# Neural Networks--Deflection Prediction of Continuous Beams with GFRP Reinforcement
## 2 Materials and Methods
In eight models, a direct division into training and test sets was performed, and in 2 models, random data selection was conducted. The cross-validation procedure (kFold-CrossValidation and LeaveOneOut-CrossValidation) performed the random data selection. The dataset was formed using data from experimental research. The total number of datasets was 355. Each dataset was obtained after each increase in load, i.e., about 30 records for each beam. From this total number of sets, 284 datasets were determined to form a training set, whereas the remaining 71 datasets formed a test set. This division was in the ratio of 80% to 20% for training and test. Before starting the network training, it was necessary to process the data, i.e., to perform their scaling so that they all fall within a certain range of sizes. Some of the methods for data scaling are standardization and normalization [28; 29]. The result of these methods is the reduction of certain data to the same order of magnitude. Additionally, they provide an opportunity to perform data analysis with the same significance during the formation of the model, which means that they will provide data analysis with a smaller size range [29]. Min-max normalization methods for data scaling and StandardScalar (Z-score normalization) were used in this study. The first step in forming a network is to determine the architecture of the network. Determining the network architecture is defining the number of layers and the number of neurons in each of the layers. Recommendations can be found in the literature, but not unambiguously defined formulas that result in the number of layers in the network as well as the number of neurons in the layers. Networks with two hidden layers have given reliable results in numerous simulations in various engineering fields. Nevertheless, the number of layers needs to be adjusted to the specifics of the problem being solved. This is the reason why in the literature we often find good prediction results and the use of neural networks with three or more hidden layers. An unadjusted number of neurons leads to overfitting or underfitting. The problem of overfitting appears in case of a large number of neurons, whereas the unsatisfactory number of neurons leads to the problem of underfitting, i.e., of the dependence between input and output quantities. The number of neurons should be such so as to enable the data to show their most useful characteristics and not cause any of the stated issues. The number of layers and the number of neurons in each of the layers was, in this study, determined experimentally. The aim of the model-defining process is finding a model with the best possible generalization capacity. Generalization is a process in which the knowledge that is valid for a set of cases is transferred to a superset of it [30], i.e., the model has the ability to result in satisfactory sizes based on data that were not presented to it during training. The possibility of improving the generalization in the prediction is provided by the use of the cross-validation procedure. In the process of finding the most reliable model, the prediction error is constantly calculated. The prediction error is the difference between the actual (desired) and the predicted value and it defines the model accuracy measure. There are a number of predictive accuracy measures in the literature. For the purpose of defining the prognostic \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Output Data** & **Output Data** & **Data Type** & **Units of Measure** & **Min** & **Max** & **Mean Value** \\ \hline Output 1 & Deflection & numerical & mm & 0.11 & 31.20 & 9.703 & \((-\infty,+\infty)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Output data of the model. model in this research, the mean absolute percentage error (MAPE) was taken as a measure of accuracy. Expression (5) shows the mean absolute percentage error, where Ai is the expected value, and Fi is the predicted value.