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Intelligent techniques for forecasting electricity consumption of buildings
Accepted Manuscript Intelligent Techniques for Forecasting Electricity Consumption of Buildings
K.P. Amber, R. Ahmad, M.W. Aslam, A. Kousar, M. Usman, M.S. Khan PII:
S0360-5442(18)30999-X
DOI:
10.1016/j.energy.2018.05.155
Reference:
EGY 12990
To appear in:
Energy
Received Date:
27 December 2017
Accepted Date:
24 May 2018
Please cite this article as: K.P. Amber, R. Ahmad, M.W. Aslam, A. Kousar, M. Usman, M.S. Khan, Intelligent Techniques for Forecasting Electricity Consumption of Buildings, Energy (2018), doi: 10.1016/j.energy.2018.05.155
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ACCEPTED MANUSCRIPT
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Intelligent Techniques for Forecasting Electricity Consumption of Buildings
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K. P. Ambera,b*, R. Ahmadc, M. W. Aslamd, A. Kousare, M. Usmanc, M.S. Khana
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aDepartment
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bFaculty
of Mechanical Engineering, Mirpur University of Science and Technology (MUST), Mirpur10250 (AJK), Pakistan
of Engineering, Science and the Built Environment, London South Bank University, London SE1 0AA, UK
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cSchool
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dDepartment
of Computer Systems Engineering, Mirpur University of Science and Technology (MUST), Mirpur-10250 (AJK), Pakistan
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eDepartment
of Electrical (Power) Engineering, Mirpur University of Science and Technology (MUST), Mirpur-10250 (AJK), Pakistan
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of Electrical Engineering and Computer Science, National University of Sciences and Technology, Islamabad, Pakistan
[email protected]*, [email protected], [email protected], [email protected], [email protected], [email protected]
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Abstract
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The increasing trend in building sector’s energy demand calls for reliable and robust energy
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consumption forecasting models. This study aims to compare prediction capabilities of five
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different intelligent system techniques by forecasting electricity consumption of an administration
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building located in London, United Kingdom. These five techniques are; Multiple Regression
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(MR), Genetic Programming (GP), Artificial Neural Network (ANN), Deep Neural Network
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(DNN) and Support Vector Machine (SVM). The prediction models are developed based on five
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years of observed data of five different parameters such as solar radiation, temperature, wind
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speed, humidity and weekday index. Weekday index is an important parameter introduced to
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differentiate between working and non-working days. First four years data is used for training the
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models and to obtain prediction data for fifth year. Finally, the predicted electricity consumption
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of all models is compared with actual consumption of fifth year. Results demonstrate that ANN
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performs better than all other four techniques with a Mean Absolute Percentage Error (MAPE) of
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6% whereas MR, GP, SVM and DNN have MAPE of 8.5%, 8.7%, 9% and 11%, respectively. The
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applicability of this study could span to other building categories and will help energy management
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teams to forecast energy consumption of various buildings.
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Keywords: Electricity forecasting, ANN, DNN, GP, MR, SVM
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1. Introduction
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Energy demand and consumption is running in parallel to increasing population across the globe [1].
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However, the building sector is the largest energy-consuming sector in the world and accounts for over one-
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third of final energy consumption globally and nearly 40% of the total primary energy consumption in
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European Union (EU) and United States of America (USA) [2]. With increasing population, building stocks
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and fast-paced economic growth, energy consumption in this sector is projected to increase by an average
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of 1.5% per year from 2012 to 2040 worldwide [3]. This increasing trend in buildings energy demand calls
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for reliable and robust energy consumption forecasting that should help in effective planning, long term
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strategies, efficient initiatives to reduce carbon emissions and controlling energy usage in the building
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sector [4]. Further, a robust forecasting is indispensable for efficient utilization of energy in the buildings
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and helps facility managers to investigate any unusual jumps or drops in their buildings energy
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consumption. Another key benefit of forecasting is that it helps facility managers in preparing reliable
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energy budget forecasts which is a vital component of successful planning [5]. In recent decades, the
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building energy consumption forecasting has gained momentum with the emergence of new building energy
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management systems.
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The total Building Energy Consumption (BEC) of higher education institutions and commercial buildings
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is 45% and 30% higher compared to residential buildings [6]. Hence, this field entails researchers to
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concentrate and work for state of the art energy consumption prediction models/techniques which should
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be more accurate, reliable and robust [7-8]. Energy usage prediction has remained a major focus of many
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researchers [9-11]. BEC forecasting involves three basic approaches; i.e. statistical, engineering and
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artificial intelligence. Engineering approach investigates architectural and climatic behavior of buildings as
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weather factors, building design, thermal characteristics of construction materials, occupants’ activities and
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their heating, ventilation and air conditioning parameters based on laws of physics and thermodynamics.
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Statistical approach uses historical data to predict BEC considering the most influential parameters.
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Regression models, Auto regressive moving average, Conditional demand analysis and Gaussian mixture
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models are some examples of statistical forecasting approach [12-15]. Artificial intelligence (AI) offers
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different processes exhibiting behavior of phenomena being modelled using historical data like statistical
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approach. AI has gained remarkable attention in the circle of analysts and forecasters efficiently reflecting
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non-linear behavior in BEC. Among all AI models, neural networks have shown significant capability to
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work on varying, non-linear functions between inputs and outputs. Artificial Neural Networks (ANN),
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Support Vector Machines (SVM), Fuzzy Logic (FL), Genetic Algorithms (GA) and Genetic Programming
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(GP) are some examples of AI largely used by researchers [16-18].
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In the recent past energy consumption has increased at exponential rates following basic changes in industry
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and economy. The forecasting of future energy needs has become an integral part of the power industry
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with the increased generation to fulfil the energy requirements. Oliveira et al. [19] in 2018 predicted
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electricity demand for the next year using monthly electricity consumption pattern from different countries.
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Their approach was based on exponential smoothing methods and Bootstrap aggregating (bagging) ARIMA
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method. In a similar study, Ding et al. [20] designed grey model to forecast electricity consumption in China
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up to 2020. A number of other researchers have adopted various forecasting approaches for predicting
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energy consumption of buildings. Of these forecasting techniques Genetic Programming (GP), Artificial
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Neural Networks (ANN), Deep Neural Networks (DNN), Support Vector Machines (SVM) and Multiple
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Regression (MR) have been widely used across the globe. For analyzing the accuracy of forecasting models,
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different researchers have used different error metrics such as Relative Error (RE), Mean Absolute
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Percentage Error (MAPE), Root Mean Square Error (RMSE), and Mean Square Error (MSE).
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GP has been widely used for estimating energy consumption in different regions. Kaboli et al. [18] used
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long term electricity consumption data (1971 to 2011) for five Asian countries i.e. Philippines, Thailand,
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Indonesia, Malaysia and Singapore. They developed forecasting models using three different forecasting
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methods i.e. GP, ANN and SVM. Their results showed that GP outperformed ANN and SVM offering
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lower MAPE values for all five countries. Kovacic and Sarler [21] used GP and MR methods to forecast
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natural gas consumption in Slovenia for a Store Steel Company which consumes nearly 1.1% of the
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country’s total gas consumption. Testing of the models revealed that GP performs better than MR. In a
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similar study, Silva et al. [22], using GP, investigated various influential factors such as political, social and
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economic, and proposed long term energy consumption forecasting model (up to 2050) for the industrial
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sector in Brazil.
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Biswas et al. [23] used Artificial Neural Networks (ANN) and predicted future energy utilization in
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residential buildings using data from TxAIRE Research Houses in USA. The accuracy of the model was
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analyzed using the coefficients of determination (R2). They found R2 values between 0.87 to 0.91. ANN
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has also found significant applications in oil industry [24-25]. Zeng et al. [25] introduced three different
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machine learning techniques to predict electricity usage on daily basis for oil driven pumps in China. Their
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models were optimized using a step by step practice of trial and error process and comparison results from
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ANN, SVM and MR were based on MAPE and RE. This comparison presented better performance for
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ANN demonstrating an error of ±5%. Szoplik [26] used ANN to forecast diurnal and seasonal gas
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consumption in Poland by considering various environmental and calendar parameters. This study
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concluded that ANN could be the most viable option to predict the hourly and daily gas consumption. The
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MAPE of this ANN model was observed 9%.
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Support Vector Machines (SVM) offers diversified applications in forecasting of electricity load [27-28],
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electricity consumption [29], heating demand [30] and hydropower consumption [31]. Photovoltaic
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installations are also supported by SVM in predicting solar irradiance of a particular site. Jiang et al. [32]
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applied SVM to forecast solar irradiance levels in China. Yang et al. [27] presented incremental model 4
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based on SVM to predict electricity load for China. Along with electricity consumption forecasting,
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investigation of heating demand encompasses important place in the studies of forecasting. Izadyar et al.
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[30] proposed a thermal model for district heating system in Iran based on SVM. The authors also compared
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the acquired results with ANN and GP models based on RMSE, Pearson Coefficient (R) and coefficient of
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determination (R2). They found that SVM performs better than ANN and GP in this particular study.
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Deep Neural Networks (DNN) is considered as the most efficient method to forecast systems which
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demonstrate nonlinear and dynamic behaviours. Fu [33] developed a DNN model to forecast the cooling
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energy demand for the buildings sector of China and Hong Kong in 2018. Testing of real data with the
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predicted data using the standard performance metrics of MAPE, RMSE, MAE, CV-RMSE and R2 proved
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the validity of the model. Dedinec et al. [34] also used DNN to forecast short term (24 hour ahead and daily
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peak) electricity load for Macedonia using historical data for the period 2008 to 2014. Suryanarayana et al.
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[35] applied three regression models and a DNN model for thermal load forecasting of two district heating
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schemes in Sweden namely Rottne and Karlshamn. It was found that despite being highly intensive, DNN
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offers better results on the basis of MAPE in both district heating schemes (8.08% and 4.15%).
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Multiple Regression (MR) is another forecasting method which is a simple statistical technique and has
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been widely used for forecasting energy consumption. It further helps researchers in identifying the
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significant and insignificant variables that have a direct linear relationship with the energy consumption.
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Pino-Mejías et al. [36] developed MR and ANN models and forecasted the energy consumption of office
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buildings in Chile. They found that MR performs better (R2 = 0.85) when the input variables are
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transformed. With no transformation of input variables, ANN outperforms MR with a R2 value of 0.998.
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Bianco et al. [37] used MR method to investigate the effect of different economic and demographic
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variables, i.e. gross domestic product (GDP), gross domestic product per capita (GDP per capita), electricity
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price and population on the electricity consumption of residential sector of Italy. They developed MR
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models and found that electricity price is not a significant variable for the electricity sector of Italy but GDP
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and GDP per capita have direct relationship with the electricity consumption. Their study concluded that 5
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Italy’s electricity consumption will increase at an average rate of 2% per year in next 20 years. Tratar and
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Strmcnik [38] collected data of heat load from a company called Energetika Ljubljana for the period
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September 2008 to February 2013 and develop MR models to predict daily, weekly and monthly heat load
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in Ljubljana, Slovenia. They observed MAPE of 3.93%. 2.77% and 1.89% for daily, weekly and monthly
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forecasting models respectively.
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This comprehensive literature review confirms that GP, ANN, DNN, SVM and MR methods have been
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widely applied by the researchers for forecasting energy consumption. There are many more similar studies
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where these methods have been applied. Fig. 1 summarizes such forecasting studies performed in different
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countries and helps in understanding which forecasting techniques were applied and which error matrix
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was used to analyze the accuracy of these forecasting models.
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This current research is inspired by the work done by Amber et al. [39] where they employed two different
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forecasting techniques:.1) MR and 2) GP for forecasting the daily electricity consumption of an
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administration building called “South Bank Technopark” located in London, United Kingdom. Fig.2 shows
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the front view of this building. Details of this building are presented in Table 2 later in Section 3.
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In this work, three new machine learning models, i.e. SVM, ANN and DNN are used for the energy
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consumption prediction of the South Bank Technopark building and their results have been compared with
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the results of MR and GP methods. These models are trained on data which contain different parameters
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such as solar radiation, temperature, wind speed, humidity and weekday index. Weekday index is an
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important parameter introduced to differentiate between WD and NWD. Its value is kept either 0 or 1,
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where 0 indicates NWD and 1 indicates WD. The observed data is spread over a period of five years. First
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four years data is used for training the prediction models and to obtain prediction data for fifth year. Finally
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the predicted data is compared with real data of fifth year and error analysis is performed.
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Fig. 1 Summary of Buildings energy forecasting studies
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Fig. 2 South Bank Technopark Building at LSBU
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This study follows the following structure. Section 1 presents related work on energy consumption
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forecasting for buildings using different techniques. A brief description of different modeling techniques 7
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and their architecture and different parameters used in this work are presented in Section 2. In Section 3,
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results are compared for all the five models and error analysis has been performed in terms of statistical
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parameters. Conclusion are drawn in Section 4.
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2. Methods
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Five energy forecasting models viz. ANN, DNN, SVM, MR and GP are selected for this study and their
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specific working as done in this research is discussed.
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2.1. Artificial Neural Network (ANN)
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Artificial Neural Networks are inspired by a mathematical model of biological neural networks and
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represent a model which mimics human brain working [11]. ANN was not in used in beginning due to
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enormous computations. But due to availability of high performance computing they became popular. ANN
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can solve complex non-linear input-output relationships that are difficult for other techniques. It is an
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adaptive system that learns and changes its structure as the input is fed to it. The basic layout of ANN
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consists of many neurons and these are linked together according to a specific network structure. These
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neurons could be divided into several layers. There are different architectures of ANN depending on the
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number of layers and the flow of information. It could be single layer, multi-layer, supervised and
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unsupervised ANN. A simple structure of ANN is shown in Fig. 3.
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Fig. 3 Simple structure of ANN
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There are two phases of ANN learning, training and testing. During training an input is fed into ANN’s
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architecture (with many layers) and outputs of layers are computed using random weights and biases. Upon
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every layer an activation function is applied and output of one layer is passed as input to next layer. For this
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research we have applied sigmoid activation function which limits the output values between 0 and 1. In
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this research ten hidden layers with 100 neurons have been used. The final output of ANN is fed back to
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adjust the weights and biases of different layers to match the target output. In this research Gradient descent
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of the loss is back propagated to adjust the weights. Mathematically if
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we can write.
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1
ℎ𝑖𝑥 =
‒
1+𝑒
(∑𝑤 𝑥 + 𝑏) 𝑗 𝑖 𝑖
ℎ𝑖𝑥 is output of ith hidden layer then
𝐸𝑞. (1)
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Where 𝑤𝑖weight at ith is layer and is the input at ith layer with j variables. This feedback process is carried
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out until the output is within a required range. A validation phase is also used in this research to overcome
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the over fitting problem.
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2.2. Deep Neural Network (DNN)
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Deep learning is an effective machine learning tool which is imparting quality results almost in every field
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of research by automatic selection and extraction of features without human intervention [50]. It is an
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extension to ANN with deeper layers and large number of neurons. Prediction is done using vague to fine
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feature extraction. Similar to ANN, recent research on DNN is possible due to availability of high
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performance computing. After the development of tensor flow library by Google and making it available
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for general public as an open source library put plethora of research in different fields [51]. Therefore, use
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of DNN for energy forecasting is carried out to establish how well DNN can perform in this field. A two
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layer Deep Model is shown in Fig. 4.
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Fig. 4 A two hidden layer Deep Neural Network
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Dependent variables or inputs are fed into the DNN from left and each variable is multiplied by some
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random weight and a bias is added to it at each layer. After this an activation function is applied to get some
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output e.g. sigmoid, tanh, etc. The output of this layer is the input to the next layer. In this way, more layers
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are introduced and computations performed using weights and biases. Sometime during layers we also
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have to apply different functions like pooling to downsize our input size. Finally for classification or
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regression we apply another function like softmax to map upon certain categories or values and linear
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function for continuous values. This phase is known as feed forward phase. In this way, all inputs are
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processed and results tweaked after certain batches of inputs and make more iteration for better results.
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Finally, weights and biases which are used to predict unknown input by passing them in feed forward
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network are determined. Mathematically the output at each layer will be; ℎ𝑖(𝑥) = 𝑚𝑎𝑥(𝑤1𝑥 + 𝑏,𝑤2𝑥 + ………….)
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𝐸𝑞. (2)
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Similarly for classification Problems we can use softmax function in last layer, which uses normalized score
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and is given by
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𝑓𝑧 =
𝑒
𝑧
∑ 𝑒𝑧
𝑎𝑛𝑑 𝑧 = 𝑤𝑥 + 𝑏
𝐸𝑞. (3)
2.3. Support Vector Machine (SVM)
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Support vector machines are well known supervised and unsupervised learning algorithms which are very
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effective for both linearly separable and not separable data sets. When data is not linearly separable then a
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transformation is applied from one dimension to another dimension so that now data is easily separable
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using hyperplane. Support vector machines are used both for classification and regression problems. In
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Support Vector regression the data set is separated by drawing a virtual line which separates each class or
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cluster among data points of a cluster or same class at a maximum distance. These points are known as
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support vectors. Then for any unknown point the previous learned weights are applied to the dependent
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variables or the input to calculate its predicted position and this will predict the output class or mapped to
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a continuous value in case of regression.
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In SVM we can use different kernels according to dataset but in this study we used dot kernel which is
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widely used kernel and implemented it using a library libSVM. SVM works in a manner that for a given
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input space of x it finds out a function which only accepts the predictions which are at maximum distance
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from
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, the support vector [39]. In mathematical form, SVM is given by Eq. (4). 𝑓(𝑥) = (𝑊,𝑥) + 𝑏
𝐸𝑞. (4)
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2.4. Genetic Programming (GP)
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GP is an evolutionary computing algorithm which was first used in 1992 by Koza [52]. The GP computer
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programs are called GP individuals. These GP individuals are in the form of mathematical formulas. Each
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individual is a solution of the given problem. GP is preferred over other methods as it has some inherent
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advantages; (1) Preprocessing of data not required, (2) Built in feature selection capability, (3) Follows
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white box model (final solution is interpretable).
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GP algorithm uses the following steps (1) A random population of GP individual is created, (2) Fitness of
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each individual is calculated according to a predefined formula, (3) New generation is created from existing
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generation using genetic operators, (4) Fitness of new generation is calculated, 5) Repeat steps 3 and 4 until
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a perfect solution is achieved.
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Important Parameters of GP
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a) Structure of GP individuals
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A GP individual is in the form of a mathematical formula and the most common structure to represent this
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formula is tree structure. A tree is composed of the root, intermediate nodes and the leaf node. The inputs
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(terminals) are at leaf nodes, the intermediate nodes represent functions operating on terminals and the root
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is the output of a GP individual.
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b) Terminal Pool Terminals represent the inputs. The independent variables constitute the terminal pool. c)
Function Pool
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Function pool consists of all the function that are applied on the inputs and these are intermediate nodes in
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a tree structure. The choice of functions is purely dependent on the problem. The functions used in this
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study are given in Table 1.
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Table 1: Parameters used for GP
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d)
Fitness Function
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A fitness function tests the ability of any GP solution in solving the problem. The choice of fitness function
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varies from problem to problem. In our study the fitness function used is the sum of absolute error. The
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fitness function used is given below in Eq. (5). 12
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𝑓𝑖𝑡𝑛𝑒𝑠𝑠 = ∑|𝑔𝑜 ‒ 𝑡𝑜|
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Eq. (5)
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where 𝑔𝑜 is the output generated by GP individual and 𝑡𝑜 is the output of the target. As per the above fitness
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function, a lower value of fitness means a better individual.
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e)
Genetic Operators
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Genetic operators operate are used to create a new generation using existing generation. Crossover and
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mutation are two popular genetic operators and the same operators have been used in this study. Crossover
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creates two children by swapping branches of two parents while mutation replaces the branch of one parent
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with a randomly generated branch to create a child.
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2.5. Multiple Regression (MR)
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MR is a statistical technique widely used for researchers for energy consumption forecasting. It establishes
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relationship among two or more variables. General form of a multiple regression model is shown in Eq. (6):
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𝑍 = ∝ 0 + ∝ 1𝐴1 + ∝ 2𝐴2 + ……………… ∝ 𝑛𝐴𝑛 + ∈
Eq. (6)
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Where Z is the dependent variable, ∝ i are the regression coefficients (i = 0, 1, 2….n), 𝐴𝑖 are the explanatory
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variables (i =1, 2, 3 …n) and ∈ is the random error term which represents the effect of all omitted
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independent variables on the dependent variable “Z” [4].
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The fitness of a MR model could be judged by its 𝑅 value which is between 0 and 1. 𝑅 is called the
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Coefficient of determination. Higher value of R2 reflects a strong association among dependent and
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independent variables and vice versa. Significance of different independent variables is judged through p-
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value or t-stat value. A variable having t-stat values greater than +1.96 or ∝ - value > 0.05 are
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considered to be significant and vice versa.
2
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3. Result Analysis
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3.1. Data Collection and Analysis:
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The building data is composed of the following parameters measured/ observed for the period Jan. 2007-
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Dec. 2011: a) Daily electricity usage (Wh/m2), b) Daily mean surrounding temperature (K), c) Daily mean
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global irradiance (W/m2), d) Daily mean humidity (%), e) Daily mean wind velocity (m/s) and f) Weekday
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Index (0/1).
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For data analysis phase, building description, electricity consumption data, weather data and building
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occupancy data were considered. All the relevant information such as area of the building, hours of
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operation, year of construction etc. were collected from the office of energy manager through on site
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interview with the London South Bank University’s (LSBU’s) energy manager. Table 2 presents building
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related information obtained from energy manager having major impact on the energy consumption of the
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building.
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Table 2: Building related information Description
Building
Building type
Offices
Gross Internal Area, m2
7,811
Year of Construction
2003
Building Orientation
South-West
Hours of Operations
8 am to 6 pm
Closing time
10 pm.
Cooling method
Natural ventilation and few dedicated split AC units
Heating equipment
Two gas fired boilers
Lighting type
CFL
Number of lifts
2
Number of LV supplies
2
Number of floors
3
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Table 3 shows the building electricity consumption statistics for non-working days (NWD) and working
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days (WD). Electricity consumption of building drops during summer mainly due to low heating
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requirements. In winter, electricity consumptions increases due to use of heating equipment such as pumps,
290
boilers, air handling units etc. The building electricity consumption patterns show that temperature plays
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an important role in the daily electricity consumption of the building. The building is naturally ventilated,
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therefore, heating is only required in winter. The building occupancy factor is somewhat constant during
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both winter and summer periods.
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Table 3: Electricity consumption (Wh/m2) statistics of WD and NWD Statistics
NWD
WD
Min
155
229
Max
311
479
Mean
222
374
Median
221
375
N
577
1249
295 296
For our study, realistic daily mean values of temperature, irradiance, wind velocity and humidity for the
297
Central London region were available from the Kings College Environment Research Group’s website [53].
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Weekday index was selected to represent the building’s occupancy. It has a value of 1 and 0 for WD and
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NWD respectively. For this variable, it was important to have an accurate data of WD and NWD for years
300
2007 to 2011. A list of public holidays was available for this period [54].
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3.2. Performance Evaluation
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All models are trained on same data set from year 2007 to 2010 while data of 2011 is used for testing. Both
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the training and the testing data set is for the same building. Comparison of actual and predicted electricity
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consumption by five models is presented in the form of box plots. Further comparison of actual and
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predicted electricity consumption during working and non-working days is also presented and discussed.
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3.3. Comparison between real and predicted electricity consumption
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Figure 5 shows a comparison between the spread of predicted energy consumption data by different
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methods and the real data in the form of box plots.
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Fig. 5 Comparison of outputs of different modelling techniques
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It can be seen from the figure that none of the methods was able to correctly predict the minimum or
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maximum value although prediction of some of the methods was closer to actual than others. Looking at
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the figure it can be said that results of ANN and GP for median, second and third quartile are very close to
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the actual values and these two methods seem to perform better than others in overall prediction.
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Figures 6 and 7 show the comparison between the actual and predicted electricity consumption for the
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working and non-working days of different months.
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Fig. 6 Comparison of actual and predicted electricity consumption on working days
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It is apparent that predicted electricity consumption of working days of different months was almost similar
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for all the methods except for GP which under predicted the consumption from January to March. The
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prediction is most accurate from March to July while the prediction is worst for the month of December.
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The poor performance for December is due to Christmas holidays where the electricity consumption
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suddenly dropped and the predicted consumption is higher than actual. A similar trend is seen for the non-
325
working days as shown in Fig. 7 except for DNN which predicts slightly higher electricity consumption
326
during the summer months. Again, all five models predicted higher electricity consumption (average 12%)
327
for the month of December for the same reason.
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Fig. 7 Comparison of actual and predicted electricity consumption on non-working days
330 331
Fig. 8 Comparison of actual and predicted monthly electricity consumption
332
For comparing the monthly electricity consumption figures, daily electricity consumption and predicted
333
consumption were converted into monthly electricity consumption figures (kWh). Figure 8 shows a 18
ACCEPTED MANUSCRIPT
334
comparison between the monthly actual and predicted electricity consumption data by five models. Again
335
it is observed that all the model over predict December’s electricity consumption. Overall, it could be seen
336
that all five models predict monthly electricity consumption of South Bank Technopark building with an
337
error less than 10%.
338
3.4. Error Analysis
339
The performance of five different forecasting models has been analyzed using Root mean Square Error
340
(RMSE), Mean Absolute Error (MAE), Mean Relative Error (MRE), Mean Absolute Percentage Error
341
(MAPE) and Normalized Root Mean Square Error (NRMSE) for all five techniques. The formulas for these
342
errors are given in Eq. 7 to 11.
R𝑀𝑆𝐸 =
∑𝑚
Eq. (7)
(𝑍𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑, 𝑖 ‒ 𝑍𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑, 𝑖)2
𝑖=1
𝑚
343 𝑚
1 |𝑍 ‒ 𝑍𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑,𝑖| 𝑀𝐴𝐸 = 𝑚𝑖 = 1 𝑜𝑏𝑠,𝑖
∑
𝑀𝑅𝐸 =
|
Eq. (9)
|
𝑍𝑜𝑏𝑠 ‒ 𝑍𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑍𝑜𝑏𝑠
𝑚 𝑍 100 𝑜𝑏𝑠, 𝑖 ‒ 𝑍𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑, 𝑖 𝑀𝐴𝑃𝐸 = 𝑚 𝑖=1 𝑍𝑖
∑
|
Eq. (8)
|
Eq. (10)
344 𝑁𝑅𝑀𝑆𝐸 = 345
𝑅𝑀𝑆𝐸
Eq. (11)
(𝑍𝑜𝑏𝑠, 𝑚𝑎𝑥 ‒ 𝑍𝑜𝑏𝑠, 𝑚𝑖𝑛)
346
Where 𝑍𝑜𝑏𝑠 is the actual value and 𝑍𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 is the forecasted value. “m” represents the sample size and
347
“i” has values from 1 to m.
19
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348
Table 4 presents the error analysis in terms of these errors.
349
It is apparent that ANN outperforms all other methods in terms of all the error measures. It achieves a
350
NRMSE of 10 % which is much better than all contemporary models. The performance of MR and GP is
351
same while the performance of SVM and DNN is also almost equal in terms of NRMSE. Similarly if we
352
analyze MAPE, it is obvious that ANN performs better compared to all other methods. In the same manner
353
MRE also tells the efficacy of ANN over all other classifiers.
354 355 356 357
Table 4: Error analysis of different prediction models Error Analysis RMSE MAE MRE MAPE NRMSE
W/m² W/m² % % %
MR
GP
34.50 34.31 21.47 24.37 7.5% 8.5% 8.5% 8.8% 12.7% 12.7%
ANN 26 17 6% 6% 10%
DNN
SVM
35 35.39 27 24.11 9.56% 8% 11.15% 9% 13.02% 13%
358
359
Figure 9 gives a comparison of MRE (%) of different methods. ANN outperforms all other methods with
360
6% error. The second-best performance is shown by MR followed by SVM, GP and DNN.
20
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361 362
The results of DNN are not as promising as expected. The reason behind this is limited amount of data used
363
in this study. The accuracy of DNN relies heavily on enormous amount of training data along with proper
364
analysis of hyper parameter selection. Although the data used in this study is limited, the results of DNN
365
are almost similar to statistical and data centric classifier. If we had more amount of training data, the
366
performance of DNN could be expected to be superior.
367
4. Conclusions
368
In this work, real historical building energy consumption data of five years is compared for different
369
intelligent forecasting techniques including MR, GP, ANN, DNN and SVM. The predicted consumption
370
figures for the weekdays, weekends and different months were compared with the actual consumption
371
figures. It was observed that all five models predicted electricity consumption of working days of different
372
months within a range of 3%. However, for the non-working days, DNN predicts slightly higher electricity
373
consumption during the summer months whereas all five models predicted higher electricity consumption
374
(average 12%) for the month of December. In terms of monthly comparison, in the first three months,
375
except GP model, all other four models predicted electricity consumption very well. Overall, all five models 21
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376
predicted monthly electricity consumption of South Bank Technopark building with a difference of less
377
than 10%.
378
In a nutshell, we conclude that ANN with the building data set under consideration performs better than all
379
other four methods. The results of ANN and GP for median, second and third quartile are very close to the
380
actual values and these two methods seem to perform better than others in overall prediction. In terms of
381
MRE, ANN outperforms all other methods with 6% error. This is followed by MR, SVM, GP and DNN
382
respectively. The performance of ANN is better than all other methods irrespective of performance
383
measures. ANN performs well with reasonable complexity compared to other exhaustive methods such as
384
DNN and SVM. Since DNN requires enormous amount of data for training along with proper analysis of
385
hyper parameter selection and the dataset in this research is rather limited, the results of DNN are not as
386
promising as expected but even with a limited data set DNN perform close to other methods. The
387
applicability of this study could span to other building categories and will help energy management teams
388
to forecast energy consumption of their buildings.
389
Acknowledgments
390
Authors would like to pay special gratitude to the Energy Manager, Mr. Anuj Saush at London South Bank
391
University for providing information and electricity data.
392
List of Acronyms
393
ANN
Artificial Neural Network
394
BEC
Buildings Energy Consumption
395
DNN
Deep Neural Network
396
GP
Genetic Programming
397
GIA
Gross Internal Area 22
ACCEPTED MANUSCRIPT
398
HE
Higher Education
399
kWh
Kilo Watt Hour
400
LSBU
London South Bank University
401
MAE
Mean Absolute Error
402
MAPE
Mean Absolute Percentage Error
403
MR
Multiple Regression
404
MRE
Mean Relative Error
405
MSE
Mean Square Error
406
NMBE
Normalized Mean Biased Error
407
NRMSE
Normalized Root Mean Square Error
408
NWD
Non-Working Day
409
RE
Regression Error
410
RMSE
Root Mean Square Error
411
RMSPE
Root Mean Square Percentage Error
412
SSE
Sum of Square Error
413
WD
Working Day
414 415
23
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416 417 418 419 420 421 422 423
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at:
ACCEPTED MANUSCRIPT 1. Manuscript Title : Intelligent Techniques for Forecasting Electricity Consumption of Buildings
2. Authors List :Khuram Pervez Amber, Rizwan Ahmad, Muhammad Waqar Aslam, Anila Kousar, Muhammad Usman, Muhammad Sajid Khan
3. Highlights :
i)
Forecasting of daily electricity consumption for administration buildings
ii)
Use of different intelligent forecasting techniques, i.e. MR, GP, ANN, DNN, SVM
iii)
ANN outperforms all other forecasting techniques
K.P. Amber, R. Ahmad, M.W. Aslam, A. Kousar, M. Usman, M.S. Khan PII:
S0360-5442(18)30999-X
DOI:
10.1016/j.energy.2018.05.155
Reference:
EGY 12990
To appear in:
Energy
Received Date:
27 December 2017
Accepted Date:
24 May 2018
Please cite this article as: K.P. Amber, R. Ahmad, M.W. Aslam, A. Kousar, M. Usman, M.S. Khan, Intelligent Techniques for Forecasting Electricity Consumption of Buildings, Energy (2018), doi: 10.1016/j.energy.2018.05.155
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ACCEPTED MANUSCRIPT
1
Intelligent Techniques for Forecasting Electricity Consumption of Buildings
2
K. P. Ambera,b*, R. Ahmadc, M. W. Aslamd, A. Kousare, M. Usmanc, M.S. Khana
3 4
aDepartment
5 6
bFaculty
of Mechanical Engineering, Mirpur University of Science and Technology (MUST), Mirpur10250 (AJK), Pakistan
of Engineering, Science and the Built Environment, London South Bank University, London SE1 0AA, UK
7 8
cSchool
9 10
dDepartment
of Computer Systems Engineering, Mirpur University of Science and Technology (MUST), Mirpur-10250 (AJK), Pakistan
11 12
eDepartment
of Electrical (Power) Engineering, Mirpur University of Science and Technology (MUST), Mirpur-10250 (AJK), Pakistan
13 14
of Electrical Engineering and Computer Science, National University of Sciences and Technology, Islamabad, Pakistan
[email protected]*, [email protected], [email protected], [email protected], [email protected], [email protected]
15
Abstract
16
The increasing trend in building sector’s energy demand calls for reliable and robust energy
17
consumption forecasting models. This study aims to compare prediction capabilities of five
18
different intelligent system techniques by forecasting electricity consumption of an administration
19
building located in London, United Kingdom. These five techniques are; Multiple Regression
20
(MR), Genetic Programming (GP), Artificial Neural Network (ANN), Deep Neural Network
21
(DNN) and Support Vector Machine (SVM). The prediction models are developed based on five
22
years of observed data of five different parameters such as solar radiation, temperature, wind
23
speed, humidity and weekday index. Weekday index is an important parameter introduced to
24
differentiate between working and non-working days. First four years data is used for training the
25
models and to obtain prediction data for fifth year. Finally, the predicted electricity consumption
26
of all models is compared with actual consumption of fifth year. Results demonstrate that ANN
27
performs better than all other four techniques with a Mean Absolute Percentage Error (MAPE) of
1
ACCEPTED MANUSCRIPT
28
6% whereas MR, GP, SVM and DNN have MAPE of 8.5%, 8.7%, 9% and 11%, respectively. The
29
applicability of this study could span to other building categories and will help energy management
30
teams to forecast energy consumption of various buildings.
31
Keywords: Electricity forecasting, ANN, DNN, GP, MR, SVM
32
1. Introduction
33
Energy demand and consumption is running in parallel to increasing population across the globe [1].
34
However, the building sector is the largest energy-consuming sector in the world and accounts for over one-
35
third of final energy consumption globally and nearly 40% of the total primary energy consumption in
36
European Union (EU) and United States of America (USA) [2]. With increasing population, building stocks
37
and fast-paced economic growth, energy consumption in this sector is projected to increase by an average
38
of 1.5% per year from 2012 to 2040 worldwide [3]. This increasing trend in buildings energy demand calls
39
for reliable and robust energy consumption forecasting that should help in effective planning, long term
40
strategies, efficient initiatives to reduce carbon emissions and controlling energy usage in the building
41
sector [4]. Further, a robust forecasting is indispensable for efficient utilization of energy in the buildings
42
and helps facility managers to investigate any unusual jumps or drops in their buildings energy
43
consumption. Another key benefit of forecasting is that it helps facility managers in preparing reliable
44
energy budget forecasts which is a vital component of successful planning [5]. In recent decades, the
45
building energy consumption forecasting has gained momentum with the emergence of new building energy
46
management systems.
47
The total Building Energy Consumption (BEC) of higher education institutions and commercial buildings
48
is 45% and 30% higher compared to residential buildings [6]. Hence, this field entails researchers to
49
concentrate and work for state of the art energy consumption prediction models/techniques which should
50
be more accurate, reliable and robust [7-8]. Energy usage prediction has remained a major focus of many
2
ACCEPTED MANUSCRIPT
51
researchers [9-11]. BEC forecasting involves three basic approaches; i.e. statistical, engineering and
52
artificial intelligence. Engineering approach investigates architectural and climatic behavior of buildings as
53
weather factors, building design, thermal characteristics of construction materials, occupants’ activities and
54
their heating, ventilation and air conditioning parameters based on laws of physics and thermodynamics.
55
Statistical approach uses historical data to predict BEC considering the most influential parameters.
56
Regression models, Auto regressive moving average, Conditional demand analysis and Gaussian mixture
57
models are some examples of statistical forecasting approach [12-15]. Artificial intelligence (AI) offers
58
different processes exhibiting behavior of phenomena being modelled using historical data like statistical
59
approach. AI has gained remarkable attention in the circle of analysts and forecasters efficiently reflecting
60
non-linear behavior in BEC. Among all AI models, neural networks have shown significant capability to
61
work on varying, non-linear functions between inputs and outputs. Artificial Neural Networks (ANN),
62
Support Vector Machines (SVM), Fuzzy Logic (FL), Genetic Algorithms (GA) and Genetic Programming
63
(GP) are some examples of AI largely used by researchers [16-18].
64
In the recent past energy consumption has increased at exponential rates following basic changes in industry
65
and economy. The forecasting of future energy needs has become an integral part of the power industry
66
with the increased generation to fulfil the energy requirements. Oliveira et al. [19] in 2018 predicted
67
electricity demand for the next year using monthly electricity consumption pattern from different countries.
68
Their approach was based on exponential smoothing methods and Bootstrap aggregating (bagging) ARIMA
69
method. In a similar study, Ding et al. [20] designed grey model to forecast electricity consumption in China
70
up to 2020. A number of other researchers have adopted various forecasting approaches for predicting
71
energy consumption of buildings. Of these forecasting techniques Genetic Programming (GP), Artificial
72
Neural Networks (ANN), Deep Neural Networks (DNN), Support Vector Machines (SVM) and Multiple
73
Regression (MR) have been widely used across the globe. For analyzing the accuracy of forecasting models,
74
different researchers have used different error metrics such as Relative Error (RE), Mean Absolute
75
Percentage Error (MAPE), Root Mean Square Error (RMSE), and Mean Square Error (MSE).
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GP has been widely used for estimating energy consumption in different regions. Kaboli et al. [18] used
77
long term electricity consumption data (1971 to 2011) for five Asian countries i.e. Philippines, Thailand,
78
Indonesia, Malaysia and Singapore. They developed forecasting models using three different forecasting
79
methods i.e. GP, ANN and SVM. Their results showed that GP outperformed ANN and SVM offering
80
lower MAPE values for all five countries. Kovacic and Sarler [21] used GP and MR methods to forecast
81
natural gas consumption in Slovenia for a Store Steel Company which consumes nearly 1.1% of the
82
country’s total gas consumption. Testing of the models revealed that GP performs better than MR. In a
83
similar study, Silva et al. [22], using GP, investigated various influential factors such as political, social and
84
economic, and proposed long term energy consumption forecasting model (up to 2050) for the industrial
85
sector in Brazil.
86
Biswas et al. [23] used Artificial Neural Networks (ANN) and predicted future energy utilization in
87
residential buildings using data from TxAIRE Research Houses in USA. The accuracy of the model was
88
analyzed using the coefficients of determination (R2). They found R2 values between 0.87 to 0.91. ANN
89
has also found significant applications in oil industry [24-25]. Zeng et al. [25] introduced three different
90
machine learning techniques to predict electricity usage on daily basis for oil driven pumps in China. Their
91
models were optimized using a step by step practice of trial and error process and comparison results from
92
ANN, SVM and MR were based on MAPE and RE. This comparison presented better performance for
93
ANN demonstrating an error of ±5%. Szoplik [26] used ANN to forecast diurnal and seasonal gas
94
consumption in Poland by considering various environmental and calendar parameters. This study
95
concluded that ANN could be the most viable option to predict the hourly and daily gas consumption. The
96
MAPE of this ANN model was observed 9%.
97
Support Vector Machines (SVM) offers diversified applications in forecasting of electricity load [27-28],
98
electricity consumption [29], heating demand [30] and hydropower consumption [31]. Photovoltaic
99
installations are also supported by SVM in predicting solar irradiance of a particular site. Jiang et al. [32]
100
applied SVM to forecast solar irradiance levels in China. Yang et al. [27] presented incremental model 4
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based on SVM to predict electricity load for China. Along with electricity consumption forecasting,
102
investigation of heating demand encompasses important place in the studies of forecasting. Izadyar et al.
103
[30] proposed a thermal model for district heating system in Iran based on SVM. The authors also compared
104
the acquired results with ANN and GP models based on RMSE, Pearson Coefficient (R) and coefficient of
105
determination (R2). They found that SVM performs better than ANN and GP in this particular study.
106
Deep Neural Networks (DNN) is considered as the most efficient method to forecast systems which
107
demonstrate nonlinear and dynamic behaviours. Fu [33] developed a DNN model to forecast the cooling
108
energy demand for the buildings sector of China and Hong Kong in 2018. Testing of real data with the
109
predicted data using the standard performance metrics of MAPE, RMSE, MAE, CV-RMSE and R2 proved
110
the validity of the model. Dedinec et al. [34] also used DNN to forecast short term (24 hour ahead and daily
111
peak) electricity load for Macedonia using historical data for the period 2008 to 2014. Suryanarayana et al.
112
[35] applied three regression models and a DNN model for thermal load forecasting of two district heating
113
schemes in Sweden namely Rottne and Karlshamn. It was found that despite being highly intensive, DNN
114
offers better results on the basis of MAPE in both district heating schemes (8.08% and 4.15%).
115
Multiple Regression (MR) is another forecasting method which is a simple statistical technique and has
116
been widely used for forecasting energy consumption. It further helps researchers in identifying the
117
significant and insignificant variables that have a direct linear relationship with the energy consumption.
118
Pino-Mejías et al. [36] developed MR and ANN models and forecasted the energy consumption of office
119
buildings in Chile. They found that MR performs better (R2 = 0.85) when the input variables are
120
transformed. With no transformation of input variables, ANN outperforms MR with a R2 value of 0.998.
121
Bianco et al. [37] used MR method to investigate the effect of different economic and demographic
122
variables, i.e. gross domestic product (GDP), gross domestic product per capita (GDP per capita), electricity
123
price and population on the electricity consumption of residential sector of Italy. They developed MR
124
models and found that electricity price is not a significant variable for the electricity sector of Italy but GDP
125
and GDP per capita have direct relationship with the electricity consumption. Their study concluded that 5
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Italy’s electricity consumption will increase at an average rate of 2% per year in next 20 years. Tratar and
127
Strmcnik [38] collected data of heat load from a company called Energetika Ljubljana for the period
128
September 2008 to February 2013 and develop MR models to predict daily, weekly and monthly heat load
129
in Ljubljana, Slovenia. They observed MAPE of 3.93%. 2.77% and 1.89% for daily, weekly and monthly
130
forecasting models respectively.
131
This comprehensive literature review confirms that GP, ANN, DNN, SVM and MR methods have been
132
widely applied by the researchers for forecasting energy consumption. There are many more similar studies
133
where these methods have been applied. Fig. 1 summarizes such forecasting studies performed in different
134
countries and helps in understanding which forecasting techniques were applied and which error matrix
135
was used to analyze the accuracy of these forecasting models.
136
This current research is inspired by the work done by Amber et al. [39] where they employed two different
137
forecasting techniques:.1) MR and 2) GP for forecasting the daily electricity consumption of an
138
administration building called “South Bank Technopark” located in London, United Kingdom. Fig.2 shows
139
the front view of this building. Details of this building are presented in Table 2 later in Section 3.
140
In this work, three new machine learning models, i.e. SVM, ANN and DNN are used for the energy
141
consumption prediction of the South Bank Technopark building and their results have been compared with
142
the results of MR and GP methods. These models are trained on data which contain different parameters
143
such as solar radiation, temperature, wind speed, humidity and weekday index. Weekday index is an
144
important parameter introduced to differentiate between WD and NWD. Its value is kept either 0 or 1,
145
where 0 indicates NWD and 1 indicates WD. The observed data is spread over a period of five years. First
146
four years data is used for training the prediction models and to obtain prediction data for fifth year. Finally
147
the predicted data is compared with real data of fifth year and error analysis is performed.
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Fig. 1 Summary of Buildings energy forecasting studies
150 151
Fig. 2 South Bank Technopark Building at LSBU
152
This study follows the following structure. Section 1 presents related work on energy consumption
153
forecasting for buildings using different techniques. A brief description of different modeling techniques 7
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and their architecture and different parameters used in this work are presented in Section 2. In Section 3,
155
results are compared for all the five models and error analysis has been performed in terms of statistical
156
parameters. Conclusion are drawn in Section 4.
157
2. Methods
158
Five energy forecasting models viz. ANN, DNN, SVM, MR and GP are selected for this study and their
159
specific working as done in this research is discussed.
160
2.1. Artificial Neural Network (ANN)
161
Artificial Neural Networks are inspired by a mathematical model of biological neural networks and
162
represent a model which mimics human brain working [11]. ANN was not in used in beginning due to
163
enormous computations. But due to availability of high performance computing they became popular. ANN
164
can solve complex non-linear input-output relationships that are difficult for other techniques. It is an
165
adaptive system that learns and changes its structure as the input is fed to it. The basic layout of ANN
166
consists of many neurons and these are linked together according to a specific network structure. These
167
neurons could be divided into several layers. There are different architectures of ANN depending on the
168
number of layers and the flow of information. It could be single layer, multi-layer, supervised and
169
unsupervised ANN. A simple structure of ANN is shown in Fig. 3.
170 171
Fig. 3 Simple structure of ANN
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There are two phases of ANN learning, training and testing. During training an input is fed into ANN’s
173
architecture (with many layers) and outputs of layers are computed using random weights and biases. Upon
174
every layer an activation function is applied and output of one layer is passed as input to next layer. For this
175
research we have applied sigmoid activation function which limits the output values between 0 and 1. In
176
this research ten hidden layers with 100 neurons have been used. The final output of ANN is fed back to
177
adjust the weights and biases of different layers to match the target output. In this research Gradient descent
178
of the loss is back propagated to adjust the weights. Mathematically if
179
we can write.
180
1
ℎ𝑖𝑥 =
‒
1+𝑒
(∑𝑤 𝑥 + 𝑏) 𝑗 𝑖 𝑖
ℎ𝑖𝑥 is output of ith hidden layer then
𝐸𝑞. (1)
181
Where 𝑤𝑖weight at ith is layer and is the input at ith layer with j variables. This feedback process is carried
182
out until the output is within a required range. A validation phase is also used in this research to overcome
183
the over fitting problem.
184
2.2. Deep Neural Network (DNN)
185
Deep learning is an effective machine learning tool which is imparting quality results almost in every field
186
of research by automatic selection and extraction of features without human intervention [50]. It is an
187
extension to ANN with deeper layers and large number of neurons. Prediction is done using vague to fine
188
feature extraction. Similar to ANN, recent research on DNN is possible due to availability of high
189
performance computing. After the development of tensor flow library by Google and making it available
190
for general public as an open source library put plethora of research in different fields [51]. Therefore, use
191
of DNN for energy forecasting is carried out to establish how well DNN can perform in this field. A two
192
layer Deep Model is shown in Fig. 4.
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Fig. 4 A two hidden layer Deep Neural Network
195
Dependent variables or inputs are fed into the DNN from left and each variable is multiplied by some
196
random weight and a bias is added to it at each layer. After this an activation function is applied to get some
197
output e.g. sigmoid, tanh, etc. The output of this layer is the input to the next layer. In this way, more layers
198
are introduced and computations performed using weights and biases. Sometime during layers we also
199
have to apply different functions like pooling to downsize our input size. Finally for classification or
200
regression we apply another function like softmax to map upon certain categories or values and linear
201
function for continuous values. This phase is known as feed forward phase. In this way, all inputs are
202
processed and results tweaked after certain batches of inputs and make more iteration for better results.
203
Finally, weights and biases which are used to predict unknown input by passing them in feed forward
204
network are determined. Mathematically the output at each layer will be; ℎ𝑖(𝑥) = 𝑚𝑎𝑥(𝑤1𝑥 + 𝑏,𝑤2𝑥 + ………….)
205
𝐸𝑞. (2)
206
Similarly for classification Problems we can use softmax function in last layer, which uses normalized score
207
and is given by
208
209
𝑓𝑧 =
𝑒
𝑧
∑ 𝑒𝑧
𝑎𝑛𝑑 𝑧 = 𝑤𝑥 + 𝑏
𝐸𝑞. (3)
2.3. Support Vector Machine (SVM)
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Support vector machines are well known supervised and unsupervised learning algorithms which are very
211
effective for both linearly separable and not separable data sets. When data is not linearly separable then a
212
transformation is applied from one dimension to another dimension so that now data is easily separable
213
using hyperplane. Support vector machines are used both for classification and regression problems. In
214
Support Vector regression the data set is separated by drawing a virtual line which separates each class or
215
cluster among data points of a cluster or same class at a maximum distance. These points are known as
216
support vectors. Then for any unknown point the previous learned weights are applied to the dependent
217
variables or the input to calculate its predicted position and this will predict the output class or mapped to
218
a continuous value in case of regression.
219
In SVM we can use different kernels according to dataset but in this study we used dot kernel which is
220
widely used kernel and implemented it using a library libSVM. SVM works in a manner that for a given
221
input space of x it finds out a function which only accepts the predictions which are at maximum distance
222
from
223
, the support vector [39]. In mathematical form, SVM is given by Eq. (4). 𝑓(𝑥) = (𝑊,𝑥) + 𝑏
𝐸𝑞. (4)
224
2.4. Genetic Programming (GP)
225
GP is an evolutionary computing algorithm which was first used in 1992 by Koza [52]. The GP computer
226
programs are called GP individuals. These GP individuals are in the form of mathematical formulas. Each
227
individual is a solution of the given problem. GP is preferred over other methods as it has some inherent
228
advantages; (1) Preprocessing of data not required, (2) Built in feature selection capability, (3) Follows
229
white box model (final solution is interpretable).
230
GP algorithm uses the following steps (1) A random population of GP individual is created, (2) Fitness of
231
each individual is calculated according to a predefined formula, (3) New generation is created from existing
232
generation using genetic operators, (4) Fitness of new generation is calculated, 5) Repeat steps 3 and 4 until
233
a perfect solution is achieved.
234
Important Parameters of GP
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a) Structure of GP individuals
236
A GP individual is in the form of a mathematical formula and the most common structure to represent this
237
formula is tree structure. A tree is composed of the root, intermediate nodes and the leaf node. The inputs
238
(terminals) are at leaf nodes, the intermediate nodes represent functions operating on terminals and the root
239
is the output of a GP individual.
240 241 242
b) Terminal Pool Terminals represent the inputs. The independent variables constitute the terminal pool. c)
Function Pool
243
Function pool consists of all the function that are applied on the inputs and these are intermediate nodes in
244
a tree structure. The choice of functions is purely dependent on the problem. The functions used in this
245
study are given in Table 1.
246
Table 1: Parameters used for GP
247 248
d)
Fitness Function
249
A fitness function tests the ability of any GP solution in solving the problem. The choice of fitness function
250
varies from problem to problem. In our study the fitness function used is the sum of absolute error. The
251
fitness function used is given below in Eq. (5). 12
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𝑓𝑖𝑡𝑛𝑒𝑠𝑠 = ∑|𝑔𝑜 ‒ 𝑡𝑜|
252
Eq. (5)
253
where 𝑔𝑜 is the output generated by GP individual and 𝑡𝑜 is the output of the target. As per the above fitness
254
function, a lower value of fitness means a better individual.
255
e)
Genetic Operators
256
Genetic operators operate are used to create a new generation using existing generation. Crossover and
257
mutation are two popular genetic operators and the same operators have been used in this study. Crossover
258
creates two children by swapping branches of two parents while mutation replaces the branch of one parent
259
with a randomly generated branch to create a child.
260
2.5. Multiple Regression (MR)
261
MR is a statistical technique widely used for researchers for energy consumption forecasting. It establishes
262
relationship among two or more variables. General form of a multiple regression model is shown in Eq. (6):
263
𝑍 = ∝ 0 + ∝ 1𝐴1 + ∝ 2𝐴2 + ……………… ∝ 𝑛𝐴𝑛 + ∈
Eq. (6)
264
Where Z is the dependent variable, ∝ i are the regression coefficients (i = 0, 1, 2….n), 𝐴𝑖 are the explanatory
265
variables (i =1, 2, 3 …n) and ∈ is the random error term which represents the effect of all omitted
266
independent variables on the dependent variable “Z” [4].
267
The fitness of a MR model could be judged by its 𝑅 value which is between 0 and 1. 𝑅 is called the
268
Coefficient of determination. Higher value of R2 reflects a strong association among dependent and
269
independent variables and vice versa. Significance of different independent variables is judged through p-
270
value or t-stat value. A variable having t-stat values greater than +1.96 or ∝ - value > 0.05 are
271
considered to be significant and vice versa.
2
272
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273
3. Result Analysis
274
3.1. Data Collection and Analysis:
275
The building data is composed of the following parameters measured/ observed for the period Jan. 2007-
276
Dec. 2011: a) Daily electricity usage (Wh/m2), b) Daily mean surrounding temperature (K), c) Daily mean
277
global irradiance (W/m2), d) Daily mean humidity (%), e) Daily mean wind velocity (m/s) and f) Weekday
278
Index (0/1).
279
For data analysis phase, building description, electricity consumption data, weather data and building
280
occupancy data were considered. All the relevant information such as area of the building, hours of
281
operation, year of construction etc. were collected from the office of energy manager through on site
282
interview with the London South Bank University’s (LSBU’s) energy manager. Table 2 presents building
283
related information obtained from energy manager having major impact on the energy consumption of the
284
building.
285
Table 2: Building related information Description
Building
Building type
Offices
Gross Internal Area, m2
7,811
Year of Construction
2003
Building Orientation
South-West
Hours of Operations
8 am to 6 pm
Closing time
10 pm.
Cooling method
Natural ventilation and few dedicated split AC units
Heating equipment
Two gas fired boilers
Lighting type
CFL
Number of lifts
2
Number of LV supplies
2
Number of floors
3
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287
Table 3 shows the building electricity consumption statistics for non-working days (NWD) and working
288
days (WD). Electricity consumption of building drops during summer mainly due to low heating
289
requirements. In winter, electricity consumptions increases due to use of heating equipment such as pumps,
290
boilers, air handling units etc. The building electricity consumption patterns show that temperature plays
291
an important role in the daily electricity consumption of the building. The building is naturally ventilated,
292
therefore, heating is only required in winter. The building occupancy factor is somewhat constant during
293
both winter and summer periods.
294
Table 3: Electricity consumption (Wh/m2) statistics of WD and NWD Statistics
NWD
WD
Min
155
229
Max
311
479
Mean
222
374
Median
221
375
N
577
1249
295 296
For our study, realistic daily mean values of temperature, irradiance, wind velocity and humidity for the
297
Central London region were available from the Kings College Environment Research Group’s website [53].
298
Weekday index was selected to represent the building’s occupancy. It has a value of 1 and 0 for WD and
299
NWD respectively. For this variable, it was important to have an accurate data of WD and NWD for years
300
2007 to 2011. A list of public holidays was available for this period [54].
301
3.2. Performance Evaluation
302
All models are trained on same data set from year 2007 to 2010 while data of 2011 is used for testing. Both
303
the training and the testing data set is for the same building. Comparison of actual and predicted electricity
304
consumption by five models is presented in the form of box plots. Further comparison of actual and
305
predicted electricity consumption during working and non-working days is also presented and discussed.
306 15
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307
3.3. Comparison between real and predicted electricity consumption
308
Figure 5 shows a comparison between the spread of predicted energy consumption data by different
309
methods and the real data in the form of box plots.
310 311
Fig. 5 Comparison of outputs of different modelling techniques
312
It can be seen from the figure that none of the methods was able to correctly predict the minimum or
313
maximum value although prediction of some of the methods was closer to actual than others. Looking at
314
the figure it can be said that results of ANN and GP for median, second and third quartile are very close to
315
the actual values and these two methods seem to perform better than others in overall prediction.
316
Figures 6 and 7 show the comparison between the actual and predicted electricity consumption for the
317
working and non-working days of different months.
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318 319
Fig. 6 Comparison of actual and predicted electricity consumption on working days
320
It is apparent that predicted electricity consumption of working days of different months was almost similar
321
for all the methods except for GP which under predicted the consumption from January to March. The
322
prediction is most accurate from March to July while the prediction is worst for the month of December.
323
The poor performance for December is due to Christmas holidays where the electricity consumption
324
suddenly dropped and the predicted consumption is higher than actual. A similar trend is seen for the non-
325
working days as shown in Fig. 7 except for DNN which predicts slightly higher electricity consumption
326
during the summer months. Again, all five models predicted higher electricity consumption (average 12%)
327
for the month of December for the same reason.
17
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328 329
Fig. 7 Comparison of actual and predicted electricity consumption on non-working days
330 331
Fig. 8 Comparison of actual and predicted monthly electricity consumption
332
For comparing the monthly electricity consumption figures, daily electricity consumption and predicted
333
consumption were converted into monthly electricity consumption figures (kWh). Figure 8 shows a 18
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334
comparison between the monthly actual and predicted electricity consumption data by five models. Again
335
it is observed that all the model over predict December’s electricity consumption. Overall, it could be seen
336
that all five models predict monthly electricity consumption of South Bank Technopark building with an
337
error less than 10%.
338
3.4. Error Analysis
339
The performance of five different forecasting models has been analyzed using Root mean Square Error
340
(RMSE), Mean Absolute Error (MAE), Mean Relative Error (MRE), Mean Absolute Percentage Error
341
(MAPE) and Normalized Root Mean Square Error (NRMSE) for all five techniques. The formulas for these
342
errors are given in Eq. 7 to 11.
R𝑀𝑆𝐸 =
∑𝑚
Eq. (7)
(𝑍𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑, 𝑖 ‒ 𝑍𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑, 𝑖)2
𝑖=1
𝑚
343 𝑚
1 |𝑍 ‒ 𝑍𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑,𝑖| 𝑀𝐴𝐸 = 𝑚𝑖 = 1 𝑜𝑏𝑠,𝑖
∑
𝑀𝑅𝐸 =
|
Eq. (9)
|
𝑍𝑜𝑏𝑠 ‒ 𝑍𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑍𝑜𝑏𝑠
𝑚 𝑍 100 𝑜𝑏𝑠, 𝑖 ‒ 𝑍𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑, 𝑖 𝑀𝐴𝑃𝐸 = 𝑚 𝑖=1 𝑍𝑖
∑
|
Eq. (8)
|
Eq. (10)
344 𝑁𝑅𝑀𝑆𝐸 = 345
𝑅𝑀𝑆𝐸
Eq. (11)
(𝑍𝑜𝑏𝑠, 𝑚𝑎𝑥 ‒ 𝑍𝑜𝑏𝑠, 𝑚𝑖𝑛)
346
Where 𝑍𝑜𝑏𝑠 is the actual value and 𝑍𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 is the forecasted value. “m” represents the sample size and
347
“i” has values from 1 to m.
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348
Table 4 presents the error analysis in terms of these errors.
349
It is apparent that ANN outperforms all other methods in terms of all the error measures. It achieves a
350
NRMSE of 10 % which is much better than all contemporary models. The performance of MR and GP is
351
same while the performance of SVM and DNN is also almost equal in terms of NRMSE. Similarly if we
352
analyze MAPE, it is obvious that ANN performs better compared to all other methods. In the same manner
353
MRE also tells the efficacy of ANN over all other classifiers.
354 355 356 357
Table 4: Error analysis of different prediction models Error Analysis RMSE MAE MRE MAPE NRMSE
W/m² W/m² % % %
MR
GP
34.50 34.31 21.47 24.37 7.5% 8.5% 8.5% 8.8% 12.7% 12.7%
ANN 26 17 6% 6% 10%
DNN
SVM
35 35.39 27 24.11 9.56% 8% 11.15% 9% 13.02% 13%
358
359
Figure 9 gives a comparison of MRE (%) of different methods. ANN outperforms all other methods with
360
6% error. The second-best performance is shown by MR followed by SVM, GP and DNN.
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361 362
The results of DNN are not as promising as expected. The reason behind this is limited amount of data used
363
in this study. The accuracy of DNN relies heavily on enormous amount of training data along with proper
364
analysis of hyper parameter selection. Although the data used in this study is limited, the results of DNN
365
are almost similar to statistical and data centric classifier. If we had more amount of training data, the
366
performance of DNN could be expected to be superior.
367
4. Conclusions
368
In this work, real historical building energy consumption data of five years is compared for different
369
intelligent forecasting techniques including MR, GP, ANN, DNN and SVM. The predicted consumption
370
figures for the weekdays, weekends and different months were compared with the actual consumption
371
figures. It was observed that all five models predicted electricity consumption of working days of different
372
months within a range of 3%. However, for the non-working days, DNN predicts slightly higher electricity
373
consumption during the summer months whereas all five models predicted higher electricity consumption
374
(average 12%) for the month of December. In terms of monthly comparison, in the first three months,
375
except GP model, all other four models predicted electricity consumption very well. Overall, all five models 21
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376
predicted monthly electricity consumption of South Bank Technopark building with a difference of less
377
than 10%.
378
In a nutshell, we conclude that ANN with the building data set under consideration performs better than all
379
other four methods. The results of ANN and GP for median, second and third quartile are very close to the
380
actual values and these two methods seem to perform better than others in overall prediction. In terms of
381
MRE, ANN outperforms all other methods with 6% error. This is followed by MR, SVM, GP and DNN
382
respectively. The performance of ANN is better than all other methods irrespective of performance
383
measures. ANN performs well with reasonable complexity compared to other exhaustive methods such as
384
DNN and SVM. Since DNN requires enormous amount of data for training along with proper analysis of
385
hyper parameter selection and the dataset in this research is rather limited, the results of DNN are not as
386
promising as expected but even with a limited data set DNN perform close to other methods. The
387
applicability of this study could span to other building categories and will help energy management teams
388
to forecast energy consumption of their buildings.
389
Acknowledgments
390
Authors would like to pay special gratitude to the Energy Manager, Mr. Anuj Saush at London South Bank
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University for providing information and electricity data.
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List of Acronyms
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ANN
Artificial Neural Network
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BEC
Buildings Energy Consumption
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DNN
Deep Neural Network
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GP
Genetic Programming
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GIA
Gross Internal Area 22
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HE
Higher Education
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kWh
Kilo Watt Hour
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LSBU
London South Bank University
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MAE
Mean Absolute Error
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MAPE
Mean Absolute Percentage Error
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MR
Multiple Regression
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MRE
Mean Relative Error
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MSE
Mean Square Error
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NMBE
Normalized Mean Biased Error
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NRMSE
Normalized Root Mean Square Error
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NWD
Non-Working Day
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RE
Regression Error
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RMSE
Root Mean Square Error
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RMSPE
Root Mean Square Percentage Error
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SSE
Sum of Square Error
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WD
Working Day
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ACCEPTED MANUSCRIPT 1. Manuscript Title : Intelligent Techniques for Forecasting Electricity Consumption of Buildings
2. Authors List :Khuram Pervez Amber, Rizwan Ahmad, Muhammad Waqar Aslam, Anila Kousar, Muhammad Usman, Muhammad Sajid Khan
3. Highlights :
i)
Forecasting of daily electricity consumption for administration buildings
ii)
Use of different intelligent forecasting techniques, i.e. MR, GP, ANN, DNN, SVM
iii)
ANN outperforms all other forecasting techniques