Novel dynamic forecasting model for building cooling loads combining an artificial neural network and an ensemble approach

Applied Energy 228 (2018) 1740–1753

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Novel dynamic forecasting model for building cooling loads combining an artificial neural network and an ensemble approach

T

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Lan Wang , Eric W.M. Lee, Richard K.K. Yuen Department of Architecture and Civil Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong Special Administrative Region

H I GH L IG H T S

building cooling forecasting model for energy saving of HVAC system. • Developing step-ahead building cooling load by time series prediction. • Forecasting step-ahead building cooling load by Fourier’s law-based analysis. • Forecasting • Improving performance of building cooling load forecasting by ensemble technique.

A R T I C LE I N FO

A B S T R A C T

Keywords: Dynamic load forecasting Building cooling loads Artificial neural network Ensemble approach

Short-term load prediction, which forecasts a building’s thermal load with a lead time ranging from seconds to a few days, is essential for not only monitoring and controlling the system operation, but also on-line scheduling. Dynamic cooling load forecasting, which belongs to short-term load prediction, is both meaningful for monitoring the system or fuzzy on-line scheduling and crucial for solving the time-lag problem to meet the heating, ventilation and air-conditioning system’s time-varying cooling loads. Numerous studies have been carried out to develop dynamic load-forecasting models, and great achievements have been made. However, limitations in their applicability persist because most previous models are calendar- and time-based data-driven models that may fail when unexpected issues occur or special schedules are adopted. What’s more, the inputs that were selected passively from the source data pools at hand rather than via active exploration may be insufficient and impair the accuracy of forecasting models. This paper proposes a novel dynamic forecasting model for building cooling loads that combines an artificial neural network with an ensemble approach. Based on physical principles other than the available data source, the inputs are explored actively and are independent from both calendar and time indicators, which make the forecasting model being capable of dealing with irregular occasions and unexpected schedules with high accuracy. A benchmark is proposed that uses the current load Q (t ) as a  (t + i ) and gives the minimum accuracy requirement for a dynamic forecasting model. forecasted cooling load Q The benchmark not only can be used to evaluate dynamic forecasting models that are validated by various case studies, but also ensures that the proposed forecasting model can be applied immediately to heating, ventilation and air-conditioning systems to tackle the time-lag problem.

1. Introduction Short-term load prediction, which forecasts a building’s thermal load with a lead time ranging from seconds to a few days (168 h, or 7 days) [1], has been discussed since the 1970s [2]. It is essential for not only monitoring and controlling the system operation, but also on-line scheduling. Dynamic load forecasting belongs to short-term load prediction, with a short lead time within 1 h, which usually corresponds to the regular time interval (15, 30 or 60 min) adopted in the optimisation

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control of the heating, ventilation and air-conditioning (HVAC) system. Dynamic load forecasting with a lead time of a single time interval is not only meaningful for monitoring the system or fuzzy on-line scheduling, but also crucial for solving the time-lag problem to meet the HVAC system’s time-varying cooling loads. Specifically, in the optimisation control of the HVAC system, which has been studied for decades, the current load is used as the input to derive the system’s optimised control variables, that is, the current load is used as the average load for the coming timestep [3] (see Fig. 1). This

Corresponding author. E-mail address: [email protected] (L. Wang).

https://doi.org/10.1016/j.apenergy.2018.07.085 Received 3 May 2018; Received in revised form 2 July 2018; Accepted 14 July 2018 0306-2619/ © 2018 Elsevier Ltd. All rights reserved.

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Nomenclature

Twb Tdb Tch, s Tch, r Tcw, s Tcw, r

Tin Tinsurf Toutsurf T∞ H∞

Hin RH hair , in

the wet bulb temperature (°C) the dry bulb temperature (°C) the temperature of chilled water being supplied from a chiller to a zone (°C) the temperature of chilled water being returned from a zone to a chiller (°C) the temperature of condenser water being supplied from a cooling tower to a chiller (°C) the temperature of condenser water being returned from a chiller to a cooling tower(°C) the dry bulb air temperature of a zone (°C) the interior surface temperature of building envelops (°C) the exterior surface temperature of building envelops (°C) the ambient dry bulb temperature of the air (°C) the ambient air humidity

hair , out Q (t )  (t ) Q ṁ ch ṁ cw ṁ air R p N Ninp Noutp Ns

The air humidity of a zone the relative humidity of air (%) the enthalpy of air being supplied to a cooling tower (J/ kg) the enthalpy of air flowing through a cooling tower (J/kg) the building cooling load at time t (KW) the forecasted building cooling load at time t (KW) the mass flow rate of the chilled water (kg/s) the mass flow rate of the condenser water (kg/s) the mass flow rate of the air (kg/s) the thermal resistance of materials (°C/W) the number of occupants the number of hidden neurons the number of inputs the number of outputs the number of training samples

Fig. 1. Diagram of model-based optimisation control. (All figures of this paper are produced by the authors.)

unexpected incidents occur. In addition, the inputs selected from the source data pools at hand may be insufficient. The use of inputs filtered from the source data pools would be reasonable only if the source data pools included all necessary factors. If the source data pools failed to include necessary inputs, the filtered inputs would be even more insufficient. The insufficiency of inputs may harm the forecasting model’s performance. In addition, no uniform benchmark can compare all kinds of forecasting models that are validated by different case studies. Therefore, the potential remains to improve the performance of forecasting models, and a reasonable benchmark should be proposed. This paper proposes a novel dynamic forecasting model for building cooling loads that combines an artificial neural network (ANN) with an ensemble approach. Based on physical principles other than the available data source, the inputs are explored actively to be trained by the

is hardly true in reality since time delay due to the slow response of the air-side of the HVAC system cannot be avoided. The step-wise optimised setting based on the current load would make the HVAC system fail to achieve maximum coefficient of performance (COP) in the coming timestep. This is the so-called time-lag problem as demonstrated in Fig. 2, which also impairs the energy efficiency of an HVAC system. For HVAC systems that work for years, tremendous energy would be saved if this time-lag problem can be solved. To solve this problem, a dynamic cooling load forecast for the next time interval is necessary. Numerous studies have examined this topic, and great achievements have been made, but limitations to their applicability persist because most studies are calendar- and time-based forecasting, which limits the forecasting model to a building schedule and makes it unsuitable when

Fig. 2. Illustration of time-lag problem in meeting an HVAC system’s time-varying cooling load. 1741

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[16]. A general regression neural network was applied for hourly load forecasting 1 day in advance [17]. An ANN and a fuzzy expert system were combined to perform hourly load forecasting 1 day in advance [18]. A nonlinear autoregressive neural network model was developed to forecast the hourly electric load 1 day in advance [19]. Two linear regression predictors were combined with an ANN using a Bayesian method to forecast the next day’s load at a given hour [20]. An autoregressive-moving average with an exogenous terms model was combined with fuzzy logic to predict the hourly load 1 day in advance [21]. AI methods have become increasingly popular in short-term load forecasting with the boom of a variety of advanced AI techniques. Although ANNs remain popular, all kinds of other techniques were widely used, such as combination of rough set theory with an ANN and data fusion, clustering algorithm, support vector regression, support vector machine and deep learning. The support vector machine was adopted to predict the mean monthly load by determining the mean monthly dry bulb temperature, the relative humidity and global solar radiation [22]. An ANN was applied to forecast the hourly electric demands of a chiller with a lead time of one time step and 1 day, respectively [23–25]. An ANN was combined with a data-fusion technique to predict the hourly load [26]. A clustering-based method was combined with a multi-layer perceptron to perform short-term load forecasting [27]. The support vector regression was applied to predict the hourly electrical load of residential buildings months in advance [28]. Two types of support vector regression technique were united to forecast the half-hourly and daily energy consumption of buildings [29]. A support vector machine and the deep learning technique were adopted to predict cooling load profiles 24 h in advance [30]. The enriched AI technique spawned various forecasting models, to select appropriate models based on building characteristics, Cui et al. [31] proposed a meta-learning based framework that effectively recommended most appropriate load forecasting model for each unique building. In summary, the evolution of modelling techniques used for shortterm load forecasting has progressed from statistical techniques to AI techniques. The AI techniques, which adapt themselves by learning from the data samples, release the forecasting model from elaborate data pre-analysis. With the application of AI techniques, the load profile can be disposed as a whole rather than being disassembled as different components as before, and the forecasting method is more concise.

proposed data-driven model. The inputs, which are independent from either calendar or time, make the forecasting model capable of dealing with unexpected schedules with higher accuracy. The benchmark, which requires the forecasted cooling load to be more accurate than simply taking the current cooling load as the target, is the minimum accuracy requirement for a forecasting model. Exceeding the benchmark guarantees that the proposed forecasting model can be applied immediately to HVAC systems to tackle the time-lag problem. In Section 2, the previous practices in short-term load forecasting are reviewed. The dynamic load-forecasting model proposed in this paper is introduced in Section 3. A case study then validates the proposed dynamic load-forecasting model in Section 4, and conclusions are drawn in Section 5. 2. Review of short-term load forecasting To the authors’ knowledge, the study of short-term load prediction can be traced to around the 1970s, and in the early literature the load mainly refers to a building’s electric load, including not only the HVAC system but also lighting and equipment. It is difficult to rely on a physics-based model to forecast the load because it is usually unrealistic to obtain sufficient necessary detailed information. Therefore, several kinds of data-driven methods that require much less information than physics-based methods have been discussed in studies. The previous studies can be reviewed from two aspects: the techniques used to deal with data and the parameters selected as the inputs for the data-driven models. These two aspects are reviewed in Sections 2.1 and 2.2, respectively. 2.1. Evolution of modelling techniques Modelling techniques have changed from statistical methods to artificial intelligence (AI) methods. Before the emergence of the AI method, around 1966 to 1990, statistical approaches were the most popular techniques in the short-term load-forecasting model [1,4,5]. The AI method’s application in short-term load-forecasting models began with its development in the 1990 s. The transition from statistical methods to AI methods occurred around 1991 to 2001, and with the booming of advanced AI techniques, a variety of AI methods and hybrids of various AI methods have been widely used ever since [6–8]. Multiple regression methods, exponential smoothing and stochastic time series are popular statistical approaches that have been applied in short-term load forecasting. Multiple linear regression was used to forecast the daily peak load (i.e. the hourly integrated load at 2 PM) [9,10]. General exponential smoothing was used for hourly load forecasting with a lead time of 1–24 h [2]. The long-term average was combined with exponential smoothing to conduct hourly load forecasting for the following day [11]. The stochastic models were adopted for hourly power system load forecasting with lead times from 1 to 24 h [12], and the stochastic time series analysis was applied to predict the daily peak load 1 day ahead [13]. The statistical approaches, which call for an explicit mathematical model to give the relationship between the output and inputs, were applied with elaborate analysis of the source data. As such, studies that use statistical approaches have tended to divide the total load into various components by their nature. For example, the total load was divided into a basic load and a weather-sensitive load [9–11]. Besides, a weekly cycle component was appended sometime [12]. During the transition period from statistical methods to AI methods, ANNs, fuzzy neural networks, combined ANNs with regression, combined ANNs with fuzzy expert system and other techniques were adopted. A three-layer ANN with historical loads and historical and forecasted dry bulb temperatures was used to predict the daily peak load, total load and hourly load [14]. A fuzzy neural approach was adopted to predict the following day’s load curve [15], and a fuzzy neural network was applied to forecast the hourly load curve using

2.2. Selection of model inputs Except for the building properties, which usually remain stable over time, the relevant factors that affect a building’s cooling load are the weather conditions, occupancy and operating equipment in the building. Due to the difficulty in collecting occupancy information, time indicators – time of day, day of the week, day type (holiday or not) – are usually chosen as inputs to represent occupancy scenarios. In addition, the historical load is a popular input because it indicates the trend of the load profile in a mathematical way. Consequently, three types of input – weather conditions, time indicators and historical loads – have been widely chosen in existing studies to include the effects of the relevant factors. Many combinations of these three types of inputs have been widely discussed. For example, only weather data – the external hourly temperature of 1 day before –was adopted as input to forecast the hourly load 1 day ahead [17]. Only historical loads were taken as input to forecast hourly loads with a lead time from 1 to 24 h [13,25,32]. Historical loads and weather data (ambient dry bulb temperature) were combined as input to forecast the daily peak load, daily total load and hourly load [14]. Historical loads and the type of day were united to forecast the hourly load with a lead time from 1 to 24 h [2,16]. Weather data and the type of day were taken as input to forecast the daily peak load and hourly loads, respectively, 24 h in advance [9,33]. The historical hourly load, weather data and type of day were combined as inputs in several 1742

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3.1. Theoretical basis for input selection

studies [11,12,15,18,19,21,23,24,34]. Through the evolution of modelling techniques, the types of inputs remained nearly the same, whilst the number of inputs increased as the modelling techniques developed. In early studies, the three types of inputs were considered by a limited number of indicators for each type. For example, only the dry bulb temperature was included to represent the weather conditions, a limited number of historical loads were included and only weekdays were considered [2,10,11]. In later studies, more indicators were included for each type of input. The wet bulb temperature, relative humidity, global solar radiation and wind speed were considered as indicators of weather conditions in addition to the dry bulb temperature [22,35,36]. More historical loads were referred, and all kinds of day types, such as weekdays, weekends and holidays, were considered [33,35]. A variety of data manipulation of inputs emerged, such as Fan et al. [30] performed feature extraction to derive inputs data for the forecasting model. And it was found that significant improvement in prediction performance can be achieved when using feature extracted by unsupervised deep learning models. The convenience of AI methods in dealing with large amounts of inputs makes it feasible to include as many factors as possible, so that the performance of the forecasting model can be improved.

Both perspectives for input selection are based on the physical principle of heat transfer, but they stress different aspects. The inputs selected based on the RTS method stressed the radiative portion of heat gain, which is absorbed by the thermal mass in the zone and then released into the space. This process creates a time lag and a dampening effect. The inputs selected based on Fourier’s law address the entire picture of heat gain, especially the convective part that contributes to building cooling loads. 3.1.1. Radiant time series method The heat balance (HB) method and the radiant time series (RTS) method are the only two load calculation methods that the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) defined in their Fundamentals Handbook ever since the 2001 edition till the latest 2017 edition. The HB method is an effective calculation method that ensures all energy flows in each zone are balanced, and the solution of a set of energy balance equations for the zone air and the interior and exterior surfaces of the envelopes are solved [37]. The RTS method, which is a simplified method derived from the HB method to compute building cooling loads [38], has effectively replaced all other simplified (non-heat-balance) methods, such as the transfer function method (TFM), the cooling load temperature difference/ cooling load factor (CLTD/CLF) method, and the total equivalent temperature difference/time averaging (TETD/TA) method. Rigorously, yet dose not require iterative calculations, the RTS method addresses two time-delay effects inherent in building heat transfer processes, namely the delay of conductive heat gain through opaque massive exterior surfaces (walls, roofs, or floors) and the delay of radiative heat gain conversion to cooling loads [39]. The total heat gain is divided into radiant, conductive and convective portions, which are then converted by coefficients into cooling loads. The convective portion is assumed to instantly become the cooling load. However, the radiative portion is absorbed first by the thermal mass and then released by convection to become the cooling load. A time lag and a dampening effect exist in this process that can be calculated using the time series method as shown in Eq. (1) [38].

2.3. Summary of the improvement potential for previous studies As stated in Sections 2.1 and 2.2, much work has been done on short-term load forecasting, and great achievements have been made. However, limitations exist, and improvements can be made in the following aspects. First, nearly all forecasting models must consider time indicators, namely, the day type, that are in fact the effect of occupancy. Interpreting the occupancy by referring to time indicators limits the applicability of a forecasting model. A forecasting model that relies heavily upon time indicators would fail to deal with irregular occasions such as special ceremonies when people gather or unexpected breaks during which people are dismissed. Applying occupancy rather than time indicators as input, the forecasting model would be applicable regardless of the type of day. Second, the selection of inputs can be improved with a more essential theoretical basis. The inputs are usually selected based on the data pools at hand by experience or by correlation analysis. In this case, if the data pool at hand fails to contain each of the necessary inputs, then the inputs filtered by experience or by correlation analysis will be even more insufficient. Instead of filtering inputs passively from an available data pool, an active exploration for inputs on an essential theoretical basis can make the selection of inputs more sufficient, and the important relevant inputs will not be neglected. The precision of the forecasting model will not be impaired by insufficient or inappropriate selection of inputs. Third, it is difficult to compare various forecasting models because no benchmark evaluates models under various circumstances [6]. A benchmark that can evaluate models in various circumstances can be determined by aiming at a specified application proposed in this paper.

Qθ = r0 qθ + r1 qθ − δ + r2 qθ − 2δ + r3 qθ − 3δ + …+r23 qθ − 23δ

(1)

where

Qθ = cooling load (Q ) for the hour (θ), qθ = heat gain for the hour (θ), qθ − nδ = heat gain n hours ago

and

r0, r1, etc. =radiant time factors. The relationship between the historical heat gain and the current or future cooling loads can be not only calculated explicitly by the time series method but also modelled implicitly with an ANN. 3.1.2. Fourier’s law–based analysis Another perspective to determine the effect factors of building cooling loads is taken from Fourier’s law by tracking factors that contribute to a building’s cooling load. The Fourier’s Law, also known as the law of heat conduction, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, which can be written specifically for a building block as Eq. (2). From the equation, it can be seen that the rate of heat transfer, which contributes to the building cooling load, is driven by temperature differences and the material thermal resistances. The temperature is a variable that can be easily measured. So, if only the factors that affect the thermal resistance can be found, then the inputs that are found out to forecast the cooling load would be

3. Proposed dynamic load-forecasting model The dynamic load-forecasting model proposed in this paper is first used to forecast the coming load from two perspectives, which are based on the radiant time series (RTS) method and Fourier’s law, respectively. Then, it combines the forecast loads with the ensemble approach to arrive at the final result. In Section 3.1, the theoretical basis for selection of inputs is introduced, namely, the RTS method and Fourier’s law. The diagram of the entire forecasting model is illustrated in Section 3.2. A benchmark as well as a comparison model for evaluation of the forecasting model are introduced in Section 3.3. 1743

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reasonably sufficient. The Fourier’s law-based analysis provides a perspective for tracking the effective factors of building cooling loads. As shown in Fig. 3, taking a building block with concrete envelopes with thickness X and area A as an example, the building cooling load can be roughly traced back to four portions as follows.

temperature, the humidity, the number of occupants and the outside surface temperature of the walls should be considered as inputs to forecast a building’s cooling load. The building properties that remain the same over a period are excluded. Heat gain from the ambient environment when shaded,

(1) The heat transferred from the ambient air to the indoor air, assuming that the building block is shaded from sunlight. The heat flow is first transferred from the ambient air to the outside surface of the walls via radiation and convection, from the outside surface to the inside surface of the walls via conduction, and finally to the indoor air via radiation and convection (see Eq. (2)). The radiant heat resistance of the ambient air is affected by the humidity and can be described as a function of the humidity (see Eq. (3)). (2) The heat gain from fresh air. Fresh air is necessary for the occupants’ health and contributes to the cooling load via sensible and latent heat gain. The sensible heat gain from fresh air can be calculated with Eq. (4), and the latent heat gain can be calculated with Eq. (5). The necessary mass flow rate of fresh air is closely related to the number of occupants (see Eq. (6)). (3) Latent heat gain from the occupants. The occupants’ main contribution to the cooling load is via sweat evaporation and is roughly a function of the occupants’ number for a building with normally one type of activity (see Eq. (7)). (4) The heat gain from solar radiation, which is reflected mainly by the outside surface temperature of the walls (see Eq. (8)).

Qe =

T∞−Tin R1 R2 R1 + R2

+ R3 +

R 4 R5 R 4 + R5

(2)

where R1 is affected by the ambient humidity [39],

R1 = f (H∞)

(3)

Heat gain from the fresh air,

Qs, f = Cp ṁ air (T∞−Tin )

(4)

Ql, f = ṁ air (H∞−Hin ) Lc

(5)

ṁ air = f (p)

(6)

where p is the number of occupants. Latent heat gain from occupants,

Qp = f (p)

(7)

Heat gain from solar radiation,

Qsol = f (Toutsurf )

(8)

where Toutsurf is the outside surface temperature of the walls. Summary of effect factors of building cooling loads,

To sum up the factors that affect the building cooling load mentioned above, a function can be written as Eq. (9). The ambient dry bulb

Q = f (building properties, p , T∞, H∞, Toutsurf )

Fig. 3. Heat transfer analysis by Fourier’s law. 1744

(9)

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current building cooling load and wet bulb temperature as constraints [50]. Because the current load is used as the average load of the coming time interval in real controls, the accuracy of the forecasted load of the coming time interval should be more accurate than that obtained by taking the current load as a forecast. Consequently, the benchmark of forecasting with the lead time of a single time interval i would be the same as taking the current cooling load Q (t ) as a forecast of the next  (t + i ) . The benchmark is applied in Section 4 to evaltime interval Q uate the performance of the proposed dynamic forecasting model.

3.2. Dynamic load-forecasting model combining artificial neural network with ensemble approach The theoretical basis illustrated in Section 3.1 provides the selection of inputs related to building cooling loads from two perspectives, based on which two forecasting models – Models A and B – can be derived. The relationship between the inputs and cooling loads can be established by an ANN, which is a dynamic inverse model that learns from examples and can approximate the behaviour of highly nonlinear systems [40]. ANNs have been widely used in short-term load forecasting [8] and have a better architecture to evaluate, estimate and predict a set of large data than statistical methods [7]. ANN with one hidden layer is adopted in this study, since the output of an ANN model with single hidden layer is in fact a superposition of numerous weighted sigmoid functions which has been proven to be a universal function approximator [41]. The input variables for Model A are historical cooling loads at time t, t−i, t−2i, t−3i, etc., namely Q (t ), Q (t −i), Q (t −2i), Q (t −3i), etc. (KW), based on the analysis of Section 3.1.1 (see Fig. 4). The input variables of Model B are the ambient dry bulb temperature (°C), the relative humidity (%), the number of occupants and the outside surface temperature of the walls (°C). The dampening effect of the building’s thermal mass and the accumulation of heat gain from the air and the occupants over time make it necessary to consider the historical value of each input at time t, t−i, t−2i, t−3i, etc. (see Fig. 5). When time t is the current time, the output is a forecast of the load for a coming time  (t + i) (KW). interval Q The number of hidden neurons in each simulation is determined by a rule-of-thumb developed by Ward System [42] described as follows.

N=

Ninp + Noutp 2

+

Ns

3.3.2. A comparison model Besides the benchmark, a model for performance comparison, which is a popular dynamic load forecasting models, is built up to further evaluate the performance of the proposed load forecasting model. With 4 previous time step inputs, including cooling loads (KW), the ambient dry bulb temperature (°C), solar horizontal radiation (W/ m2) and room temperature setpoint(°C), a 3-layer ANN model has been developed to perform a one time step ahead building cooling load (KW) forecasting [51]. The transfer function is hyperbolic tangent function in the hidden neurons and a linear function is used in the output neuron. The training function is the Levenberg-Marquardt back- propagation algorithm. 4. Case study A building, whose parameters were derived from a real 90-floor commercial skyscraper, was developed using the transient system simulation tool (TRNSYS). The simulation was verified by comparing the simulated building cooling loads with the measured loads. The simulation overcame the limitations of measured data by providing sufficient information such as the envelopes’ outside surface temperature and by avoiding unreasonable building cooling loads due to improper manipulations of the HVAC system by the occupants. Based on the simulated data, the proposed dynamic load-forecasting model was successfully validated.

(10)

where N is the number of neurons; Ninp and Noutp are the number of input and output parameters, respectively; and Ns is the number of training samples. Models A and B emphasise different aspects of the cooling load composition and are developed independently based on diverse theories. The combination of Models A and B by the ensemble approach is supposed to give more accurate forecasts. The ensemble approach is an idea that by the combination of different predictors, it is possible to improve the overall prediction accuracy [43]. This idea has been used to improve the performance of prediction models successfully in several researches [44–46]. The technique of the ensemble approach used in this paper is the bagging approach [47], which averages the inputs to give outputs. Concretely, Models A and B are trained by the relevant historical data, which cover the latest weather and occupancy scenarios. The building properties are assumed to be in the same state for a period, at least a few months. After Models A and B are trained, they can be used for forecasting. With relevant inputs, cooling loads are forecast by Models A and B, and the final forecasted cooling load can be obtained using the ensemble approach (see Fig. 6).

4.1. Building description The sample building of this study is a mega grade A office building, which is located at the hub centre of Hong Kong. Multi-national financial companies coming from all over the world are working in this

3.3. Benchmark and a comparison model for evaluation of the dynamic load-forecasting model 3.3.1. Benchmark The current load combining with the current weather information are usually taken as constraints to derive the optimum HVAC system settings to minimize the electrical energy consumption [48]. Current wet bulb temperature and building cooling load are taken as constraints in optimising the condenser water loop of HVAC system [3]. An energy optimization methodology was proposed to derive the optimized operation decisions for chiller plants at regular intervals based on the building thermal load and the weather condition [49]. A varying searching bounds optimization control method was proposed by taking

Fig. 4. Architecture of the ANN for Model A. 1745

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energy systems [54,55]. The Type 56 Multi-zone Building model, which solves coupled differential equations using matrix inversion techniques, provides a more efficient way to calculate the interaction between two or more zones. The building envelopes were modelled according to the ASHRAE transfer function approach [54], which has been verified as a reliable method to calculate a building’s cooling load [39]. Several popular simulation codes for modelling buildings’ thermal behaviour and cooling loads, including EnergyPlus, DOE-2.1E, TRNAYS-TUD and ESP-r were compared, and discovered that TRNSYS simulation gives results with satisfying accuracy [56]. The building cooling loads of domestic and public buildings have been modelled with TRNSYS in a variety of studies [57–61]. The building cooling load simulated by TRNSYS was compared with measured data to verify the simulation. Fig. 9 compares the building cooling load profiles. The variation trend and the magnitude of timevarying loads were both captured by TRNSYS simulation. The profiles were well matched from around 6650 to 6775 h, from around 7507 to 7107 h and from around 7200 to 7275 h. The discrepancies occurred mainly during peak load hours, which can also be observed from the scatter plot of Fig. 10 for its heteroscedastic nature, and it was possibly due to improper manipulation of the HVAC system by the building’s occupants. The coefficient of determination was taken to evaluate the accuracy of simulation, as shown in Eqs. (11) and (12). The coefficient of determination:

Fig. 5. Architecture of the ANN for Model B.

building with 24 h services including air conditioning, power supply, security access and so on. It was simulated in TRNSYS with a standard floor area of 1800 m2, and the 90 floors were divided into nine zones of 10 floors each. A window belt (1.5 m high) was embedded in the facades in all four directions for each floor (see Fig. 7). Table 1 shows the construction and thermal properties. The time frame is chosen as from 6550 h to 7300 h (from Oct. 1, 2009 to Oct. 31, 2009 approximately) since the performance data of the sample building are only available during that time. The data collected including measured hourly building cooling loads, the meteorological data and occupancy level. The hourly monitored meteorological data includes the ambient dry bulb temperature and the relative humidity. The building’s occupancy level, which was managed according to the Code of Practice for Fire Safety in Buildings [52] of Hong Kong, was measured by the electricity energy consumption of the escalators [53]. Apart from the building cooling loads, the monitored ambient dry bulb temperature, relative humidity and occupancy level are plotted in Fig. 8. The monitored data were all applied in the TRNSYS simulation, and solar radiation was read from the TMY2 meteorology file of Hong Kong provided by TRNSYS 16.

R2 = 1−

∑ (yi −y )̂ 2 ∑ (yi −y )2

(11)

where yi is the measured value, y ̂ is the modelled output,

and y =

1 n

n

∑

yi

i=1

(12)

The indoor temperature can be ensured to be extremely constant in TRNSYS simulation, which is hardly possible in a real building due to the delayed responses of the HVAC system or the manipulations of occupants. Therefore, discrepancies between simulated and measured data cannot be avoided. Compared with the measured data which can be noisy since the delayed response of the HVAC system or the improper manipulations of occupants, etc. the simulated data is more qualified by excluding the noise that may not be explained by physical terms. Combining the observation that (a) the mainly curving trends of the measured cooling load profile have been tracked well by the simulated data; (b) the simulation model explains 87% of all the variability of the measured data (R2 is 0.87, see Fig. 10); (c) average deviation of simulation is 9.7 KW (see Fig. 11), which is less than 0.2% of the measured data mean, we may conclude the data that simulated by TRNSYS could reasonably represent the sample building. The hourly cooling loads that were calculated from TRNSYS are taken as the real

4.2. TRNSYS simulation verification The TRNSYS program, developed continuously by the Solar Energy Laboratory at the University of Wisconsin since 1975, is a flexible simulation tool that can simulate the transient performance of thermal

Fig. 6. Diagram of dynamic load forecasting method. 1746

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Fig. 7. Geometry and construction detail for sample building.

and B, and the latter one third of the data were used to test the performance of the dynamic forecasting model. Previous inputs of nine time steps and three time steps for Models A and B, respectively, were adopted after a series of trials. An early-stop validation approach showed no significant improvement in the validation error over a predefined number of epochs after the minimum level was reached. The intermediate state of the model with the minimum validation error was selected as the trained model. One thousand epochs were adopted in this case study (refer to Fig. 12). As shown in Fig. 13a, the building loads forecasted by Models A and B were distributed around the real load profile with diverse patterns. During the peak load period, the results of Model A (dashed line with hollow squares) tend to be higher than the real load profile (thick solid line with crosses). Sometimes, the deviations are huge: around 7110, 7146, 7182, 7206 and 7266 h. However, the results of Model B (thin solid line with solid triangles) tend to be randomly distributed around the real load during the peak load periods. For example, the results of Model B match the real load profile well around 7116, 7137, 7161,

Table 1 Construction layers and thermal properties of the envelope.

Wall/Roof Window

Construction

U-value (W/ m2 K)

g-Value

200 mm concrete 50 mm insulation layer 6 mm glass and 16 mm air and 6 mm glass

0.580

–

1.26

0.397

load of the sample building in the case study. 4.3. Results and discussion 4.3.1. Results Overall, 742 valid data samples were derived from the TRNSYS simulation from 6553 to 7294 h. The first two thirds of the data were trained by an ANN with Bayesian regularisation to develop Models A

Fig. 8. Weather and occupancy profile applied in TRNSYS simulation. 1747

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Fig. 9. Comparison of simulated and measured cooling load profile.

7233, 7157 and 7263 h; underestimates occur around 7140 and 7143 h, whilst overestimates occur around 7185, 7191, 7212 and 7236 h. During the trough load period, the results of Model A and Model B match the real load profile well. During the period that loads are increasing or decreasing, the results of Model A match the real load profile well and Model B performs well when the load increases whilst underestimates happen when load decreases, such as around 7146 and 7170 h. The differences in the forecasting patterns derived from Models A and B make the combination of the results of the two models meaningful. The final results (thin solid line with solid circle) were drawn after using an ensemble approach to average the results of Models A and B. As shown in Fig. 13b, both Model A’s large deviations during the peak load periods and Model B’s underestimates during the decreased load periods were alleviated after ensemble. As such, the final results match the real load profile better than the results of either model alone. The benchmark (dashed line with half hollow square), which takes the current load as a forecast, plots a profile that behaves as a shift of the real load profile. Large deviations could not be avoided by the benchmark profile when loads varied dramatically as increasing or decreasing. As indicated by the value of R2, the proposed forecasting model considerably improved the accuracy, as compared with the benchmark. The load profile forecasted by the comparison model tend to overestimate at both peak and trough load periods, see Fig. 13c. The deviation can be huge at some hours, such as around 7113, 7167 and 7239 h. With an R2 of 0.8633, the performance of the comparison model is inferior to that of the proposed forecasting model. The errors of the forecasting models were analysed by both error distribution analysis and scatter plot as shown in Fig. 14. From the error distribution histograms, it can be seen that the 95% confidence interval of the error distributions was located in a similar range for Models A and B. The mean error of the model after ensemble was the average of the means of Models A and B, yet the deviation (sigma) was smaller than that of either Model A or B. The 95% confidence interval of the error distribution of the model after ensemble was only two thirds that of Models A and B. The mean error of the benchmark was between that of Models A and B, whilst the deviation was the greatest, and the benchmark’s 95% confidence interval of error distribution was nearly double that of the model after ensemble. Both the mean error and the deviation of the comparison model are larger than those of the model after ensemble. The 95% confidence interval of error distribution of the comparison model is around 1.75 times that of model after ensemble. The scatter plots in Fig. 14 show that, relatively, the deviations are relatively large at high load period whilst small at low load period for Model A. For Model B, the deviations occur at both high load period and low load period. After the ensemble procedure, the deviations are reduced obviously for all load scenarios. The deviations are averagely distributed at high load period and low load period besides some

Fig. 10. Scatter plot of simulated cooling loads with measured cooling loads.

Fig. 11. Error distribution of simulated cooling loads.

Fig. 12. Early-stop validation for ANN training.

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Fig. 13a. Comparison of cooling load profiles.

better than Model A on the inflection points in general, with smaller deviations. However, during the trough loading periods, when the environmental factors remained more stable, Model B performed worse than Model A with a few underestimates. The diversity of Models A and B made it reasonable to combine them to form a better forecasting model, which was proved by the results of the case study. The load profile showed that most of the large deviations were eased by the model after ensemble. The R2 values of Models A and B were both around 0.93, indicating similar accuracies of the two models. The R2 value increased to around 0.96 by combining the two models, and such a large improvement in accuracy could not occur if the two models were not complementary. The error deviations of Models A and B were both around 830 KW, whilst the residual deviation of the model after ensemble was reduced to around 630 KW. The decrease in the residual deviation also indicated the complementary status of Models A and B. Compared with the benchmark as well as the comparison model, the proposed ensemble model greatly improved the forecasting accuracy. The residual range of the model after ensemble was also considerably smaller than that of the benchmark and the comparison model. The forecasting model proposed in this paper differed from previous studies in input selection. As stated in the Introduction section, inputs in previous studies were usually selected from available source data pools. A passive method that contained the implicit premise that the available data pools included all necessary inputs, if not, the inputs selected from the data pools would have been even more insufficient. However, the accessible source of data pools might not be sufficient for cooling load prediction, as they were usually collected by the bureau according to the basic requirements of weather sampling. Instead of passive selection of relevant inputs based on the accessible data pool, extra inputs were actively explored based on physical modelling. Without a presumed condition, the inputs explored actively based on physical modelling are possibly be used to supplement the source data. Occupancy, rather than the type of day, was chosen to be one input,

outliers for the benchmark, and the results of the comparison model tend to overestimate a lot.

4.3.2. Discussion As shown in Fig. 13a and summarized in Table 2, the building loads forecasted by Models A and B were distributed around the real load profile with diverse patterns because they were based on different theories and stressed different aspects of the cooling load composition. Based on the RTS method, Model A stressed the radiant heat gain portion, which depended completely upon the cooling loads that already existed from the current time back into the past whilst the future was excluded. With the adoption of Model A, the cumulative effects of the cooling loads were well presented, but the inflection points that were driven mainly by sudden changes in the weather or occupancy were hardly reflected. Therefore, huge deviations mainly occurred with the adoption of Model A for forecasting when the real load profile came to an inflection point on each day, changing from ascending to descending. During the trough load periods, when the real load profile changed much more moderately, Model A performed better. Based on Fourier’s law, Model B stressed both the conductive and convection heat gain portions by considering all relevant environmental factors, indicating the heat gain that affected instant and future cooling loads. The current and historic sensor-based inputs affected future cooling loads due to the time they consumed with either the dampening effect of the building thermal mass or the process of metabolism. Concretely, the outside surface temperature of the envelope affected the future cooling load due to the time consumed by conductive heat transfer through the envelope’s thermal mass; the ambient dry bulb temperature and the relative humidity influenced the future cooling load as fresh air with the time needed to disperse evenly into a large room. The number of occupants affected the future cooling load with the time required by human metabolism to contribute latent heat gain. For the essence of stressing instant and future heat gains by considering all environmental affecting factors, Model B performed

Fig. 13b. Comparison of cooling load profiles. 1749

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Fig. 13c. Comparison of cooling load profiles.

of occupants could be monitored in a variety of ways, such as lift electricity consumption [53], Wi-Fi connections [62] and passive infrared sensors [28]. In addition, the envelope’s outside surface temperature was used as

which enriched the forecasting model to handle unexpected schedules. The use of the type of day to indicate the occupancy scenario had limitations when unexpected incidents occurred and invalidated the usual schedule. With the development of sensor techniques, the number

(a1)

(a2)

(b1)

(b2)

(c2)

(c1) Fig. 14. Forecasting error distributions. 1750

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(d1)

(d2)

(e1)

(e2) Fig. 14. (continued)

Table 2 Summary of forecasting performance of Model A and Model B.

Peak load period Trough load period Inflection points

From ascending to stable or descending From descending to stable or ascending

Forecasting performance of Model A

Forecasting performance of Model B

Mainly overestimates Mainly match

Underestimates & overestimates Mainly match with a few underestimates

Mainly overestimates Mainly match

Mainly match with a few overestimates Mainly match

an input for the first time. The surface temperature, which reflects the heat gain from solar radiation and the heat loss due to wind speed, has been neglected in other studies. Compared with the use of solar radiation and wind speeds as inputs, the surface temperature is more closely related to the building’s thermal behaviour and can ease computation loads by reducing the number of inputs and can be collected with sensors. The framework of the proposed model differed from those in previous studies. Although ANNs are frequently used in dynamic load forecasting, the ensemble approach was adopted here for the first time to combine two complimentary models. The forecasting model proposed in this paper essentially used an ANN and the ensemble approach to determine how a building transforms different portions of heat gain – radiation, conduction and convection – to the building cooling load with assumption that the building thermal properties do not change much with time. By applying the framework of the proposed model, the qualified training data are necessary. According to the previous study that evaluated a variety of AI methods [63], the more qualified training data are accessible, the better the model performance will be. The proposed forecasting model achieves accurate and reliable one step-ahead forecasting for building cooling load, which can be applied to tackle the time-lag problem of HVAC system control, the HVAC system optimisation as well as other building management tasks.

5. Conclusions A dynamic load-forecasting model that combines two sub-models – Models A and B – has been proposed in this paper using an artificial neural network and an ensemble approach. Based on the radiant time series method, Model A stresses the historical radiant heat gain portion of cooling loads; and according to Fourier’s law, Model B emphasises the instantaneous and future conduction and convection heat gain portions of cooling loads. By bringing together the complimentary submodels, all the heat gain portions that contribute to building cooling loads are covered in the dynamic load-forecasting model, and it provides improved accuracy compared with previous popular forecasting model (the comparison model). It was also demonstrated by the benchmarking test which represents an ordinary operation in practice. The proposed Model A and Model B are based on structured analysis of the widely used theories for cooling load calculation rather than relying heavily on data manipulation. Based on radiant time series method, Model A generally provides highly accurate forecasting whilst overestimates at inflection points; based on Fourier’s Law, Model B achieves high accuracy generally with underestimates at trough load period. The forecasting accuracy after the ensemble of Model A and Model B further improve the forecasting performance than each individual model with an obvious alleviation of overestimates and underestimates. The theoretical bases–radiant time series method and Fourier’s law, which have been proved to be effective on calculating 1751

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building cooling loads and heat transfer problems, indicate the feasibility of Model A and Model B on forecasting cooling loads for a variety of buildings, so as the model after ensemble. By active exploration of model inputs, the number of occupants and outside surface temperature of the envelope are included as inputs. By applying the number of occupants rather than a calendar or time-based input, the Model B breaks the limitation of specific building schedules and is capable of dealing with irregular occasions and unexpected schedules. A benchmark was formulated to evaluate the performance of the proposed forecasting model based on practical operation, and it can also be used to evaluate other dynamic forecasting models that are validated by different case studies. The proposed dynamic load-forecasting model is practically applicable since it can be applied to tackle the time-lag problem in HVAC system control. The time-lag problem, which means the cooling load cannot be reflected by the temperature change instantly due to the time delay in air mixing, would make the cooling load be either over-met or un-met by the HVAC system. The problem can be alleviated by integrating the proposed dynamic load forecasting model into the HVAC system control. For HVAC systems that work for years, large amount of energy could possibly be saved. It can also be applied to other building management operations such as optimization control as well as fault detection. With a reasonable one time step-ahead load forecasting, the system setting for chiller plants’ optimization can be developed in advance to minimize the electrical energy consumption. The deviation between the forecasted loads with the observed loads can also be used as an indicator to indicate the anomalies in building operation. Developing more dynamic load forecasting models to further enhance the performance by ensemble technique and integrating the proposed dynamic load-forecasting model into HVAC system control to save energy would be the future works of this study.

[17] Ben-Nakhi A, Mahmoud M. Cooling load prediction for buildings using general regression neural networks. Energy Convers Manage 2004;45:2127–41. [18] Kim K, Park J, Hwang K, Kim S. Implementation of hybrid short-term load forecasting system using artificial neural networks and fuzzy expert systems. IEEE Trans Power Syst 1995;10(3). [19] Chow T, Leung C. Nonlinear autoregressive integrated neural network model for short-term load forecasting. IEE Proc – Generat Transm Distrib 1996;143(5). [20] Kiartzis S, Kehagias A, Bakirtzis A, Petridis V. Short term load forecasting using a Bayesian combination method. Electr Power Energy Syst 1997;19(3):171–7. [21] Yang H, Huang C. A new short-term load forecasting approach using self-organizing fuzzy ARMAX models. IEEE Trans Power Syst 1998;13(1). [22] Dong B, Cao C, Lee S. Applying support vector machines to predict building energy consumption in tropical region. Energy Build 2005;37:545–53. [23] Yang J, Rivad H, Zmeureanu R. On-line building energy prediction using adaptive artificial neural networks. Energy Build 2005;37:1250–9. [24] Gonzalez P, Zamarreno J. Prediction of hourly energy consumption in buildings based on a feedback artificial neural network. Energy Build 2005;37:595–601. [25] Wang J, Wang J, Li Y, Zhu S, Zhao J. Techniques of applying wavelet de-noising into a combined model for short-term load forecasting. Electr Power Energy Syst 2014;62:816–24. [26] Hou Z, Lian Z, Yao Y, Yuan X. Cooling-load prediction by the combination of rough set theory and an artificial neural-network based on data-fusion technique. Appl Energy 2006;83:1033–46. [27] Tang F, Kusiak A, Wei X. Modeling and short-term prediction of HVAC system with a clustering algorithm. Energy Build 2014;82:310–21. [28] Massana J, Pous C, Burgas L, Melendez J, Colomer J. Short-term load forecasting for non-residential buildings contrasting artificial occupancy attributes. Energy Build 2016;130:519–31. [29] Zhang F, Deb C, Lee S, Yang J, Shah K. Time series forecasting for building energy consumption using weighted support vector regression with different evolution optimization technique. Energy Build 2016;126:94–103. [30] Fan C, Xiao F, Zhao Y. A short-term building cooling load prediction method using deep learning algorithms. Appl Energy 2017;195:222–33. [31] Cui C, Wu T, Hu M, Weir JD, Li X. Short-term building energy model recommendation system: a meta-learning approach. Appl Energy 2016;172:251–63. [32] Xu X, Huang G, Liu H, Chen L, Liu Q. The study of the dynamic load forecasting model about air conditioning system based on the terminal user load. Energy Build 2015;94:263–8. [33] Powell K, Sriprasad A, Cole W, Edgar T. Heating, cooling and electrical load forecasting for a large-scale district energy system. Energy 2014;74:877–85. [34] Sun Y, Wang S, Xiao F. Development and validation of a simplified online cooling load prediction strategy for a super high-rise building in Hong Kong. Energy Convers Manage 2013;68:20–7. [35] Wong S, Wan K, lam T. Artificial neural networks for energy analysis of office buildings with daylighting. Appl Energy 2010;87:551–7. [36] Lim H, Kim G. Prediction model of cooling load considering time-lag fore preemptive action in buildings. Energy Build 2017;151:53–65. [37] Pedersen C, Fisher D, Liesen R. Development of a heat balance procedure for calculating cooling loads. ASHRAE Trans 1997;103(Part 2):459–68. [38] Spitler J, Fisher D, Pedersen C. The radiant time series cooling load calculation procedure. ASHRAE Trans 1997;103(Part 2):503–15. [39] American Society of Heating, Refrigerating and Air-Conditioning Engineers.. ASHRAE handbook: fundamentals. Inch-pound ed. Atlanta (GA): ASHRAE; 2013. p. 4.15–6. [40] Zhang G, Patuwo B, Hum Y. Forecasting with artificial neural networks: the state of the art. Int J Forecast 1998;14:35–62. [41] Cybenko G. Approximation by superpositions of sigmoidal function. Math Control Signals Syst 1989;2(4):303–14. https://doi.org/10.1007/BF02551274. [42] NeuroShell 2 manual. Frederick (MA): Ward Syst. Group Inc.; 1995. Ward. [43] Carney J, Cunningham P. Tuning diversity in bagged ensembles. Int J Neural Syst 2000;10(4):267–79. [44] Leung P, Lee E. Estimation of electrical power consumption in subway station design by intelligent approach. Appl Energy 2013;101:634–43. [45] Yuen J, Lee E, Lo S, Yuen R. An intelligence-based optimization model of passenger flow in a transportation station. IEEE Trans Intell Transport Syst 2013;14(3). [46] Yuen J, Lee E, Lam W. An intelligence-based route choice model for pedestrian flow in a transportation station. Appl Soft Comput 2014;24:31–9. [47] Jain A, Dube R, Chen C. Bootstrap techniques for error estimation. IEEE Trans Pattern Anal Mach Intell 1987;PAMI-9(5):628–33. [48] Chua K, Chou S, Yang W, Yan J. Achieving better energy-efficient air conditioning: a review of technologies and strategies. Appl Energy 2013;104:8–104. [49] Lu L, Cai W, Soh Y, Xie S, Li S. HVAC system optimization-condenser water loop. Energy Convers Manage 2004;45(4):613–30. [50] Wang L, Lee E, Yuen R. A practical approach to chiller plants’ optimisation. Energy Build 2018;169:332–43. [51] Li Z, Huang G. Re-evaluation of building cooling load prediction models for use in humid subtropical area. Energy Build 2013;62:442–9. [52] Buildings Department. Code of practice for fire safety in buildings. Buildings Department; 2011. p. 25–7. [53] Kwok S, Lee E. A study of the importance of occupancy to building cooling load in prediction by intelligent approach. Energy Convers Manage 2011;52:2555–64. [54] University of Wisconsin-Madison. TRNSYS 16: A TRaNsient SYstem Simulation Program – Volume 5 mathematical reference. Madison: University of Wisconsin; 2006. p. 137–40. [55] A TRaNsient SYstems Simulation Program. Solar Energy Laboratory University of Wisconsin; 2003.

Acknowledgement This work described in this paper was fully supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region, China [Project No. CityU 11257816]. References [1] Gross G, Galiana F. Short-term load forecasting. Proc IEEE 1987;75(12):1558–73. [2] Christiaanse W. Short-term load forecasting using general exponential smoothing. IEEE Trans Power Apparat Syst 1971;PAS-91(5). [3] Thangavelu S, Myat A, Khambadkone A. Energy optimization methodology of multichiller plant in commercial buildings. Energy 2017;123:64–76. [4] Mahmoud A, Comerford R, Adams J, Dawson E. Load forecast bibliography. IEEE Trans Power Apparat Syst 1980;PAS-99(1). [5] Mohamed A, Naresh S. Short-term load demand modeling and forecasting: a review. IEEE Trans Syst Man Cybern 1982;SMC-12(3). [6] Zhao H, Magoules F. A review on the prediction of building energy consumption. Renew Sustain Energy Rev 2012;16:3586–92. [7] Kumar R, Aggarwal R, Sharma J. Energy analysis of a building using artificial neural network: a review. Energy Build 2013;65:352–8. [8] Srivastava A, Pandey A, Singh D. Short-term load forecasting methods: s review. International conference on emerging trends in electrical, electronics and sustainable energy systems (ICETEESES-16). 2016. [9] Heinemann G, Nordman D. The relationship between summer weather and summer loads – a regression analysis. IEEE Trans Power Apparat Syst 1966;PAS-85(11). [10] Corpening S, Reppen N, Ringlee R. Experience with weather sensitive load models for short and long term forecasting. IEEE Trans Power Apparat Syst 1973;PAS92(6). [11] Lijesen D, Rosing J. Adaptive forecasting of hourly loads based on load measurements and weather information. IEEE Trans Power Apparat Syst 1971;PAS-90(4). [12] Gupta P, Yamada K. Adaptive short-term forecasting of hourly loads using weather information. IEEE Trans Power Apparat Syst 1972;PAS-91(5). [13] Goh T, Ong H, Lee Y. A new approach to statistical forecasting of daily peak power demand. Electr Power Syst Res 1986;10:145–8. [14] Park D, El-Sharkawi M, Marks R, Atlas L, Damborg M. Electric load forecasting using an artificial neural network. IEEE Trans Power Syst 1991;6(2). [15] Srinivasan D, Liew A, Chang C. Forecasting daily load curves using a hybrid fuzzyneural approach. IEEE Proc-Generat Transm Distrib 1994;141(6). [16] Bakirtzis A, Theocharis J, Kiartizis S, Satsios K. Short term load forecasting using fuzzy neural network. IEEE Trans Power Syst 1995;10(3).

1752

Applied Energy 228 (2018) 1740–1753

L. Wang et al.

Build 2015;86:93–103. [61] Ruiz-Calvo F, Montagud C, Cazorla-Marin A, Corberan J. Development and experimental validation of a TRNSYS dynamic tool for design and energy optimization of ground source heat pump systems. Energies 2017;10:1510. https://doi.org/10. 3390/en10101510. [62] Martani C, Lee D, Robinson P, Britter R, Ratti C. ENERNET: Studying the dynamic relationship between building occupancy and energy consumption. Energy Build 2012;47:584–91. [63] Banko M, Brill E. Scaling to very very large corpora for natural language disambiguation. ACL’01 Proceedings of 39th annual meeting on association for computational linguistics, Toulouse, France 2001. p. 26–33. https://doi.org/10.3115/ 1073012.1073017.

[56] Loutzenhiser P, Manz H, Felsmann C, Strachan P, Frank T, Maxwell G. Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation. Sol Energy 2007;81:254–67. [57] Al-ajmi F, Hanby V. Simulation of energy consumption for Kuwaiti domestic buildings. Energy Build 2008;40:1101–9. [58] Chargui R, Sammouda H. Modeling of a residential house coupled with a dual source heat pump using TRNSYS software. Energy Convers Manage 2014;81:384–99. [59] Cacabelos A, Eguia P, Migues J, Granada E, Arce M. Calibrated simulation of public library HVAC system with a ground-source heat pump and a radiant floor using TRNSYS and GeoOpt. Energy Build 2015;108:114–26. [60] Djedjig R, Bozonnet E, Belarbi R. Analysis of thermal effects of vegetated envelopes: Integration of a validated model in a building energy simulation program. Energy

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