1. Introduction
More recently, the ubiquity of the internet of things makes distributed energy systems smarter by optimizing energy efficiency for reducing losses and creates a new era named as the internet of energy (IoE), which is equipped with intelligent forecasting systems that employ meteorological forecasts and other explanatory information to predict future energy consumption. IoE brings energy forecasting into the forefront along with the smart grids and microgrids wherein buildings occupy the majority of the energy consumption. According to the one of the latest reports of the International Energy Agency, the buildings account for the largest portion of global final energy use with a share of 36%, which increases the significance of building energy forecasting to redress the balance between supply and demand for a more energy efficient future for the next generations of humanity [
1].
An accepted standard is still not available for the classification of energy forecasting, but Hong and Fan grouped forecasting categories as very short-term, short-term, medium-term, and long-term with cut-off horizons of one day, two weeks, and three years [
2]. Principally, short-term forecasts refer to an hour, day, or week ahead predictions, and it is considered that this concept can be applied to building electrical energy consumption forecasting as well [
3]. Short-term building electrical energy consumption forecasting is an essential tool that is not merely required for the integration of smart grids to current electric power systems. It enhances a building’s quality of energy management and planning as well by monitoring energy consumption, finding base and peak demands, reducing losses, minimizing risks, securing reliability for uninterrupted operation, playing an active role in making viable decisions in regard to maintenance planning and future investments, including both renewable and non-renewable energy technologies, such as photovoltaic, landfill, and tri-generation fueled by natural gas.
A variety of machine learning algorithms in the literature are currently implemented to short-term building electrical energy consumption forecasting problems, as explained in
Section 2 in detail, but nonetheless, most of them do not have the ability to generate easily comprehensible model equations among explanatory variables and response variables. The exceptions are GEP and GMDH networks, which are able to create simple analytical expressions between input variables and target variables without the need for application of feature selection (to avoid verbose presentation, GMDH-type polynomial neural networks are noted as GMDH networks throughout this study). Having model equations for forecasting tasks is advantageous owing to the fact that it reduces the computational complexity of the on-line forecast process for building energy management systems. Moreover, it is easy to understand and applicable for building energy staff whether an automation for building energy management system exists. Furthermore, there is a plethora of parameters and considerations differing from building to building and affecting energy consumption, such as mass, orientation, surface area to volume ratio, glazing ratio, occupancy pattern, activity level, and so on; the data set of this study covers electrical, meteorological, and calendar variables.
The original contributions of this study are clarified as noted below:
An application of real-time short-term electrical energy consumption forecasting study with comprehensive meteorological observations is conducted for a large-scale hospital complex, including data acquisition, wrangling, and visualization in detail. Studies appertaining to short-term building electrical energy consumption forecasting is limited, especially for detailed real-time applications, and it is thought that this study will bridge the emphasized gap and strengthen the literature.
Among various machine learning algorithms, GEP and GMDH networks are selected as forecasting methods for their capability of generating simple model equations between predictor variables and target variables without the necessity of performing feature selection. As far as is known, this study is the first attempt in the literature that compares GEP and GMDH networks for the prediction of short-term building electrical energy consumption. Both methods are implemented under identical constraints during a one-year period. Performing analyses with the same criteria reveals the genuine performance of each method for benchmarking purposes with respect to coefficient of determination (R), root mean squared error (RMSE), and mean absolute percentage error (MAPE). For the first time, overall results of GEP and GMDH networks are interpreted from the points of accuracy, number of input parameters and complexity of model equations, and computational time. In addition to those, generated model equations in the context of this study can be employed for future studies regarding buildings having similar climatological conditions and electrical energy consumption profiles.
To the best of one’s knowledge, an in-depth investigation of performance metrics acquired from the results of short-term building electrical energy consumption forecasting is firstly fulfilled in terms of several explanatory variables. Effects of short-wave irradiation, start and end of the shift hours, weekends and holidays, and seasonal transitions over short-term building electrical energy consumption forecasting are deduced along with hourly, daily, and monthly trends of prediction complexity in reference to MAPE.
The rest of the study is organized as follows:
Section 2 presents the state-of-the-art review consisting of review studies intersecting building electrical energy consumption forecasting with artificial intelligence (AI), case studies in the field of short-term building electrical energy consumption prediction focusing on statistical and AI techniques for nonresidential buildings, and research studies utilizing GEP and GMDH networks for forecasting short-term electric load, demand, or electrical energy consumption;
Section 3 introduces data source and acquisition, data wrangling, data set properties, and forecasting methods comprising the fundamentals of GEP and GMDH networks;
Section 4 hosts discussion and experimental results of in-depth analyses; and finally,
Section 5 concludes the study by emphasizing the prominent results for future studies.
2. Related Work
The literature contains a variety of successful reviews, which attempted to summarize building energy consumption forecasting methodologies from diverse perspectives. Firstly, Zhao and Magoules reviewed building energy consumption forecasting by classifying the methodologies, such as engineering methods, statistical methods, and AI methods [
4]. Ahmad et al. summarized the applications of artificial neural networks (ANN) and support vector machines (SVM) for building energy consumption prediction by emphasizing the potential of a hybrid method that merges GMDH networks with least squares SVM (LSSVM) [
5]. Raza and Khosravi conducted a review study on AI-based load demand forecasting techniques not only for buildings but also for smart grids by explaining all phases of short-term load forecasting comprehensively [
6]. Daut et al. reviewed on the prediction of building electrical energy consumption by dividing the methodologies as conventional, AI, and hybrid methods [
7]. Wang and Srinivasan compared single and ensemble models for AI-based building energy consumption forecasting within a review study [
8]. Wei et al. presented a review of data-driven approaches for both prediction and classification of building energy consumption by mentioning practical applications of the approaches [
9]. In a similar manner, Amasyali and El-Gohary reviewed data-driven building energy consumption forecasting studies by particularly focusing on the scopes of prediction, data properties and preprocessing methods, machine learning algorithms, and performance measures [
10]. Lastly, Runge and Zmeureanu suggested a review for forecasting energy use in buildings utilizing ANN by highlighting applications, data, forecasting models, and performance metrics [
11].
There are a limited number of studies in the literature that concentrated on short-term electrical energy consumption forecasting based on statistical and AI techniques for nonresidential buildings. Initially, Fan et al. presented a rigorous work about day-ahead building energy consumption forecasting, which employs an ensemble model in which weights are optimized by a genetic algorithm (GA), and the ensemble model consists of a single ANN, auto-regressive integrated moving average (ARIMA), boosting tree (BT), k-nearest neighbors (kNN), multivariate adaptive regression splines (MARS), multiple linear regression (MLR), random forests (RF), and support vector regression (SVR) [
12]. Ke et al. analyzed the load profile and implemented hours-ahead building load forecasts by obtaining data from a substation feeder at the Centennial Campus of North Carolina State University and using similar day approach (SDA), direct curve fitting (DCF) with polynomial regression (PR), and MLR [
13]. Wang et al. performed ensemble bagging trees (EBT) for forecasting hour-ahead energy consumption of Rinker Hall building in the University of Florida against a regression tree (RT) model [
14]. Shabani and Zavalani utilized an incremental ANN approach against target mean (TM) for forecasting hour-ahead loads of a commercial building [
15]. Zhu et al. compared performances of ANN by applying different strategies for neuron numbers, activation functions, data filtering, and regrouping for forecasting day-ahead loads acquired from two buildings in the City University of Hong Kong [
16]. Yong et al. suggested implementing a combination of SDA and long-short term memory (LSTM) networks in comparison with ANN and a hybrid approach containing particle swarm optimization (PSO) and ANN for short-term load forecasting of a hotel building in Shanghai [
17]. Ahmad et al. conducted a comprehensive work by obtaining data from a hotel building in Madrid and applied deep highway networks (DHN), SVR, and a tree-based ensemble (TBE) model for forecasting hour-ahead building heating, ventilation, and air-conditioning (HVAC) energy consumption [
18]. Fang et al. tried to improve forecast accuracy by performing wavelet decomposition (WD) and ARIMA together as compared to the Holt-Winters method (HWM), LSTM, and seasonal auto-regressive integrated moving average (SARIMA) for daily energy consumption prediction of an office building in Qingdao, Shandong [
19]. Fan et al. assessed deep network strategies including gated recurrent unit (GRU), LSTM, and recurrent neural networks (RNN) with several prediction approaches, such as direct, multi-input and multi-output (MIMO), and recursive approaches in order to forecast day-ahead energy consumption of an educational building in Hong Kong [
20]. Finally, Divina et al. benchmarked different forecasting strategies, including ANN, ARIMA, ensemble, evolutionary algorithms (EA) for regression trees (EVTree), extreme gradient boosting (XGBoost), generalized boosted regression models (GBM), MLR, RF, and recursive partitioning and regression trees (RPart) for forecasting short-term electrical energy consumption of thirteen buildings belonging to a university campus in the south of Spain [
21]. Comparative analysis of the aforementioned studies that processed short-term building electrical energy consumption forecasting is tabulated in
Table 1, according to performed models, building type, temporal granularity of data set, forecast horizon, benchmark models, and performance results, respectively.
The literature comprises several studies that employed GEP and GMDH networks for short-term electrical energy consumption forecasting. Huo et al. developed an improved GEP model for short-term load forecasting and compared their model with traditional models of genetic programming (GP) and GEP [
22]. Fan and Zhu indicated that a combination of empirical mode decomposition (EMD) and GEP may perform higher accuracy than WD and GEP combination for short-term load forecasting [
23]. Hosseini and Gandomi compared GEP models with multiple least squares regression (MLSR) and generalized regression neural networks (GRNN) for forecasting day ahead peak and total loads of a North American electric utility [
24]. Deng et al. used artificial fish swarm based hybrid GEP along with cloud computing in order to model distributed electric load forecasting in comparison with ANN, PSO-SVM, SVR, and traditional GEP on the data set of EUNITE competition [
25].
Sforna used GMDH networks for acquiring a function between electric load and temperature variables and compared GMDH networks with ANN on electrical and meteorological data of four major Italian cities containing Florence, Milan, Naples, and Rome [
26]. Huang and Shih utilized a combination of fuzzy modeling and GMDH networks on Taiwan’s electric load data in order to improve the performance of their short-term load forecast model against ANN and ARIMA [
27]. Abdel-Aal employed GMDH networks on Seattle’s electrical and weather data to obtain analytical expressions between input and output variables in forecasting hourly and daily electric loads with different variations of ANN, abductive networks, and network committees (NC) [
28,
29,
30]. Elattar et al. proposed a generalized locally weighted GMDH networks based EA for short-term load forecasting and performed the algorithm along with local support vector regression (LSVR), locally weighted GMDH networks (LWGMDH), locally weighted support vector regression (LWSVR), and traditional GMDH networks on two different data sets belonging to New York City and Victorian electricity market of Australia [
31]. Xu et al. applied GMDH networks in comparison with ARIMA for short-term load forecasting of New South Wales in Australia [
32]. Koo et al. presented a comparative study that performed ANN, simple exponential smoothing (SES), and GMDH networks for forecasting Korean electric load data on an hourly basis [
33], and another study that wavelet transform was firstly applied for decomposition before the implementation of Holt-Winters method, ANN, and GMDH networks for one day ahead forecasting of hourly electric loads [
34]. Jacob et al. employed GMDH networks and linear regression (LR) for forecasting short-term electrical energy consumption of a university campus in Nigeria [
35]. Zjavka and Snasel proposed a method named as differential polynomial neural network that merges the functionality of GMDH networks with differential equation substitutions and carried out short-term load forecasting against ANN, SVM, and GMDH networks for the UK electricity transmission network and Canadian detached houses [
36]. Yuniarti et al. tried to integrate wavelet transform with GMDH networks for short-term load forecasting of a power company in Sumatara, Indonesia, and collated it with the coefficient method (CM), which is currently used by the company [
37]. Liu et al. enhanced GMDH networks by introducing elastic net regression and enriching with difference degree weighting optimization for forecasting hourly loads in data sets pertaining to three locations in China [
38] against ANN, SVM, least absolute shrinkage and selection operator (LASSO), ridge regression (RR), and traditional GMDH networks. For South Korea’s hourly load data, Yu et al. suggested a forecasting methodology based on SVR, which implements GMDH networks and bootstrap methods for the input selection procedure in comparison with different variations of linear correlation (LC) and mutual information (MI) based filter methods [
39]. Izzatillaev and Yusupov analyzed hourly electrical energy consumption forecasting in a grid-connected microgrid within a commercial bank by employing GMDH networks and ANN [
40].
Benchmark analysis of the studies that utilized from GEP and GMDH networks for short-term electrical energy consumption forecasting is demonstrated in
Table 2 in terms of performed models, application type, forecast horizon, and compared models, consecutively.
4. Results and Discussion
All computations in the scope of this work were performed on a Macintosh computer with OS version of 10.15.2, a processor of 2.4 GHz (Intel Core i5), and a memory size of 8 GB. For all computing tasks, RStudio was used as an integrated development environment for R programming language, which is one of the most popular languages for statistical computing and data analytics with elegant graphics [
55].
Values stored in input variables of the data set are scaled between 0 and 1 for normalization, which provides elimination of units of various data types, reducing computational time and covering less memory for data integrity, and benchmarking multiple data columns in a similar way. In the assessment of performances belonging to GEP and GMDH networks, R
2, RMSE, and MAPE are utilized in this study. Formulae of the performance metrics are as follows:
where
is actual or measured output,
is predicted output,
is mean of
, and
n indicates the number of observations [
41].
For model testing and evaluation, random sampling method is implemented to GEP and GMDH networks in such a manner that 20% of the data set is employed to constitute training data, and 80% of the data set is adopted to form validation data randomly.
4.1. Parameters of GEP
Model building parameters for GEP are used as 50 for population size, 10,000 for the number of maximum tries for initial population, 4 for genes of chromosome, 8 for gene head length, 2000 for number of maximum generations, 1000 for number of generations without improvement, and 1.0 for the best chromosome’s fitness score stop. Fitness properties are determined as MSE for fitness function, 1% for hit tolerance, and 100 for selection range. During computations, allowed functions are addition (+), subtraction (−), multiplication (×), division (/), and square root (), while algebraic simplifications are conditionally permitted. The rates of evolution parameters are specified as 4.4% for mutation, 10% for gene, inversion, insertion sequence transposition, root insertion sequence transposition, and gene transposition, and 30% for both one-point and two-point. Addition (+) is employed as the link function for all genes. Features of random constants are adjusted as 10 for random real constants per gene, −10 and 10 for minimum and maximum constant values, and 1% for mutation rate.
Generations required for the training model and simplification are 2001 and 407, respectively. The complexity of the model is reduced from 25 to 15 by simplification. Evaluations of fitness function are numbered as 125,150. The best GEP model containing four input variables is demonstrated in
Figure 8 and yields the following equation
where
is the predicted electrical energy consumption,
and
represent the outdoor temperature and short-wave irradiation values taken from MERRA-2,
corresponds to the electrical energy consumption value for the previous one hour, and
is the value of calendar variable standing for hour of day.
4.2. Parameters of GMDH Networks
For GMDH networks, the quadratic reference function with two variables stated in Equation (
5) is employed. Parameters for the GMDH networks are predetermined as 20 for the number of both maximum network layers and neurons per layer, 16 for maximum polynomial order, and
for convergence tolerance. Allowed network configuration for the neurons in the next layer is designated as the selection of neurons in the previous layer and original input variables. A hold-out sample of 20% is utilized for protection control in order to avoid overfitting.
The best GMDH network model having seven input variables is found as
where
N corresponds to neurons from
to
such that each neuron represents a quadratic equation,
and
stand for transducer device temperature and relative humidity,
symbolizes the calendar variable type of day, and
indicates the electrical energy consumption for the previous day at the same hour. Detailed parameters and coefficients of Equation (
7) are given in
Table 6.
4.3. Overall Results
Correlation coefficients of input, target, and predictor variables are visualized as a map in
Figure 9 according to Pearson’s correlation prior to mentioning overall results. Pearson’s correlation indicates a number between −1 and 1 that shows the extent to which two variables are linearly correlated. It should be emphasized that blank squares within the correlation map represent statistically insignificant p-values that are smaller than 0.01.
When overall performances of the applied methods are evaluated in terms of accuracy, it is seen that GMDH networks give slightly better results than GEP according to R
2, RMSE, and MAPE for the short-term building electrical energy consumption forecasting problem, as shown in
Table 7.
However, it should be noted that the best GMDH network model employs seven input variables with different variations in several equations having high polynomial order, while the best GEP model executes four input variables in one simple equation. Therefore, the simplicity of the GEP model reveals the fact that the computational time required to reach the best model by using GEP is one fourth of the time needed for GMDH networks, as indicated in
Figure 10.
Thus, the selection of each method for short-term building electrical energy consumption forecasting problem depends on the order of importance. If accuracy is more important than computational time and simpleness, GMDH networks are recommended. Otherwise, GEP is suggested for its low computational complexity and run time.
Additionally, graphs consisting of actual and predicted values by employing GEP and GMDH networks are demonstrated in
Figure 11 for 9–10 October 2017 and 23–24 April 2018, which are the days possessing the largest errors because of seasonal transitions (from summer to winter and from winter to summer).
4.4. Discussion of In-Depth Investigation Results
Daylight utilization is one of the crucial topics not only for electrical energy efficiency studies but also for architectural indoor lighting studies. Short-wave irradiation is active during daylight and considered as a prominent variable that affects energy consumption of sustainable buildings. One distinctive finding of this study is related to the effect of short-wave irradiation over short-term building electrical energy consumption forecasting.
is encountered in both model equations; hence, it draws the attention and is advised to be included as an explanatory variable for further studies. Short-wave irradiation affects outdoor and indoor temperature, which also have impacts on the building HVAC temperature set point that influences electrical energy consumption. This study unveils that if short-wave irradiation does not equal zero, the arduousness level of short-term building electrical energy consumption prediction significantly increases, as indicated in
Table 8.
Another innovative result of this work, which has never processed in the literature to the best of one’s knowledge, are in-depth investigations of the error-related performance metrics regarding short-term forecasts with respect to hour of day, name of day, type of day, and name of month. Short-term forecasts are examined according to the hour of day, in order to deduce the challenging hours in building electrical energy consumption prediction. It is inferred from the obtained results presented in
Table 9 that two hours and an hour before the shift start (06:00–07:00 and 07:00–08:00) have the largest errors and are difficult to predict along with the previous hour of the shift end (16:00–17:00). The forecasts in terms of the name of day are analyzed in detail and the results are shared in
Table 10. In regard to
Table 10, the complexity level of prediction shows a tendency to decrease from the first day of the week (Monday) to the end of the week (Sunday). In the forecasts according to the type of day, in-depth analyses indicate that forecasting working days are more difficult than predicting weekends and holidays, as illustrated in
Table 11.
Months with peak errors are elaborated in
Table 12 wherein October and April possess the largest errors in comparison with the others owing to the fact that in the mentioned months, significant meteorological changes occur due to seasonal transitions from summer to winter and vice versa.
Key results of the in-depth investigations are summarized in
Figure 12. Effect of shift start and end on an hourly basis, decreasing trend from Monday to Sunday, and peak errors of months during seasonal transitions are highlighted in
Figure 12 with respect to GEP and GMDH networks.
5. Conclusions
Share of buildings energy consumption in the global final energy use and evolution of existing electric power systems to smart grids and IoE are considered together, the significance of short-term building electrical energy consumption forecasting is comprehended. Complexity of the forecasting process comes from the fact that there are so many factors influencing building energy consumption and every building has its own characteristics, such as physical properties and operational schedule.
Recent studies in the literature show an interest in the application of machine learning algorithms to predict short-term building electrical energy consumption. However, most of them produce an abstruse analytical expression among explanatory variables and response variables. In this study, GEP and GMDH networks are employed to forecast short-term building electrical energy consumption for a large hospital complex in the Eastern Mediterranean owing to their capability of generating easily understandable model equations between input variables and target variables without the need of implementing feature selection. Both methods are performed under identical constraints and evaluated in terms of R2, RMSE, and MAPE.
According to the results of the analyses, the best MAPE scores of GMDH networks and GEP are calculated as 0.620% and 0.641%, respectively. It is considered that GEP can be chosen for its low computational complexity and run time, while GMDH networks may be selected for predictions holding slightly better accuracy. In-depth investigations are carried out in this study to generalize and highlight the increase in forecasting complexity during challenging transitional periods by investigating MAPE values. Acquired results deduce the effects of short-wave irradiation, start and end of the working hours, weekends and holidays, and seasonal transitions over short-term building electrical energy consumption forecasting along with hourly, daily, and monthly trends of the prediction arduousness with respect to MAPE.
Consequently, it should be emphasized that this study is the first attempt in the literature that benchmarks GEP and GMDH networks for short-term building electrical energy consumption forecasting to create genuine and simple model equations by interpreting remarkable results with regards to accuracy, number of input parameters and complexity of model equations, and computational time. Furthermore, produced model equations in this study can be utilized for future studies related to buildings possessing similar meteorological conditions and electrical energy consumption profiles.