Issue 45

S. Harzallah et al, Frattura ed Integrità Strutturale, 45 (2018) 147-155; DOI: 10.3221/IGF-ESIS.45.12 151 5. Calculation of the prediction error, through statistical indices, adopting the testing set; 6. Comparisons and final choice of the best ANN configuration. M ATERIAL AND METHOD eural networks can be classified into dynamic (e.g. Elman) and static (e.g. MLP) categories. MLP is the most commonly used static networks [18], in which the input is presented to the network along with the desired output, and the weights are adjusted so that the network attempts to produce the desired output. The MLP network has three layers of neurons (nodes) an input layer, a hidden layer and an output layer (Fig. 5). The Neurons are the fundamental elements in each layer, and every neuron in one layer is associated and interacts with other layers. The outputs of every neuron in the hidden and output layers are determined by the previous output ( ij j   Σ w x , j x is the input signals), activation function (   ij j  f Σ w x ), and weighting coefficients ( ij w ) [19]. The MLP network is processed as follows: the information flow is input into the input layer and passes through the hidden and output layers to achieve the output information. The Tan-sigmoid activation function is used in the neurons of hidden and output layers in this work. In detail, neurons sum the weight-controlled input production to apply the nonlinear activation function as follows: n i ij j  j 1 a w x    (8)   i i i 2a 2 y f a 1 1 e      (9) where ij w is the weight coefficient, j x is the input signals, i a is the summation of the weighted inputs, and i y . is the output at neuron i of the output layer. Figure 5 : Architecture of MLP neural network. M ODEL VALIDATION or the estimation of the depth and length, a type of neural network (MLP) is used. Fig. 6 represents the steps of inversion. The accuracy and performance of the derived correlations in predicting of global solar radiation was evaluated on the basis of the following statistical error tests which are coefficient of determination R², root mean square error (RMSE) and its normalised value (nMBE), relative root mean square error (rRMSE), mean absolute error (MAE) and its normalised value (nMAE). These error indices are defined as [20,21]: N F