# Neural Networks--Deflection Prediction of Continuous Beams with GFRP Reinforcement
## 3 Results and Discussion  
Based on the defined input and output variables and other necessary parameters, models of artificial neural networks--multilayer perceptron (MLP)--were defined. The number of layers, as well as the number of neurons in hidden layers, is determined experimentally, and the number of neurons in the input and output layer is determined based on the number of input and output values. The number of hidden layers was increased from one to three during the model formation. The largest number of hidden neurons in each of the hidden layers is 15. Ten models of artificial neural networks were formed. In five models, the data were scaled using the min-max procedure, while in the remaining five models, the StandardScalar procedure was used. All neural networks in the model have three input values and one output value. Models of neural networks with min-max standardization for predicting the deflection of continuous beams are shown in the following table (see Table 6). It also lists the characteristics of each model with a measure of accuracy determined by means of the mean absolute percentage error (MAPE). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Function** & **Mark** & **Explanation** & **Range** \\ \hline Identity & \(x\). & by in the output layer & \((-\infty,+\infty)\) \\ \hline \multirow{6}{*}{Rectified Linear units} & \multirow{6}{*}{\(max(0,x)\)} & Activation of neurons is transmitted directly as an output if it is positive, and if it is negative, 0 is transmitted. It has been proven to have 6 times better convergence compared to the hyperbolic tangent function. & \multirow{2}{*}{\((0,+\infty)\)} \\ \cline{1-1}  & & & \\ \cline{1-1} \cline{3-4}  & & & \\ \cline{1-1} \cline{3-4}  & & & \\ \cline{1-1} \cline{3-4}  & & & \\ \cline{1-1} \cline{3-4}  & & & \\ \cline{1-1} \cline{3-4}  & & & \\ \cline{1-1} \cline{3-4}  & & & \\ \cline{1-1} \cline{3-4}  & & & \\ \cline{1-1} \cline{3-4}  & & & \\ \cline{1-1} \cline{3-4}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Activation functions of a multilayer perceptron model of an artificial neural network. In two models, random data selection was performed. In one model, it was conducted using kFold-CrossValidation for k = 10 and in the other one using LeaveOneOut-CrossValidation (LOOCV). The accuracy measure of these models is determined using the mean absolute percentage error (MAPE) (see Tables 8 and 9). In models where dividing data was conducted by using kFold-CrossValidation, the data were scaled with Standard-Scalar, and in those models in which the division was performed using LOOCV, the data were scaled through the min-max function. The two models that gave the best results in each of the random data selections are presented here. Considering and comparing the presented models, it is noticed that the NND3 model has the best performances, i.e., gives the smallest error in the prediction. For the NND3 model, data scaling was applied using StandardScaler. It defines one input, three hidden and one output layer of neurons. There are three neurons in the input layer. In the hidden layers, from the first to the third, there are seven, 15 and three neurons. There is one \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model Name**} & **Model** & **Activation Function** & **Activation Function** & **MAPE Training** & **MAPE Test Set** \\  & **Characteristics** & **of Hidden Layers** & **of Output Layer** & **Set [\%]** & **[\%]** \\ \hline NND4 & MLP 3-7-14-3-1 & ReLu & Identity & 9.89 & 13.40 \\ \hline NND5 & MLP 3-7-13-3-1 & Tanh & Identity & 13.82 & 13.55 \\ \hline NND6 & MLP 3-7-9-3-1 & Swish & Identity & 13.48 & 13.45 \\ \hline NND8 & MLP 6-7-7-3-1 & ReLu & Identity & 11.75 & 12.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Models of artificial neural networks for continuous beam deflection estimate (min-max).