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Applications of Artificial Neural Networks to Renewable Energies: History
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Contributor: Íñigo Manuel Iglesias-Sanfeliz Cubero , Andrés Meana-Fernández , Juan Carlos Ríos-Fernández ,
Thomas Ackermann
, Antonio José Gutiérrez-Trashorras

Artificial neural networks (ANNs) have become key methods for achieving global climate goals. The applications of ANNs to renewable energies such as solar, wind, and tidal energy were studied. 

  • machine learning
  • artificial neural network
  • big data
  • energy transition

1. Introduction

Currently, the most accurate, most efficient, and most powerful machine for performing operations is the human brain, which can provide solutions to problems that PCs are not capable of solving. Researchers and scientists have developed artificial intelligence (AI) models to reproduce, to some extent, the processes that take place in the human brain [1]. Currently, AI is divided into different groups: artificial neural networks (ANNs) and different hybrid systems. Among them, ANNs are the best method as they are accurate, fast, and simple and have the ability to model a multivariate system [2].
The neural network (NN) concept has more than half a century of history; however, it is only in the last 20 years that the largest number of applications have been developed in the fields of defense, engineering, mathematics, economics, medicine, meteorology, and many others.
The history of neural networks dates to the 1940s. It was Warren McCulloch and Walter Pitts who first built a very simple neural network using electrical circuits [3]. Later, Donald Hebb proposed that neural pathways strengthen with each use, an important concept in human learning [4]. Then, in the 1950s, Nathaniel Rochester of IBM Research Laboratories first attempted to simulate complex neural networks [5]. In 1959, Bernard Widrow and Marcian Hoff developed models called “ADALINE” and “MADALINE” [6][7]. After the publication of the book “Perceptrons” by Marvin Minsky and Seymour Papert in 1969, there was a period of slowdown in research. This book argued that the concept of a single perception approach to neural networks did not have an effective correlation in multilayer neural networks [8]. In the 1970s, two competing models emerged in the conception of neural networks, called symbolism and connectionism [9]. The controversy ended with the acceptance of the symbolic paradigm as the most viable line of research. In the early 1980s, however, connectionism resurfaced, based on Werbos’s 1974 studies. These studies made it possible to rapidly develop the formation of multilayer neural networks using the so-called “backpropagation” algorithm [10][11]. Since then, the field of neural networks has seen significant advances. Some of these advances were the introduction and development of max-pooling in three-dimensional data recognition [12]. On the other hand, advances included the development of deep learning and its application to a wide variety of fields such as renewable energy [12].
However, ANNs are not the only ones that learn by example. There are other methods, such as the following. Supervised learning: this method trains algorithms on the basis of sample input and output data labeled by humans [13]; deep learning: it uses neural networks to learn from the data and to improve performance by increasing the number of samples that are available during the learning process [14]; machine learning paradigms for unsupervised classification such as conceptual clustering [15], which is an unsupervised learning method that focuses on generating concept descriptions for the generated classes. Other machine learning paradigms that learn by example are semi-supervised learning [16], active learning [17], transfer learning [18], and online learning [19].
The data collection needed to train ANNs must be a sufficiently complete and consistent set of information [20]. The development of machine learning models requires historical data from several years, supplemented by information that is more recent. This information amounts to thousands of data points [20]. In the context of different energy transition scenarios and geographical locations, it is essential to ensure that the data collection is as complete, impartial, and representative as possible. This is achieved by managing diverse and reliable sources of information. Some of the most used sources are public repositories, data from official agencies and organizations, research centers, and geographic databases [21][22]. To ensure that the data are impartial, complete, and representative of all the energy transition scenarios analyzed, it is necessary to perform careful data selection and apply measures such as domain adaptation and data augmentation [23]. Model performance can also be improved, and training data can be augmented by using pretrained models in other domains [23]. The authors, based on the objective pursued and the exact geographical location, have analyzed all data obtained in the various studies, with latitude and longitude coordinates provided in many of them. Similarly, much of the data provided are based on measurements made by the authors themselves when using AI.
ANNs have gained momentum to the point where they have become popular and useful models for classification, clustering, recognition, and prediction in a wide variety of applications [24]. ANNs are increasingly being used for different applications due to their ability and effectiveness in solving different problems. They have proven to be very efficient when it is complex to cull through a mass of existing data, for example, in the evaluation of public transportation of people and goods [25], image recognition [26], medical analysis [27], efficiency analysis in nonlinear contexts, or to adjust production functions, among other applications [28][29].
ANN consists, in most cases, of an input layer, at least one hidden layer (in the case of a simplified model), an output layer, the weight, the connection biases, the activation function, and the sum node. The layers in turn are made up of several connected units (called neurons) [30], considered to be the fundamental building blocks for the correct functioning of a neural network. The link between neurons is achieved by so-called connecting links [2]. The basic diagram of a neuron is shown in Figure 1 [31].
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Figure 1. Schematic diagram of a neuron [31].
The main characteristic feature of ANNs compared to other approaches is their ability to learn by example. ANNs can be applied to any situation where there is a relationship between input and output variables [32]. The procedure for the learning process is what is known as a learning algorithm, the purpose of which is to alter the synaptic weights of the networks in order to achieve a previously set goal [33].
ANNs must be trained by feeding the network a set of quantified data to achieve the desired output using a pool of input data [34]. The learning process continues until the NN output matches the expected output [35]. The problem with ANN models lies precisely in overtraining, i.e., when the network capacity for training is too high or too many training iterations are allowed per network [36]. The degree of training accuracy obtained in the different applications where the ANN technique is used is very high, in the order of 10−5 to complete the training processes [2]. NNs can be grouped into different categories depending on their structure [37]. This classification is shown in Figure 2. The most commonly used are single-layer feed-forward networks, multilayer feed-forward networks, radial basis networks, and dynamic (differential) or recurrent neural networks. Of these, single-layer power supply networks are the best known and most widely used. Single-layer power supply networks were the first and simplest networks devised. Information travels in only one direction: from input nodes, through hidden nodes, to output nodes. This type of NN can be designed based on different unities, and among them, the perceptron is the most famous and simplest example [38]. Rosenblatt created the perceptron in 1958, thanks to the creation of the training algorithm [39]. The perceptron is composed of a single neuron with adjustable synaptic weights and thresholds [40]. The most frequently used algorithm is the so-called backpropagation (BP) algorithm [41]. The BP algorithm consists of training and correcting the weights until the error function is below the desired tolerance limit [37].
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Figure 2. Artificial Neural Networks classification.

2. Applications of ANNs to Renewable Energies

This section details the different research carried out in the field of renewable energies and more specifically in wind, solar, and tidal energy. These three types of renewable energies have been selected as they are the ones that have the largest contributions to the national energy balances [42] as well as due to the greater abundance of works found.

2.1. Applications of ANNs for Wind Power and Speed Prediction

Within the renewable energy mix, wind energy is currently considered the most economical way to generate electricity. Recently, there has been new research into methods capable of predicting wind speed. This is of great importance due to the continuous growth of wind power generation worldwide [43]. For proper operation of wind farms, a constant stream of data about wind speed and wind direction is required. Artificial neural networks are an excellent method for short-, medium-, and long-term wind speed forecasting.
The following Table 1 summarizes the main research pieces found. The studies have been classified according to the ANN structure, journal and region, input and outputs for the network, and the activation function employed.
Table 1. Uses of artificial neural networks for wind power and speed prediction.
  Authors
and Year		 ANN Type and Structure Journal Country/
Region		 I/O
Setting		 Activation Function Notes
Input Output
1 [44] Multilayer Perceptron (MLP)
3-4-1		 Renewable Energy Muppandal,
India		 Wind speed (Ws), relative humidity (RH),
generation hours		 Energy output of wind farms logsig
(hidden layer)
purelin
(output layer)		 Trained by BP
algorithm
Input data
normalized to
[0, 1]
2 [45] ANN
4-X-2		 Renewable Energy Turkey Longitude (lon), latitude (lat), altitude (A),
measurement height		 Ws, related power logsig
(hidden and output layer)		 Trained by BP
algorithm
Input and Output data normalized to [0, 1]
3 [46] MLP
5-10-5-1		 Renewable Energy Turkey Ws, month (M) Ws logsig
(hidden layer)
purelin
(output layer)		 Resilient propagation (RP)
algorithm was adopted
4 [47] Radial Basis Function (RBF)
1-7-2		 Renewable and
Sustainable Energy
Reviews		 Iran Ws Proportional and integral (PI) gains - Use Gaussian function for hidden layer
Gravitational search algorithm (GSA) is adopted
5 [48] MLP
3-(2-100)-24		 Renewable Energy Medina city, Saudi Arabia Mean daily Ws Ws
prediction of the next day		 tansig
(hidden
layer)
purelin
(output
layer)		 Input data
normalized to
[0, 1]
Trained by Levenberg–Marquardt (LM) BP algorithm
Compared and
outperforms
support vector machine (SVM)
SVM used Gaussian kernel
2000 days used for training and 728 days used for
testing
6 [49] MLP
6-7-5-1
MLP
4-7-5-1		 Renewable and
Sustainable Energy
Reviews		 Alberta,
Canada		 Wind power (Wp)
WP1 (t − 1),
WP1 (t − 2),
WP1 (t − 3),
WP1 (t − 4),
WP1 (t − 5),
WP1 (t − 6)		 Short-term forecasting of the Wp time series tansig
(hidden layer)
purelin
(output layer)		 Input data
normalized to
[−1, 1]
Imperialist
competitive
algorithm (ICA), GA, and particle swarm
optimization (PSO) are
employed for training the neural
network
1200 data used for training and 168 data used for
testing
7 [50] ANN
2-(16-32)-(16-32)-1		 Renewable Energy Coquimbo, Chile Ws, wind
direction (Wd)		 Turbine power - ADAM algorithm is adopted
103,308 data used for training and 52,560 data used for testing
8 [51] RBF
2-3-1
MLP
2-4-1
ADALINE
2-4-1		 Applied Energy North Dakota, USA Mean hourly Ws Forecast value of next hourly average Ws - Trained by LM algorithm
5000 data used for training and 120 data used for
testing
9 [52] MLP
5-5-3		 Renewable Energy Guadeloupean archipelago, French West Indies Ws, 30 min moving average speed Wp (t + kt) tansig
(hidden layer)
purelin
(output layer)		 Bayesian regularized (BR)
10 [53] ANN
7-20-1		 Renewable Energy China Actual Ws, Wp Ws - Trained by BP algorithm
11 [54] MLP
6-7-1		 Renewable Energy Albacete, Spain Wsp1, Wsp2, temperature (T) Tp2, solar cicle1, solar cicle2, Wdp1 Ws forecast (48 h later) - LM algorithm is adopted
12 [55] ANN
3-3-1
ANN
3-2-X
ANN
3-1
ANN
2-1		 Renewable Energy Oaxaca, México Previous
values of hourly Ws		 Current value of Ws - 550 data used for training and 194 data used for
testing
13 [56] ANN
-		 Renewable Energy Basque
Country, Spain		 Ws data in the last 3 h Ws in 1 h sigmoid
(output layer)		 Trained by BP
algorithm
14 [57] MLP
X-8-X		 Renewable Energy Rostamabad, Iran Standard
deviation,
average, slope		 Ws (k + l), …, Ws (k + 2), Ws (k + 1) - Trained by BP
algorithm
672 patterns used for training
15 [58] MLP
5-3-3-1		 Communications in
Nonlinear Science and Numerical Simulation		 Italy Ws, RH, generation hours, T,
maintenance hours		 Total wind energy tansig (first hidden layer)
sigmoid
(second hidden layer)
purelin
(output layer)		 Trained by BP
algorithm
16 [59] MLP
6-25-1		 Renewable Energy Himachal
Pradesh, India		 Average temperature (TAVG),
maximum temperature (Tmax),
minimum
temperature (ax), air
pressure (Pair), solar
irradiance (G), A		 Average daily Ws
for 11 H.P. locations		 - Trained by LM algorithm
Scaled conjugate gradient (SCG)
algorithm is adopted
Input and target data are
normalized to
[−1, 1]
60% data used for training, 20% used for testing, and 20% used for
validation
17 [60] MLP
4-15-15-1		 Applied
Energy		 Nigeria lat, lon, A, M Mean monthly Ws tansig
(hidden layers)
purelin
(output layer)		 SCG and LM algorithms are adopted
Input and target data normalized to [−1, 1]
18 [61] MLP
14-15-1		 WSEAS Transactions on Systems Portugal Average hourly values of Ws Average hourly Ws - Trained BP algorithm
87.75% patterns used for training, 9.75% used for validation, and 2.5% used for
testing
19 [62] MLP
5-6-6-6-2		 - Cyprus M, mean monthly
values of Ws at two levels
(2 and 7 m)		 Mean monthly
values of Ws of a third station		 tansig
(hidden layer)
logsig
(output layer)		 Trained by BP algorithm
90% patterns used for training and 10% patterns used for testing
20 [63] MLP
9-10-1		 Energy
Conversion and Management		 Marmara,
Turkey		 9 stations Ws Ws - Trained by BP
algorithm
21 [64] MLP
4-8-1		 Theoretical and Applied Climatology Tabriz,
Azerbaijan,
Iran		 Pair, air
temperature (Tair), RH,
precipitation		 Monthly Ws logsig
(hidden layer)
purelin
(output layer)		 Trained by LM
algorithm
Input and output data normalized to [0, 1]
75% of data used for training and 25% used for
testing
22 [65] MLP
31-63-31		 Knowledge-Based
Systems		 Minqin, China Historical daily average Ws during March
previous year		 Daily average Ws
during March target year		 tansig
(hidden layer)
logsig
(output layer)		 Trained by BP
algorithm
23 [66] MLP
X-25-1		 2014 4th IEEE International Conference on
Information
Science and Technology		 Colorado, USA T, RH, Wd, wind gust, pressure (P), historical Ws Ws tansig
(hidden layer)		 Trained by BP with momentum
1000 input/output pairs used for training and 200 input/output pairs used for testing
The applications have different characteristics in several aspects, such as the ANN structure, the input data, the activation function used, and the training algorithm. As can be seen from the literature, various studies on wind speed prediction have been carried out for more than twenty years in different parts of the world, most of them located in Turkey, India, China, or Iran.
The main characteristics of the networks studied are detailed below.
  • ANN type: from the 23 references analyzed, the MLP network has been used in 17 of them, followed by the RBF in two of them. Five of them did not specify the type of ANN used.
  • Structure of the ANN: the predominant type is simple with one hidden layer (70%) and the rest with two hidden layers (26%) with the exception of the investigation of [41], which uses three hidden layers. The number of neurons in the hidden layer is usually around 15, while in other cases more than 63 are selected [67].
  • Amount of data: the percentage of research that makes use of data for validation is 8.69%.
  • I/O configuration: the inputs to the models usually take in situ measured features such as past wind speeds, temperature, relative humidity, altitude, month, or pressure.
  • Activation function: only 13 of the 23 cases detail the activation function used. In the hidden layer, linear functions are used, with tansig and logsig being the most commonly used, while in the output layer, linear functions of the purelin type are adopted.
Figure 3 details the most common inputs and outputs used by ANNs in wind power and wind speed prediction and the operating scheme.
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Figure 3. Inputs and outputs in ANNs applied to wind energy and wind speed prediction.
ANNs are highly recommended for predicting wind speed and power generation for several reasons, including self-learning, low error, and high efficiency predictability [68].

2.2. Applications of ANNs for Solar Energy Systems

Within solar energy, the ANN technique has proven to be an alternative to conventional methods, providing great benefits in terms of precision, performance, and modeling. The study indicates that the advantage of ANN techniques over conventional techniques is that they do not require knowledge of internal system parameters, require less computational effort, and offer robust outputs to multivariate problems. NN modeling requires data representing the history, the current performance of the real system, and a correct selection of a NN model. Mellit et al. [69] conducted an overview of the different AI techniques for sizing PV systems. The research shows that one of the advantages of AI in modeling PV systems is that it allows good optimization in isolated areas, where meteorological data are not always available. Mellit and Kalogiriu [70] have applied AI techniques to model, predict, simulate, optimize, and control photovoltaic systems.
The applications of ANNs to solar energy go beyond that, as there is also research such as the one carried out in [71], in which the application of the ANN technique seeks to optimize and predict the performance of the different devices involved in a solar energy system such as solar collectors, heat pumps, or solar air. The research shows how the application of ANNs can save time and reduce the financial costs of the system since it is not necessary to carry out so many experimental tests to determine the relationship between the input and output variables. Another application of ANNs is shown in the research of [72], where the performance of solar collectors is predicted, thus improving the efficiency of the system as a whole. The developed model also showed advantages over conventional computational methods in terms of calculation and prediction time.
Solar radiation data are very important because in most cases they are not available due to the lack of a meteorological station. It is therefore necessary to have techniques to accurately predict solar radiation. ANNs are the solution to the problems of conventional methods [73].
Different ANN models have been applied for solar irradiance prediction, such as the MLP neural network, the RBF neural network, or the general regression neural network (GRNN). The different studies have been classified, taking into account different factors such as network structure and type, input/output configuration, or the activation function and tuning algorithm employed, as is shown in Table 2.
Table 2. Uses of artificial neural networks for solar energy prediction.
  Authors
and Year		 ANN Type and
Structure		 Journal Country/
Region		 I/O Setting Activation Function Notes
Input Output
1 [74] RBF
6-11-24
RBF
6-15-24		 Solar Energy Huazhong, China G (t + 1), Ws (t + 1), Tair (t + 1), RH (t + 1), t, power (Pw) (t) Pw1 (t + 1), Pw2 (t + 1), …, Pw24 (t + 1) - k-fold (validation)
Input and output data
normalized to [0, 1]
2 [75] MLP
2-3-1		 Renewable Energy Jaen, Spain G, module cell
temperature
(TC)		 G, ambient temperature (Ta) - Trained by LM BP
algorithm
3 [76] MLP
3-3-1
MLP
4-3-1		 Energy Corsica Island, France
Bastia
Ajaccio		 RH, sunshine duration (S), nebulosity (Y)
Y, S, P,
differential pressure (DGP)		 Global
radiation
(GR)		 tansig (hidden layer)
purelin (output layer)		 Trained by LM algorithm
Input data normalized to
[−1, 1]
80% data used for training, 10% for validation, and 10% used for testing
4 [77] MLP
8-3-1		 Solar Energy Ajaccio,
Corsica Island, France		 Clearness index (KT) KTt−1, KTt−2, KTt−3, KTt−4, KTt−5, KTt−6, KTt−7, KTt−8 Daily global solar
radiation (GSR)		 purelin (output layer) Trained by LM algorithm
Use Gaussian function for hidden layer
Input data normalized to [0, 1]
80% data used for training, 10% for validation, and 10% used for testing
5 [78] MLP
3-11-17-24		 Solar Energy Trieste, Italia G, Tair, hour or day (t) G1 (t + 1), G2 (t + 1), …, G24 (t + 1) - Trained by LM BP
Algorithm k-fold validation
Input and output data
normalized to [−1, 1]
6 [79] RBFN
(2-3-4)-
(4-5-7)-1
MLP
(2-3-4)-
(2-3-5)-1		 Energy Al-Medina, Saudi Arabia Tair, S, RH, t Daily global solar
radiation
(GD)		 - 1460 data used for training and 365 data used for testing
7 [80] MLP
6-5-1		 Applied
Energy		 Turkey lat, lon, A, M, S, T G logsig (hidden layer) Trained by BP algorithm
SCG, Pola–Ribiere
conjugate gradient (CGP), and LM algorithms are adopted
Input and output data normalized to [−1, 1]
8 [81] MLP
3-20-1		 Renewable and
Sustainable Energy Reviews		 Morocco lon, lat, A Mean annual and monthly G - Trained by BP algorithm
Input and output data
normalized to [0, 1]
9 [82] MLP
2-36-1
MLP
3-20-1		 Energy Sources, Part A: Recovery, Utilization, and Environmental
Effects		 Abha, Saudi Arabia Tair, RH, hour or day (t) Diffuse solar radiation
(DSR)		 logsig (hidden layer) Trained by BP algorithm
1462 days used for training and 250 days used for testing
10 [83] MLP
5-8-1		 Expert
Systems with Applications		 Anatolia,
Turkey		 lat, lon, A, S, average cloudiness G tansig (hidden layer)
purelin (output layer)		 Trained by BP algorithm
11 [84] MLP
7-5-1		 Applied
Energy		 Nigeria lat, lon, A, M, S, T, RH G tansig (hidden layer)
purelin (output layer)		 SCG and LM algorithms are adopted
Input data normalized to [−1, 1]
11,700 datasets used for training and 5850 datasets used for validation and
testing
12 [85] MLP
4-X-1		 International Journal of Photoenergy Malaysia lat, lon, day or hour (t), S KT logsig (hidden layer) Trained by BP algorithm
13 [86] MLP
4-4-1		 International Journal of Computer Applications India lat, lon, S, A G tansig (hidden layer)
purelin (output layer)		 LM algorithm is adopted
14 [87] MLP
5-40-1		 Energy Egypt GSR, like long-wave atmospheric emission, Tair, RH, P Diffuse
fraction (KD)		 sigmoid (output layer) Trained by BP algorithm
15 [88] MLP
7-15-1		 Solar Energy Jaen, Spain t (day), t (hour), KT, hourly clearness index (kt) kt−1, kt−2, kt−3, S Solar
radiation maps		 - Trained by BP algorithm (with momentum and
random presentations)
Input data normalized to [0, 1]
16 [89] MLP
6-X-1		 Solar Energy Helwan, Egypt Wd, Ws, Ta, RH, cloudiness, water vapor G sigmoid (output layer) Trained by LM BP
algorithm
Input data normalized to [0, 1]
17 [90] MLP
2-X-1
MLP
3-X-1
MLP
3-X-X-1		 Solar Energy Athalassa,
Cyprus		 S, theoretical sunshine
duration (S0d), M, Tmax		 GD tansig (hidden layer) Trained by BP algorithm
90% data used for training and 10% used for testing
18 [91] MLP
7-9-1		 Renewable Energy India lat, lon, A, M, S,
rainfall
ratio, RH		 KT tansig (hidden layer)
purelin (output layer)		 Trained by BP algorithm
19 [92] MLP
2-5-1		 Energy Policy China Kt, S (%) Monthly mean daily KD tansig (hidden layer)
purelin (output layer)		 Trained by BP algorithm
TRAINLM algorithm is adopted
Input and output data normalized to [0, 1]
20 [93] MLP
6-15-1		 Solar Energy Uganda S, Tmax, Total Cloud Cover (TCC), lat, lon, A Monthly
average daily GSR on a horizontal surface		 tansig (hidden layer)
purelin (output layer)		 Trained by LM BP
algorithm
Input data normalized to [−1, 1]
21 [94] MLP
6-6-1		 Applied
Energy		 Turkey lat, lon, A, M, DSR, mean beam radiation G logsig (hidden layer)
purelin (output layer)		 SCG and RP algorithms are adopted
22 [95] GRNN
6-1.0-1		 Energy Turkey lat, lon, A, surface emissivity (ε4), surface emissivity (ε5), land surface
temperature		 G - -
23 [96] MLP
7-4-1		 Energy
Conversion and Management		 Iran Tmax, Tmin, RH, VP,
total precipitation, Ws, S		 GSR logsig (hidden layer)
purelin (output layer)		 Trained by BP algorithm
65 months used for training and 7 months used for testing
24 [97] ANN
6-6-1		 Applied Energy Turkey lat, lon, A, M, S, T G logsig (hidden layer) SCG, CGP, and LM
algorithms are adopted
Trained by BP algorithm
Input and output data normalized to [−1, 1]
25 [98] MLP
3-6-1		 Renewable Energy Khuzestan, Iran Tmax, Tmin, extra-terrestrial
radiation (Ra)		 GSR logsig (hidden layer) Trained by LM BP
algorithm
Input data normalized to [0, 1]
70% data used for training and 30% patterns used for testing
26 [99] MLP
5-3-1		 Energy
Procedia		 Bechar,
Algeria		 M, t (day),
t (hour), T, RH		 GSR tansig (hidden layer)
purelin (output layer)		 Trained by LM BP
algorithm
81% data used for training and 19% used for testing
27 [100] MLP
9-11-1		 Renewable and
Sustainable Energy
Reviews		 Republic of
Indonesia		 T, RH, S, Ws,
precipitation, lon, lat, A, M		 GSR - Trained by BP algorithm
28 [101] RBF
4-50-2		 Energy Sources, Part A: Recovery, Utilization, and Environmental Effects Saudi Arabia Ta, RH, GSR, t DSR, direct normal
radiation (DNR)		 - Use Gaussian function for hidden layer
1460 values used for
training and 365 values used for testing
29 [102] MLP
8-15-1		 Renewable Energy Sultanate of Oman Location (L), M, P, T, VP, RH, WS, S GR - Trained by BP algorithm
In contrast to the previous case, there is more literature available and the existing research from 1998 to 2012 has been collected. Most of the studies focus on countries that enjoy strong and prolonged hot climates such as the countries bordering the Mediterranean Sea as well as Saudi Arabia and China. As in the previous section and as mentioned at the beginning, the different applications are analyzed. The main characteristics of the networks studied are detailed below.
  • ANN type: in most of the investigations, the MLP network has been used (24 out of 29 cases) followed by the RBF.
  • Structure of the ANN: most studies use simple structures with a single hidden layer (96%), and the remaining with two hidden layers. The number of neurons in the hidden layer is usually in the order of 10, reaching 50 neurons in the research of [101]. In some cases, the number of neurons in the hidden layer is not specified, as in [89][90].
  • Amount of data: the percentage of research that make use of data for validation is 6.9%.
  • I/O configuration: altitude, latitude, longitude, relative humidity, or month of the year are used as the most common inputs.
  • Activation function: only 19 of the 29 investigations detail the activation function used. In the hidden layer, linear functions are used, with tansig and logsig being the most commonly used, while in the output layer, linear functions of the purelin type are adopted.
Figure 4 details the most common inputs and outputs used by ANNs in solar energy prediction and the operating scheme.
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Figure 4. Inputs and outputs in ANNs applied to solar energy systems.

2.3. Applications of ANNs for Wave Prediction

Tidal energy, like other renewable energies, is fundamental to achieving the European climate targets for 2030 and 2050. Recently, the use of NNs for wave height (H) and period prediction has gained importance. ANNs have also been applied in different fields of ocean, coastal, and environmental engineering [103]. The following table summarizes the main research pieces found. The studies have been classified according to the ANN structure, journal and region, input and outputs for the network, and the activation function employed. The following Table 3 shows the H predictions.
Table 3. Uses of artificial neural networks for wave height prediction.
  Authors
and Year		 ANN Type
and Structure		 Journal Country/
Region		 I/O Setting Activation Function Notes
Input Output
1 [104] ANN
28-15-4
28-9-4
28-4-4
28-7-4		 Journal of Atmospheric and Oceanic Technology Gulf of Maine, Gulf of Alaska, Gulf of Mexico 7 days of significant H 6, 12, 18, 24 h forecast logsig
(hidden and output layer)		 Input data normalized to [0, 1]
Conjugate gradient
algorithm with Fletcher–Reeves is adopted
2 [105] MLP
3-5-5-2		 Ocean
Engineering		 Bombay, India Deep water wave height (Ho), wave energy
period (Te)		 Breaking wave height (Hb), water depth at the time of breaking (db) sigmoid
(output layer)		 Trained by BP
algorithm
Input and output data normalized to [0, 1]
3 [106] MLP
48-97-24		 Ocean
Engineering		 Ireland 48 h history wave
parameters		 H and zero-up-
crossing peak wave period (Tp) over hourly intervals from 1 h to 24 h		 logsig
(hidden layer)
purelin
(output layer)		 Trained by resilient BP algorithm
4 [107] MLP
6-5-1		 Proceedings of the
Institution of Civil
Engineers-Maritime Engineering		 Anzali, Iran H, Tp Energy flux (Fe) over horizon of
1 to 12 h		 sigmoid
(output layer)		 Conjugate gradient
algorithm is adopted
80% data used for training and 20% used for testing
5 [108] MLP
2-4-3
MLP
4-4-4		 Ocean
Engineering		 Karwar, India Ws 3-hourly values of H and average cross-period - Trained by BP
algorithm
80% data used for training and 20% data used for testing
6 [109] Deep Neural Network (DNN)
6-64-32-32-1		 Ocean
Engineering		 Pacific and
Atlantic coasts and the Gulf of Mexico		 H, Te, Fe, weighted average
period, Tp, Ws, Wd		 Fe, Te, H - SCG BP algorithm is adopted
Input data normalized to [0, 1]
75% data used for training and 25% data used for testing
7 [110] MLP
3-300-300-2		 Ocean
Engineering		 Lake Michigan, United Sates of America Wind field, db, ice
coverage		 H, Te ReLU
(hidden
layer)		 Stochastic gradient-based algorithm is adopted
80% data used for training and 20% data used for testing
8 [111] MLP
1-x-1		 Marine Structures Goa, India H Fe sigmoid
(output layer)		 Trained by BP cascade correlation algorithms
80% patterns used for training and 20%
patterns used for
testing
9 [112] MLP
6-5-1		 Ocean
Engineering		 Persian Gulf Ht, Ht−1, Ht−2, Utcos(Φt − θ), Ut−1cos(Φt – 1 − θt),
Ut−2cos(Φt − 2 − θ2)		 H for the next 3, 6, 12, 24 h sigmoid
(output layer)		 Conjugate gradient and LM algorithms are adopted
80% data used for training and 20% data used for testing
10 [113] MLP
3-4-4-1		 Applied
Soft
Computing		 Spain H, Te, θm Fe tansig
(hidden layer)
purelin
(output layer)		 Trained by BP algorithm
67% data used for training and 33% data used for testing
11 [114] MLP
3-3-1		 Ocean
Engineering		 Lake Superior, USA Ws, weather station
index (W)		 H sigmoid
(hidden and output layer)		 Trained by BP algorithm
Input and output data normalized to [−1, 1]
Compared with SVM, Bayesian networks, and adaptive neuro-fuzzy inference
system (ANFIS)
345 patterns used for training and 54 patterns used for testing
12 [115] MLP
5-2-1		 Renewable Energy Brazil Wind shear velocity (U) U1, U2, Un, Y (t − 1),
Y (t − i)		 Wave energy potential tansig
(hidden layer)
purelin
(output layer)		 Trained by LM BP
algorithm
90% data used for training and 10% data used for testing
13 [116] MLP
X-15-1		 Applied Ocean
Research		 Canary Islands, Spain H, Tp Predict Fe tansig
(hidden layer)
purelin
(output layer)		 Gradient descent with momentum and BP
algorithm are adopted
89% data used for training and 11% data used for testing
Input and output data normalized to [−1, 1]
14 [117] MLP
4-4-1		 Applied Ocean
Research		 India H values of the preceding 3, 6, 12, and 24th hour H subsequent 3, 6, 12 and 24th hour - Trained by LM BP
algorithm
60% data used for training and 40% data used for testing
15 [118] RBF
21-13-1
MLP
21-9-1		 Marine Structures India H(1–21) H(SW3) - Use Gaussian function for hidden layer
BP, SCG, conjugate gradient Powell–Beale (CGB), Broyden–Fletcher–Goldfarb (BFG), and LM algorithms are adopted
80% data used for training and 20% data used for testing
16 [119] MLP
8-4-1
MLP
2-2-1		 Ocean
Engineering		 Taiwan Significant wave height (H1/3),
highest one-tenth wave height (H1/10), highest wave height (Hmax), mean wave height (Hmean)
(stations A and B)		 H1/3
(station C)		 sigmoid
(output layer)		 Trained by BP
algorithm
Input data normalized to [0, 1]
17 [120] MLP
2-5-1		 Marine Structures Yanam, India Ht, Ht−1 Ht+1 - Trained by BP
algorithm
Conjugate gradient and cascade
correlation algorithms are adopted
80% data used for training and 20% data used for testing
18 [121] ANN
9-1-1
ANN
4-1-1
ANN
9-8-1
ANN
9-1-1		 Applied Ocean Research Ratnagiri, Pondicherry,
Gopalpur, Kollam, India		 t − 24,
t − 21,
t − 18,
t − 15,
t − 12, t − 9,
t − 6, t − 3		 t + 24
(24 h ahead
predicted
error)		 logsig
(hidden layer)
purelin
(output layer)		 Trained by LM algorithm
Input data normalized to [0, 1]
70% data used for training and 15% used for validation and
testing
19 [122] MLP
4-9-3
MLP
4-7-1
MLP
2-5-1
MLP
4-8-1		 Applied Ocean Research Lake Ontario, Canada/USA Ws, Wd, fetch length, wind duration H, Tp,
(wave
direction) Θ		 tansig/
sigmoid
(hidden layer)
purelin
(output layer)		 Trained by BP
algorithm
10-fold cross-
validation used
Input data normalized to [0, 1]
611 data used for
training and 326 data used for testing
20 [123] MLP
1-3-1		 Ocean
Engineering		 Lake Superior, Canada/USA Ws H sigmoid (transfer function) Compared and
outperforms with model tree
4045 data used for training and 3259 data used for testing
While it is true that studies appear in the literature since 2001, unlike the two previous cases, there has been an increase in the number of studies carried out in recent years. Most of the research is concentrated in India, Canada, and the United States and applies to both lakes and the open sea. The main characteristics of the networks studied are detailed below.
  • ANN type: as in previous cases, the MLP has been the structure chosen by most researchers (17 out of 20 cases). Research using the DNN [109] and RBF [118] has also been found.
  • Structure of the ANN: most of the studies analyzed use simple structures with a single hidden layer. Research has also been found that uses two hidden layers or even the research of [109], which uses three. The number of neurons in the hidden layer is usually in the order of 10, reaching 300 neurons in the research of [110].
  • Amount of data: in most research, the volume of data is in the order of hundreds or thousands. Normally, a major part of the data is used for training, with the remainder applied to testing. The percentage of studies that make use of data for validation is 5%.
  • I/O configuration: temperature, wind speed, wind direction, and historical wave data are normally used as inputs. Outputs predict wave heights from one hour to 24 h in advance.
  • Activation function: the activation function is specified in 15 out of the 20 research. In the hidden layer, linear functions are used, with tansig and logsig being the most commonly used, while in the output layer, linear functions of the purelin and sigmoid types are adopted.
As a summary of all the previous sections, in the case of renewable energies, the predominant structure chosen is the multilayer perceptron structure with one or two hidden layers, because it may act as a universal function approximator. In addition, together with the backpropagation algorithm, it is able to learn any type of continuous function between a set of input and output variables.
Figure 5 details the most common inputs and outputs used by ANNs in wave height prediction and the operating scheme.
Applsci 14 00389 g005
Figure 5. Inputs and outputs in ANNs applied to wave prediction.

This entry is adapted from the peer-reviewed paper 10.3390/app14010389

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