and P. Canner.1992. Guideline for Energy Simulation of Commercial Buildings. Portland: Bonneville Power Administration.

O'Neill, Z., Eisenhower, B., Yuan, S., Bailey, T., Narayanan, S. and Fonoberov, V. 2011. Modeling and calibration of energy models for a DoD Building. ASHRAE Transactions, 117(2): 358-365.

Tuluca, A. 2010. Modeling for Existing Buildings. ASHRAE Existing Building Conference. New York, NY.

Wetter, M. and J, Wright. 2003. Comparison of a generalized pattern search and a genetic algorithm optimization method. Proceedings of the Eighth International IBPSA Conference, Eindhoven, Netherlands, pp. 1401-1408.

Zheng O'Neill, PhD, PE


Bryan Eisenhower, PhD


Vladimir Fonoberov, PhD

Trevor Bailey, PhD

Zheng O'Neill is research engineer. Trevor Bailey is project leader at United Technologies Research Center, East Hartford, CT. Bryan Eisenhower is associate director at the Center for Energy Efficient Design, University of California, Santa Barbara, CA. Vladimir Fonoberov is chief scientist at Aimdyn, Inc., Santa Barbara, CA.
COPYRIGHT 2012 American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
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Author:O'Neill, Zheng; Eisenhower, Bryan; Fonoberov, Vladimir; Bailey, Trevor
Publication:ASHRAE Transactions
Article Type:Report
Geographic Code:1USA
Date:Jul 1, 2012
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