Smart building Ensemble predictors Neural network Particle swarm optimization Bayesian model averaging Wavelet transform

1. Contents lists available at ScienceDirect
Applied Energy
journal homepage: www.elsevier.com/locate/apenergy
Demand forecast of PV integrated bioclimatic buildings using ensemble
framework
Muhammad Qamar Raza
⁎
, Mithulananthan Nadarajah, Chandima Ekanayake
School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, QLD 4072, Australia
School of Engineering, Griffith University, Gold Coast 422, Australia
H I G H L I G H T S
• A novel ensemble forecasting framework for PV integrated bioclimatic buildings.
• Five different predictors along with their wavelet transformed are combined.
• Bayesian model averaging technique is used to aggregate the multiple predictors.
• Forecast framework is analyzed for multiple forecast horizons and buildings.
• Significant error reduction in different test case studies using the framework.
A R T I C L E I N F O
Keywords:
Smart building
Ensemble predictors
Neural network
Particle swarm optimization
Bayesian model averaging
Wavelet transform
A B S T R A C T
Buildings are one of the major sources of electricity and greenhouse gas emission (GHG) in urban areas all
around the world. Since a large integration of solar energy is observed in the form of rooftop photovoltaic (PV)
units, electricity use of buildings is highly uncertain due to intermittent nature of solar output power. This leads
to poor energy management for both network operators and building owners. In addition, uncertain metrological
conditions, diversity and complexity of buildings are big hurdles to accurate prediction of the demand. To
improve accuracy of load demand forecast of PV integrated smart building, a hybrid ensemble framework is
proposed in this paper. This is based on a combination of five different predictors named as backpropagation
neural network (BPNN), Elman neural network (EN), Autoregressive Integrated Moving Average (ARIMA), feed
forward neural network (FNN), radial basis function (RBF) and their wavelet transform (WT) models. WT is
applied to historical load data to remove the spikes and fluctuations. FNN and RBF network were trained with
particle swarm optimization (PSO) for higher forecast accuracy. The output of each predictor in the ensemble
network is combined using Bayesian model averaging (BMA). The proposed framework is tested using real data
of two practical PV integrated smart buildings in a big university environment. The results indicate that the
proposed framework show improvement in average forecast normalized root mean square error (nRMSE) around
17% and 20% in seasonal daily and seasonal weekly case studies, respectively. In addition, proposed framework
also produces lowest of nRMSE about 3.88% in seasonal monthly forecast of smart buildings with rooftop PV as
compared to benchmark model. The proposed forecast framework provides consistent forecast results for global
change institute (GCI) and advance engineering building (AEB) during seasonal daily and weekly comparison.
1. Introduction
The built environment is one of the major consumers of energy and
source of environmental pollution. One study highlights that, world-
wide the energy demand of buildings is up to 32% and it’s up to 40% of
total demand in the United States [1]. It is reported for densely popu-
lated cities that buildings account for a staggering 94% of electricity use
and the greenhouse gas emission (GHG) is up to 75% [1]. Buildings
contributed about 36% of CO2 emission in Europe [2]. Therefore, in
order to address this issue, European Union (EU) has set an energy
target for 2020 with emission reduction. The target is to reduce the EU
greenhouse emission equal to the level in 1990 and improvement in
energy efficiency by 20% [3]. Therefore, characterizing and forecasting
the demand of smart building will reduce the excess usage of electricity
and consequently environmental pollution. In addition, accurate load
demand forecasting will help the design of more effective energy
http://dx.doi.org/10.1016/j.apenergy.2017.08.192
Received 5 May 2017; Received in revised form 29 July 2017; Accepted 18 August 2017
⁎
Corresponding author at: Power and Energy System Group, School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, QLD 4072, Australia.
E-mail addresses: Qamar.raza@uq.edu.au (M.Q. Raza), mithulan@itee.uq.edu.au (M. Nadarajah), c.ekanayake@griffith.edu.au (C. Ekanayake).
Applied Energy 208 (2017) 1626–1638
Available online 09 September 2017
0306-2619/ © 2017 Elsevier Ltd. All rights reserved.
MARK

2. management system. It will be beneficial to implement energy effi-
ciency programs with greater outcome. Accurate demand forecast of PV
integrated smart buildings is also important due to higher penetration
of solar energy. However, it is a difficult task to precisely forecast the
load demand as several factors affect it. These factors are uncertain PV
output power, meteorological conditions, uncertain occupant’s usage
behavior, building comfort level and structure.
In the last decade, a large number of accurate load demand forecast
models have been developed and deployed. The forecasting models are
based on statistical forecast [4], support vector machine (SVM) based
models [5], fuzzy logic [6], grey model [7] and artificial neural net-
works (ANN) [8]. Among the reported load demand forecasting tech-
niques, ANN is the most widely used technique with various degrees of
success.
Neural networks (NN) have been found as a worthwhile competitor
to several conventional time series models [9,10]. Therefore, NN has
received considerable attention by researchers due to numerous ad-
vancements in the model performance and suitability for different
prediction, optimization, and classification problems. However, there
are some drawbacks of NN based models for load demand forecast. The
output performance of NN is greatly affected by the learning of the
network, learning rates, network structures, number and quality of
forecast model inputs. In addition, the output performance of NN
forecast model also varies due to change in evaluation metrics and the
sites of data collection. The poor learning of the NN leads to lower
generalization capability of the network [11]. Therefore, it is difficult to
declare that, a single NN model will outperform the other forecast
models for different predictions applications and forecast conditions
[12]. In [13], authors suggest a short term load demand forecast model
based on NN method for bioclimatic building. The investigation of this
study finds that, the load demand of a building varies with change in
outdoor solar radiation and temperature. However, a single NN model
cannot provide a higher level of generalization and prediction perfor-
mance in PV integrated smart buildings.
Some research studies proposed hybrid models to enhance the
forecast accuracy by overcoming the drawback of single model. For
example in [14], authors present a SVM and self-organized map (SOM)
based two-stage hybrid load forecast model. The proposed model de-
monstrates better results than single SVM model for different time
series data sets. A chaotic particle swarm optimization (CPSO) with
ANN based forecast model is proposed in [15]. The prediction results
demonstrate that, proposed model produces better forecast accuracy
compared with Levenberg Marquardt (LM) NN model. A number of
other techniques was applied to forecast the load demand of buildings
[16–23].
However, there is still room to enhance the forecast accuracy,
especially in PV integrated smart building.
It is a difficult task due to higher uncertainty of PV output power
and volatility of building load demand. In previously reported research,
the hybrid model tries to precisely forecast with two or more models
that depends on each other. As a result, the overall forecast accuracy is
affected due to bad performance of any of the models. Therefore, there
is a need to design multi predictor based forecast model, in which each
predictor doesn’t affect the performance of each other. It is also re-
ported that, the forecast performance of independent predictors, even
with low quality solutions in ensemble network will increase the fore-
cast accuracy [24,25]. The individual predictor produces different
forecast output with the same input data due to different operational
principles. The diverse output of individual independent predictor
provides an opportunity to enhance the overall forecast output by ex-
ploring other possible solutions.
The NN ensemble is a method to aggregate the multiple models or
predictors to generate the output accurately rather than relying on a
single model. Neural network ensemble is a method for creating a
multiple NN and train them individually. After that, the outputs of all
individual networks are combined to generate output of ensemble
model. Such a combination of networks is also referred as aggregation,
combination, and fusion. In order to overcome the limitation of single
model and enhancement in predictive accuracy, network ensembles
based forecast models are suggested by many researchers [26]. The
ensembles based forecast model for wind speed is presented in [27].
The performance of ensemble based forecast model demonstrate the
possibility to apply ensemble models to load demand forecasts. There-
fore, five independent predictors in ensemble network along with their
WT based approach is proposed and implemented for load demand
forecast of a PV integrated smart building in this work.
The proposed NN ensembles based forecast framework is designed
in multiple phases. In first phase, the historical load demand data is
preprocessed with the wavelet transform technique. An ensemble fra-
mework is made by designing multiple predictors in it. However, the
number of predictors in an ensemble network may be varied depending
on the nature and complexity of forecasting problem. Then, wavelet
transformed load demand data and correlated metrological variables
were applied as forecast model inputs. In next stage, the individual
network produced forecasted output, which is reconstructed using WT
reconstruction process. After that, generated output of each predictor
will be combined using aggregation techniques. In this research study,
Bayesian model averaging technique is used to integrate the output of
individual predictors and to generate forecast output. The details of
each phase are discussed in later section of the paper. The major con-
tributions of the proposed novel ensemble approach are highlighted as
follows:
(1) Development and integration of the five neural networks and time
series predictors along with the WT models in ensemble network.
(2) Aggregation of predicators output using Bayesian model averaging
for efficient selection and contribution of each of them in final
forecast results.
(3) Implementation of proposed forecast framework on two real PV
integrated smart buildings to achieve the long-term net-zero energy
building (NZEB) goal.
(4) Training of neural predictors (FNN and RBF) using particle swarm
optimization (PSO) for higher forecast accuracy of individual pre-
dictor.
(5) Incorporating the wavelet transformed historical load demand data
with metrological variables such as wind speed (Ws), temperature
(T), humidity (H) and exogenous variables (type, week and hour of
the day) as forecast model inputs.
(6) Improvement in average forecast normalized root mean square
error (nRMSE) more than 17% in seasonal daily and 20% in sea-
sonal weekly evaluation case studies in comparison with the ex-
isting model.
Rest of the paper is organized as follows. Section 2 describes a ty-
pical load profile of PV integrated smart building. Section 3 highlights
the major components of proposed framework. The proposed hybrid
framework for demand forecast of PV integrated smart building is
discussed in Section 4. Numerical results and discussion are presented
in Section 5. The conclusions of the paper are summarized in Section 6.
2. Load profile of PV integrated smart building
2.1. Practical PV integrated smart buildings
In this study, two practical PV integrated bioclimatic buildings at
The University of Queensland (UQ), Australia namely GCI and AEB are
selected for validation of proposed forecast framework. The design
objective of GCI building is to closely work with the natural environ-
ment. It is also aimed to achieve the target of zero carbon emission and
zero net energy building. The GCI building is equipped with modern
sun shading, which tracks the sunlight and provide the natural air
ventilation for reduction in energy demand. The net zero energy
M.Q. Raza et al. Applied Energy 208 (2017) 1626–1638
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3. objective is achieved by cross ventilation system (natural air circula-
tion), shading control from solar gain, optimal lighting and solar PV
integration. These PV arrays are connected with batteries and solar hot
water.
138 kW rooftop PV is installed at GCI building and excess energy is
stored in batteries. Electrical energy flow diagram of GCI building is
shown in Fig. 1.
AEB is the second smart building, which is considered in this study.
AEB is designed in energy efficient way by implementing the mix mode
of air conditioning system. In this building, 95.75 kW rooftop PV
system comprises of tilt mounted 383 modules. AEB is connected with
11 kV UQ internal grid and rooftop PV. The voltage is step down to
415 V for AEB distribution network. In addition, PV is connected to low
voltage (LV) distribution network of AEB. The electrical power is ab-
sorbed by the electrical load and water production system. The pure
electrical load consists of building lighting, lifts, fans etc. In addition,
chilled water production system that consists of a chiller station is also
run using electrical power.
2.2. Historical load data and PV output profile
Fig. 2 represents the PV output power profile of year 2014 from 1
January to 31 December. In this graph, number of days on X axis, solar
data points in a day on Y axis and magnitude of power on Z axis. The
solar output power is available for 24 h of the day in solar data
management system. However, PV output power is available from 7am
to 5 pm due to absence of solar radiations. The PV output power other
than 7 am to 5 pm is considered zero or not significant. There are
219,000, 43,800 and 7300 measurements in the 1-min, 5-min and 30-
min dataset within the range of 7am to 5 pm. However, 0.62% of data is
missing in online data management system, which might be due to
instrumental and other errors. Therefore, the missing data is replaced
with average value of last 4 weeks at same time. It can be observed from
Fig. 2, that the PV output power is highest during the first 100 days of
the year. The PV output goes down to lowest level in next 125 days of
the year. Afterwards, PV output power start climbing and reached up to
medium level. This indicates that, the PV output varies throughout the
year with change in season and environmental conditions. The solar
output power rose to a maximum level in December and January due to
increase in solar irradiation and temperature. A real-time data of PV
output power and respective weather variables with one-minute re-
solution were recorded to train and validate the proposed framework.
Electrical power is fed to AEB distribution network using four feeder
lines called 49.1, 49.2, 49.3 and 49.7 of UQ internal grid network. In
AEB power distribution network, 49.7 is connected with AEB roof top
PV unit and other three feeders are connected with UQ internal grid.
The PV output power is variable and uncertain due to different factors.
Therefore, the additional power supply from UQ internal grid fulfills
AEB load demand.
Fig. 3 illustrates the hourly load profile of AEB for 2014. It can be
observed that, the load demand of AEB varies throughout the year in
different season. The load demand of this building varies due to change
of metrological conditions and occupant’s usage pattern. The load de-
mand is at medium level during the month of December and January
(Summer) as the regular semester is off. However, due to raise in
temperature in summer season, air conditioning load takes it to medium
level with start of new semester. The load demand is relatively at higher
level in February due to increase in occupants’ usage and fairly higher
temperature.
The load demand of AEB building is reduced from higher to medium
level in autumn season and it further deceased in winter season. The
peak load demand of AEB is reached at 0.9 normalized value between
October and November 2014. Fairly similar seasonal load demand
pattern is observed for GCI building. The higher level of fluctuations in
load demand can be observed from AEB and GCI building load profiles.
The variability of PV output power also adds more uncertainty in load
demand from grid side. It will lead towards lower power system relia-
bility and quality. In addition, the higher level of fluctuations can be
observed at building than the electrical grid due to sharp changes in
metrological conditions and occupants’ usage. This makes it more
Fig. 1. Electrical power flow diagram of GCI building.
Fig. 2. Aggregated solar output power profile of UQ solar of year 2014.
M.Q. Raza et al. Applied Energy 208 (2017) 1626–1638
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4. difficult to forecast accurately the load demand due to higher fluctua-
tions.
Figs. 4 and 5 depict the hourly load profile of AEB for one month
(January 2014) and one week (January 1 to 7, 2014) respectively. It
can be observed from one week and month hourly load profile that the
load demand of AEB is highly fluctuating. The load demand varies
through the month of January 2014 and it goes to peak of the month
during the last week. In addition, the demand varies throughout the day
and it is also different between hours. It is observed from load profile
analysis that load demand curve was much more stable than PV in-
tegrated smart buildings.
On the other hand, the load demand of buildings is highly volatile in
comparison with grid load demand profile. Therefore, the load demand
forecast of PV integrated smart buildings is more difficult and forecast
models are less accurate. There is a need to accurately forecast the load
demand of buildings in order to correctly characterize, reduce energy
use and CO2 emission of buildings.
3. Components of ensemble forecast framework
Proposed forecast framework components such as wavelet trans-
form, ensemble predictors, particle swarm optimization and Bayesian
model averaging (BMA) are described below in detail.
3.1. Wavelet transform
It can be observed that from historical load demand, time series data
contains oscillations, peaks, and different types of non-stationary data
components. These are due to variable PV output power as a result of
sudden changes in metrological conditions and exogenous variables.
The PV output varies throughout the day due to above mentioned
factors. The forecast accuracy of prediction model can be enhanced by
Fig. 3. Advance Engineering Building (AEB)
hourly load profile during 2014.
Fig. 4. AEB Load profile of one month, January 2014.
M.Q. Raza et al. Applied Energy 208 (2017) 1626–1638
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5. smoothing the historical demand data, which is applied as forecast
model to train it. Therefore, Wavelet transform (WT) technique has
potential to apply on historical data in order to treat as forecast model
inputs for higher forecast accuracy.
The WT can be separated into two groups known as continuous WT
(CWT) and discrete WT (DWT). The historical demand data can be
decomposed into a series of constitutive components using wavelet
transform. These transformed constitutive components demonstrate
more stable behavior with less variations, which can contribute to
better forecast accuracy. The two basic functions of WT are mother
wavelet signal ψ t( ) and scaling function ϕ t( ). The series of function can
be derived as given below in Eq. (1) and (2) [28].
= ∗ −φ t φ t k( ) 2 (2 )j k
j j
,
/2 /2
(1)
= ∗ −ψ t ψ t k( ) 2 (2 )j k
j j
,
/2 /2
(2)
where scaling and translating integer variables are j and k. The φ and ψ
represents the scaling and wavelet function. The signal S(t) can be ex-
pressed by using the scaling φj k, and wavelet function ψj k, as given in Eq.
(3).
∑ ∑ ∑= − + −
=
∞
S t C k φ t k d k ψ t k( ) ( )2 (2 ) ( )2 (2 )
k
j
j j
k j j
j
j j/2 /2
0
0 0
0 (3)
where d k( )j and Cj0
represents the detailed and approximations coef-
ficients of the signal respectively. The symbol j0 represents pre-scaling
coefficient in the above signal equation.
Mallat’s algorithm is a method to implement the wavelet transform
using different high and low pass filters [29]. In this algorithm, firstly
the original signal is decomposed into different detailed and approx-
imation components by using low and high pass filters as shown in
Fig. 6.lefttop A research study utilize the wavelet transform (WT) for
short-term load forecast. In this study, two-level decomposition is used
for preprocessing historical load data [28]. In [30], authors used three-
level WT decomposition for electricity price forecasting. The forecast
results demonstrate the effectiveness of three-level WT decomposition
in terms of model predication performance. Therefore, the three-level
decomposition is applied on historical load data in this study. However,
WT is not applied to other forecast model input variables.
During the decomposition process of WT, high pass (H.P.) filter
generates the high frequency or detailed components of the signal
named as w D1, D2 and D3. The approximate component (low frequency
components) A3 is obtained by down sampling with low pass filters.
These detailed and approximate components of historical load demand
data signals (A3, D1, D2 and D2) were applied as forecast model inputs
along with other variables. The output of predictor is reconstructed
using reconstruction process. In reconstruction process is applied to
detailed ( ̂ ̂D D,1 2 and ̂D3) and approximate ̂A3 components to generate the
predictor output.
3.2. Ensemble predictors
ANN consists of different layers such as input, hidden and output
layer. ANN models attempt to achieve the best performance through
densely interconnected small processing units called neurons. The
network of artificially interconnected neurons explores multiple com-
peting hypotheses by simultaneously massive processing for the better
results.
In this research, five different types of predictors are applied to
forecast the load demand. These predictors are backpropagation neural
network (BPNN), Elman neural network (EN), Autoregressive
Integrated Moving Average (ARIMA), feed forward (FNN) and radial
basis function (RBF). The purpose of different predictor’s in ensemble
network is based on their applicability for forecast application and
achieve the diverse forecast output. This diverse forecast output is
combined using aggregation technique. Therefore, the overall forecast
accuracy of ensemble network will be increased as each predictor will
dissimilar forecast results. The details of predictors are given below.
3.2.1. BPNN
The first predictor is BPNN. In the last decade, BPNN is applied to
vast range of forecast applications such as electrical load, price and
wind forecast with good level of success. In BPNN, backpropagation
process tries to determine the nodes connections weights values. The
weights values of the network are updated using error function. The
network learning error is calculated with difference of network pre-
dicted and actual. The error between the predicted and actual output
values is back-propagated and weight values are updated based on
network learning error. Therefore, the network learning error is mini-
mized by back propagating the error and updating the connections
weight values.
Fig. 5. AEB Load profile of one week, January 1 to 7, 2014.
M.Q. Raza et al. Applied Energy 208 (2017) 1626–1638
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6. 3.2.2. EN
EN is considered as another type of recurrent neural network. In EN,
special copy layer of hidden layer is connected through linking path.
Therefore, the Elman neural network training process depends on three
processes named as previous state, current inputs of the system and
network output. The standard backpropagation algorithm can also be
used for training of the neural network as the special layer treated as
another set of inputs [31,32].
3.2.3. ARIMA
ARIMA is the third predictor employed for load demand forecast in
ensemble network. In ARIMA based forecast model, differenced series
appearing in the forecasting equation and lags of the forecast errors are
named as autoregressive and moving average respectively. The purpose
of including a time series predictors in ensemble network is to achieve
the diverse forecast output. In ensemble network, each standalone
predictor will explore the different forecast possibilities. As a result, the
overall forecast accuracy of the proposed ensemble would be enhanced
by integrating the each predictor.
3.2.4. FNN
FNN is the third neural and fourth ensemble predictor in the net-
work. In FFN, the input information of the network is proceeded in
forward direction only. The input data of NN is applied to input layer
and pass to network output layer though hidden layer. There is no
backward path for the information like backpropagation network. In
the study, a three-layer FNN is used which contains one input, hidden
and output layer. Hyperbolic tangent (tansig) and linear (purelin)
functions activation functions were used for hidden and output layer
respectively.
3.2.5. RBF
The fourth neural and fifth ensemble network predictor is RBF
neural network. It consists of three layers named as input, hidden and
output layer. Gaussian function is chosen as the radial basis function
and network output is expressed in the form of Gaussian function. The
training algorithm is applied to RBF network learning and it tries to find
the optimum values of connection weights to reduce the learning error
of the network in iterative manner.
3.3. Particle swarm optimization
The performance of NN predictor is highly dependent on network
training. The objective of neural network training is to find the op-
timum values of weights. It is reported that, backpropagation learning
algorithm is used for training neural networks. However, back-
propagation learning technique of the NN uses gradient learning tech-
nique. It has drawbacks such as slow convergence, higher probability to
become trapped in local minima and inefficient training of the network
[33]. In order to obtain an accurate forecast output, network should
converge to global optimum solution rather than local optimum. In
addition, BP algorithm is highly dependent on learning rate, mo-
mentum, initial weight and biases values.
PSO is one of the most efficient training techniques, which can be
utilized for NN training. Therefore, PSO is utilized in this study to en-
hance the forecast performance of neural predictors. PSO is population
based optimization technique which inspired by sociological behavior
of flock of birds or school of fishes moving in search for food. The birds
or fishes try to find the food by own best search experience as well as
social experience. In PSO population based optimization technique, in
which each candidate of population is called particle and each particle
tends to find the best solution based on own and neighbor experience in
a multidimensional search space. A group of particles is called swarm
and swarm tends to find the optimal solution for certain objective
function. The one major advantage of PSO techniques is to adjust only
two parameters which are velocity and position of particles. Each
particle updates his position and velocity based on his own and social
experience according to Eqs. (4) and (5) [33].
= + − + −+
v wv c r Pbest x c r gbest x( ) ( )i
k
i
k
i
k
i
k k
i
k( 1)
1 1 2 2 (4)
= ++ +
x x vi
k
i
k
i
k1 1
(5)
where
c1 and c2 are positive constants which control the personal and
global component of algorithm,
r1 and r2 are randomly generated numbers within a range of [0,1], w
is the inertia weight,
Pbesti
k
is the personal particle best position achieved, which is based
on its own experience,
gbestk is the global particle best position achieved by the all particle,
Fig. 6. Wavelet Transformation process of signal.
M.Q. Raza et al. Applied Energy 208 (2017) 1626–1638
1631

7. which is based on overall swarm’s experience,
k is the iteration index.
vi
k
Current velocity of the particle.
+
vi
k( 1)
New velocity of the particle.
xi
k
Current of the position.
+
xi
k 1
New particle position.
3.4. Ensemble network aggregation using Bayesian model averaging (BMA)
The objective of ensemble network aggregation process is to com-
bine the individual predictors output in an optimal way for final ac-
curate forecast. In NN ensemble based forecast method, each predictor
forecast the load demand, which is independent from each other. Each
ensemble predictors will also produce the forecast error according to
individual predictor performance. The idea is to combine individual
result together in an intelligent manner. This allows to compensate
individual predictor errors using better performing aggregation tech-
nique. In this way, the final prediction error of ensemble will be re-
duced. One of the simplest ways to aggregate the outcomes of all ap-
plied predictors is averaging. However, individual predictor averaging
is not the optimal way as the equal weightage is given to bad and good
performing models. As a result, it leads to higher forecast error.
Several studies have reported that, the BMA has potential to be used
as good aggregation tool. It can produce more adaptive and reliable
predictions results as demonstrated for different applications in
[34–37]. BMA is a statistical procedure to infer consensus results of
different predictors to combine them. Recently, BMA techniques is used
to aggregate the output of the neural network ensembles for different
forecast applications [36]. The results of proposed framework demon-
strate the significance of BMA aggregation in terms forecast accuracy.
BMA technique opposes the individual model dependence and entire
data set take part in inference making process. Based on posterior
model probabilities, the combinational weights are assigned to each
individual network in aggregation process of BMA method. Weights
values of any individual NN model are based on the network perfor-
mance. The higher weight values are assigned to better performing
forecast models as compared to lower performing models [36,37].
In [38,39], authors present the method to estimate the coefficients/
weight for the BMA technique. Let b will represent the coefficients/
weight of BMA model. The j number of models in M model space as
= …Mj J(1,2,3, , ) and these are predicting the PV output y. Fj is the
output of forecast model j and D denotes the training data of each
network [40]. The average of posterior distributions of each model is
=P Mj D( | ) and weighted by their posterior probabilities =P y Mj D( | , )
for probability density function. The calculation of the BMA probabil-
istic forecast are given in Eq. (6).
∑= ∗
=
p y D wj p y Mj D( | ) ( | , )
j
j
1 (6)
The BMA forecast posterior mean and variance can be calculated as:
∑ ∑= ∗ = ∗
= =
E y D p Mj D E y Mj D wj fj[ | ] ( | ) [ | , ]
j
j
j
j
1 1 (7)
∑ ∑ ∑=
⎛
⎝
⎜ −
⎞
⎠
⎟ + ∗
= = =
Var y D Wj fj wifi wj σ[ | ]
j
j
i
j
j
j
j
1 1
2
1
2
(8)
For training data D, the variance associated with model prediction fj is
σj
2
. The posterior probability of the jth model is − dw p(f | )j i for steady
observations. The average by weighting each forecast with corre-
sponding posterior model probability represents the BMA combination.
The forecast is basically combination of different model components.
The calculation of posterior model probability is one of the most im-
portant parts of BMA combination process. The estimated coefficients
and errors are put into a matrix called coefficient matrix b. After that,
estimated BMA weight coefficients are multiplied with individual
output of the individual predictor in order obtain the combined forecast
using BMA model. The Youtput is the output of each NN forecast model.
BMA output can be calculated as given in Eq. (9).
= ∗YBMA Y boutput (9)
This aggregation technique is also known as BMA combination algo-
rithm. It is also applied to different forecast applications [27].
Fig. 7. Schematic diagram of the proposed ensemble framework.
M.Q. Raza et al. Applied Energy 208 (2017) 1626–1638
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8. 4. Proposed ensemble forecast framework
Fig. 7 depicts the schematic diagram of the proposed framework for
load forecast of smart building using neural ensemble predictors,
Bayesian model averaging and WT. The load forecast procedure, which
consists of six phases, for a PV integrated smart building is explained as
follows:
Phase 1: The first phase of the forecast process is to select the most
influential model input variables. The forecast input variables of
individual neural predictors are hourly historical load data values of
smart building, day of the week (DW), type of the day (D) (i.e.
working or holyday), and hour of the day (H). In addition, tem-
perature (T), humidity (HDt), and wind speed (WSt) are also applied
as predictors inputs [41]. Hourly historical load and metrological
data is used to train the predictors at t hour for accuracy forecast.
Phase 2: WT technique is applied to historical load data. The his-
torical load series is decomposed into three detailed and one ap-
proximate component. The detailed or high-frequency components
named as D1, D2, and D3 are obtained using high pass filter. The
approximate or low frequency component (A3) is obtained by down
sampling with low pass filter. The schematic diagram of individual
predictor is shown in Fig. 8.
Phase 3: The connection weight vectors of neural predictors are
initialized using the PSO algorithm. Initial particle position of PSO
algorithm is assigned as initial weight values of NN. These weight
values are used during the training process of NN based predictors.
The network is trained using initial weights values (particle posi-
tions). The network will generate learning error on the basis of
provided network weight values during training process.
The particle positions (weight and bias) are updated in order to
minimize the learning error of the network. Fitness function of NN
(network learning error which is mean square error, MSE) is calculated.
The lowest error of each particle’s is Pbest value of PSO. The lowest
learning error achieved during the entire learning process is considered
as gbest in swarm. If the fitness value is better than the best fitness value
(Pbest) in a search history, then current value is set as the new Pbest. The
particle with the best fitness value of all the particles is selected as the
Gbest. The “Pbest” and “Gbest” values are used to calculate the new ve-
locity according to Eq. (5) for new position of particle for targeted
learning error. The new calculated particle positions (weight, bias of
NN). The new velocity is added in old position according to Eq. (4).
These new set of positions are applied to network and it will produce
the new learning error. The flow chart of PSO trained predictors in the
proposed framework is shown in Fig. 9.
Phase 4: The neural predictors are initialized in ensemble network.
These predictors are BPNN, EN, ARIMA, FNN, and RBF. The learning
of parameters and network configuration of each predictor is dif-
ferent from each other. Therefore, the performance of each predictor
is different due to individual network performance. A diverse range
of forecast output is obtained using these predictors. As a result, the
overall forecast performance of ensemble network is enhanced by
combining them. The historical load data wavelet transformed
components and exogenous variables are applied as each predictor’s
model input. This process will be repeated until NN termination
criteria are met. In this research, RBF and FNN were trained using
PSO algorithm in order to enhance the forecast accuracy of in-
dividual predictors. As a result, the overall forecast accuracy of
ensemble network will be enhanced by aggregating the individual
predictor output.
Phase 5: The output components of each NN predictor is re-
constructed as shown in Fig. 8. The output decomposed components
named as approximation ( ̂A2) and detailed signals ( ̂ ̂D D,1 2 and ̂D2)
are reconstructed by up sampling using combination of low and high
pass filters. The individual ensemble predictors output is re-
constructed.
Phase 6: The output forecast of each predictor is combined using
ensemble network aggregator as shown in Fig. 7. Averaging model is
used to aggregate the output of ensemble network. However, the
forecast accuracy of ensemble model is affected due to equal weight
assignment to bad and good performing models. Therefore, BMA
technique is used to aggregate the output of ensemble network in
proposed framework.
Load Demand
Wavelet decomposition
Predictor
Wavelet reconstruction
Predicted Load
Demand
Ldt
D1 D2 D3 A3
Tt
WSt
HDt
Temprature
Wind Speed
Humidity
Day of the Week (DW)
Type of the Day (D)
Hour of the Day(H)
Fig. 8. Schematic diagram of individual Predictor in
the proposed framework.
M.Q. Raza et al. Applied Energy 208 (2017) 1626–1638
1633

9. 5. Numerical results and discussion
The proposed ensemble forecast framework is tested using recorded
data by building management system (BMS) of AEB and GCI building at
UQ, Australia. In order to evaluate the performance of proposed fra-
mework, the forecast results are compared with persistence forecast and
individual predictors such as BPNN, EN, ARIMA, FNN, and RBF models.
WT is applied to each individual predictor in the ensemble network.
The forecast results of each predictor with and without WT are pre-
sented in order to analyse the effectiveness of the WT techniques. The
historical load values, wind speed (WSt), humidity (HDt), Temperature
(Tt), Type (D), Day (DW) and hour of the day are applied as inputs of
neural predictors in ensemble network. The output of each independent
predictors in ensemble is combined using aggregation techniques as
discussed earlier. In this study, normalized root-mean-square error
(NRMSE) is calculated to evaluate the performance of predictors as
given in Eq. (10) [42].
∑ ⎜ ⎟= ∗ ⎛
⎝
− ⎞
⎠
∗
=
NRMSE
N
LD LD
LD
(%)
1
100
t
N
t
Actual
t
Forecast
t
Peak
1
2
(10)
where N is number of load demand data points. The N = 24 for daily
load demand (LD) forecast and N = 168 for the week LD forecast. The
LDt
Actual
is actual demand at time t, LDt
Forecast
is forecasted demand and
LDt
Peak
represents peak demand at tth hour. In addition, normalized
mean absolute error (NMAE) is calculated for each predictor and case
study in order to assess the forecast performance of proposed and other
predictors.
∑= ∗
−
∗
=
NMAE
N
LD LD
LD
(%)
1
100
t
N
t
Actual
t
Forecast
t
Peak
1 (11)
In this study, seasonal one day, seasonal one week and month ahead
forecast case studies were designed in order to assess the performance
proposed forecast model along with other comparative predictors. Due
to similar pattern of results only four randomly selected days and weeks
are presented in this paper. In addition, MATLAB® and its neural net-
work tool is used to do simulations.
5.1. Seasonal daily forecast case study
In order to assess the forecast models’ performance, one day is se-
lected from each season of the year 2014. In this study, one day is se-
lected from each season such as summer (December 15), autumn (April
2), winter (July 16) and spring (October 30) of 2014. The 24 h ahead
load demand forecast case studies were designed for AEB and GCI PV
integrated smart buildings. The historical one year historical data with
30 min. resolution were used to train the forecast model. The actual
data of 30 min. resolution data of forecasted days were used to validate
the performance of proposed framework. The nMAE and nRMSE is
calculated for each individual predictor and ensemble network. In ad-
dition, proposed forecast framework results are also compared with
persistence model for all test case studies. Table 1 presents the seasonal
daily forecast nRMSE and nMAE comparison of proposed ensemble
forecast framework with persistence model and other individual pre-
dictors for AEB.
It can be observed that, the persistence method produces higher
nRMSE (8.81%, 7.92%, 9.12% and 8.78%) in comparison of proposed
framework (4.48%, 4.11%, 4.61% and 4.21%) for selected seasonal
forecast days of AEB. In order to assess, similar forecast models were
applied to GCI building, where nRMSE values were obtained from
persistence method are also higher (9.36%, 9.11%, 8.36%, and 7.86%)
compared to proposed model (5.27%, 4.99%, 4.16% and 4.17%) for
under consideration seasonal days. In addition, in seasonal daily load
forecast case study, BPNN predictors produces higher forecast nRMSE
than the persistence method for all seasonal days as given in Table 1.
Fig. 10 highlights the comparison of different predictors with proposed
framework. The designed framework is more close to actual load de-
mand in comparison with other models.
START
Forecast model Input
Selection
Wavelet Decomposition
Ensemble Network
Initialization
NN weight vectors
Initialization using PSO
Update Weight vectors
Network MSE<NN
criteria
PSO algorithm
Wavelet Reconstruction
Yes
END
Predicted Output
NO
Y1,Y2,Y3,…,Y3
Forecast Model Inputs
D1,D2,D3,A1
Fig. 9. Flowchart for the neural predictor trained with PSO
in a proposed framework.
M.Q. Raza et al. Applied Energy 208 (2017) 1626–1638
1634

10. It can be observed that, the prediction performance of models is
inconsistent over the different seasonal days. Therefore, average of four
season’s nRMSE is calculated for better comparison. In the most of
seasonal daily load forecast cases, the prediction performance
WT+RBF+PSO and WT+FNN+PSO are found closer to each other.
The forecasted output of proposed framework is close to real load and
follow the variation pattern in better way. However, average forecast
nRMSE results indicate that, the WT+FNN+PSO model produces less
forecast error (5.77%) in comparison with WT+RBF+PSO (5.87%).
Furthermore, the average forecast nRMSE values of EN and ARIMA
model are close with 7.49% and 7.33% respectively. In most of seasonal
daily forecast cases of AEB, ARIMA model gives higher forecast accu-
racy than the EN.
The proposed forecast framework produces higher forecast accuracy
than the individual predictors and persistence forecast model. It is also
observed that, the forecast performance of the proposed ensemble fra-
mework and other models varies during seasonal daily case study. It is
concluded that from daily seasonal forecast, the forecast model per-
formance is sensitive to seasonal variations. Therefore, inconsistent
forecast results are obtained.
Table 2 represents the seasonal daily forecast error comparison of
GCI building. The proposed framework and persistence model were
applied for the same selected seasonal days. The similar forecast error
pattern of ensemble framework, individual predictor and persistence
model were observed for seasonal daily load forecast of GCI building.
The forecast nRMSE values obtained from BPNN model are larger
(9.38%, 9.82%, 8.65% and 8.57%) than the persistence (9.36%, 9.11%,
8.26% and 7.86%) and proposed method (5.27%, 4.96%, 4.42% and
4.27%) for GCI building. As mentioned earlier, historical load data
contains non-stationary components and different spikes. Therefore,
WT technique is used to remove the fluctuations and smoothing the
model input data. The effectiveness of WT techniques can be observed
from AEB and GCI daily forecast error Tables. The EN model gives
average nRMSE value 7.89% without WT for GCI building case study.
The forecast average nRMSE reduced to 7.17%, when EN is in-
tegrated with WT. The average nRMSE indicates that, the proposed
hybrid framework outperforms the persistence model and individual
predictor in terms of forecast accuracy with average nRMSE 4.35% for
GCI building. The forecast nRMSE comparison of persistence, BPNN,
FNN+PSO, WT+BPNN, WT+FNN+PSO and proposed framework is
presented in Fig. 11. It can be observed form forecast error comparison,
that the proposed framework is robust and accurate for load demand
forecast of seasonal days.
5.2. Seasonal weekly forecast case study
In order to assess the performance of proposed framework, the
second case study is designed to forecast the week ahead load demand
of different season for AEB and GCI building. In this case study, one
week is selected from each season e.g. December 22–27 (summer), April
Table 1
Daily forecast error comparison for AEB.
Summer Autumn Winter Spring Avg.
E1 E2 E1 E2 E1 E2 E1 E2
M1 8.81 6.78 7.92 5.96 9.12 7.19 8.78 6.91 8.65
M2 9.92 7.86 8.36 6.73 9.26 7.35 8.81 7.12 9.08
M3 8.15 6.56 6.94 5.11 7.68 5.98 7.19 5.29 7.49
M4 7.23 5.38 7.09 5.24 8.16 6.62 6.86 5.11 7.33
M5 6.42 4.94 6.13 4.56 7.13 5.57 6.06 4.18 6.43
M6 6.52 5.16 5.96 4.42 7.19 5.83 5.91 4.26 6.39
M7 8.96 7.18 7.81 6.11 8.62 7.16 8.14 6.38 8.38
M8 7.23 5.63 6.38 4.24 6.79 5.05 6.36 4.47 6.69
M9 6.56 4.78 6.29 4.28 7.34 5.68 6.46 4.43 6.66
M10 5.46 3.96 5.74 4.16 6.54 4.83 5.76 3.87 5.87
M11 5.67 4.12 5.46 3.92 6.32 4.98 5.64 3.92 5.77
N12 4.48 3.26 4.11 3.06 4.61 3.43 4.21 2.95 4.35
M1 = Persistence, M2 = BPNN, M3 = EN, M4 = ARIMA, M5 = RBF + PSO,
M6 = FNN + PSO, M7 = WT + BPNN, M8 = WT + EN, M9 = WT + ARIMA,
M10 = WT + RBF + PSO, M11 = WT + FNN + PSO, M12 = Proposed, E1 = nRMSE,
E2 = nMAE.
Fig. 10. One day ahead load demand forecast error comparison.
Table 2
Daily forecast error comparison of GCI building.
Summer Autumn Winter Spring Avg.
E1 E2 E1 E2 E1 E2 E1 E2
M1 9.36 7.12 9.11 6.84 8.26 6.71 7.86 6.72 8.64
M2 9.82 7.76 9.38 7.11 8.65 7.46 8.57 7.09 9.10
M3 8.02 6.59 7.92 6.53 7.92 6.26 7.72 5.91 7.89
M4 7.96 6.45 7.48 6.31 7.47 5.84 6.76 5.37 7.41
M5 7.19 6.03 6.94 5.39 6.56 5.17 6.14 4.92 6.70
M6 7.36 5.95 6.73 5.08 6.48 5.31 5.85 4.64 6.60
M7 8.8 7.12 8.56 6.45 7.81 6.47 7.97 6.56 8.28
M8 7.55 6.04 7.16 5.94 6.61 5.33 7.37 5.51 7.17
M9 6.92 5.71 6.86 5.61 6.56 5.16 6.02 4.79 6.59
M10 6.16 4.92 5.98 4.51 5.72 4.51 5.57 4.28 5.85
M11 5.98 4.84 5.82 4.39 5.79 4.47 5.38 4.03 5.7
M12 5.27 3.79 4.96 3.41 4.42 3.21 4.27 3.12 4.73
M1 = Persistence, M2 = BPNN, M3 = EN, M4 = ARIMA, M5 = RBF + PSO,
M6 = FNN + PSO, M7 = WT + BPNN, M8 = WT + EN, M9 = WT + ARIMA,
M10 = WT + RBF + PSO, M11 = WT + FNN + PSO, M12 = Proposed, E1 = nRMSE,
E2 = nMAE.
Fig. 11. Daily load demand forecast nRMSE Comparison of AEB.
M.Q. Raza et al. Applied Energy 208 (2017) 1626–1638
1635

11. 7–13 autumn (April 2), July 14–16 (winter) and October 20–26
(spring). Seasonal weekly forecast error comparison of proposed and
benchmark model along with individual predictor is presented in Tables
3 and 4 for AEB and GCI building respectively. The persistence, BPNN,
EN, ARIMA, RBF+PSO, FNN+PSO models produce average forecast
nRMSE values 8.16%, 8.44%, 7.4%, 7.04%, 6.21% an 6.1% respectively
without WT for AEB. The forecast nRMSE reduced to 7.91%, 6.90%,
6.42%, 5.70% and 5.62% respectively with WT.
Therefore, forecast results indicate the effectiveness of WT in terms
of prediction error reduction. The proposed ensemble forecast frame-
work outperform the persistence model with average nRMSE of 4.45%
for AEB. Table 4 illustrates the seasonal weekly forecast error com-
parison of GCI building. The seasonal weekly forecast performance of
proposed framework and other comparative model are presented by
calculating the nRMSE and nMAE. The results indicate that, proposed
ensemble network outperform the comparative models in week ahead
forecast case study with nRMSE 3.97%, 4.32%, 4.23% and 4.11%.
Furthermore, histogram error plot of persistence, BPNN, FNN+PSO,
WT+BPNN, WT+FNN+PSO and proposed framework is presented in
Fig. 12.
The predicted load using proposed framework is close enough to
real load due lower forecast error. This indicates the effectiveness of
proposed forecast framework. Seasonal daily and weekly forecast re-
sults indicate that, the prediction performance of forecast framework is
seasonal sensitive. Therefore, the forecast results are inconsistent.
5.3. Monthly forecast case study
Third case study is designed to forecast the monthly load demand of
AEB building to analyze the performance of proposed framework under
various weather conditions. Table 5 presents the monthly forecast error
comparison of proposed and persistence framework. The proposed
forecast framework produce average monthly forecast nRMSE (4.19%)
as compared to persistence model (8.20%). Fig. 13 presents the histo-
gram error comparison of proposed and persistence model.
It can be observed that, the proposed hybrid framework gives better
forecast results than the persistence model in monthly forecast. It can
be concluded that from forecast results, the proposed framework
highlights significant improvement in load demand forecast of PV in-
tegrated smart buildings.
5.4. Forecast error comparison of GCI and AEB
This case study is designed to compare the prediction median error
of proposed forecast framework for AEB and GCI in seasonal daily and
weekly scenario. Figs. 14 and 15 represent the box plot of seasonal daily
and weekly nRMSE for AEB and GCI respectively. As Fig. 14 highlights
that, forecast results of AEB provides steady error in comparison with
GCI. It is can also observed from box plot as the size of upper and lower
quartile is small. However, GCI forecast results are less steady as
compare to AEB in same selected days. Proposed forecast framework
produced about 4.70% nRMSE for GCI, while it is less than 4.30% for
AEB. Improper training of ensemble predictors and uncertain
Table 3
Weekly forecast comparison of AEB.
Summer Autumn Winter Spring Avg.
E1 E2 E1 E2 E1 E2 E1 E2
M1 7.96 5.89 7.92 6.1 8.59 6.92 8.18 5.95 8.16
M2 8.46 6.77 8.06 6.37 8.93 7.06 8.31 6.14 8.44
M3 7.34 5.71 7.17 5.29 7.81 6.21 7.29 5.82 7.40
M4 7.12 5.41 6.78 4.93 7.66 5.91 6.61 5.26 7.04
M5 6.42 4.8 5.75 4.06 6.73 5.01 5.94 4.36 6.21
M6 6.32 4.67 5.68 4.1 6.59 4.98 5.83 4.21 6.10
M7 7.62 5.86 7.71 6.01 8.21 6.35 8.11 5.91 7.91
M8 6.76 5.23 6.96 5.37 7.09 5.07 6.81 5.61 6.90
M9 6.59 4.7 5.78 4.02 6.92 5.17 6.42 5.26 6.42
M10 5.73 3.98 5.21 3.63 6.18 4.29 5.71 4.02 5.70
M11 5.65 3.93 5.36 3.82 5.91 4.19 5.57 3.84 5.62
M12 4.18 3.12 4.26 3.21 4.49 3.23 4.87 3.68 4.45
M1 = Persistence, M2 = BPNN, M3 = EN, M4 = ARIMA, M5 = RBF + PSO,
M6 = FNN + PSO, M7 = WT + BPNN, M8 = WT + EN, M9 = WT + ARIMA,
M10 = WT + RBF + PSO, M11 = WT + FNN + PSO, M12 = Proposed, E1 = nRMSE,
E2 = nMAE.
Table 4
Weekly forecast error comparison of GCI building.
Summer Autumn Winter Spring Avg.
E1 E2 E1 E2 E1 E2 E1 E2
M1 7.71 5.91 8.07 6.36 7.86 6.04 7.83 5.81 7.86
M2 7.65 5.74 8.28 6.51 8.15 6.32 8.13 6.24 8.05
M3 7.02 5.37 7.19 6.13 6.97 5.12 6.81 5.19 6.99
M4 6.91 5.1 6.79 5.37 6.47 4.58 6.56 4.84 6.68
M5 5.89 4.27 6.41 4.54 6.14 4.17 5.84 4.33 6.07
M6 6.06 4.51 6.29 4.63 5.98 4.11 5.71 3.99 6.01
M7 6.84 5.24 7.83 5.92 7.24 5.67 7.48 5.63 7.34
M8 6.44 4.6 6.69 5.16 6.49 4.54 6.29 4.47 6.47
M9 6.24 4.52 6.13 4.59 5.76 3.98 5.93 4.14 6.01
M10 5.19 3.48 5.61 3.89 5.32 3.46 4.98 3.16 5.27
M11 5.32 3.53 5.72 4.03 5.24 3.34 5.1 3.44 5.34
N12 4.97 2.94 4.32 3.25 4.23 3.06 4.11 3.21 4.40
M1 = Persistence, M2 = BPNN, M3 = EN, M4 = ARIMA, M5 = RBF + PSO,
M6 = FNN + PSO, M7 = WT + BPNN, M8 = WT + EN, M9 = WT + ARIMA,
M10 = WT + RBF + PSO, M11 = WT + FNN + PSO, M12 = Proposed, E1 = nRMSE,
E2 = nMAE.
Fig. 12. Weekly load demand forecast nRMSE Comparison of GCI Building.
Table 5
Monthly AEB forecast nRMSE comparison.
Month Persistence model (nRMSE) Proposed framework (nRMSE)
January 7.75 3.94
February 8.21 4.45
March 8.23 4.21
April 8.07 3.91
May 9.12 4.61
June 7.89 4.11
July 8.18 4.36
August 7.58 4.12
September 8.26 3.88
October 8.62 4.11
November 9.06 4.61
December 7.53 3.98
Average 8.20 4.19
M.Q. Raza et al. Applied Energy 208 (2017) 1626–1638
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12. occupancy of GCI are potential cause of increased forecast nRMSE.
Prediction results of proposed forecast framework for AEB and GCI are
more consistent in seasonal weekly case study. Median forecast nRMSE
AEB and GCI are about 4.80% and 4.40% respectively in seasonal
weekly forecast case study. The distribution of prediction nRMSE of
AEB and GCI are also closer to each other. In conclusion, prediction
results are more stable in seasonal weekly case study.
5.5. Potential practical applications
An accurate forecast of load demand and renewable energy re-
sources can be utilized for smart building demand side management
[43]. The power generation at certain instant is matched with by con-
trolling the energy demand of smart buildings are considered as
building demand side management. Energy demand of buildings is
managed by shifting the appliances time of use from peak to off time.
Therefore, peak demand can be shifted by using accurate prediction of
building level load demand. It is important to optimize the electricity
use in building as they consume more than 30% of total [44].
The proposed framework can also be used in building to optimize
the energy use of PV integrated buildings [45]. Furthermore, storage
devices can be charged and discharged depending on the availability of
PV output power. As a result, this will reduce the building operational
cost significantly. In addition, an efficient heating ventilation and air
conditioning (HVAC) system can also be designed with minimal elec-
tricity use with the help of an accurate forecasting. The proposed
forecast can also be utilized for different prediction application such as
wind speed, load demand of power grid and PV output power forecast
etc. [46–49].
6. Conclusions
A novel hybrid framework has been proposed in this work for ac-
curate load demand forecast of PV integrated smart buildings. The
proposed forecast framework is based on five different predictors
named as BPNN, EN, ARIMA, FNN, RBF and their wavelet transformed
models in an ensemble network. WT is applied to historical load data to
remove the sharp fluctuations and spikes. Individual predictors such as
RBF and FNN were trained with PSO algorithm to enhance the pre-
diction performance of individual predictor. The combination of
Fig. 13. nRMSE histogram of monthly AEB load demand
forecast.
Fig. 14. Seasonal daily nRMSE comparison of AEB and GCI.
Fig. 15. Seasonal weekly nRMSE comparison of AEB and GCI.
M.Q. Raza et al. Applied Energy 208 (2017) 1626–1638
1637

13. different independent predictors generates diverse forecast output due
its operational principle. After that, the output of each predictor and
WT predictors were aggregated using Bayesian model averaging. The
objective of aggregation is to achieve higher forecast accuracy of PV
integrated smart building’s load demand through selection of better
performing models. The overall forecast accuracy is enhanced by
combining the predictors in an intelligent manner, in which more
weight is given to best performing models. The performance of pro-
posed forecasting framework is tested on two practical PV integrated
smart buildings located at a big university campus environment using a
massive data captured through building data management system.
The performance of the proposed framework is compared with other
models such as the persistence model, BPNN, EN, ARIMA, FNN, RBF
and their WT models. The forecast results demonstrate that the pro-
posed forecast shows improvement in average forecast nRMSE around
17% in seasonal daily and 20% in seasonal weekly in comparison with
each compared models. The proposed framework produces approxi-
mately consistent forecast results for GCI and AEB during seasonal daily
and weekly forecast comparison. In addition, proposed framework
provides minimum nRMSE of 3.88% in monthly forecast. The effec-
tiveness of WT is also observed with forecast error reduction. The
proposed hybrid and intelligent forecast framework is significantly in-
creased the prediction accuracy during different seasonal and monthly
case studies. In future, the proposed forecast framework can be applied
to electrical load, price and PV output power forecast including other
prediction applications. It can also be applied for efficient management
system and different demand response programs for smart grid and
buildings.
References
[1] Jain RK, Smith KM, Culligan PJ, Taylor JE. Forecasting energy consumption of
multi-family residential buildings using support vector regression: Investigating the
impact of temporal and spatial monitoring granularity on performance accuracy.
Appl Energy 2014;123:168–78.
[2] OECD/IEA. International Energy Agency. http://www.iea.org/aboutus/faqs/
energyefficiency/; 2014.
[3] Bagnasco A, Fresi F, Saviozzi M, Silvestro F, Vinci A. Electrical consumption fore-
casting in hospital facilities: an application case. Energy Build 2015;103:261–70.
[4] Ma Y-J, Qi M, Zhou X-S, Zhang S-r, Zhang H-T. Application of chaos theory in
cascaded five levels variable frequency and variable speed system. In: Power and
Energy Engineering Conference (APPEEC), 2010 Asia-Pacific; 2010. p. 1–4.
[5] Li Q, Meng Q, Cai J, Yoshino H, Mochida A. Applying support vector machine to
predict hourly cooling load in the building. Appl Energy 2009;86:2249–56.
[6] Khotanzad A, Enwang Z, Elragal H. A neuro-fuzzy approach to short-term load
forecasting in a price-sensitive environment. IEEE Trans Power Syst
2002;17:1273–82.
[7] Bahrami S, Hooshmand R-A, Parastegari M. Short term electric load forecasting by
wavelet transform and grey model improved by PSO (particle swarm optimization)
algorithm. Energy 2014;72:434–42.
[8] Hao Q, Srinivasan D, Khosravi A. Short-term load and wind power forecasting using
neural network-based prediction intervals. IEEE Trans Neural Networks Learn Syst
2014;25:303–15.
[9] Raza MQ, Khosravi A. A review on artificial intelligence based load demand fore-
casting techniques for smart grid and buildings. Renew Sustain Energy Rev
2015;50:1352–72.
[10] Baharudin Z, Raza MQ. A review on short term load forecasting using hybrid neural
network techniques. In: Power and Energy (PECon), 2012 IEEE international con-
ference on. IEEE; 2012. p. 846–51.
[11] Gao Z, Ming F, Hongling Z. Bagging neural networks for predicting water con-
sumption. J Commun Comput 2005;2:19–24.
[12] Burnham KP, Anderson DR. Model selection and multimodel inference: a practical
information-theoretic approach. Springer Science & Business Media; 2002.
[13] Mena R, Rodríguez F, Castilla M, Arahal MR. A prediction model based on neural
networks for the energy consumption of a bioclimatic building. Energy Build
2014;82:142–55.
[14] Shu F, Luonan C. Short-term load forecasting based on an adaptive hybrid method.
IEEE Trans Power Syst 2006;21:392–401.
[15] He H-d, Lu W-Z, Xue Y. Prediction of particulate matter at street level using arti-
ficial neural networks coupling with chaotic particle swarm optimization algorithm.
Build Environ 2014;78:111–7.
[16] Benedetti M, Cesarotti V, Introna V, Serranti J. Energy consumption control auto-
mation using Artificial Neural Networks and adaptive algorithms: proposal of a new
methodology and case study. Appl Energy 2016;165:60–71.
[17] Chou J-S, Ngo N-T. Time series analytics using sliding window metaheuristic
optimization-based machine learning system for identifying building energy con-
sumption patterns. Appl Energy 2016;177:751–70.
[18] Li X, Wen J, Bai E-W. Developing a whole building cooling energy forecasting
model for on-line operation optimization using proactive system identification.
Appl Energy 2016;164:69–88.
[19] Lü X, Lu T, Kibert CJ, Viljanen M. Modeling and forecasting energy consumption for
heterogeneous buildings using a physical–statistical approach. Appl Energy
2015;144:261–75.
[20] Cui C, Wu T, Hu M, Weir JD, Li X. Short-term building energy model re-
commendation system: a meta-learning approach. Appl Energy 2016;172:251–63.
[21] Vu DH, Muttaqi KM, Agalgaonkar AP. A variance inflation factor and backward
elimination based robust regression model for forecasting monthly electricity de-
mand using climatic variables. Appl Energy 2015;140:385–94.
[22] Raatikainen M, Skön J-P, Leiviskä K, Kolehmainen M. Intelligent analysis of energy
consumption in school buildings. Appl Energy 2016;165:416–29.
[23] Deb C, Eang LS, Yang J, Santamouris M. Forecasting diurnal cooling energy load for
institutional buildings using Artificial Neural Networks. Energy Build
2016;121:284–97.
[24] Hassan S, Khosravi A, Jaafar J. Examining performance of aggregation algorithms
for neural network-based electricity demand forecasting. Int J Electr Power Energy
Syst 2015;64:1098–105.
[25] Siwek K, Osowski S. Improving the accuracy of prediction of PM 10 pollution by the
wavelet transformation and an ensemble of neural predictors. Eng Appl Artif Intell
2012;25:1246–58.
[26] Sloughter JM, Gneiting T, Raftery AE. Probabilistic wind speed forecasting using
ensembles and Bayesian model averaging. J Am Stat Assoc 2010;105:25–35.
[27] Li G, Shi J, Zhou J. Bayesian adaptive combination of short-term wind speed
forecasts from neural network models. Renew Energy 2011;36:352–9.
[28] Li S, Wang P, Goel L. Short-term load forecasting by wavelet transform and evo-
lutionary extreme learning machine. Electric Power Syst Res 2015;122:96–103.
[29] Catalao J, Pousinho H, Mendes V. Hybrid wavelet-PSO-ANFIS approach for short-
term electricity prices forecasting. IEEE Trans Power Syst 2011;26:137–44.
[30] Mandal P, Haque AU, Julian M, Srivastava AK, Martinez R. A novel hybrid approach
using wavelet, firefly algorithm, and fuzzy ARTMAP for day-ahead electricity price
forecasting. IEEE Trans Power Syst 2013;28:1041–51.
[31] Khatib T, Mohamed A, Sopian K, Mahmoud M. Assessment of artificial neural
networks for hourly solar radiation prediction. Int J Photoenergy 2012; 2012.
[32] Singh NK, Singh AK, Tripathy M. Short-term load/price forecasting in deregulated
electric environment using ELMAN neural network. In: Energy Economics and
Environment (ICEEE), 2015 International Conference on: IEEE; 2015. p. 1–6.
[33] Mirjalili S, Mohd Hashim SZ, Moradian Sardroudi H. Training feedforward neural
networks using hybrid particle swarm optimization and gravitational search algo-
rithm. Appl Math Comput 2012;218:11125–37.
[34] Raftery AE, Gneiting T, Balabdaoui F, Polakowski M. Using bayesian model aver-
aging to calibrate forecast ensembles. Monthly Weather Rev 2005;133:1155–74.
[35] Duan Q, Ajami NK, Gao X, Sorooshian S. Multi-model ensemble hydrologic pre-
diction using Bayesian model averaging. Adv Water Resour 2007;30:1371–86.
[36] Li G, Shi J. Application of Bayesian model averaging in modeling long-term wind
speed distributions. Renew Energy 2010;35:1192–202.
[37] Bayesian Wasserman L, Selection Model, Averaging Model. J Math Psychol
2000;44:92–107.
[38] Magnus J, Powell O, Prufer P. A comparison of two model averaging techniques
with an application to growth empirics. J Econ 2010;154:139–53.
[39] De Luca G, Magnus J. Bayesian model averaging and weighted average least
squares: equivariance, stability, and numerical issues. Stata J 2011;11:518–44.
[40] Raza MQ, Nadarajah M, Ekanayake C. An improved WT and NN ensemble demand
forecast model for PV integrated smart buildings. In: Innovative Smart Grid
Technologies-Asia (ISGT-Asia), 2016 IEEE: IEEE; 2016. p. 781–6.
[41] Raza MQ, Baharudin Z, Badar-Ul-Islam B-U-I, Nallagownden P. A comparative
analysis of neural network based short term load forecast models for anomalous
days load prediction. J Comput 2014;9:1519–24.
[42] Haque AU, Nehrir MH, Mandal P. A hybrid intelligent model for deterministic and
quantile regression approach for probabilistic wind power forecasting. IEEE Trans
Power Syst 2014;29:1663–72.
[43] Tascikaraoglu A, Boynuegri AR, Uzunoglu M. A demand side management strategy
based on forecasting of residential renewable sources: A smart home system in
Turkey. Energy Build 2014;80:309–20.
[44] Asadi E, Silva MGd, Antunes CH, Dias L, Glicksman L. Multi-objective optimization
for building retrofit: a model using genetic algorithm and artificial neural network
and an application. Energy Build 2014;81:444–56.
[45] Qamar Raza M, Nadarajah M, Ekanayake C. On recent advances in PV output power
forecast. Solar Energy 2016;136:125–44.
[46] Li G, Shi J. On comparing three artificial neural networks for wind speed fore-
casting. Appl Energy. 2010;87:2313–20.
[47] Li Y, He Y, Su Y, Shu L. Forecasting the daily power output of a grid-connected
photovoltaic system based on multivariate adaptive regression splines. Appl Energy
2016;180:392–401.
[48] Muhammad Qamar Raza, Mithulananthan Nadarajah, Duong Quoc Hung, Zuhairi
Baharudin, An intelligent hybrid short-term load forecasting model for smart power
grids, Sustainable Cities and Society, vol. 31; 2017. p. 264–75. ISSN 2210-6707.
[49] Meer Dvd, Mouli GRC, Morales-Espana G, Elizondo LR, Bauer P. Energy manage-
ment system with PV power forecast to optimally charge EVs at the workplace. In:
IEEE transactions on industrial informatics; 2016. p. 1.
M.Q. Raza et al. Applied Energy 208 (2017) 1626–1638
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