## 2 Methodology
### ANN-Based Hybrid Models for Wind Speed Estimation  
ANNs are intelligent systems that work by mimicking the biological nervous system and are inspired by the electrochemical information processing technique of the human brain. An ANN model is comprised of neurons that use inputs across the network and transform inputs using transfer functions to produce results [52]. In this study, a Multi-Layer Feed-Forward Backpropagation ANN structure, as demonstrated in Figure 4, is utilized for the estimation of wind speed. Each cell in an ANN is called a neuron, which connect with each other through connections of different weights. Sets of neurons form  
Figure 3: Monthly variation in mean wind power densities (\(W\)/m\({}^{2}\)) for the Canakkale Province. layers that are divided into three layers: input, output, and hidden. As seen in Figure 4, 12 neurons (\(x_{1}\), \(x_{2}\), \(x_{3}\), \(\ldots\), \(x_{12}\)) representing the wind direction, wet bulb temperature, actual pressure, maximum and minimum temperature, relative humidity, average temperature, total global solar radiation, areal precipitation, amount of cloudiness, sea water temperature and hours of sunshine are used in the input layer, whereas one neuron (\(y_{1}\)) is employed In the output layer, denoting the daily average wind speed. Each neuron's input is determined by adding a bias term to the weighted sum of its previous layer's outputs [53]. The inputs of each neuron are processed by a transfer function, from which the linked neuron's output is produced. The sigmoid and hyperbolic tangent functions are the most frequently used activation functions [52]. The hyperbolic tangent sigmoid (tansig) is preferred as the transfer function in that configuration because  
Figure 4: Feed-forward backpropagation ANN structure with two hidden layers. the relation between input and output neurons is nonlinear. Equation (14) can be employed to mathematically define the output of the network. \[\overset{\wedge}{y}=f_{3}\left(\sum_{k=1}^{p}w_{ks}.f_{2}\left(\sum_{j=1}^{m}w_{ jk}.f_{1}\left(\sum_{i=1}^{n}w_{ij}.\ x_{i}+\varphi_{j}\right)+\varphi_{k}\right)+\varphi_{s}\right) \tag{14}\]  
where \(x_{i}\) represents the input values and \(\hat{y}\) is the output values of the network; \(w_{ij}\) represents the weights used to establish connections between the \(i\)th node of the input layer and the \(j\)th node of the first hidden layer; \(w_{jk}\) is the weights used to establish connections between the first and second hidden layers; and \(w_{ks}\) denotes the weights used to establish connections between the output layer and the second hidden layer. The transfer function is represented by \(f_{1},f_{2},\) and \(f_{3}\), whereas the biases on the nodes of the first hidden, second hidden, and output layers are indicated by \(\varphi_{j}\), \(\varphi_{k}\), and \(\varphi_{s}\), respectively. One of the main objectives and novelties of this study is to introduce two hybrid approaches consisting of ANNs' dual combinations with GA and PSO algorithms to predict the wind speed and wind power potential. These hybrid approaches are more effective than the conventional ANN method alone. To overcome the lack of a single ANN model, the parameters of the ANN model are optimized by GA and PSO, resulting in higher prediction performance. Most recent studies have focused on hybrid approaches, where an ANN and metaheuristic optimization methods have been combined [54; 55; 56; 57]. A network of interconnected artificial neurons that have been trained utilizing a learning algorithm is known as an ANN. In the ANN-GA hybrid model, a GA is used as a learning algorithm and trains the ANN in order to optimize the estimation technique. Similarly, in the ANN-PSO hybrid model, PSO is employed as a learning algorithm and trains the ANN to optimize the model and learning parameters. Figure 5 illustrates the flowchart of the presented hybrid ANN-GA and ANN-PSO algorithms.