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International Construction Specialty Conference of the Canadian Society for Civil Engineering (ICSC) (5th : 2015)

Development and validation of regression models to predict annual energy consumption of office buildings… Amiri, Shideh Shams; Mottahedi, Mohammad; Asadi, Somayeh; Riley, David Jun 30, 2015

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5th International/11th Construction Specialty Conference 5e International/11e Conférence spécialisée sur la construction    Vancouver, British Columbia June 8 to June 10, 2015 / 8 juin au 10 juin 2015   DEVELOPMENT AND VALIDATION OF REGRESSION MODELS TO PREDICT ANNUAL ENERGY CONSUMPTION OF OFFICE BUILDINGS IN DIFFERENT CLIMATE REGIONS IN THE UNITED STATES Shideh Shams Amiri1,Mohammad Mottahedi 2, Somayeh Asadi1, 3,David Riley1 1 Pennsylvania State University, United State 2 University of Texas at San Antonio, United State  3asadi@engr.psu.edu Abstract: Energy consumption in commercial buildings has been growing substantially in recent years. Recently, building energy consumption estimation tools have been used to calculate energy savings and emissions reduction. Energy performance of building is complicated since it depends on multiple variables associated to building characteristics, equipment and systems, weather, occupants, and sociological influences. Therefore, the objective of this study is to develop the multi-linear regression models to predict energy consumption of an office building in five different climate regions in the United States. In order to achieve this objective, a typical commercial building was selected and the effect of 17 key building design parameters on its energy performance was investigated. To quantify building energy consumption, eQuest and DOE-2, which are building energy simulation software programs, were used to develop the building profile and perform annual energy simulation. In addition, Monte Carlo simulation technique was used to create a ten thousands comprehensive dataset covering the full range of design parameters for each studied climate region. An in-house computer program was developed to implement the Monte Carlo simulation. Statistical analysis was performed using R statistical analysis program to develop a set of linear regression equations predicting energy consumption of each design scenario. The difference between obtained results from regression model and DOE-2 are largely within 5%. In addition, standardized regression coefficient was calculated to assess the sensitivity of heating, cooling, and total energy loads to different building design parameters across five climate zones. It is believed that the developed regression models can be used to estimate the energy consumption of office buildings in different climate regions when designers and engineers consider various building envelope designs in the early stages of the design. 1 INTRODUCTION  In recent years, the contribution of modern world to energy consumption has been increased significantly. World energy consumption has increased from 524 quadrillion Btu in 2010 to 630 quadrillion Btu in 2010 and 820 quadrillion Btu in 2040, a 30 year increase of 56% (EIA 2010). The same trend was seen in the United States in which total energy consumption was approximately 97.9 quadrillion Btu in 2010 with an increase rate of 8.3% (EIA 2010). According to the EIA (2010), building sector in the U.S. consume 40% of total energy which is higher than transportation and industrial sectors. Therefore, proper tools are needed to estimate and optimize energy consumption in buildings. Several studies have been conducted to study building energy performance. In addition, there are different methods including simple regression analysis and dynamic simulation software programs (e.g. 078-1 EnergyPlus and DOE-2 (Repice 2011) to model building energy performance (Lam et al. 2010, Broun et al. 2014, Catalina et al. 2013, Asadi et al. 2012). In a study conducted by Hygh et al. (2012), EnergyPlus software was used to perform energy simulation and calculate annual building energy consumption of a commercial building in four different climate zones. Mohammadpour et al.(2014) employed EnergyPlus to model energy consumption of three retrofit projects and compared energy consumption before and after the retrofit. Asadi et al. (2014) developed multiple linear regression models to predict building energy consumption for a typical residential building in the hot and humid climate. The effect of 7 buildings shapes as well as 17 building design parameters including HVAC schedule, orientation, building envelop, etc. on building energy performance were investigated. Results of their study showed that there is a good agreement between results of the DOE-2 and regression equations and the error was less than 5% in most cases. In another study, Catalina et al. (2013) developed regression models to investigate monthly heating load in residential building in France. The inputs of the regression model include the window to wall ratio, building envelope U-value, and building shape factor. Their analysis indicated that there is a strong relationship between building shape and energy consumption. Later, Lam et al. (2010) developed regression models using DOE-2 simulation results to determine the impact of 12 building design sensitive variables on building energy performance. The authors reported that there is a strong correlation between annual building energy consumption and design parameters in the warm climates. This paper proposes a simple and realistic approach to estimate energy consumption of a typical office building in five different climate zones. The primary objective of this study is to develop a multi-linear regression model to predict and quantify energy consumption of a commercial building in the early stages of building design. 2 MATERIAL AND METHOD  Building energy simulation models are commonly used to predict energy performance. They are powerful computational tools helping users to model a building as a system and to identify potential opportunities to reduce building energy consumption. In the present study, a comprehensive set of inputs such as internal loads, mechanical and electrical system, orientation and occupancy schedule was considered to calculate energy consumption. Also five major climate zones including cold dry, cool dry, mixed humid, warm marine and hot humid were considered in this study (Table 1).  Table 1: Five selected cities in each climate region. Climate Representative city HDD CDD Cold dry Billings >7000 <2000 Cool dry Salt lake City <5500-7000 <2000 Mixed humid Washington DC <4000-5499 <2000 Warm marine San Jose <4000 <2000 Hot humid Houston <4000 ≥2000 HDD=Average heating degree-days, CDD= Average cooling degree-days (EIA, Noaa 2012)   Monte Carlo simulation was performed by randomly selecting 17 variables based on uniform distribution  to generate a new input file for the simulation software. This process was repeated 10000 time to effectively examine the configuration space. The eQuest and DOE-2 software programs were utilized to calculate the annual heating and cooling consumption for each design scenario based on Monte Carlo simulation. eQUEST software, which adds an additional graphical wizards capability to DOE-2, facilitates creation of building envelope and climate zones. Using DOE-2 avoids imprecisions introduced by simplifying algorithms, and since it is a configurable tool, it can be utilized for detailed design. Based on the Monte Carlo simulation, 10,000 simulation runs were defined for each of the five climate zones, covering a complete range of design parameters. In addition, a code was written in Python’s programming language to help extracting required data from DOE-2. Then, these data were used to develop the multiple linear regression equations and investigate the relationship between different parameter and annual energy consumption. Figure 1 illustrates the framework of the analysis.  078-2  Figure 1: Framework of present study 2.1 Base Case Model Description and Design Variables Table 2 shows the list of parameters that were used to build the office building model using eQuest and Table 3 represents the implemented variables in the Monte Carlo Simulation. As it can be seen in Table 2, 17 design parameters including building envelop, orientation and occupant schedules were considered. The properties of all building components including wall, roof, ceiling, foundation, and floors were defined in this study. For each parameter, set of values and ranges are selected based on AHRAE 90.1 (ASHRAE 2007). In addition, a comprehensive data set was generated based on random distribution to examine all possible configuration of building envelope. Uniform distribution was applied to each parameter ensuring that all values within the specified range are investigated equally for each design choice. Table 2: Description of eQuest inputs.  Constant parameters  Building type Office bldg., two story Jurisdiction ASHRAE 90.1 Building Area 2322.6 m2 Cooling Equip Chilled water coils Heating Equip Hot water coils Analysis Year 2013 Day Light Control Daylight control Usage details Hourly end use profile Zoning Pattern One per floor Floor-To-Floor 2.74 m Floor-To-Ceiling 2.43 m Door type Opaque Door Construction Wood, hollow core flush, 0.02-0.096m  Windows Area method Present of Gross wall area  Floor to Floor Window ratio 40% Net Floor to Ceiling Window ratio 53.3% Window High  1.59 m Cooling source (HVAC)  Evaporate resistance Heating Source Furnace System type Direct Number of Occupants  105 People Activity  0.131 kw/hr.     078-3 Table 3: Implemented variables in the Monte Carlo Simulation Variable Range U –value (W/m2k) Variable Range U –value (W/m2k) Top floor ceiling interior finish  • Acoustic Tile  • Drywall Finish  • Plaster Finish •4.50 •12.6 •10.1 Floor Construction • 0.05m Concrete • 0.10m Concrete • 0.15m Concrete • 0.20m Concrete •20.0 •17.8 •11.7 •8.84 Top floor ceiling exterior insulation • No Board Insulation • Polyurethane (R-6) • polyurethane  (R-9)  •0.90 •0.72 Exterior wall absorbance  • light • Medium • Dark  N/A N/A N/A Top floor batt insulation • R-30       • R-45 • R-11       • R-19 •No Batt •0.17  •0.7 •0.47  •0.27 Roof absorbance • light • Medium • Dark N/A N/A N/A Ceiling Interior finish  • Acoustic Tile  • Drywall Finish  • Plaster Finish •4.50 •12.6 •10.1 Roof Construction •ASHRAE Roof # 2,9,11, 16,20 26,28,33,35 •min =0.35 •max=0.74 Ceiling Insulation Parameters  • Wool Batt (R11)  • Wool Batt (R19)  • Wool Batt (R30) •0.47 •0.27 •0.17 Interior Wall •ASHRAE Wall #       3,10,11,17 23,27,31,32,34,38,39,41,43,35,47 •min=0.17 •max=3.3 Ground Floor Construction Concrete • 0.1m          •0.3m • 0.15m        •0.2m •17.8  •7.69 •17.7  •8.84 Exterior Wall  •ASHRAE Wall #1, 3,6,11,12,19 25,27,29,30,32 •Min=0.19 •max=2.65 Ground Floor Interior Finish •Carpet (No Pad) •Vinyl Tile •Ceramic/Stone Tile •0.21 •0.007 •0.004 Glass Category  • Single Low-e • Double Low-e • Triple Low-e •2.0 •1.0 •7.0 Floor Interior Finish •No Surface Finish • Carpet (No Pad) • Vinyl Tile/Stone  •4.7 •11.1 Building Orientation •360 °            •180° •90  °             •270°  Occupant  Schedule • 08:00:00 AM to 05:00:00 PM (Monday-Friday) +HVAC 1 • 08:00:00 AM to 06:00:00 PM (Monday-Thursday) +HVAC 1 • 07:00:00 AM to 05:00:00 PM (Monday-Thursday) +HVAC 1 • 07:00:00 AM to 04:00:00 PM (Monday-Friday) +HVAC1 • 08:00:00 AM to 05:00:00 PM (Monday-Friday) +HVAC2 …………… •07:00:00 AM to 04:00:00 PM (Monday-Friday) +HVAC3 1HVAC system turns on 1 hour before working hours and turn off 1 hour after working hours. 2HVAC system is on 24/7. 3HVAC system is on only during workings hours.  078-4 2.2 Regression Analysis  The aim of regression analysis in this study is to develop simple and accurate models to predict energy consumption in commercial buildings. A multiple regression model with more than one explanatory variable may be written as:  [1]Y= β0+ β1χ1+ β2χ2+...+ βnχn Where y is the output, βi is the regression parameters and χ i  is the input variables. The least-squares method is generally used for estimation purposes in the multiple-regression model. Once regression coefficients are identified, a prediction equation can then be used to estimate the value of a continuous output as a linear function of one or more independent inputs.  A comprehensive dataset was developed based on the randomly generated building parameters using energy simulation model. Eighty percent (80%) of the simulation runs were selected randomly and used to develop the regression equations. Remaining twenty percent (20%) of the runs were used to validate the developed model. The generated dataset was used to develop regression equations predicting annual building energy consumption.  3 RESULTS AND DISCUSSION 3.1 Interaction between parameters Analysis of the Interaction between parameters represents the combined effects of the independent parameters on the dependent variable. When an interaction effect is present, the impact of one factor depends on the level of the other factor. One of the methods to determine the interaction between parameter is to identify multicollinearity. Multicollinearity is a statistical phenomenon in which two or more predictor variables in a multiple regression model are strongly correlated. It arises when two or more predictors in the model are correlated and provide redundant information about the response. Generalized variance-inflation factor (GVIF) can be used to detect multicollinearity in the regression equation. The GVIF indicates the degree to which the confidence interval for that variable regression parameter is expanded relative to a model with uncorrelated predictors. As a general rule, GVIF>4 indicates a multicollinearity problem. The GVIF results are presented in Table 4. As it can be seen in this table, the GVIF values in all cases are less than 1.3 indicating that there is no correlation between predictor variables in the multiple regression models. Table 4: Generalized variance-inflation coefficients  Billings Houston Washington, D.C. San Jose Salt Lake City Building Orientation 1.038285 1.035407 1.028915 1.034806 1.030121 Top Floor Batt Insulation 1.03594 1.035997 1.034708 1.038009 1.036116 Ceiling Interior Finish 1.023482 1.021158 1.020389 1.02523 1.024162 Ceiling Insulation 1.026014 1.02497 1.023632 1.02252 1.024083 Floor Construction 1.038519 1.034395 1.037726 1.03494 1.026742 Top Floor Ceiling Exterior Insulation 1.039947 1.034008 1.037932 1.031834 1.034814 Top Floor Ceiling Interior finish 1.048875 1.044126 1.045476 1.047932 1.047745 Ground Floor Construction 1.022871 1.024229 1.018244 1.022585 1.024278 Ground Floor Interior Finish 1.038625 1.032505 1.034519 1.028883 1.032269 Floor Interior Finish 1.025238 1.025422 1.022385 1.018312 1.02167 078-5 Interior Wall 1.230111 1.215584 1.214586 1.220215 1.200708 Exterior Wall 1.197334 1.210685 1.204963 1.199288 1.18698 Roof Construction 1.093883 1.110539 1.101251 1.094528 1.099383 Exterior Wall Absorbance 1.021308 1.02599 1.028086 1.01917 1.025674 Roof Absorbance 1.025294 1.025288 1.023411 1.020919 1.022567 Occupant Schedule 1.129032 1.118156 1.117025 1.115387 1.118505 3.2 Regression Results and Discussion Table 5 shows the regression equations associated with each climate zones. Five different regression equations were developed for each climate zone. The R2, root mean square error (RMSE) and F-Test values are shown in this table. R2 measures how close the data are to the fitted regression line. As it can be seen, the R2 value is more than 0.94 in all cases which indicates that the model fits with the data.   Table 5: Regression equations associated with each climate zones Regression Coefficient   = 𝛽𝛽1𝑥𝑥1 + 𝛽𝛽2 𝑥𝑥2+𝛽𝛽3 𝑥𝑥3 + 𝛽𝛽4𝑥𝑥4 + 𝛽𝛽5𝑥𝑥5 + 𝛽𝛽6 𝑥𝑥6+𝛽𝛽7𝑥𝑥7          + 𝛽𝛽8𝑥𝑥8 + 𝛽𝛽9 𝑥𝑥9 +𝛽𝛽10𝑥𝑥10+𝛽𝛽11𝑥𝑥11 + 𝛽𝛽12 𝑥𝑥12          + 𝛽𝛽13𝑥𝑥13 + 𝛽𝛽14𝑥𝑥14 + 𝛽𝛽15 𝑥𝑥15+𝛽𝛽16 𝑥𝑥16 + 𝛽𝛽17𝑥𝑥17    San Jose Washington, DC Houston Billings Salt Lake City  -2.20 -0.68 1.68 -2.10 -0.41  -1.35 0.70 1.19 -3.52 -0.87  -2.07 -3.16 0.49 -5.02 1.80  0.19 -4.14 -1.62 -8.93 -7.37  1.30 1.02 0.73 0.49 -0.03  0.04 -0.10 0.31 -0.42 -0.12  0.57 -3.32 -1.78 -2.94 -2.15  1.40 1.41 2.56 -2.78 -2.64  -0.47 1.91 -7.04 -1.57 -2.37  -0.97 -2.83 2.65 2.26 -3.01  0.48 0.42 -0.10 0.21 0.28  -0.40 -0.89 -0.33 -1.33 -1.70  -0.42 0.09 1.30 -0.21 0.44 078-6 To demonstrate the variation in energy consumption for each climate zone, identical parameter samples were used for all locations, but the observed range and variability of total energy were unique in different locations (Fig 3). It can be seen that number of outliers is highest in Billings where the first and third quartiles makes up less than half of the range between the minimum and maximum observed. The high variability in Billings is driven by the cold winters and hot summers, which exhibits wide variation depending on the combination of the values for the design parameters.  Figure 3: Distribution of total energy consumption for the five locations 3.3 Regression Model Validation Model validation is one of the most important steps in finding the best fit for the regression model. R2 and RMSE values are commonly used to validate the model. In this study two thousands of simulations runs were set aside to test the regression model performance and validate the results. Figure 4 shows the validation results for each climate region.  It can be observed that the results from the model are well correlated with the data from simulations with acceptable error of less than 5%.    078-8    Figure 4: Validation of the total energy consumption models 4 CONCLUSION The goal of this study was to develop simple regression models for office building in the five major climates including cold dry, cool dry, mixed humid, warm marine and hot humid. A total of 17 key building design variables were identified and considered as inputs in the regression models. The coefficient of determination R2 varies from 0.94 to 0.95 indicating that 95% of the variation in annual building energy consumption can be explained by change in 17 parameters. The analysis indicates that there is a strong interaction between building location and level of energy consumption. It also shows Billings (cold-dry) with cold winters and hot summers consume the highest amount of energy in comparison with other location. On the other hand, San Jose (warm marine) with the subtropical Mediterranean climate has the least temperature variation and subsequently has the least annual energy consumption. The difference between regression-predicted and DOE-simulated annual building energy use are largely within 5%. Consequently, the developed regression models can be used for comparative energy studies to estimate the potential energy savings during the early stage of design when different building schemes and design concepts are being considered. Climates with the least temperature variation, subsequently have the least annual energy consumption. The difference between regression-predicted and DOE-simulated annual building energy use are largely within 5%. Consequently, the developed regression models can be used for comparative energy studies to estimate the potential energy savings during the early stage of design when different building schemes and design concepts are being considered. The models for energy consumption prediction presented in this study, will be expanded in future and will be validated using case studies on physical commercial building to better estimate the prediction accuracy. 078-9 References Asadi., S., Amiri., S.S., Mottahedi., M., 2014, On the development of multi-linear regression analysis to assess energy consumption in the early stages of building design, Energy and Buildings, 85:246-255. Asadi, S., Hassan, M., and Beheshti, A., 2012. Development and validation of a simple estimating tool to predict heating and cooling energy demand for attics of residential buildings. Energy and Buildings, 54:12-21. ASHRAE, ASHRAE 90.1-2007, American Society of Heating, Refrigeration, and Air-Conditioning Engineers, Atlanta, GA, 2007. Broun, R., Babaizadeh, H., Zakersalehi, A., and Menzies, G.F., 2014. Integrated Life Cycle Energy and Greenhouse Gas Analysis of Exterior Wall Systems for Residential Buildings. Sustainability, 6 (12):8592-8603. Catalina, T., Iordache, V., and Caracaleanu, B., 2013. Multiple regression model for fast prediction of the heating energy demand. Energy and Buildings, 57:302-312. Department of Energy (DOE) EnergyPlus 7,2011. Department of Energy (DOE), DOE-2., Building Energy Use and Cost Analysis Tool, 2009, Available from: http://doe2.com/DOE2/index.html. Energy Information Administration (EIA), Annual Energy Review, DOE/EIA03842010, U.S. Energy Information Administration, 2011. Hygh, J.S.,  DeCarolis, J.F.,  Hill, D.B., Ranji Ranjithan, S., 2012, Multivariate regression asan energy assessment tool in early building design, Building and Environment, 57, 165–175. Lam, J.C., Wan, K., Liu, D., and Tsang., C.L, 2010. Multiple regression models for energy  use in air-conditioned office buildings in different climates.  Energy Conversion and Management, 51(12): 2692-2697. Mohammadpour, A., Alanqar, I., Anumba, C., and Messner, J., 2014, Cross Case Energy Simulation Modeling Analysis in Healthcare Facilities Retrofit, Computing in Civil and Building Engineering Conference, Orlando, FL, USA. Repice, R., 2011. Annual Energy Review 2010. DOE/EIA-0384 (2010), US Energy Information Administration, Washington, DC.   078-10  5th International/11th Construction Specialty Conference 5e International/11e Conférence spécialisée sur la construction    Vancouver, British Columbia June 8 to June 10, 2015 / 8 juin au 10 juin 2015   DEVELOPMENT AND VALIDATION OF REGRESSION MODELS TO PREDICT ANNUAL ENERGY CONSUMPTION OF OFFICE BUILDINGS IN DIFFERENT CLIMATE REGIONS IN THE UNITED STATES Shideh Shams Amiri1,Mohammad Mottahedi 2, Somayeh Asadi1, 3,David Riley1 1 Pennsylvania State University, United State 2 University of Texas at San Antonio, United State  3asadi@engr.psu.edu Abstract: Energy consumption in commercial buildings has been growing substantially in recent years. Recently, building energy consumption estimation tools have been used to calculate energy savings and emissions reduction. Energy performance of building is complicated since it depends on multiple variables associated to building characteristics, equipment and systems, weather, occupants, and sociological influences. Therefore, the objective of this study is to develop the multi-linear regression models to predict energy consumption of an office building in five different climate regions in the United States. In order to achieve this objective, a typical commercial building was selected and the effect of 17 key building design parameters on its energy performance was investigated. To quantify building energy consumption, eQuest and DOE-2, which are building energy simulation software programs, were used to develop the building profile and perform annual energy simulation. In addition, Monte Carlo simulation technique was used to create a ten thousands comprehensive dataset covering the full range of design parameters for each studied climate region. An in-house computer program was developed to implement the Monte Carlo simulation. Statistical analysis was performed using R statistical analysis program to develop a set of linear regression equations predicting energy consumption of each design scenario. The difference between obtained results from regression model and DOE-2 are largely within 5%. In addition, standardized regression coefficient was calculated to assess the sensitivity of heating, cooling, and total energy loads to different building design parameters across five climate zones. It is believed that the developed regression models can be used to estimate the energy consumption of office buildings in different climate regions when designers and engineers consider various building envelope designs in the early stages of the design. 1 INTRODUCTION  In recent years, the contribution of modern world to energy consumption has been increased significantly. World energy consumption has increased from 524 quadrillion Btu in 2010 to 630 quadrillion Btu in 2010 and 820 quadrillion Btu in 2040, a 30 year increase of 56% (EIA 2010). The same trend was seen in the United States in which total energy consumption was approximately 97.9 quadrillion Btu in 2010 with an increase rate of 8.3% (EIA 2010). According to the EIA (2010), building sector in the U.S. consume 40% of total energy which is higher than transportation and industrial sectors. Therefore, proper tools are needed to estimate and optimize energy consumption in buildings. Several studies have been conducted to study building energy performance. In addition, there are different methods including simple regression analysis and dynamic simulation software programs (e.g. 078-1 EnergyPlus and DOE-2 (Repice 2011) to model building energy performance (Lam et al. 2010, Broun et al. 2014, Catalina et al. 2013, Asadi et al. 2012). In a study conducted by Hygh et al. (2012), EnergyPlus software was used to perform energy simulation and calculate annual building energy consumption of a commercial building in four different climate zones. Mohammadpour et al.(2014) employed EnergyPlus to model energy consumption of three retrofit projects and compared energy consumption before and after the retrofit. Asadi et al. (2014) developed multiple linear regression models to predict building energy consumption for a typical residential building in the hot and humid climate. The effect of 7 buildings shapes as well as 17 building design parameters including HVAC schedule, orientation, building envelop, etc. on building energy performance were investigated. Results of their study showed that there is a good agreement between results of the DOE-2 and regression equations and the error was less than 5% in most cases. In another study, Catalina et al. (2013) developed regression models to investigate monthly heating load in residential building in France. The inputs of the regression model include the window to wall ratio, building envelope U-value, and building shape factor. Their analysis indicated that there is a strong relationship between building shape and energy consumption. Later, Lam et al. (2010) developed regression models using DOE-2 simulation results to determine the impact of 12 building design sensitive variables on building energy performance. The authors reported that there is a strong correlation between annual building energy consumption and design parameters in the warm climates. This paper proposes a simple and realistic approach to estimate energy consumption of a typical office building in five different climate zones. The primary objective of this study is to develop a multi-linear regression model to predict and quantify energy consumption of a commercial building in the early stages of building design. 2 MATERIAL AND METHOD  Building energy simulation models are commonly used to predict energy performance. They are powerful computational tools helping users to model a building as a system and to identify potential opportunities to reduce building energy consumption. In the present study, a comprehensive set of inputs such as internal loads, mechanical and electrical system, orientation and occupancy schedule was considered to calculate energy consumption. Also five major climate zones including cold dry, cool dry, mixed humid, warm marine and hot humid were considered in this study (Table 1).  Table 1: Five selected cities in each climate region. Climate Representative city HDD CDD Cold dry Billings >7000 <2000 Cool dry Salt lake City <5500-7000 <2000 Mixed humid Washington DC <4000-5499 <2000 Warm marine San Jose <4000 <2000 Hot humid Houston <4000 ≥2000 HDD=Average heating degree-days, CDD= Average cooling degree-days (EIA, Noaa 2012)   Monte Carlo simulation was performed by randomly selecting 17 variables based on uniform distribution  to generate a new input file for the simulation software. This process was repeated 10000 time to effectively examine the configuration space. The eQuest and DOE-2 software programs were utilized to calculate the annual heating and cooling consumption for each design scenario based on Monte Carlo simulation. eQUEST software, which adds an additional graphical wizards capability to DOE-2, facilitates creation of building envelope and climate zones. Using DOE-2 avoids imprecisions introduced by simplifying algorithms, and since it is a configurable tool, it can be utilized for detailed design. Based on the Monte Carlo simulation, 10,000 simulation runs were defined for each of the five climate zones, covering a complete range of design parameters. In addition, a code was written in Python’s programming language to help extracting required data from DOE-2. Then, these data were used to develop the multiple linear regression equations and investigate the relationship between different parameter and annual energy consumption. Figure 1 illustrates the framework of the analysis.  078-2  Figure 1: Framework of present study 2.1 Base Case Model Description and Design Variables Table 2 shows the list of parameters that were used to build the office building model using eQuest and Table 3 represents the implemented variables in the Monte Carlo Simulation. As it can be seen in Table 2, 17 design parameters including building envelop, orientation and occupant schedules were considered. The properties of all building components including wall, roof, ceiling, foundation, and floors were defined in this study. For each parameter, set of values and ranges are selected based on AHRAE 90.1 (ASHRAE 2007). In addition, a comprehensive data set was generated based on random distribution to examine all possible configuration of building envelope. Uniform distribution was applied to each parameter ensuring that all values within the specified range are investigated equally for each design choice. Table 2: Description of eQuest inputs.  Constant parameters  Building type Office bldg., two story Jurisdiction ASHRAE 90.1 Building Area 2322.6 m2 Cooling Equip Chilled water coils Heating Equip Hot water coils Analysis Year 2013 Day Light Control Daylight control Usage details Hourly end use profile Zoning Pattern One per floor Floor-To-Floor 2.74 m Floor-To-Ceiling 2.43 m Door type Opaque Door Construction Wood, hollow core flush, 0.02-0.096m  Windows Area method Present of Gross wall area  Floor to Floor Window ratio 40% Net Floor to Ceiling Window ratio 53.3% Window High  1.59 m Cooling source (HVAC)  Evaporate resistance Heating Source Furnace System type Direct Number of Occupants  105 People Activity  0.131 kw/hr.     078-3 Table 3: Implemented variables in the Monte Carlo Simulation Variable Range U –value (W/m2k) Variable Range U –value (W/m2k) Top floor ceiling interior finish  • Acoustic Tile  • Drywall Finish  • Plaster Finish •4.50 •12.6 •10.1 Floor Construction • 0.05m Concrete • 0.10m Concrete • 0.15m Concrete • 0.20m Concrete •20.0 •17.8 •11.7 •8.84 Top floor ceiling exterior insulation • No Board Insulation • Polyurethane (R-6) • polyurethane  (R-9)  •0.90 •0.72 Exterior wall absorbance  • light • Medium • Dark  N/A N/A N/A Top floor batt insulation • R-30       • R-45 • R-11       • R-19 •No Batt •0.17  •0.7 •0.47  •0.27 Roof absorbance • light • Medium • Dark N/A N/A N/A Ceiling Interior finish  • Acoustic Tile  • Drywall Finish  • Plaster Finish •4.50 •12.6 •10.1 Roof Construction •ASHRAE Roof # 2,9,11, 16,20 26,28,33,35 •min =0.35 •max=0.74 Ceiling Insulation Parameters  • Wool Batt (R11)  • Wool Batt (R19)  • Wool Batt (R30) •0.47 •0.27 •0.17 Interior Wall •ASHRAE Wall #       3,10,11,17 23,27,31,32,34,38,39,41,43,35,47 •min=0.17 •max=3.3 Ground Floor Construction Concrete • 0.1m          •0.3m • 0.15m        •0.2m •17.8  •7.69 •17.7  •8.84 Exterior Wall  •ASHRAE Wall #1, 3,6,11,12,19 25,27,29,30,32 •Min=0.19 •max=2.65 Ground Floor Interior Finish •Carpet (No Pad) •Vinyl Tile •Ceramic/Stone Tile •0.21 •0.007 •0.004 Glass Category  • Single Low-e • Double Low-e • Triple Low-e •2.0 •1.0 •7.0 Floor Interior Finish •No Surface Finish • Carpet (No Pad) • Vinyl Tile/Stone  •4.7 •11.1 Building Orientation •360 °            •180° •90  °             •270°  Occupant  Schedule • 08:00:00 AM to 05:00:00 PM (Monday-Friday) +HVAC 1 • 08:00:00 AM to 06:00:00 PM (Monday-Thursday) +HVAC 1 • 07:00:00 AM to 05:00:00 PM (Monday-Thursday) +HVAC 1 • 07:00:00 AM to 04:00:00 PM (Monday-Friday) +HVAC1 • 08:00:00 AM to 05:00:00 PM (Monday-Friday) +HVAC2 …………… •07:00:00 AM to 04:00:00 PM (Monday-Friday) +HVAC3 1HVAC system turns on 1 hour before working hours and turn off 1 hour after working hours. 2HVAC system is on 24/7. 3HVAC system is on only during workings hours.  078-4 2.2 Regression Analysis  The aim of regression analysis in this study is to develop simple and accurate models to predict energy consumption in commercial buildings. A multiple regression model with more than one explanatory variable may be written as:  [1]Y= β0+ β1χ1+ β2χ2+...+ βnχn Where y is the output, βi is the regression parameters and χ i  is the input variables. The least-squares method is generally used for estimation purposes in the multiple-regression model. Once regression coefficients are identified, a prediction equation can then be used to estimate the value of a continuous output as a linear function of one or more independent inputs.  A comprehensive dataset was developed based on the randomly generated building parameters using energy simulation model. Eighty percent (80%) of the simulation runs were selected randomly and used to develop the regression equations. Remaining twenty percent (20%) of the runs were used to validate the developed model. The generated dataset was used to develop regression equations predicting annual building energy consumption.  3 RESULTS AND DISCUSSION 3.1 Interaction between parameters Analysis of the Interaction between parameters represents the combined effects of the independent parameters on the dependent variable. When an interaction effect is present, the impact of one factor depends on the level of the other factor. One of the methods to determine the interaction between parameter is to identify multicollinearity. Multicollinearity is a statistical phenomenon in which two or more predictor variables in a multiple regression model are strongly correlated. It arises when two or more predictors in the model are correlated and provide redundant information about the response. Generalized variance-inflation factor (GVIF) can be used to detect multicollinearity in the regression equation. The GVIF indicates the degree to which the confidence interval for that variable regression parameter is expanded relative to a model with uncorrelated predictors. As a general rule, GVIF>4 indicates a multicollinearity problem. The GVIF results are presented in Table 4. As it can be seen in this table, the GVIF values in all cases are less than 1.3 indicating that there is no correlation between predictor variables in the multiple regression models. Table 4: Generalized variance-inflation coefficients  Billings Houston Washington, D.C. San Jose Salt Lake City Building Orientation 1.038285 1.035407 1.028915 1.034806 1.030121 Top Floor Batt Insulation 1.03594 1.035997 1.034708 1.038009 1.036116 Ceiling Interior Finish 1.023482 1.021158 1.020389 1.02523 1.024162 Ceiling Insulation 1.026014 1.02497 1.023632 1.02252 1.024083 Floor Construction 1.038519 1.034395 1.037726 1.03494 1.026742 Top Floor Ceiling Exterior Insulation 1.039947 1.034008 1.037932 1.031834 1.034814 Top Floor Ceiling Interior finish 1.048875 1.044126 1.045476 1.047932 1.047745 Ground Floor Construction 1.022871 1.024229 1.018244 1.022585 1.024278 Ground Floor Interior Finish 1.038625 1.032505 1.034519 1.028883 1.032269 Floor Interior Finish 1.025238 1.025422 1.022385 1.018312 1.02167 078-5 Interior Wall 1.230111 1.215584 1.214586 1.220215 1.200708 Exterior Wall 1.197334 1.210685 1.204963 1.199288 1.18698 Roof Construction 1.093883 1.110539 1.101251 1.094528 1.099383 Exterior Wall Absorbance 1.021308 1.02599 1.028086 1.01917 1.025674 Roof Absorbance 1.025294 1.025288 1.023411 1.020919 1.022567 Occupant Schedule 1.129032 1.118156 1.117025 1.115387 1.118505 3.2 Regression Results and Discussion Table 5 shows the regression equations associated with each climate zones. Five different regression equations were developed for each climate zone. The R2, root mean square error (RMSE) and F-Test values are shown in this table. R2 measures how close the data are to the fitted regression line. As it can be seen, the R2 value is more than 0.94 in all cases which indicates that the model fits with the data.   Table 5: Regression equations associated with each climate zones Regression Coefficient   = 𝛽𝛽1𝑥𝑥1 + 𝛽𝛽2 𝑥𝑥2+𝛽𝛽3 𝑥𝑥3 + 𝛽𝛽4𝑥𝑥4 + 𝛽𝛽5𝑥𝑥5 + 𝛽𝛽6 𝑥𝑥6+𝛽𝛽7𝑥𝑥7          + 𝛽𝛽8𝑥𝑥8 + 𝛽𝛽9 𝑥𝑥9 +𝛽𝛽10𝑥𝑥10+𝛽𝛽11𝑥𝑥11 + 𝛽𝛽12 𝑥𝑥12          + 𝛽𝛽13𝑥𝑥13 + 𝛽𝛽14𝑥𝑥14 + 𝛽𝛽15 𝑥𝑥15+𝛽𝛽16 𝑥𝑥16 + 𝛽𝛽17𝑥𝑥17    San Jose Washington, DC Houston Billings Salt Lake City  -2.20 -0.68 1.68 -2.10 -0.41  -1.35 0.70 1.19 -3.52 -0.87  -2.07 -3.16 0.49 -5.02 1.80  0.19 -4.14 -1.62 -8.93 -7.37  1.30 1.02 0.73 0.49 -0.03  0.04 -0.10 0.31 -0.42 -0.12  0.57 -3.32 -1.78 -2.94 -2.15  1.40 1.41 2.56 -2.78 -2.64  -0.47 1.91 -7.04 -1.57 -2.37  -0.97 -2.83 2.65 2.26 -3.01  0.48 0.42 -0.10 0.21 0.28  -0.40 -0.89 -0.33 -1.33 -1.70  -0.42 0.09 1.30 -0.21 0.44 078-6 To demonstrate the variation in energy consumption for each climate zone, identical parameter samples were used for all locations, but the observed range and variability of total energy were unique in different locations (Fig 3). It can be seen that number of outliers is highest in Billings where the first and third quartiles makes up less than half of the range between the minimum and maximum observed. The high variability in Billings is driven by the cold winters and hot summers, which exhibits wide variation depending on the combination of the values for the design parameters.  Figure 3: Distribution of total energy consumption for the five locations 3.3 Regression Model Validation Model validation is one of the most important steps in finding the best fit for the regression model. R2 and RMSE values are commonly used to validate the model. In this study two thousands of simulations runs were set aside to test the regression model performance and validate the results. Figure 4 shows the validation results for each climate region.  It can be observed that the results from the model are well correlated with the data from simulations with acceptable error of less than 5%.    078-8    Figure 4: Validation of the total energy consumption models 4 CONCLUSION The goal of this study was to develop simple regression models for office building in the five major climates including cold dry, cool dry, mixed humid, warm marine and hot humid. A total of 17 key building design variables were identified and considered as inputs in the regression models. The coefficient of determination R2 varies from 0.94 to 0.95 indicating that 95% of the variation in annual building energy consumption can be explained by change in 17 parameters. The analysis indicates that there is a strong interaction between building location and level of energy consumption. It also shows Billings (cold-dry) with cold winters and hot summers consume the highest amount of energy in comparison with other location. On the other hand, San Jose (warm marine) with the subtropical Mediterranean climate has the least temperature variation and subsequently has the least annual energy consumption. The difference between regression-predicted and DOE-simulated annual building energy use are largely within 5%. Consequently, the developed regression models can be used for comparative energy studies to estimate the potential energy savings during the early stage of design when different building schemes and design concepts are being considered. Climates with the least temperature variation, subsequently have the least annual energy consumption. The difference between regression-predicted and DOE-simulated annual building energy use are largely within 5%. Consequently, the developed regression models can be used for comparative energy studies to estimate the potential energy savings during the early stage of design when different building schemes and design concepts are being considered. The models for energy consumption prediction presented in this study, will be expanded in future and will be validated using case studies on physical commercial building to better estimate the prediction accuracy. 078-9 References Asadi., S., Amiri., S.S., Mottahedi., M., 2014, On the development of multi-linear regression analysis to assess energy consumption in the early stages of building design, Energy and Buildings, 85:246-255. Asadi, S., Hassan, M., and Beheshti, A., 2012. Development and validation of a simple estimating tool to predict heating and cooling energy demand for attics of residential buildings. Energy and Buildings, 54:12-21. ASHRAE, ASHRAE 90.1-2007, American Society of Heating, Refrigeration, and Air-Conditioning Engineers, Atlanta, GA, 2007. Broun, R., Babaizadeh, H., Zakersalehi, A., and Menzies, G.F., 2014. Integrated Life Cycle Energy and Greenhouse Gas Analysis of Exterior Wall Systems for Residential Buildings. Sustainability, 6 (12):8592-8603. Catalina, T., Iordache, V., and Caracaleanu, B., 2013. Multiple regression model for fast prediction of the heating energy demand. Energy and Buildings, 57:302-312. Department of Energy (DOE) EnergyPlus 7,2011. Department of Energy (DOE), DOE-2., Building Energy Use and Cost Analysis Tool, 2009, Available from: http://doe2.com/DOE2/index.html. Energy Information Administration (EIA), Annual Energy Review, DOE/EIA03842010, U.S. Energy Information Administration, 2011. Hygh, J.S.,  DeCarolis, J.F.,  Hill, D.B., Ranji Ranjithan, S., 2012, Multivariate regression asan energy assessment tool in early building design, Building and Environment, 57, 165–175. Lam, J.C., Wan, K., Liu, D., and Tsang., C.L, 2010. Multiple regression models for energy  use in air-conditioned office buildings in different climates.  Energy Conversion and Management, 51(12): 2692-2697. Mohammadpour, A., Alanqar, I., Anumba, C., and Messner, J., 2014, Cross Case Energy Simulation Modeling Analysis in Healthcare Facilities Retrofit, Computing in Civil and Building Engineering Conference, Orlando, FL, USA. Repice, R., 2011. Annual Energy Review 2010. DOE/EIA-0384 (2010), US Energy Information Administration, Washington, DC.   078-10  Shideh Shams AmiriPhD StudentThe Pennsylvania State UniversityVancouver, British ColumbiaJune 8 to June 10, 2015 2 Building sector 40% of total energy use 65% of electricity consumption 30% of greenhouse gas emissions By 2030, an estimated 80% more coal will be neededSpase Heating , 41%Air-Conditioning 8%Water Heating , 20%Refrigerators5%Other Appliances and Lighting, 26%Commercial buildingU.S. Energy Information Administration3 Develop multi-linear regression model to predict and quantify energy consumption in commercial building in the early stages of building design.4Frame work of the research DOE-2 software is used to perform energy simulationand calculate annual building energy consumption.The eQUEST software program is used to facilitatecreation of building geometry and climate zone.A program is written in Python to automate thesimulation process and extract the necessary datafrom simulation report generated by DOE-2 software.6DOE-2 inputsConstant Parameters Constant ParametersBuilding type Office building, two story Floor-To-ceiling 2.43mJurisdiction ASHRAE 90.1 Window Area method Percent of gross wall areaBuilding Area 2322.6m2 Door type OpaqueCooling Equipment Chilled water coils Floor-Ceiling Window Ratio53.3%Heating Equip Hot water coils Window High 1.5mAnalysis Year 2013 Cooling source (HVAC) Evaporation  resistanceFloor-To-Floor 2.74m Usage Details Hourly end use profile7 A number of building envelop, building orientation, climateregion and occupant schedule are considered as inputparameters All the components of the building including walls, roof,ceiling, foundation, and floors are considered. ASHRAE 90.1 is used to identify the building envelopmaterials.8Variable Range Variable RangeCeilingInterior finish▪Acoustic Tile▪Drywall Finish▪Plastic FinishBuildingOrientation▪360◦ ▪180◦▪90◦ ▪270◦Ground FloorConstructionConcrete:▪0.1m ▪0.15m ▪0.2m▪0.3mRoofConstructionASHRAE Wall:#2,9,11,16,20,..,28,33Exterior wall ASHRAE Wall:#3,6,11,12,19,26,30Ceiling InteriorinsulationWool Batt (R11)▪Wool Batt (R19)▪Wool Batt (R30)Top Floor BattInsulation▪R-30 ▪R-11▪R-45 ▪R-19Roof Absorbance ▪Light▪Medium▪DarkGlass Category ▪Single low-e▪Double Low-e▪Triple Low-eOccupantScheduleMon-Fri ,8am-5pm1Mon-Thur,8am-6pm2Mon-Fri,7am-4pm3Sample variation and association level1HVAC system turns on 1hour before & turns off 1 hour after working hours.2HVAC system is on 24/7. 3HVAC system is on only during workings hours 9Five selected cities in each climate region. Climate Representative cityCold Dry BillingsCool Dry Salt Lake CityMixed Humid Washington DC Warm Marine Sa n JoseHot Humid Houston Uniform probability distribution was used to randomlyselect different levels of each variable using Monte Carlomethod and replace them in each building file. A numerical code was developed using Python programinglanguage to perform these simulations, Interface with DOE-2 software. Extracting the useful data from simulation report files andconduct the multi-linear regression analysis. In total 50,000 simulations were carried out to cover fivedifferent climate zone. A full annual simulation was run foreach design scenario.11 Multiple linear regression models the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. y=β0+β1X1+β2X2+β3X3+…+βPXP Where y is the predicting heating, cooling, or total energy, xipresents the value of parameter and βi is the corresponding regression coefficient. Multiple-linear regression is a method demonstrating how a dependent variable  y, varies with a set of independent variables   x1-xn.12Generalized variance-inflation coefficients x1= Building Orientation, x2= Top Floor Batt Insulation, x3 = Ceiling Interior Finish,x4= Ceiling Insulation,x5= Floor Construction, x6= Top Floor Ceiling Exterior Insulation, x7= Top Floor Ceiling Interior Finish, x8= Ground Floor Construction, x9= Ground Floor Interior Finish,x10= Floor Interior Finish,x11= Interior Wall, x12= Exterior Wall,x13= Roof Absorbance,x14= Exterior Wall Absorbance, x15= Roof Absorbance, x16= Occupant Schedule,x17= Glass Category. 14Accuracy of the model: Determination of Coefficient (R2) Root Mean Square Error (RMSE)Regression Coefficient y= 𝛽𝛽1𝑥𝑥1 + 𝛽𝛽2 𝑥𝑥2+𝛽𝛽3 𝑥𝑥3 + 𝛽𝛽4𝑥𝑥4 + 𝛽𝛽5𝑥𝑥5 + 𝛽𝛽6 𝑥𝑥6+𝛽𝛽7𝑥𝑥7+ 𝛽𝛽8𝑥𝑥8 + 𝛽𝛽9 𝑥𝑥9 +𝛽𝛽10𝑥𝑥10+𝛽𝛽11𝑥𝑥11 + 𝛽𝛽12 𝑥𝑥12+ 𝛽𝛽13𝑥𝑥13 + 𝛽𝛽14𝑥𝑥14 + 𝛽𝛽15 𝑥𝑥15+𝛽𝛽16 𝑥𝑥16 + 𝛽𝛽17𝑥𝑥17San Jose Washington, DC Houston Billings Salt Lake CityR2 0.95 0.94 0.95 0.94 0.95RMSE 226.2 221.3 218.4 223.6 222.015Residual scatter plot16Sample of  Validation of the total energy consumption models Distribution of total energy consumption for the five locations  Climate has the least temperature variation has the least annual energy consumption. The difference between regression predicted and DOE-2 simulation annual use building energy consumption are largely within 5%. The regression model will act as pre-diagnostic tool to predict the energy performance in the office buildings. 19Thank you Shideh@psu.edu.com

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