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Prediction of Hydropower Generation Using Grey Wolf Optimization Adaptive Neuro-Fuzzy Inference System

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Hydropower is among the cleanest sources of energy. However, the rate of hydropower generation is profoundly affected by the inflow to the dam reservoirs. In this study, the Grey wolf optimization (GWO) method coupled with an adaptive neuro-fuzzy inference system (ANFIS) to forecast the hydropower generation. For this purpose, the Dez basin average of rainfall was calculated using Thiessen polygons. Twenty input combinations, including the inflow to the dam, the rainfall and the hydropower in the previous months were used, while the output in all the scenarios was one month of hydropower generation. Then, the coupled model was used to forecast the hydropower generation. Results indicated that the method was promising. GWO-ANFIS was capable of predicting the hydropower generation satisfactorily, while the ANFIS failed in nine input-output combinations.
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Energies 2019, 12, 289; doi:10.3390/en12020289 www.mdpi.com/journal/energies
Article
Prediction of Hydropower Generation Using Grey
Wolf Optimization Adaptive Neuro-Fuzzy Inference
System
Majid Dehghani 1, Hossein Riahi-Madvar 2, Farhad Hooshyaripor 3, Amir Mosavi 4,5,
Shahaboddin Shamshirband 6,7,*, Edmundas Kazimieras Zavadskas8 and Kwok-wing Chau 9
1 Technical and Engineering Department, Faculty of Civil Engineering, Vali-e-Asr University of Rafsanjan,
P.O. Box 518, 7718897111 Rafsanjan, Iran; m.dehghani@vru.ac.ir
2 College of Agriculture, Vali-e-Asr University of Rafsanjan, P.O. Box 518, 7718897111 Rafsanjan, Iran;
h.riahi@vru.ac.ir
3 Technical and Engineering Department, Science and Research, Branch, Islamic Azad University,
1477893855, Tehran, Iran; hooshyarypor@gmail.com
4 Institute of Automation, Kando Kalman Faculty of Electrical Engineering, Obuda University, 1034
Budapest, Hungary; amir.mosavi@kvk.uni-obuda.hu
5 School of the Built Environment, Oxford Brookes University, OX3 0BP Oxford, UK
6 Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi
Minh City, Viet Nam
7 Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
8 Institute of Sustainable Construction, Vilnius Gediminas Technical University, LT-10223 Vilnius,
Lithuania; edmundas.zavadskas@vgtu.lt
9 Department of Civil and Environmental Engineering, Hong Kong Polytechnic University, Hong Kong,
China; dr.kwok-wing.chau@polyu.edu.hk
* Correspondence: shahaboddin.shamshirband@tdtu.edu.vn
Received: 31 December 2018; Accepted: 16 January 2019; Published: 17 January 2019
Abstract: Hydropower is among the cleanest sources of energy. However, the rate of hydropower
generation is profoundly affected by the inflow to the dam reservoirs. In this study, the Grey wolf
optimization (GWO) method coupled with an adaptive neuro-fuzzy inference system (ANFIS) to
forecast the hydropower generation. For this purpose, the Dez basin average of rainfall was
calculated using Thiessen polygons. Twenty input combinations, including the inflow to the dam,
the rainfall and the hydropower in the previous months were used, while the output in all the
scenarios was one month of hydropower generation. Then, the coupled model was used to forecast
the hydropower generation. Results indicated that the method was promising. GWO-ANFIS was
capable of predicting the hydropower generation satisfactorily, while the ANFIS failed in nine
input-output combinations.
Keywords: hydropower generation; hydropower prediction; dam inflow; machine learning; hybrid
models; artificial intelligence; prediction; grey wolf optimization (GWO), deep learning; adaptive
neuro-fuzzy inference system (ANFIS), hydrological modelling; hydroinformatics; energy system;
drought; forecasting; precipitation
1. Introduction
Hydropower is a renewable source of energy that is derived from the fast reservoir water flows
through a turbine. One of the main purposes of dam construction is to generate the hydropower via
installation of a hydropower plant near the dam site. The rate of hydropower generation depends on
the dam height and the inflow to the dam reservoir. Nonetheless, hydropower is one of the major
Energies 2019, 12, 289 2 of 20
sources of power supply in each country. In addition, the power consumption varies strongly during
the year. Therefore, an insight on the value of hydropower energy to be produced in the coming
months would be an important tool in managing the electricity distribution network and operation
of the dam. Consequently, hydropower generation forecasting could be a key component in dam
operation. Hamlet et al. [1] evaluated a long-lead forecasting model in the Colombia river and stated
that long-lead forecasting model led to an increase in annual revenue of approximately $153 million
per year in comparison with no forecasting model. Several researches carried out based on the inflow
forecasting to the dam and executing an operating reservoir model to determine the hydropower
generation [2–8]. While these researches are promising, some challenges arise during the
implementation of these models. First, forecasting the precipitation is needed and in the next step the
inflow to the river and then a reservoir model needs to be run. Each step, including the precipitation
or inflow forecasting and reservoir modeling, is associated with uncertainty and the results are highly
affected by the uncertainty in these models. Second, an optimization algorithm seems to be needed
to optimize the parameters of predictive models.
During the past two decades, several artificial intelligent models were utilized for hydrologic
model prediction [9] and hydropower stream flow forecasting [10]. Among them, the ensemble
models [11–13] and hybrid models [14] have recently become very popular. Recently, to produce
novel hybrid models, different optimization algorithms were coupled with these models to improve
their performance [15–20]. Among the optimization algorithms, Grey wolf optimization (GWO) has
shown promising results in a wide range of application when coupled with machine learning
algorithms [21]. Consequently, in this study, to reduce the source of uncertainty, an artificial
intelligent model was used for hydropower generation forecasting. For this purpose, the adaptive
neuro-fuzzy inference system (ANFIS) was coupled with GWO to forecast the monthly hydropower
generation directly based on the precipitation over the basin, the inflow to the dam and the
hydropower generation in previous months. This method is capable to facilitate the hydropower
generation forecasting. The rest of this chapter is organized as follows. In section 2, the coupled model
of ANFIS and GWO and study area are presented. Section 3 involves the results of hydropower
forecasting and its reliability. Finally, section 4 includes the conclusion of the study.
2. Methodology and Data
2.1. Study Area
The Dez dam is an arch dam constructed in 1963 on the Dez river southwestern of Iran (Figure
1). The dam is 203 m high and has a reservoir capacity of 3340 Mm3. The upstream catchment of the
dam with the mean elevation of 1915.3 m above sea level and average slope of 0.0084 has an area of
17843.3 Km2. The catchment length is about 400km and ends with the dam reservoir at the outlet.
Flow to the reservoir was measured at the Tele-Zang hydrometric station (Figure 1). The precipitation
stations that were used in the present study include four precipitation stations in the catchment and
10 others around the catchment (Figure 1). The hydrometric data was taken from Iran's Water
Resources Management Company (http://www.wrm.ir/index.php?l=EN) and the precipitation data
is available from Iran Meteorological Organization (http://www.irimo.ir/eng/index.php). The
monthly data used here covered the range of October 1963 to September 2017. The average Inflow to
the reservoir and precipitation were calculated and shown in Figure 2. According to Figure 2, the
most precipitation occurred from October to May. Precipitation in the winter accumulated as
snowpack over the high mountainous area and in the spring the river flow increased as a result of
snowmelt. Summer was dry with almost no considerable precipitation.
Energies 2019, 12, 289 3 of 20
Figure 1. Location of the Dez dam and the precipitation stations in Iran.
Figure 2. Average monthly precipitation in the catchment and mean monthly inflow to the Dez dam
reservoir.
The primary purpose of the Dez dam is the flood control, hydroelectric power generation and
irrigation supply for 125000 ha downstream agricultural area, as well. The Dez hydropower plant
consists of eight units with a total installed capacity of 520 MW. The monthly power generation was
#
*
%,Tele_Zang
AZNA
ARAK
DOROUD
KHOMEIN
MALAYER
NAHAVAND
KOOHRANG
ALESHTAR
BROUJERD
GOLPAIGAN
ALIGOODARZ
KHORRAMABAD
MASJED SOLEYMAN
SAFIABAD DEZFUL
50°30'0"E50°0'0"E49°30'0"E49°0'0"E48°3 0'0"E48°0'0"E47°30'0"E
34°30'0"N34°0'0"N33°30'0"N33°0'0"N32°30'0"N32°0'0"N
Legend
%,Hydrometry S t.
#
*
Dez Dam
Precipitation St.
River
DEZ BASIN
Subbasin
±
#*
Persian Gulf
Caspian sea
61°30'0"E58°0'0"E54°30'0"E51°0'0"E47°30'0"E44°0'0"E
39°30'0"N36°0'0"N32°30'0"N29°0'0"N25°30'0"N
Legend
khazar-khalijPoly3
DEZ BASIN
Subbasin
±
0
200
400
600
800
1000
1200
1400
1600
1800
0
10
20
30
40
50
60
70
80
90
100
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Inflow (Mm3)
Precipitation (mm)
Month
P (mm)
I (MCM)
Energies 2019, 12, 289 4 of 20
gathered between 1963 and 2017 from Iran's Water Resources Management Company. Figure 3
illustrates monthly hydroelectric generation in the Dez hydropower plant. Table 1 shows the
statistical characteristics of the precipitation over the Dez basin, the inflow to the dam reservoir and
the hydropower generation time series.
Figure 3. Average power generation in the Dez hydropower plant.
Table 1. Presenting the datasets and the statistical characteristics.
Parameter Mode Mean Min S.D. First
Quartile Median Third
Quartile Max Skew. Kurtosis.
Ht 26545.98 165297.70 26545.98 56093.06 130338.42 168568.96 203734.07 354879.53 −0.10 2.76
Qt 63.28 651.71 63.28 615.23 209.87 430.22 842.41 3643.84 1.86 6.91
Pt 0.00 42.82 0.00 46.91 0.47 27.97 71.81 238.47 1.10 3.69
Ht: Hydroelectric Energy (MWH) at month t; Qt: River Inflow (m3/s) at month t; Pt: precipitation (mm)
at month t; S.D.: Standard Deviation.
2.2. ANFIS: Adaptive Neuro-Fuzzy Inference System
Jang (1993) [22] developed ANFIS as a joint of artificial neural network and the fuzzy inference
system [23]. The learning ability of artificial neural networks (ANN) and the fuzzy reasoning create
a valuable capability to fit a relationship between input and output spaces [24]. On the other hand,
the ANFIS uses the training capability of ANN to assign and adjust the membership functions. The
back-propagation algorithm enables the model to adjust the parameters until an acceptable error is
reached [25]. Suppose that the system of fuzzy inference include x & y as inputs and z as output. Two
if-then rules could be utilized for Sugeno model as follows:
Rule one: if x and y = 1
A
and 1
B
, respectively, then 1111
ryqxpf
Rule two: if x and y = 2
A
and 2
B
, respectively, then 2222
ryqxpf
where 1
A
,1
B
,2
A
, 2
B
are considered as the labels of linguistic. Furthermore, 1
p
,2
p
,1
q
,2
q
,1
r
and
2
r
are the output function parameters [26].
The architecture of ANFIS is presented in Figure 4. It includes five layers; all are fixed nodes,
except the first and fourth nodes, which are adaptive nodes.
100000
110000
120000
130000
140000
150000
160000
170000
180000
190000
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Precipitation (mm)
Month
Energies 2019, 12, 289 5 of 20
Figure 4. Architecture of adaptive neuro-fuzzy inference system in this study.
Layer 1: The nodes act adaptive in generating the membership grades of the inputs [24]:
)(
,1
xO
Aii
, for i = 1, 2, or
(1)
)(
2,1
yO
Bii
, for i = 3, 4.
It should be noted that i is the number of inputs and i
O
,1 to i
O
,5 are the output of each layer.
Several memberships could be used for this purpose; among all Gaussian functions presented in the
Equation (1), the following was utilized in this study:
 
2
5.0exp
i
i
cx
x
(2)
where i
c and i
are set parameters with maximum and minimum of one and zero, respectively
[22].
Layer 2: this layer is a rule node with AND/OR operator to get an output which called firing
strengths i
O
,2 :
)()(
,2
yxO
BiAii
, i = 1, 2 (3)
Layer 3: presents an average node computing the normalized firing strength as follows:
21
,3
ww
w
wO
i
ii
, i = 1, 2 (4)
Layer 4: this layer contains the consequent nodes for which the p, q and r parameters were
tuned during the learning process:
)(
,4 iiiiiii
ryqxpwfwO
(5)
Layer 5: this layer contains the output nodes which compute the total average of output through
a sum of entire input signals [27]:
Energies 2019, 12, 289 6 of 20
i
iii
fwfO
,5
(6)
While the ANFIS has high capability to map the input to the output as a black-box model, it
suffers from a long training time to assign the proper values to the parameters of membership
function. To overcome this problem we use the optimization algorithm of grey wolf.
2.3. Grey Wolf Optimization (GWO)
The optimization algorithm of Grey wolf known as GWO is known as an advanced meta-
heuristic nature-inspired for an efficient optimization [28]. This algorithm was developed through
imitating the foraging behavior of grey wolfs performing in groups of five-12 individuals which are
at the top of food chain [29]. Grey wolves follow a social hierarchy strictly.
The leaders include a couple of female and male, called alpha (
), who are in charge of decision
making while hunting, resting and so on. Beta (
) is the next level helping alpha in making
decisions, while they should obey the alpha. The beta wolves can be male and female and the role of
them is disciplining the group. They are the best candidate for substituting the alpha when they
become older or die. The next level is called delta (
) and play the role of scouts, sentinels, hunters
and so on. The last level is called omega (
), which are the weakest level. They act as babysitters.
While this level is the weakest, without omega wolves, internal fights may be observed in the group.
Hunting, along with the social hierarchy, is a major social behavior of grey wolves. Muro et al. [30]
expressed the three steps in the grey wolves hunting:
1. Identifying, following and approaching the prey;
2. Encircling the prey;
3. Attacking the prey.
These two social behaviors are considered in the GWO algorithm [29]. In mathematical modeling
of the algorithm,
is considered as the fittest solution, and in the next steps,
,
and
. The
mathematical formulation of encircling could be presented as follows [28]:
p
 
  (7)
( 1) ( )
p
X t X t A D
 
 
(8)
where,
A
and
C would work as the vectors of the coefficient. Furthermore,
p
X would
determine the positions of prey and
X
is the wolf's positions. Here,
D
would be the vector for
specifying a new position of the GW and
t
is the iteration time. The
C and
A
formulated as
[28]:
1
2
A a r a
 
 
(9)
2
2C r
 
 
(10)
where
a presents the set of vectors over the iteration that change in value from 2 to 0 linearly. The
1
r and
2
r represent random vectors in
 
0,1
.
Energies 2019, 12, 289 7 of 20
The
leads the hunting, while
and
contribute in this task occasionally. For
mathematical representation of hunting, it was assumed that the alpha, bata and delta include better
knowledge on the prey’s locations. Thus, the optimal solutions for the three positions can be
registered. Consequently, the rest of the wolves will follow and update their postions accordingly.
1
D C X X
 
 
(11)
2
D C X X
 
 
 
(12)
3
D C X X
 
  
 
(13)
1 1
X X A D
 
 
 
(14)
2 2
X X A D
 
 
 
(15)
3 3
X X A D
 
 
 
(16)
3
)1( 321 XXX
tX
(17)
When the prey stops, the grey wolves start to attack. The vector A is a random value in the
interval
 
2 , 2a a. The 1A leads to grey wolves’ attack while 1A force them to move
away to find a better solution. Figure 5 shows the framework of the GWO algorithm.
Figure 5. The flowchart of ANFIS-GWO modeling.
Energies 2019, 12, 289 8 of 20
2.4. Performance Criteria.
The assessment of the proposed model’s efficiencies, including accuracy and agreement, was
evaluated using statistical criteria, such as the confidence index (CI), root mean square error (RMSE),
Nash-Sutcliffe Efficiency (NSE), coefficient of determination (R2), index of agreement (d), relative
absolute error (RAE) and mean absolute error (MAE).
The evaluation criteria of RMSE and MAE are common mean error indicators that indicated how
close data points are to a best fit line (Equations (18) & (19)) [31].
According to Nash and Sutcliffe [32], the NSE is defined as the sum of the absolute squared
differences of the observed and estimated data normalized by the variance minus one. (Equation
(21)). As determined by [33], the range of NSE is from one to −∞. When NSE is less than 0, the mean
observed value have been a better predictor than the model. It describes the plot of observed data
versus estimated data, and how well they fit the 1:1 line.
Furthermore, according to Bravais-Pearson, the R2 presents the squared value of the correlation
coefficient describing how much of the observed dispersion is delivered by the prediction. The value
of R2 may vary from 1 and 0. The 0, and 1 values would present no correlation between observed and
predicted data, and dispersion of the estimation data is equal to that of the observation, respectively
[33] (Equation (20)).
The index of agreement d [34] prevail over the insensitivity of NSE and R2 to differences in the
means and variances of the observed and estimated data [35]. The index of agreement demonstrates
the ratio of the mean square error and the potential error [36] (Equation (22)). The range of d similar
to R2 changes from 0 for the no correlation to 1, which is a perfect fit.
The RAE is a non-negative index that indicates a ratio of the overall agreement level between
observed and estimated datasets. The range of RAE may change from 0 for a perfect fit to ∞, which
means no upper bound. The Confidence index (CI) is the product of NSE and d, which ranges
between 1 (perfect fit) and −∞. Lower than zero values means that the mean observed values have
been a better predictor than the model.
The evaluation criteria were calculated based on the following equations:
 
2
1
1N
i i
i
RMSE O P
N
 
,
RMSE0
(18)
N
i
ii
PO
N
MAE
1
1
,
MAE0
(19)
 
 
2
1 1
22
1
2
 
 
N
i
N
iii
N
iii
PPOO
PPOO
R
, 10 2r (20)
 
 
N
ii
N
iii
OO
PO
NSE
1
2
1
2
1,
1
NSE
(21)
 
 
N
iii
N
iii
OOOP
OP
d
1
2
1
2
1 ,
10
d
(22)
Energies 2019, 12, 289 9 of 20
 
 
N
iii
N
iii
OO
PO
PI
1
2
1
1
2
1,
PI
(23)
NSEdCI
,
1
CI
(24)
N
ii
N
iii
OO
PO
RAE
1
1,
RAE0
(25)
In which the Oi is observation value, Pi is the predicted model output, Ō is the average of
observations,
P
is the average of model outputs and N is number of data.
3. Results
In this study, the inflow of the Dez dam and the average precipitation over the whole basin were
utilized to forecast the hydropower generation. For this purpose, the time series divided into two
subsets as the train and test subsets. 70% of data was assigned as the train and the remaining 30% for
test phase.
Different input combinations were evaluated and used in the modeling process. The final
selection of input combinations was based on the correlation analysis of variables in Table 3, the
physical nature of variables and applicability of models presented in Table 2. Based on the availability
of different measured parameters in the dam, one can choose which model is applicable for prediction
of hydropower, and these different combinations strengthen the applicability of model in different
data availability of the study. Some models were only based on inflow to the dam and rainfall such
as: M1, M2, M3, M13, M14, M15, M18, M19 and M20. These models did not require the hydropower
generation of the dam in previous time steps and, based on inflow and precipitation, can predict the
hydropower generation in the plan. Some models used lagged values of hydropower generation of
the dam in previous time steps as input vectors and these models did not require further information
of inflow or precipitation in prediction of hydropower generation. These models, such as M5, M7
M10, M11 and M12, are lagged based models. The other models are based on combination of lagged
values of hydropower generation, inflow and precipitation, such as M4, M6, M8, M9, M16 and M17.
Table 2. Different input combination used for ANFIS and GWO-ANFIS modeling.
Model Input Parameters Output
M1 Qt Ht
M2 Qt, Pt Ht
M3 Qt-1, Qt Ht
M4 Qt-1, Qt, Ht-1 Ht
M5 Ht-1 Ht
M6 Qt-1, Qt, Pt, Ht-1 Ht
M7 Ht-2, Ht-1 Ht
M8 Qt, Ht-2, Ht-1 Ht
M9 Qt-1, Qt, Ht-2, Ht-1 Ht
M10 Ht-12, Ht-2, Ht-1 Ht
M11 Ht-12, Ht-1 Ht
M12 Ht-12 Ht
M13 Qt-4, Qt-3, Qt-2, Qt-1, Qt Ht
Energies 2019, 12, 289 10 of 20
M14 Qt-3, Qt-2, Qt-1, Qt Ht
M15 Qt-2, Qt-1, Qt Ht
M16 Qt-3, Qt-2, Ht-12, Ht-1 Ht
M17 Qt-3, Ht-2, Ht-1 Ht
M18 Qt-4, Qt-3 Ht
M19 Pt-5, Pt-4, Qt-4, Qt-3, Qt-2 Ht
M20 Pt-5, Pt-4, Qt-3, Qt-2 Ht
According to Table 2, the discharge, precipitation, and the hydropower generation with different
lags were used to forecast the hydropower generation for the next month. The correlation coefficients
between the input variables were calculated and are presented in Table 3; they oscillate between 0.01
and 0.67. It should be noted that Q is the inflow of the dam, but not the inflow of the turbine.
Therefore, as the Dam is multipurpose, and the water stored in the dam is also used for irrigation, it
is possible to use Qt to predict the Ht. All 20 input combinations were used for modeling by ANFIS
and GWO-ANFIS to evaluate the capability of GWO in optimizing the ANFIS parameters, which
shows better performance. The results of ANFIS modeling are presented in Table 4. Among the
different input combinations, the first three models were not capable to reproduce satisfying results.
Negative values were assigned to the NSE and CI, which show the poor application of models. The
same procedure is visible in M13, M14, M15, M18, M19 and M20. However, the M4 to M11, M16 and
M17 performed well. Among these combinations, M4 is the best and M8, M10 and M9 are the next in
row. It should be noted that although the M4 was the best based on the evaluation criteria, according
to Table 2, M17 was selected as the best model. This was because all the inputs of M17, i.e., Qt-3, Ht-
2 and Ht-1, have at least a one-month lag. In addition, the results of M4 and M17 were not
considerably different. This pattern was repeated for the test phase. Consequently, it can be
concluded that, ANFIS was capable to forecast the hydropower generation satisfactorily.
In the next step, the coupled model of GWO-ANFIS was utilized for hydropower generation
forecasting. Results are presented in Table 5. According to Table 5, the model performed well in all
input combinations. As the d, NSE and CI values were positive in all the models, the new modeling
technique of GWO-ANFIS provided a superior capability in forecasting hydropower generation,
while the ANFIS results failed in nine models. In addition, based on the evaluation criteria, the
accuracy of forecasting was higher for GWO-ANFIS.
The time series of observed and forecasted hydropower in train and test phases for M4, M8, M10
and M117 are presented in Figures 6 and 7. Both ANFIS and GWO-ANFIS performed well, while the
GWO-ANFIS was superior due to less error. In addition, it can be observed that the M4 and M10
presented better input combinations, while for dam operation and reservoir management, M17 was
more practical.
Although Figures 6 and 7 and Tables 4 and 5 show the observed and forecasted values and
evaluation criteria for all models, the error distribution among models could not be discussed via
these figures and tables. Therefore, the box plot of error during the train and test phases was plotted
in Figure 8. In Figure 8, it can be observed that the GWO-ANFIS was superior to the ANFIS
considerably in almost all input combinations. Nevertheless, the error of ANFIS in nine models was
considerably higher than the GWO-ANFIS.
Energies 2019, 12, 289 1 of 20
Table 3. Correlation coefficients between parameters.
Ht Qt Pt Ht-1 Ht-2 Ht-3 Ht-4 Ht-5 Ht-6 Ht-12 Qt-1 Qt-2 Qt-3 Qt-4 Qt-5 Qt-6 Pt-1 Pt-2 Pt-3 Pt-4 Pt-5
Ht 1
Qt 0.11 1
Pt 0.05 0.13 1
Ht-1 0.66 0.01 0.1 1
Ht-2 0.34 0 0.07 0.66 1
Ht-3 0.15 0.02 0.02 0.34 0.66 1
Ht-4 0.06 0.02 0 0.16 0.35 0.66 1
Ht-5 0.02 0.01 0.02 0.06 0.16 0.35 0.67 1
Ht-6 0.01 0 0.08 0.02 0.06 0.16 0.35 0.66 1
Ht-12 0.18 0.01 0.06 0.14 0.08 0.04 0.02 0.01 0.01 1
Qt-1 0.27 0.46 0 0.11 0.01 0 0.02 0.02 0.01 0.09 1
Qt-2 0.31 0.14 0.09 0.27 0.11 0.01 0 0.02 0.02 0.15 0.46 1
Qt-3 0.31 0 0.19 0.31 0.26 0.11 0.01 0 0.02 0.17 0.14 0.46 1
Qt-4 0.24 0.02 0.24 0.31 0.31 0.26 0.11 0.01 0 0.13 0 0.14 0.46 1
Qt-5 0.11 0.11 0.18 0.24 0.31 0.31 0.26 0.11 0.01 0.05 0.03 0 0.14 0.46 1
Qt-6 0.02 0.17 0.04 0.11 0.24 0.31 0.31 0.26 0.11 0 0.11 0.03 0 0.14 0.46 1
Pt-1 0 0.45 0.23 0.06 0.1 0.07 0.02 0 0.02 0.01 0.13 0 0.09 0.19 0.24 0.18 1
Pt-2 0.04 0.39 0.06 0 0.06 0.1 0.07 0.02 0 0 0.45 0.13 0 0.09 0.19 0.24 0.23 1
Pt-3 0.11 0.29 0 0.04 0 0.06 0.1 0.07 0.02 0.03 0.39 0.45 0.13 0 0.09 0.19 0.06 0.23 1
Pt-4 0.2 0.14 0.06 0.1 0.04 0 0.06 0.1 0.07 0.08 0.28 0.39 0.45 0.13 0 0.09 0 0.06 0.23 1
Pt-5 0.21 0.02 0.2 0.2 0.1 0.04 0 0.06 0.1 0.12 0.14 0.28 0.39 0.45 0.13 0 0.06 0 0.06 0.23 1
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Table 4. Results of ANFIS modeling in train and test phases.
Train
ANFIS1 ANFIS2 ANFIS3 ANFIS4 ANFIS5 ANFIS6 ANFIS7 ANFIS8 ANFIS9 ANFIS10
RSQ 0.08 0.12 0.17 0.68 0.62 0.51 0.63 0.69 0.66 0.67
RMSE 179477 179882 179305 29260 32165 38263 31488 29768 30164 29991
MAE 171981 172397 171840 21000 23451 28172 22869 21539 21599 22521
RAE 4.10 4.11 4.11 0.50 0.56 0.67 0.55 0.51 0.52 0.54
d 0.31 0.31 0.31 0.90 0.88 0.83 0.88 0.90 0.89 0.89
NSE −11.02 −11.08 −11.01 0.68 0.61 0.45 0.63 0.67 0.66 0.67
CI −3.41 −3.42 −3.41 0.61 0.54 0.38 0.56 0.60 0.59 0.60
ANFIS11 ANFIS12 ANFIS13 ANFIS14 ANFIS15 ANFIS16 ANFIS17 ANFIS18 ANFIS19 ANFIS20
RSQ 0.66 0.12 0.22 0.26 0.23 0.64 0.65 0.35 0.22 0.32
RMSE 30579 51150 179856 179647 179438 31253 30884 179512 180465 180470
MAE 23091 40660 172323 172134 171954 22451 22071 172115 172932 172973
RAE 0.55 0.97 4.12 4.11 4.11 0.54 0.53 4.12 4.13 4.13
d 0.89 0.54 0.31 0.31 0.31 0.88 0.89 0.31 0.31 0.31
NSE 0.66 0.04 −11.06 −11.02 −11.01 0.64 0.64 −11.02 −11.11 −11.11
CI 0.58 0.02 −3.41 −3.41 −3.41 0.56 0.57 −3.41 −3.43 −3.43
Test
ANFIS1 ANFIS2 ANFIS3 ANFIS4 ANFIS5 ANFIS6 ANFIS7 ANFIS8 ANFIS9 ANFIS10
RSQ 0.12 0.15 0.21 0.73 0.70 0.64 0.67 0.72 0.69 0.66
RMSE 155453 155740 155021 31265 33984 36654 35367 32951 33508 35003
MAE 143490 143773 143018 24498 26694 28267 28096 25989 25890 26600
RAE 2.85 2.85 2.83 0.49 0.53 0.56 0.56 0.51 0.51 0.53
d 0.38 0.37 0.38 0.92 0.91 0.89 0.89 0.91 0.90 0.89
NSE −5.67 −5.69 −5.60 0.73 0.68 0.63 0.66 0.70 0.69 0.66
CI −2.13 −2.13 −2.11 0.67 0.62 0.56 0.59 0.64 0.62 0.59
ANFIS11 ANFIS12 ANFIS13 ANFIS14 ANFIS15 ANFIS16 ANFIS17 ANFIS18 ANFIS19 ANFIS20
RSQ 0.68 0.15 0.51 0.42 0.31 0.68 0.69 0.45 0.39 0.37
RMSE 34307 59395 154896 154929 154933 34157 33456 154793 155475 155535
MAE 25910 45123 142788 142914 142926 26613 25956 142809 143361 143448
RAE 0.51 0.89 2.82 2.83 2.83 0.53 0.51 2.82 2.83 2.83
d 0.90 0.64 0.38 0.38 0.38 0.90 0.90 0.38 0.38 0.38
NSE 0.68 0.03 −5.56 −5.60 −5.60 0.68 0.69 −5.55 −5.61 −5.61
CI 0.61 0.02 −2.10 −2.11 −2.11 0.61 0.62 −2.10 −2.11 −2.11
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Table 5. Results of GWO-ANFIS modeling in train and test phases. G-A is the abbreviation of GWO-ANFIS.
Train
G-A1 G-A2 G-A3 G-A4 G-A5 G-A6 G-A7 G-A8 G-A9 G-A10
RSQ 0.09 0.31 0.28 0.73 0.63 0.63 0.65 0.70 0.72 0.65
RMSE 49503 42889 43809 26857 31477 32559 30770 28414 27482 31016
MAE 40463 33764 35873 19773 22984 25600 22453 20854 20365 22675
RAE 0.97 0.81 0.86 0.47 0.55 0.61 0.54 0.50 0.49 0.54
d 0.39 0.68 0.66 0.92 0.88 0.84 0.88 0.91 0.91 0.88
NSE 0.09 0.31 0.28 0.73 0.63 0.60 0.65 0.70 0.72 0.65
CI 0.03 0.21 0.19 0.67 0.55 0.51 0.57 0.63 0.65 0.57
G-A11 G-A12 G-A13 G-A14 G-A15 G-A16 G-A17 G-A18 G-A19 G-A20
RSQ 0.64 0.18 0.48 0.42 0.33 0.68 0.61 0.32 0.41 0.37
RMSE 31073 47263 37224 39510 42411 29521 33028 42668 39952 41037
MAE 23219 37781 29617 30810 33846 21076 23585 32684 30033 31964
RAE 0.55 0.90 0.71 0.74 0.81 0.50 0.56 0.78 0.72 0.76
d 0.88 0.53 0.80 0.75 0.68 0.90 0.88 0.68 0.75 0.73
NSE 0.64 0.18 0.48 0.42 0.33 0.68 0.59 0.32 0.41 0.37
CI 0.57 0.09 0.39 0.32 0.22 0.61 0.52 0.22 0.30 0.27
Test
G-A1 G-A2 G-A3 G-A4 G-A5 G-A6 G-A7 G-A8 G-A9 G-A10
RSQ 0.11 0.21 0.26 0.79 0.69 0.71 0.70 0.75 0.76 0.70
RMSE 62420 58695 56473 28402 34128 40849 34151 30535 29928 34293
MAE 50699 45595 46289 21439 27079 32838 27480 24131 23811 27566
RAE 1.01 0.90 0.92 0.42 0.54 0.65 0.54 0.48 0.47 0.55
d 0.44 0.58 0.54 0.93 0.89 0.79 0.89 0.92 0.92 0.89
NSE -0.07 0.05 0.12 0.78 0.68 0.54 0.68 0.74 0.75 0.68
CI -0.03 0.03 0.07 0.72 0.61 0.43 0.61 0.68 0.69 0.60
G-A11 G-A12 G-A13 G-A14 G-A15 G-A16 G-A17 G-A18 G-A19 G-A20
RSQ 0.69 0.13 0.51 0.48 0.35 0.73 0.65 0.35 0.45 0.43
RMSE 33816 59590 47204 49583 54710 31377 36526 54756 48849 52456
MAE 26205 46902 37185 38988 43489 24547 28006 42243 37949 41320
RAE 0.52 0.93 0.73 0.77 0.86 0.49 0.55 0.83 0.75 0.82
d 0.90 0.51 0.68 0.64 0.56 0.92 0.89 0.55 0.68 0.61
NSE 0.69 0.02 0.39 0.32 0.18 0.73 0.63 0.18 0.35 0.25
CI 0.61 0.01 0.27 0.21 0.10 0.67 0.57 0.10 0.24 0.15
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M4
M10
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M8
M17
Figure 6. Observed and forecasted time series of hydropower generation using ANFIS.
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M4
M10
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M8
M17
Figure 7. Observed and forecasted time series of hydropower generation using GWO-ANFIS.
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Figure 8. Box plot of errors for ANFIS and GWO-ANFIS modeling in training and testing phases. F
and G refer to ANFIS and GWO-ANFIS, respectively.
The meta-heuristic optimization algorithm of GWO-ANFIS showed an acceptable efficiency in
the optimization of the unknown parameters in ANFIS. Although the number of optimization
parameters in ANFIS and GWO-ANFIS was the same, the main complexity quantifier was the
number of unknown parameters to be tuned for model training. The present research sought to
ensure that the numerical complexity of the two modeling approaches was similar. Furthermore, the
ANFIS models required the derivative calculation for unknown parameters, which increased the
computational time and space necessary for training. While the GWO-ANFIS models did not need
the derivative calculation, this would lead to less computation and faster convergence.
4. Conclusions
In this study, a coupled of adaptive neuro-fuzzy inference system and grey wolf optimization
was utilized for one month ahead hydropower generation. For this purpose, 53 years of monthly data
of inflow to the dam reservoir and the hydropower generation were used. Twenty input-output
combinations were considered to evaluate the model robustness and to find the best input-output
combination. Based on the results, GWO was capable to improve the ANFIS performance
Energies 2019, 12, 289 2 of 20
considerably. GWO-ANFIS performed well in all 20 combinations based on the evaluation criteria
while the ANFIS failed in nine out of 20 combinations. Additionally, the box plot of error in all
combinations shows the superiority of GWO-ANFIS. Overall, it can be concluded that, GWO-ANFIS
is capable to forecast the hydropower generation satisfactorily, which makes it a suitable tool for
policymakers. Furthermore, for the future research direction, it is important to mention that, not all
the rules in the model architecture are essential; thus, it is necessary to reduce trained models
complexity through eliminating the noncontributing rules which leads to the reduction of network’s
computational cost. To improve the proposed method, utilizing the other optimization algorithms
for creating novel hybrid prediction models, as well as applying ensemble models in this application
is suggested for the future research. In fact, the potential of ensemble machine learning models have
not yet been fully explored in the prediction of hydropower generation, which leaves great room for
future investigations. In addition, a limitation of our proposed model was that while the effective
factors for which the model was implemented were the most critical factors, there may be other
relevant factors that should be used. For instance, climate change and drought variations need to be
separated from the general trend of the data set. Therefore, the addition of these concepts is left for
future work.
Author Contributions: Conceptualization, M.D., H.R.-M. and F.H.; Data curation, M.D., H.R.-M. and F.H.;
Formal analysis, M.D., A.M., H.R.-M. and F.H.; Methodology, M.D., H.R.-M., S.S. and F.H.; Resources, H.R.-M.
and F.H.; Software, H.R.-M., M.D. and F.H.; Supervision, K.-w.C. and E.K.Z.; Visualization, F.H., A.M., S.S. and
K.-w.C.; Writing–original draft, M.D., H.R.-M., F.H. and A.M.; Writing–review & editing, M.D., H.R.-M., F.H.,
A.M., S.S. and K.-w.C.
Conflicts of Interest: The authors declare no conflict of interest.
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(CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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It finds successful applications in healthcare, where AI enhances diagnostics and treatment planning, cybersecurity by enhancing threat detection and protection of data, energy, where it is used to optimize renewable energy systems. Applied AI integrates advanced computational techniques with domain-specific knowledge and closes the gap between theory and practice. Technological advancement and complex challenges faced by society are driven forward by Applied AI. The motivation for the literature review in applied AI is to address the dynamic and interdisciplinary nature of the field that has undergone rapid growth over the last decade. Applied AI cuts across a wide domain of cybersecurity, healthcare, energy, and construction, each with unique challenges and transformative potential. However, the large and fragmented body of research makes it hard to draw overarching insights or identify emerging trends. The following review systematically analyzes and synthesizes contributions from the author's research and fundamental studies in the field to give an overview of the evolution of applied AI, showing how advances in theory have translated into impactful real-world solutions. The originality and added value of this review lie in consolidating findings from various disciplines into one holistic view to bridge the gaps among these isolated studies. Success stories are highlighted, persistent challenges identified, and patterns unveiled that may direct further research and application. Reviewing such barriers to scalability, ethical considerations, and technological constraints develops a more accurate understanding of the current status and potentials of applied AI. It thereby contributes to the scientific debate and, equally, provides actionable insights for practitioners and policymakers in their search to deploy AI responsibly across many domains. Applied AI focuses on the implementation of AI techniques to address practical, real-world challenges across various industries. By applying machine learning, deep learning, and optimization algorithms, applied AI creates solutions that enhance efficiency, accuracy, and decision-making. In cybersecurity, for instance, Nadeem et al. (2023) developed a two-layer symmetric cryptography algorithm to protect sensitive data, while Farooq et al. (2023) employed a fused machine learning approach to enhance intrusion detection systems. These advancements illustrate how applied AI directly contributes to improving security frameworks and combating modern threats. In construction, energy, and materials science, applied AI has demonstrated its ability to optimize processes and innovate solutions. Kazemi et al. (2023) applied AI techniques to analyze the effects of medium-density fiberboard waste ash on concrete properties, aiding in sustainable construction practices. Similarly, Dehghan Manshadi et al. (2022) utilized deep learning to model offshore hybrid wind-wave energy systems, advancing renewable energy technologies. These applications underscore how applied AI bridges computational power and domain knowledge to address pressing challenges in engineering and environmental sustainability. Beyond technical industries, applied AI has found success in healthcare, agriculture, and organizational decision-making. Rehman et al. (2022) integrated blockchain with federated learning to create a secure and scalable healthcare 5.0 system, demonstrating AI's potential to enhance data security in biomedical contexts. In agriculture, Mallah et al. (2022) employed
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Hydropower operation and planning requires streamflow forecasts at both short (typically, the first 4–5 days) and long ranges (a few months or a season ahead) over different spatial scales. Operational streamflow forecasting services a variety of decisions, made under conditions of risk and uncertainty, e.g., flood protection, dam safety, system’s operation, optimization, and planning of power production. In areas where snow falls in significant quantities during winter, spring freshet poses additional challenges given the uncertainties related to the timing and volume of melt water flowing into hydropower reservoirs. Reservoir levels need to be gradually lowered over the winter to make it possible to store snowmelt water in spring. Reservoirs are thus important regulators of streamflow natural variability. They act as a storage place to water that can be used later to meet periods of higher electricity demands or to sell surplus electricity to the power distribution grid. They also usually are multipurpose, and their operation must take into account the different water uses, which can, in some cases, be conflictual. The importance of accurate and reliable streamflow forecasts is therefore unquestionable. The hydropower sector has long recognized that streamflow forecasting is intrinsically uncertain and the use of ensemble forecasts is progressing fast. Key challenges today are related to the integration of state-of-the-art weather services, the implementation of systematic, advanced data assimilation schemes, to the assessment of the links between forecast quality and value, and to the enhancement of risk-based decision-making.
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This book, compiles, presents, and explains the most important meta-heuristic and evolutionary optimization algorithms whose successful performance has been proven in different fields of engineering, and it includes application of these algorithms to important engineering optimization problems. In addition, this book guides readers to studies that have implemented these algorithms by providing a literature review on developments and applications of each algorithm. This book is intended for students, but can be used by researchers and professionals in the area of engineering optimization.