A systematic approach to manual calibration and validation of building energy simulation

Abstract

Purpose

This study aims to create an efficient approach to validate building energy simulation models amidst challenges from time-intensive data collection. Emphasizing precision in model calibration through strategic short-term data acquisition, the systematic framework targets critical adjustments using a strategically captured dataset. Leveraging metrics like Mean Bias Error (MBE) and Coefficient of Variation of Root Mean Square Error (CV(RMSE)), this methodology aims to heighten energy efficiency assessment accuracy without lengthy data collection periods.

Design/methodology/approach

A standalone school and a campus facility were selected as case studies. Field investigations enabled precise energy modeling, emphasizing user-dependent parameters and compliance with standards. Simulation outputs were compared to short-term actual measurements, utilizing MBE and CV(RMSE) metrics, focusing on internal temperature and CO₂ levels. Energy bills and consumption data were scrutinized to verify natural gas and electricity usage against uncertain parameters.

Findings

Discrepancies between initial simulations and measurements were observed. Following adjustments, the standalone school 1’s average internal temperature increased from 19.5 °C to 21.3 °C, with MBE and CV(RMSE) aiding validation. Campus facilities exhibited complex variations, addressed by accounting for CO₂ levels and occupancy patterns, with similar metrics aiding validation. Revisions in lighting and electrical equipment schedules improved electricity consumption predictions. Verification of natural gas usage and monthly error rate calculations refined the simulation model.

Originality/value

This paper tackles Building Energy Simulation validation challenges due to data scarcity and time constraints. It proposes a strategic, short-term data collection method. It uses MBE and CV(RMSE) metrics for a comprehensive evaluation to ensure reliable energy efficiency predictions without extensive data collection.

Citation

Tomrukcu, G., Kizildag, H., Avgan, G., Dal, O., Ganic Saglam, N., Ozdemir, E. and Ashrafian, T. (2024), "A systematic approach to manual calibration and validation of building energy simulation", Smart and Sustainable Built Environment, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/SASBE-10-2023-0296

Abbreviations

ASHRAE

American Society of Heating and Air-Conditioning Engineers

ACH

Air Change per Hour

BES

Building Energy Simulation

CIBSE

Chartered Institution of Building Services Engineers

CV(RMSE)

Coefficient of Variation of Root Mean Square Error

FEMP

Federal Energy Management Program

GOF

Goodness Of Fit

HVAC

Heating, Cooling and Air Conditioning

IPMVP

International Performance Measurement and Verification Protocol

MBE

Mean Bias Error

NMBE

Normalized Mean Bias Error

ppm

parts per million

RMSE

Root Means Square Error

1. Introduction

Building energy simulation (BES) is a physical-based mathematical model that comprehensively calculates building energy performance (Chong et al., 2021). BES models are essential for accurately assessing energy savings and building retrofitting strategies (Clarke et al., 1993). They encompass various input data such as climate, building geometry, thermal loads, construction details, density, Heating, Cooling, and Air Conditioning (HVAC) systems, occupant behavior, occupant profile, and thermophysical building data, including U-value (Ali et al., 2021; Ferreira and Pinheiro, 2011). Therefore, BES plays a significant role in energy performance analysis, retrofit analysis, optimization and control operations, and model validation to enhance the credibility of simulation results (Chong et al., 2021).

When comparing measured and simulated data, two leading causes of inaccuracy arise: (1) model error resulting from the simulation, and (2) measurement error present in the actual data. Measurement errors stem from technical specifications. Several studies have attempted to identify the sources and extent of uncertainties in building modeling (Hopfe and Hensen, 2011; Macdonald and Strachan, 2001; Macdonald and Clarke, 2007; Spitz et al., 2012). According to de Wit and Augenbroe (Wit and Augenbroe, 2002), three main factors cause uncertainty:

1. Specification issues: Arising when the structure and systems of a building are incompletely or incorrectly documented.

2. Modeling issues: Stemming from the simulated model’s principles, which represent an abridged version of reality.

3. Scenario issues: Wherein the model’s internal and external variables, such as occupant behavior and weather, often deviate from reality.

Dynamic factors associated with occupants are recognized as a substantial cause of uncertainty. Thus, developing stochastic models tailored to specific occupancy cases is crucial (Royapoor and Roskilly, 2015).

1.1 Simulation validation

Calibration and validation are distinct processes. Model calibration involves adjusting numerical parameters to establish model credibility by aligning simulation predictions with actual results. Validation, on the other hand, assesses the model’s accuracy in representing the real world. Verification involves assessing the model’s accuracy against the developer’s initial statement (Chong et al., 2021).

Discrepancies between simulation and actual results may occur during the validation process. Uncertainty in this context can arise from errors or misrepresentations in input data due to occupational and operational scenarios, model intricacies, and abstraction (Chong et al., 2021). This uncertainty is often referred to as an “energy performance gap” in literature (Cozza et al., 2021). Effective management of the validation process is crucial for establishing a credible BES model (Hou et al., 2021). However, Malhotra et al. reported that among 72 reviewed articles, only 7% conducted a validation study, indicating a limited practice (Malhotra, 2022).

Validation primarily focuses on temperature and building energy consumption due to the continuous interplay between indoor air temperature and energy demands (Chong et al., 2021). Key parameters influencing simulation results include weather data (Beagon et al., 2020), building envelope, internal gains, zone set points, and HVAC system settings (heating and cooling set points) (Al-Shargabi et al., 2022; Afroz et al., 2018; Beagon et al., 2020; Bellagarda et al., 2022). Internal gains encompass occupant profiles and density, lighting, equipment, and operational schedules, significantly impacting energy end-users (Koulamas et al., 2018). Several studies emphasize the criticality of occupant behavior in causing disparities in indoor temperature and building energy demand results (Cipriano et al., 2015; Malhotra, 2022). However, few papers in the literature have discussed occupant behavior typology specifically in school buildings (Franceschini and Neves, 2022).

1.2 Simulation calibration methods

Building model calibration is a metric of model accuracy that remains significantly affected within the specified parameter space despite increasing complexities (Cipriano et al., 2015). The primary approaches can be categorized as manual and automated (Hou et al., 2021; Zuhaib et al., 2019), with 74% of calibration approaches being manual (Coakley et al., 2014). The manual calibration method aligns with the standards of the ASHRAE Guideline (ASHRAE, 2002) and the International Performance Measurement and Verification Protocol (IPMVP).

Several calibration methods are mentioned in the literature: root mean square error (RMSE), coefficient of the variation of the root mean square error (CV(RMSE)), statistical mean bias error (MBE), normalized mean bias error (NMBE), goodness of fit (GOF), and coefficient of determination (R2). These methods are suitable for calculating indoor air temperature and building energy demands using electricity and natural gas. Table 1 comprises the error limits and standardizations of these validation methods.

Apart from these methods, others include mean absolute percentage error (MAPE), annual percentage error (APE), mean square error (MSE), R-value, mean absolute error (MAE), coefficient variation (CV), Spearman-rho, and MSE-R (Al-Shargabi et al., 2022). However, the literature lacks information on their acceptable limits, calibration, and formulations.

The most commonly used calibration method is RMSE, followed by R-squared (R2), mean absolute error (MAE), and mean absolute percentage error (MAPE) (Al-Shargabi et al., 2022; Dahlström et al., 2022; Franceschini and Neves, 2022). The combination of CV(RMSE) and NMBE, as utilized in this study, provides a practical approach for calibrating and validating energy simulation models. This combination offers a comprehensive assessment of both prediction accuracy and precision.

CV(RMSE) measures the relative variability of prediction errors, indicating model precision by dividing RMSE by the mean value of observed data. A lower CV(RMSE) signifies a more precise model with reduced variation in prediction errors.

NMBE evaluates the bias or systematic error of the model by dividing MBE by the mean value of observed data and expressing it as a percentage. Lower NMBE values indicate a model with less bias, where predicted and observed average values are closer.

Combining CV(RMSE) and NMBE provides complementary information about the model’s performance. While CV(RMSE) focuses on prediction precision, NMBE highlights the model’s bias or accuracy, offering insights into strengths and weaknesses.

Moreover, the adaptability of CV(RMSE) and NMBE allows for adjustments, making them convenient for model evaluation and enhancement. Analyzing changes in CV(RMSE) and NMBE values enables effective comparison of model versions, experimentation with input parameters, or assessment of simulation model alterations for accuracy and precision.

1.3 Building energy simulation validation challenges

The accuracy of BES models heavily relies on their validation against actual measured data. In practice, validating BES models involves comparing the results of actual values obtained from buildings to the simulation results. This process ensures that the simulation accurately predicts the energy performance of buildings when adequately calibrated. However, validating BES encounters significant time constraints stemming from the comprehensive nature of these models (Agdas and Srinivasan, 2014) and the intricacies involved in data collection and validation processes (Giraldo-Soto et al., 2022). Implementing a thorough validation procedure necessitates time-intensive efforts, including acquiring empirical data, meticulous calibration of simulation parameters, and comparing simulated results against actual measurements.

Furthermore, the duration required for data collection often extends beyond practical limits due to resource constraints or the need for extended monitoring periods. Balancing the need for accurate validation with time constraints poses a challenge, requiring innovative approaches that optimize validation strategies within feasible timeframes without compromising the reliability and precision of the simulation outcomes (Judkoff et al., 2008). The scarcity of available data for calibration makes the process highly under-determined and overparameterised. This lack of data significantly increases the time and cost of collecting detailed measured information, posing a significant obstacle in ensuring model accuracy (Hong et al., 2018).

Another significant challenge in the validity of BES of incredibly complicated and multi-zone buildings is the high number of dataloggers that need to be utilized, the longitudinal measurement and the variation of the operation during that measurement period (van Dronkelaar et al., 2016). Each zone or area may require several dataloggers to capture the diverse internal conditions and variables such as temperature, humidity and CO₂ level. Also, validating energy simulations often requires collecting data over an extended period. During this measurement period, the building’s operation is not consistent. Factors such as changes in occupancy, weather conditions, maintenance schedules, or equipment usage can cause significant fluctuations in energy consumption. These variations make it more challenging to accurately model and simulate energy usage, especially in intricate buildings with multiple zones.

The study aims to overcome the challenges of BES validation by proposing a systematic approach to be used during the model calibration process. It uses a strategic, short-term data collection approach to precise model calibration. Using both MBE and CV(RMSE) together allows for a comprehensive evaluation of the model’s performance regarding bias, variation, and relative accuracy, thereby enabling a more robust assessment of the energy efficiency predictions without relying on extensive data collection.

2. Methodology

The methodology is based on a detailed framework that incorporates manual calibration, actual data collection through measurement, and statistical techniques, aiming to mitigate constraints imposed by the analytic program. The methodology utilized the ASHRAE Guideline 14 for energy model calibration. The study encompasses four distinct phases:

• Phase 1: essential data gathering

Initially, data collection and measurement were conducted, obtaining weather data, physical attributes, and energy bills related to the school buildings. To enhance data accuracy, parameters like exterior wall U-values and indoor air quality were measured.

• Phase 2: simulation process

The simulation process involved calculating occupancy-related activity rates, equipment usage, lighting requirements, and mechanical operations.

• Phase 3: building energy modeling

Building energy models were developed using DesignBuilder, a specialized software tool.

• Phase 4: building energy model calibration

In this phase, simulation results were compared with actual energy bill data using two error calculation methods: NMBE and CV(RMSE). The energy model underwent adjustments until inaccuracies fell within the accepted error rate bounds.

Figure 1 depicts the methodology frameworks and the flow of the steps.

2.1 Case study description

In the initial step of the validation process, distinct schools with varied characteristics were chosen in Istanbul. The primary aim was to ensure access to reliable building data within the area of study. Bakırköy and Tuzla were selected as pilot areas due to their substantial population and proximity to the Istanbul seashore, experiencing a moderately temperate and humid climate as most of Istanbul’s regions. Criteria for selecting buildings included the availability of comprehensive information such as architectural, mechanical, and electrical projects, energy consumption records, and detailed data on building structure and energy systems. Furthermore, considerations were made regarding the potential applicability of findings to schools nationwide. Both chosen educational facilities are public schools, with one being a single building (School 1) following a typical school layout found nationwide (Köse and Barkul, 2012) and the other being a campus facility (School 2).

School 1, located in the Bakirkoy district of Istanbul, is a five-story building comprising four regular floors and a basement. Constructed in 2008, it accommodates 31 standard classrooms, each with a capacity for 20 students. Additionally, the building includes a multi-purpose hall, a computer laboratory, a gymnasium, a small dining area, and a library.

School 2, situated in Istanbul’s Tuzla district, is an educational campus established in 2004. It consists of a main educational building, three vocational atelier buildings, a refectory, and a dormitory. The main building, also spanning five stories, houses administrative offices, teachers' rooms, and classrooms. The vocational buildings, spanning two to three floors each, contain laboratories and classrooms. The refectory building comprises a dining hall and a kitchen serving lunch.

Both schools employ similar heating systems. School 1 utilizes non-condensing boilers of 300 kW capacity, connected to radiators to meet heating needs. In contrast, School 2 features two central condensing boilers in the main building totaling 1,163 kW capacity. These boilers supply baseboard radiators across campus buildings through underground pipes. Both heating systems are manually controlled based on outdoor temperature and occupancy behavior, typically active from November to March annually.

Regarding cooling, split air conditioners are installed in specific zones, including administrative offices in both schools. School 1 also equips some classrooms in the southern part of the building with split air conditioners. Electric water heaters cater to hot water needs in both schools, while thermosiphons are utilized in the kitchen area. School 1 additionally features a thermosiphon in the guard room, which is operational on weekdays and weekends except during school hours.

Neither school relies on mechanical ventilation, favoring natural ventilation methods. Users, particularly teachers, manage window openings. Observations indicate windows are often open during recess and midday for ventilation, decreasing frequency as the indoor-outdoor temperature difference rises. Natural ventilation schedules were established based on user input and on-site visits. Detailed information about materials used in both schools is provided in Table 2 and Table 3.

2.2 Obtained and measured data

The study primarily focused on simulating and calibrating BES models, involving extensive efforts to collect, preserve, and analyze input information. The data collection process commenced by obtaining annual and monthly weather data from the closest weather stations to the case study buildings. Two weather stations within a one-kilometer distance from the case study buildings have been determined, and required data has been obtained for the measurement period and a year before when energy bills are covered. Architectural drawings, encompassing floor plans, sections, elevations, technical drawings, electrical plans, material details, and structures, were acquired from the schools. Detailed information regarding the HVAC systems, encompassing operation and maintenance schemes, was identified through interactions with school administration, label information, and on-site observations. Monthly electricity and natural gas bills were retrieved from the case study buildings. Surveys and field observations gathered occupancy-related data, including zone capacities, working hours, and habits related to natural ventilation through window openings. For domestic hot water usage, impacting gas and electricity consumption, standard consumption rates based on liters per day per person in educational buildings, informed by local experts, were considered.

Lighting and equipment significantly influence electricity consumption for cooling and indoor air temperature regulation, impacting calibration. Information regarding power and usage schedules of lighting fixtures and electrical equipment was obtained through on-site visits and label information. Generally, classroom and corridor lighting systems are controlled by teachers. Observations during site visits revealed that corridor lights were typically left on during the day while lighting in classrooms and offices was based on outdoor illuminance levels. CIBSE standards recommend design illuminance levels ranging from 300 to 500 lux for various classroom types, with a target illuminance of 400 lux for interior lighting operations.

Validation of the energy model is critical for BES. To enhance model accuracy, several measures were undertaken, including indoor air quality and U-value measurements of external walls, along with thermal analysis of the building envelope. Combined with audits and on-site measurements, these measures aimed to support the validation process and attain more precise and reliable results. The manufacturer’s specifications indicate a unit error rate of ±0.5 for the indoor air quality and U-value measurement devices used in this study.

2.2.1 Indoor air quality measurements

Datalogger devices were used to measure indoor air quality, including temperature, relative humidity, and CO₂ levels. The devices’ accuracy rate for the temperature recording is ±0.5 °C, and their resolution is 0.1 °C. The measuring range for CO₂, when the relative humidity is between 0 and 99%, is 0–5,000 ppm, and their accuracy rate is ±50 ppm at 25 °C. All devices were connected to the power supply and the Wi-Fi during the measurement period. To simplify the validation process, relative humidity has been excluded from the process, although it was used to check for unforeseen conditions and inconsistencies in the reporting.

While monitoring or tracking window openings for natural ventilation in a school environment might be challenging, measuring CO₂ levels offers an indirect but reliable method for gauging ventilation. CO₂ levels tend to rise indoors with insufficient ventilation because humans exhale CO₂. When windows are closed or there is inadequate airflow, CO₂ accumulates. Therefore, a sharp decrease in CO₂ emissions signals a potential increase in ventilation. Observing the changes in CO₂ concentrations over time makes it possible to infer when windows are open or when there is improved airflow, allowing fresher outdoor air to replace the CO2 accumulations indoors.

Several considerations influenced the selection criteria for rooms and the duration of the measurement period. Factors such as location, orientation, and safety precautions were taken into account, and the following criteria were applied:

Location: Rooms on typical floors were chosen to minimize the impact of ground and roof heat flux on the measurements.

Orientation: Rooms with at least two opposite and/or different orientations were selected to analyze variations resulting from diverse orientation parameters.

Internal wall placement: Rooms with an internal wall available for device placement, away from direct sunlight, were preferred to ensure accurate measurement results.

Table 4 provides information on the selected zones, orientations, and measurement period.

The thermal camera was used to inspect the interior walls of the designated rooms, to analyze heat leakage and identifying any thermal bridges caused by pipes and systems carrying hot water. This investigation also aimed to determine the optimal placement for the device, as illustrated in Figure 2. The data loggers were positioned at approximately 1.5 meters above ground level, aligned with the typical sitting height.

Between February and March 2022, indoor air quality measurements were undertaken at School 1. Specifically, the study covered classrooms facing both south and north. These zones possessed similar geometric characteristics, as well as identical occupant capacities and user schedules. The heating system remained operational throughout the measurement period, and the school was open. The positions of the Datalogger devices employed for these measurements are illustrated in Figure 3.

In the case of School 2, a campus comprising multiple buildings posed challenges in selecting zones with similar functions and user schedules but in opposing directions. Consequently, optimal measurement locations were identified as follows: the classroom (C) and teachers' room (F) in the main building, and classrooms in buildings E1 (D) and E2 (E) within the atelier buildings. It’s important to note that the classrooms in the atelier buildings had distinct user schedules compared to those in the main building.

Short-term indoor temperature monitoring data were collected and averaged across the respective areas to compare simulated indoor temperature outputs. Additionally, heating programs and set point temperatures were monitored and analyzed based on indoor temperature graphics for various thermal zones. CO₂ levels within the selected thermal zones were measured to assess indoor ventilation and leakage rates, as illustrated in Figures 4 and 5.

During the analysis conducted in February and March, School 1, zone B maintained an active heating system throughout the measurement period. The average CO₂ level recorded was 710 parts per million (ppm), notably increasing during lesson hours. Although the ppm values stayed below the average, it was evident that spaces were ventilated by opening windows and doors, particularly on weekdays during recess and lunch breaks. On weekends, CO₂ values were lower, indicating less active school use.

Per ASHRAE 62.1-2013 standards, CO₂ concentrations should not exceed 1,000 ppm to avoid health issues. However, the measured CO₂ levels in School 1, zone B exceeded this recommended range by 12.5%. The highest recorded CO₂ level reached 2,855 ppm, significantly surpassing standard guidelines.

Indoor air quality measurements were conducted in School 2, focusing on four distinct zones: classrooms, laboratories, teachers' rooms, and offices. The average CO₂ levels recorded in these zones were 670, 710, 1000, and 390 ppm, respectively. Throughout the measurement period, CO₂ levels exceeded 1,000 ppm in 18% of the classroom and laboratory measurements, with a 15% rate in the teachers' room. At noon, the highest recorded CO₂ level in the school exceeded 1,350 ppm. This pattern indicates higher CO₂ levels during school hours on weekdays, with lower levels observed during weekends and holidays.

Based on these findings, natural ventilation schedules were established for simulation purposes. The schedules were designed to mirror observed patterns, featuring reduced ventilation during class hours and increased ventilation during recess, as indicated by the measurement data.

2.2.2 U-value measurement of the external walls

The thermal properties of construction materials and the thermal transmittance of building façades significantly impact overall building performance. It is essential to recognize that the actual conditions of buildings may vary from their initial design due to changes in the building envelope’s properties over time (Asdrubali et al., 2014). Therefore, on-site measurements of the U-value are crucial to accurately assess thermal performance, especially considering potential variations from calculated values based on material data (Ficco et al., 2015).

Specific key parameters were considered in selecting the measurement zone and method. Firstly, based on our device’s manufacturer catalogue, a minimum temperature difference of 10 °C between indoor and outdoor environments was required. Additionally, the measurement period had to be at least 1 h. U-value measurements were conducted in January when both schools' heating systems were active. School B’s measurement occurred in the main building, assuming similar U-values for other campus buildings due to similar building materials and construction years.

These measurements determined the thermal transmittance (U-value) of external walls as 1.473 W/m²K for School 1 and 1.844 W/m²K for School 2.

2.2.3 Thermal analysis of the envelope

The condition of the building envelope significantly influences overall building performance. To analyze heat leakages in the building envelope, a thermal camera was used during winter when indoor air temperature exceeds outdoor air temperature. This device assesses building surfaces based on their temperatures, identifying potential areas of heat leakage. Figure 6 presents the samples of the thermal camera pictures used for the related analysis.

Thermal camera analysis pinpointed an optimal location without heat leaks for the U-value measurement. The analysis highlighted the vulnerability of window lintels to heat permeation. Considering a 5% error rate specified in the U-value measuring device’s technical handbook, the estimated value range was determined, factoring in the impact of the lintels.

2.3 Building energy simulation model

The study employed EnergyPlus and DesignBuilder, renowned simulation tools for building energy analysis. EnergyPlus was chosen for its robust simulation capacities and alignment with research objectives. DesignBuilder, similarly recognized for its modeling features, was selected based on its suitability within the study’s context. Integrating these tools into the methodology enabled simulations of building energy consumption and indoor conditions, validated against measured data for accuracy.

The collected data and measurements were compiled for BES modeling. The buildings' model based on their construction drawings was created in DesignBuilder. Weather data from the nearest meteorological stations were processed using the Elements program to generate usable “epw” weather files for modeling and simulation purposes.

In the initial phase of the BES process, zones with similar functions and properties were grouped together. Architectural characteristics were defined, encompassing both transparent and opaque elements of the buildings. Material inputs for the building models were derived from data provided by the schools' administration. On-site measurements determined the U-values of the exterior walls for each building, while specific heat capacity, density, and conductivity values for the building envelope materials were aligned with TS 825 standards, explicitly chosen to validate the measured U-values.

Regarding the HVAC system, equipment and electrical information for the building and lighting systems were defined using EnergyPlus software for simulation purposes. The selected schools utilized air conditioners for cooling demands, whereas heating requirements were met through baseboards connected to boilers. Subsequently, occupancy behaviors and schedules for equipment operation were generated within the simulation. Figure 7 depicts the buildings' models created in DesignBuilder.

2.4 Calibration process

The calibration procedure followed the ASHRAE guidelines, encompassing five primary stages: gathering building information, conducting building energy simulation, comparing simulated and measured data, and adjusting fuzzy simulation parameters to achieve an acceptable error range.

The study adopted a two-step methodology: first, calibrating interior temperature and then calibrating energy consumption. The calibration process involved comparing and validating the BES model. Initial steps involved collecting data inputs, including case study building data, annual weather files, and on-site measurements. Subsequently, adjustments were made to the BES model.

The first calibration step concentrated on validating hourly indoor temperatures by comparing output results with measured data to determine error rates. Energy end-use simulation results were compared and analyzed with actual energy bills in the second calibration step. If error rates, such as MBE and CV(RMSE), fell outside the acceptable range, the BES model underwent resetting using a new set of parameters. Figure 8 depicts the study’s calibration process.

2.4.1 Uncertainty analysis

Uncertainty and sensitivity analysis aim to detect potential inconsistencies in a system’s input and output (Lomas and Eppel, 1992), assessing a simulation model’s robustness. Among the strategies for determining an energy simulation model for a whole building outlined by Neymark et al. (2002), this study adopted an empirical validation method, comparing recorded data from an actual building or experiment with simulated data.

Following the calibration process, validating the energy models involved comparing measured and simulated indoor air temperature values and energy consumption rates. This was done to minimize uncertainties and achieve accurate BES models. To assess the models, two statistical indices, recommended by ASHRAE Guideline 14 (ASHRAE, 2002) and commonly used in similar studies (Clarke et al., 1993; Afroz et al., 2018), were utilized: MBE and CV(RMSE).

ASHRAE Guideline 14 sets limits for NMBE and Coefficient of CV(RMSE). For monthly calibration, models must have an NMBE of 5% and a CV(RMSE) of 15%. These criteria should be 10 and 30% for hourly calibration, respectively.

Yu et al. evaluated unbiased symmetric metrics with commonly used metrics to assess relative bias and inaccuracy between predicted and observed values, depending on the factor between measured and observed values. While most of these relative differences are normalized by the measured values, normalization might lead to incorrect conclusions (Yu et al., 2006). Therefore, two methods, MBE and CV(RMSE), are used in this study to calibrate the case buildings' energy consumption. The equations utilized were based on Mi (energy consumption data from bills), Si (energy consumption simulation result), Np (amount of data), and Mp (average energy consumption of actual data). These methods were employed for calibrating both internal temperature and energy consumption.

(1)MBE=∑i=1Np(Mi−Si)∑i=1NpMi

(2)CV(RMSE)=∑i=1Np((Mi−Si)²/Np)Mp

2.4.2 Calibration-related assumptions

Numerous parameters significantly influence building energy consumption and indoor conditions. While some of these parameters can be accurately determined through comprehensive data collection, others involve uncertainties during determination. These variables include building envelope material properties, occupancy patterns, infiltration rates, lighting and equipment efficiencies and usage patterns, HVAC system efficiency, controls and setpoints, natural ventilation system efficiency, renewable energy systems, and climate data. Calibration and validation of these parameters in simulation models are crucial to ensure accuracy and reliability in predicting real-world performance.

In relatively newly constructed buildings without visible material deterioration and thermal imaging indicating no related issues, it’s assumed that material properties align with manufacturers' reports. Buildings with specific users and predictable conditions allow for occupancy pattern determination with minimal uncertainty. Lighting and equipment efficiencies typically match manufacturer-reported values in new and well-maintained conditions. Like occupancy patterns, lighting and equipment usage patterns are conveniently established in buildings with predictable usage.

Yearly weather data from nearby weather stations typically suffice for simulations, although microclimate conditions might influence results. To understand microclimate impacts, on-site weather stations measure parameters for comparison with local weather station data.

Certain parameters cannot be directly measured or reliably obtained on-site. One such parameter is boiler efficiency. The range for boiler efficiency was determined by considering technical specifications, production date, maintenance, and potential obsolescence due to lack of regular maintenance. The companies' product brochures were consulted to establish the highest and lowest values. School 1’s range spanned from 85% to 95% for a non-condensing single hot water boiler, with the simulation adopting an efficiency of 87%. School 2, with two condensing hot water boilers, ranged from 85% to 98%, settling at an efficiency of 85% after simulation fitting.

Air infiltration, another uncertain parameter affecting simulation results, was validated within the 0.1–0.5 value range from CIBSE standards (CIBSE, 2015). Ultimately, the validation settled on rates of 0.2 1/h for School 1 and 0.3 1/h for School 2.

Heating setpoint temperatures were uncertain, given the absence of thermostat systems. Estimated ranges were derived from indoor air measurements: 23–25 °C for School 1 and 20–22 °C for School 2. Simulation runs using these ranges concluded with setpoints of 25 °C for School 1 and 23 °C for School 2.

Natural ventilation rates, influenced by occupant habits in window operations, were determined based on interior and exterior temperature differences from surveys. A range of 2–5 1/h in winter and 5–8 1/h in summer was simulated, with the final values chosen as best fit to consumption data.

Four parameters with uncertainty were identified to create the calibrated energy model. ASHRAE Guideline 14’s (ASHRAE, 2002) MBE and CV(RMSE) formulas were utilized to quantify error rates, considering potential parameter variations. Table 5 indicates the uncertain parameters and their range used during calibration.

3. Results

The validation of a building through energy modeling simulations inherently carries a wide range of uncertainty. Therefore, the BES model underwent repeated revisions through iterative simulation attempts, aligning with uncertain variable parameters to achieve an acceptable error margin. Upgraded assumptions regarding uncertain factors were employed to assess the calibrated building model’s performance across multiple levels, including validation of internal temperature during the measurement period and the energy consumption rates throughout the year.

The calibration process initially focused on School 1, specifically the south-facing classroom. During internal temperature measurement validation, a base file was established using measurements and standards. Initial results pre-calibration revealed an average temperature of 19.5 °C, with the highest at 24.4 °C and the lowest at 15.5 °C. Notable temperature variations were observed at night and on weekends. Figure 9 illustrates the measured indoor air temperature and its variation during the calibration process in School 1, Zone A.

Simulation outcomes indicated faster cooling rates when the heating system was not active compared to measured results. Datalogger device readings showed an average temperature of 21.6 °C, ranging from 17.9 °C to 26.1 °C, remaining consistently lower than the simulations. Consequently, revisions were made to uncertain parameters, particularly addressing the air infiltration value within the building envelope, aligning it with specified standard ranges.

Additionally, the heating setpoint temperature was increased in the simulation, reflecting the higher weekday temperatures that were measured. Post-revision results demonstrated decreased discrepancies between simulation and measurement. The measured average indoor temperature stood at 21.3 °C, with a 0.26 °C difference from the average simulation temperature. The lowest measured temperature was 17.7 °C, with a 0.19 °C difference from the simulation, while the highest reached 25.3 °C. Differences between measurement and simulation results were analyzed using the CV(RMSE) and MBE methods to complete the indoor temperature validation. The calculated CV(RMSE) for School 1, Zone A, was 4.0%, and MBE was 1.1%, falling within the recommended standard range.

The second zone considered in the internal air temperature calibration for School 1 was a classroom in the North. The average temperature measured was 21.8 °C, with the highest value at 27 °C and the lowest at 16.6 °C. Before model calibration, simulation results indicated an average temperature of 19.7 °C, with a maximum of 24.5 °C and a minimum of 12.5 °C. Notably, the northern area exhibited higher average temperatures than the southern area. Figure 10 illustrates the measured indoor air temperature and its variation during the calibration process in School 1, Zone B.

Observations during field measurements suggested lesser natural ventilation in the northern areas, supported by CO₂ values obtained during measurements. Simulation outcomes, like those in the southern class, were lower than the measurements. Thus, revising uncertain parameters brought the simulation closer to the actual measurements. Post-revision, the simulation model’s maximum temperature matched the measurements at 27 °C. On average, the minimum temperatures were recorded at 15.4  and 19.7 °C. After internal temperature calibration, the MBE error margin for the calibrated energy model was 2.6%, and the CV(RMSE) error margin for School 1, Zone B, was 0.7%.

Measurement for School 2, Zone C, was conducted in November in a southeast-facing laboratory of the atelier building. The average temperature recorded in this zone was 20.2 °C, with the highest at 24.7 °C and the lowest at 16.6 °C. Pre-calibration simulation results suggested higher peak temperatures than actual, prompting adjustments in set points and ventilation rates during unoccupied periods. Post-calibration, School 2, Zone C’s simulation reflected 1.6 and 0.3% values using CV(RMSE) and MBE, respectively. Figure 11 illustrates the measured indoor air temperature and its variation during the calibration process of School 2, Zone C.

Measurements in School 2, Zone D, were taken in November in another laboratory south of the atelier building. The average temperature recorded in this zone was 21.6 °C, with the highest at 24.2 °C and the lowest at 16.6 °C. After calibration, the optimized temperature values for School 2, Zone D, showed CV(RMSE) and MBE rates of 1.6% and −0.5%, respectively. Figure 12 illustrates the measured indoor air temperature and its variation during School 2, Zone D, calibration process.

Measurement in School 2, Zone E, took place in November in the teachers' room at the main school building, east side. The average temperature here was 17.9 °C, peaking at 24.7 °C, an unusual high for the average. However, the lowest was 13.1 °C, creating a substantial gap. After reprogramming user-dependent parameters and optimizing ventilation rates according to CO₂ levels, temperature values' CV(RMSE) and MBE rates for School 2, Zone E, reached 1.9% and −0.2%, validating within the 10% error range. Figure 13 illustrates the measured indoor air temperature and its variation during the calibration process in School 2, Zone E.

The measurement in School 2, Zone F, took place in December in another zone at the main school building, specifically a classroom on the north side. The average temperature in this zone was 16.5 °C, notably lower than in other zones. Due to these lower temperatures, the heating system’s schedule underwent revision. Significant temperature drops during specific periods, particularly at night during the first and last weeks, suggested the possibility of windows being left open after school hours. After optimizing the mentioned parameters, temperature values' CV(RMSE) and MBE rates for School 2 - F Zone reached 3.0% and −1.4%, respectively. Figure 14 illustrates the measured indoor air temperature and its variation during the School 2, Zone F, calibration process.

After completing indoor temperature validations at different locations in both schools, the next step involved comparing the bills. These temperature validations helped determine the heating set point. During the bill validation process, the temperature set points for simulations were set at 25 °C for School 1, 21 °C for the main building, and 22 °C for other facilities in School 2.

The School 1 simulation and bills were compared using the CV(RMSE) and MBE methods. For electricity in January, the bill value was 8.963 kWh, and the simulation outcome was 8.560 kWh. CV(RMSE) was calculated at 5.7% and MBE at 4.5%. Differences in January stemmed from unpredictable usage during the holidays. Values obtained in March and April were 2.4 and 4.3% using CV(RMSE) and 1.8 and 3.4% using MBE, respectively. Figure 15 indicates the electricity consumption error rates under the MBE and CV(RMSE) calibration process in School 1.

Similarly, in May, differences were 3.8% using CV(RMSE) and 3.6% using MBE. Variances in electricity consumption during these months were due to varying usage patterns, especially in conference rooms and meeting rooms without fixed schedules. Between June and August, only administrative staff used the school. Air conditioner usage significantly contributed to this difference, and its schedule was considered after consulting with the managers.

From September to December, simulation results were generally higher than the bills. The usage of electric thermosiphons also played a role in this discrepancy, as it depends on the electrical equipment’s consumption. However, all values obtained fell within the recommended error ranges.

Only months with active heating systems were included in the validation process for natural gas consumption, as there is no natural gas consumption between May and October when the heating system is off. In January, the bill value was 36,599 kWh, while the simulation outcome was 37.195 kWh. The CV(RMSE) was calculated at 1.9%, and MBE at −1.6%. This difference could be due to mid-term holidays when the heating system was operated part-time as informed by the authorities. In February, CV(RMSE) was calculated at 4.2% and MBE at −3.2%, potentially attributed to user-based ventilation variations despite defining a natural ventilation range. Figure 16 indicates the natural gas consumption error rates under the MBE and CV(RMSE) calibration process in School 1.

Upon analysis, simulations consistently appeared higher than the bills, notably in April, possibly due to user comfort, as the heating system was not used due to higher outside temperatures. CV(RMSE) values for November and December were 0.4 and 2.7%, while MBE was −0.5% and −2.2% respectively. Simulation results surpassing bills in December might be linked to reduced natural ventilation in winter. However, overall CV(RMSE) and MBE error rates were within the acceptable range.

The simulation and energy consumption bills for School 2 were compared and carried out similarly. For electricity, CV(RMSE) was 7.4% in January, and MBE was 5.7%, possibly influenced by the holiday season. In February, differences were minimal. In April, higher simulation results could be due to less usage of user-dependent equipment. Inconsistencies in usage calendars for common areas contributed to these variations. Lower differences were observed in June–August due to holidays and low usage. Higher simulation results were attributed to user-generated parameters like electrically operated thermosiphons in September–November. Despite differences, overall error rates calculated using CV(RMSE) and MBE were within the acceptable range when considering all values. Figure 17 indicates the electricity consumption error rate under the MBE and CV(RMSE) calibration process in School 2.

The HVAC system modeling for an individual school building and a campus settlement varies among branches. In the campus buildings, boilers serve as heating sources for multiple buildings, addressing both heating and DHW demand. However, heat loss may occur during hot water transfer from the main building to other facilities. Consequently, the energy performance analysis for School 2 exhibits a higher error rate (Figure 18). The validation process aligned with School 1, focusing on the active heating system. Figure 18 indicates the natural gas consumption error rates under the MBE and CV(RMSE) calibration process in School 2.

The bill values exceeded the simulation results for January, March, and April. This disparity might be due to reduced ventilation during winter months, influenced by observations indicating varying window opening and closing rates for occupant comfort. These averages were based on relevant standards. Notably, there was a marked difference in February, where simulation results surpassed actual usage, potentially linked to water heaters connected to the boiler.

No natural gas consumption occurred between May and November as the heating system remained inactive. CV(RMSE) values were calculated in November and December at 1.7 and 3.1%, and MBE at 4.8 and 2.5% respectively. Despite these fluctuations, overall CV(RMSE) and MBE values remained within the recommended error range when considering all results.

4. Discussion

Representing an existing building through BES poses several challenges and constraints, primarily due to occupant-related factors and equipment depreciation. This study identified the main variables influencing simulation outcomes and quantified their effects on consumption rates.

Boiler efficiency, a critical variable affecting natural gas consumption, was determined within a range. Various simulations were conducted, highlighting that a ±0.10 change in boiler efficiency can cause a 12–14% difference in natural gas energy consumption (Tomrukçu et al., 2022). Consequently, an appropriate efficiency value was determined based on invoices.

In both cases, the absence of a thermostat system made defining the heating set point temperature challenging, significantly impacting simulation results. Simulation evaluations showed that a ±1 change in heating set point temperature affected natural gas consumption by 12–15% (Tomrukçu et al., 2022). Higher set temperatures notably increased energy consumption.

The hydrothermal aspects of a building, influenced by natural ventilation and infiltration, were challenging to determine precisely. A range for hourly ventilation rates was set within EnergyPlus software, considering usage calendars for lesson and break hours. Simulations revealed that a 0.1% change in air changes per hour (ACH) affected natural gas consumption by 0.9–1.3% (Tomrukçu et al., 2022).

Internal thermal mass significantly influences a building’s heat transmission. While this study considered the impacts of internal partitions on the simulation model, defining furniture details presented time limitations.

Temperature calibration significantly enhances the accuracy of energy predictions in buildings by aligning simulated temperatures with actual measured data. This fine-tuning of building energy models ensures a more precise reflection of the specific thermal characteristics of the building, considering various parameters. Refining these parameters based on observed data makes the model more accurate and reliable, reducing discrepancies and improving its ability to predict real-world behavior. Accurate temperature calibration leads to more reliable estimations of heating and cooling loads, directly impacting energy consumption predictions. Moreover, it enables a better understanding of how building systems respond to temperature changes, facilitating optimization for efficient operation. With calibrated temperature data, scenario analyses become more insightful, allowing exploration of diverse weather conditions and potential energy-saving strategies under various scenarios for retrofit projects or new builds.

Following the optimization of these parameters in the BES calibration process, error rates for indoor temperature and energy consumption calibration were calculated. For indoor air temperature, in School 1, Zone A has a CV(RMSE) of 4.00% and an MBE of 1.10%, while Zone B has a CV(RMSE) of 0.70% and an MBE of 2.60%. In School 2, Zone C has a CV(RMSE) Max of 1.62% and an MBE of −0.30%, Zone D has a CV(RMSE) Max of 1.63% and an MBE of −0.50%, Zone E has a CV(RMSE) Max of 1.99% and an MBE of −0.25%, and Zone F has a CV(RMSE) Max of 3.00% and an MBE of −1.44%.

In the Shin et al. (2022) study, one case has a CV(RMSE) of 3.71% and an MBE of −1.63%, while the second case has a CV(RMSE) of 2.94% and an MBE of −0.94% that shows a good similarity with this study’s results. Table 6 presents a comparison of the error rates of this study and Shin et al.

The study results have been compared with three similar studies regarding monthly energy consumption. Kunwar et al. (2021) reported a relatively high CV(RMSE), while Monetti et al. (2015) depicted a lower MBE error rate. The study’s results, however, show good consistency with the error rates reported in these selected studies. Table 7 compares the maximum MBE and CV(RMSE) error rates for monthly energy analysis in the current study and the three selected studies.

Another aim was to test the validation method’s reliability for single and campus buildings and explore their potential differences. The results indicated no substantial difference between these educational building types, confirming the method’s applicability to singular and campus educational facilities.

The calibration method employed in this study for BES, focusing on parameters like heating set-points, ventilation rates, infiltration, and heating system efficiencies, is applicable across diverse buildings and situations, especially buildings with predictable occupancy patterns and without material failures and deteriorations. These parameters are fundamental to most buildings, regardless of their specific characteristics. While buildings may differ in design or size, they commonly share heating and ventilation requirements, allowing for a similar calibration approach. Energy conservation concerns are universal, making the calibration of these parameters relevant across buildings aiming for improved energy efficiency. Its adaptability, universality, and focus on essential parameters make this calibration method suitable for various buildings seeking to optimize energy performance.

5. Conclusion

Transferring data to simulation programs and obtaining results closely matching reality are critical steps in building energy simulation. This study aimed to validate two existing educational buildings, a singular building (School 1) and a campus facility (School 2), through in situ observations and measurements and applying relevant standards for user-dependent parameters. The analysis and measurement results were incorporated into simulation programs for validation purposes.

Initially, internal temperature measurements were compared with simulation outputs using the CV(RMSE) and MBE methods. In School 1, the simulation outputs initially showed lower temperatures than the measurements, with an average internal temperature of 21.6 °C measured, which was initially simulated at 19.5 °C and revised to 21.3 °C. Revisions were made considering uncertain and user-dependent parameters. School 2 presented a more complex scenario, with some areas showing higher measured temperatures than the simulations. CO₂ measurements were then supposed to differentiate occupancy and vacancy periods for adjustments similar to the revisions made in School 1.

Subsequently, analyses were conducted on invoices and consumption data, verifying natural gas and electricity consumption. Various simulations within specific parameter ranges were performed, and error rates were calculated in monthly verifications. Adjustments were made to electrical equipment and lighting schedules to optimize electricity consumption based on user activity. Natural ventilation values were evaluated across intervals to verify natural gas consumption.

This study outlines the validation steps for building energy simulations to predict accurate energy consumption. Challenges encountered during verification included air infiltration values obtained from references rather than measured via a blower door method. Moreover, during the internal temperature validation phase, precise measurement and data input regarding building zone materials, as well as defining this data as internal mass, will yield more accurate results concerning consumption and internal temperatures. Variations in these uncertain parameters during indoor air temperature calibration need consideration to verify invoice values. These steps should be sequential, ensuring the most accurate values for unknown parameters.

A limitation of this study is that the microclimate impact on the weather data, building energy consumption and indoor conditions has been neglected. The study lacks consideration of how small-scale variations in climate conditions specific to the building’s immediate surroundings might impact weather data accuracy, building energy consumption patterns, and indoor environmental conditions. Addressing these microclimate influences could provide a more comprehensive and accurate analysis of the studied parameters.

Future studies should comprehensively analyze microclimate influences on the validation and calibration process. This entails conducting localized assessments to understand how specific topographical, environmental, and land-use factors impact the accuracy of weather data, affect building energy consumption patterns, and influence indoor environmental quality. Incorporating microclimate considerations will provide a more detailed understanding of the interplay between local climate variations and their effects on building energy simulation, thus enhancing the accuracy and applicability of findings in real-world scenarios.

Figures

Figure 1

The methodology framework of the study

Figure 2

Internal wall thermal camera analysis and placement of Datalogger device

Figure 3

School 1 Datalogger devices’ location (shown in red dots)

Figure 4

Measured CO₂ levels (ppm) from Datalogger in School 1, zone B

Figure 5

Measured CO₂ levels (ppm) from Datalogger in School 2, zone D

Figure 6

Thermal camera analysis of School 1 (a) and School 2 (b)

Figure 7

Building energy simulation models of School 1 and School 2 in DesignBuilder interface

Figure 8

Calibration process

Figure 9

Indoor air temperature measurement results and calibration, School 1, zone B

Figure 10

Indoor air temperature measurement results and calibration, School 1, zone B

Figure 11

Indoor air temperature measurement results and calibration, School 2 – C zone

Figure 12

Indoor air temperature measurement results and calibration, School 2, zone D

Figure 13

Indoor air temperature measurement results and calibration, School 2, zone E

Figure 14

Indoor air temperature measurement results and calibration, School 2, Zone F

Figure 15

Annual electricity consumption validation’s error rates, School 1

Figure 16

Annual natural gas consumption validation’s error rates, School 1

Figure 17

Annual electricity consumption validation’s error rates, School 2

Figure 18

Annual natural gas consumption validation’s error rate, School 2

Table 1

Calibration methods and the error limits allowed in each method

Metric	Standardized by	Error limits	References
RMSE	ASHRAE Guideline 14	10–20%	Ali et al. (2021), Al-Shargabi et al. (2022), ASHRAE (2002), Chong et al. (2021), Dahlström et al. (2022), Franceschini and Neves (2022)
CV(RMSE)	ASHRAE Guideline, IPMVP, FEMP	15–30% (monthly and hourly results)	ASHRAE (2002), IPMVP (2022), Hou et al. (2021), Li et al. (2017)
MBE	ASHRAE Guideline, IPMVP, FEMP	5–20% (monthly and hourly results)	ASHRAE (2002), Franceschini and Neves (2022), Hou et al. (2021)
NMBE	ASHRAE Guideline, IPMVP, FEMP	5–20% (monthly and hourly results)	Ali et al. (2021), ASHRAE (2002), Chong et al. (2021)
GOF	ASHRAE Guideline	0.5–1%	ASHRAE (2002), Chong et al. (2021), Cipriano et al. (2015)
R2	–	Close to 0.999 (monthly and hourly measurements)	ASHRAE (2002), Chong et al. (2021), Singaravel et al. (2018)

Source(s): Created by the authors, 2023

Table 2

Details of building components in School 1

School 1	Material	Thickness [m]	Conductivity [W/m-K]	U-value [W/m2-K]
Above ground walls	Plaster	0.03	0.7	1.42
	Concrete	0.4	0.89
	Plaster	0.03	0.7
Ground and internal floors	Plaster	0.02	0.14	1.65
	Concrete	0.15	0.89
	Sloping Screed	0.05	0.7
	Ceramic tile	0.01	0.8
Pitched roof	Clay Tile	0.01	0.84	0.41
	Flakeboard	0.018	0.3
	EPDM	0.018	0.3
	Air Gap	0.5	N. A
	Rockwool	0.08	0.045
	Concrete	0.15	0.89
	Plaster	0.02	0.7

Source(s): Created by the authors, 2023

Table 3

Details of building components in School 2

School 2	Material	Thickness [m]	Conductivity [W/m-K]	U-value [W/m2-K]
Above ground walls	Plaster	0.03	0.51	1.72
	Clay	0.2	0.68
	Plaster	0.03	0.51
Ground and internal floors	Plaster	0.02	0.14	1.99
	Concrete	0.15	1.6
	Sloping Screed	0.03	0.7
	Ceramic tile	0.01	0.8
Pitched roof	Clay Tile	0.01	0.84	0.41
	Flakeboard	0.018	0.3
	EPDM	0.018	0.3
	Air Gap	0.5	N. A
	Rockwool	0.08	0.045
	Concrete	0.15	0.89
	Plaster	0.02	0.7

Source(s): Created by the authors, 2023

Table 4

Datalogger measurement details

Building	Zone type	Orientation	Code	Measurement period
School 1
Main building	Classroom	South	A	08.02.2022–02.03.2022
	Classroom	North	B	08.02.2022–15.03.2022
School 2
Atelier building/E1	Classroom	Southeast	C	30.06.2021–11.01.2022
Atelier building/E2	Classroom	South	D	10.10.2021–11.01.2022
Main building	Teachers' Room	East	E	10.10.2021–11.01.2022
Main building	Classroom	Northeast	F	02.12.2021–11.01.2022

Source(s): Created by the authors, 2023

Table 5

Presumption of uncertain values for input parameters

Uncertain parameters	Unit	Value range		Calibrated value
		School 1	School 2	School 1		School 2
Boiler efficiency	%	85–95	85–98	89		85
Air infiltration	air changes per hour (ACH)	0.1–0.5	0.1–0.5	0.2		0.3
Heating set point	°C	23–25	21–23	25		Main Building: 22 Atelier Buildings: 23
Natural ventilation	1/h	Warmer months: 4–8 Colder months: 2–6		Lesson	Break	Lesson	Break
		Jan/Feb/Mar/Nov/Dec		1–2	2–4	2–3	3–4
		Apr/May/Sep/Oct		2–4	4–6	3–5	4–6
		Jun/Jul/Aug		4–6	6–8	5–7	7–8

Source(s): Created by the authors, 2023

Table 6

Hourly temperature analysis maximum error rate in this study and a study by Shin et al

Zone	CV(RMSE)	MBE
School 1: hourly temperature analysis maximum error rate
A	4.00%	1.10%
B	0.70%	2.60%
School 2: hourly temperature analysis maximum error rate
C	1.62%	−0.30%
D	1.63%	−0.50%
E	1.99%	−0.25%
F	3.00%	−1.44%
Shin et al. (2022) hourly temperature analysis maximum error rate
Case 1	3.71%	−1.63%
Case 2	2.94%	−0.94%

Source(s): Created by the authors, 2023

Table 7

Monthly energy analysis maximum error rate in this study and three other studies

	MBE	CV(RMSE)
School 1: monthly energy analysis maximum error rate
Electricity	4.50%	5.73%
Natural gas (heating)	−4.95%	4.22%
School 2: monthly energy analysis maximum error rate
Electricity	−5.78%	7.18%
Natural gas (heating)	−5.80%	6.28%
Kunwar et al. (2021) monthly Energy Analysis Maximum Error Rate
East oriented room	−5.10%	39.50%
South oriented room	−13.00%	33.10%
West oriented room	−7.50%	36.50%
Monetti et al. (2015) monthly energy analysis maximum error rate
Climatic Room	0.83%	20.40%
Office	−0.14%	3.51%
Office on first floor	0.06%	1.54%
Buffer zone	−0.01%	0.19%
Pan et al. (2007) monthly energy analysis maximum error rate
Electricity	n.a	4.71%
Natural gas (heating)	n.a	8.94%

Source(s): Created by the authors, 2023

Data availability statement: The data underpinning this study are currently unavailable to the public due to restrictions imposed by the funding authority. However, the data can be shared five years later after the project’s conclusion. If you are interested in accessing the data after 2028, please feel free to reach out to the corresponding author, who can assist you in making the request.