## 2 Methodology
### Multilayer Feedforward Neural Network (MFNN)  
ANNs are computer algorithms that simulate human central nervous system information processing. When a human brain receives information, it is processed in the central nervous system and a final decision is made. The nervous system is made up of cells called neurons, and ANNs have neuron-like nodes. ANNs have a special ability to define the correlation of data in nonlinear relationships [33]. The neural network, first introduced by [PERSON] and [PERSON] [50], has since been developed into various types of network models. Among these, the most efficient and widely used model is the multilayer feedforward neural network (MFNN) [51]. The structure of a general MFNN assuming the number of hidden nodes is \(J\) is shown in Figure 8. As shown in the figure, the MFNN consists of an input layer for inputting data, a hidden layer for computing with the input data, and an output layer for predicting the target value. Each layer consists of many nodes. The nodes of each layer are mathematically connected to the nodes of adjacent layers (input layer-hidden layer, hidden layer-output layer). Weights are assigned to the connections between layers. In addition, a bias is assigned to each node of the hidden layer and the output layer. In order for the ANN to accurately predict the target value, the optimal weight and bias should be determined, which is done through training. The process of training an artificial neural network is as follows. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Girder**} & \multicolumn{4}{c}{**Training Data**} & \multicolumn{2}{c}{**Test Data**} \\ \cline{3-6}  & & **Min.** & **Max.** & **Min.** & **Max.** \\ \hline \multirow{4}{*}{Longitudinal Strain (=input)} & S2 & \(-1.9485\times 10^{-5}\) & \(20.1969\times 10^{-5}\) & \(-4.1586\times 10^{-6}\) & \(4.0053\times 10^{-5}\) \\  & S1 & \(-1.4692\times 10^{-5}\) & \(12.5891\times 10^{-5}\) & \(-4.3175\times 10^{-6}\) & \(5.3966\times 10^{-5}\) \\  & CG & \(-0.7784\times 10^{-5}\) & \(9.0571\times 10^{-5}\) & \(-4.7890\times 10^{-6}\) & \(4.3134\times 10^{-5}\) \\  & N1 & \(-0.7014\times 10^{-5}\) & \(9.5812\times 10^{-5}\) & \(-2.9181\times 10^{-6}\) & \(2.5414\times 10^{-5}\) \\  & N2 & \(-2.6651\times 10^{-5}\) & \(16.3720\times 10^{-5}\) & \(-3.4250\times 10^{-6}\) & \(1.5924\times 10^{-5}\) \\ \hline \multirow{4}{*}{Vertical Displacement (=output, unit: mm)} & S2 & \(-16.0033\) & \(1.0827\) & \(-3.4275\) & \(0.4020\) \\  & S1 & \(-10.2574\) & \(0.5583\) & \(-3.4660\) & \(0.2214\) \\ \cline{1-1}  & CG & \(-6.6549\) & \(0.4138\) & \(-2.9460\) & \(0.2268\) \\ \cline{1-1}  & N1 & \(-7.8640\) & \(0.5330\) & \(-2.1045\) & \(0.2295\) \\ \cline{1-1}  & N2 & \(-12.0705\) & \(2.4387\) & \(-1.2924\) & \(0.2450\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ranges of strain and displacement values. Figure 8: Structure of MFNN used in this study (architecture 55-J-55). First, training data must be prepared for the learning process. These training data consist of input (\(I\)) and target output (\(T\)) values. In this study, 55 strain values were used as input values and 55 displacement values as output values. The prepared input values are used in a calculation along with the first weight and bias generated randomly, and the calculated values are input to the hidden layer  
\[net\_hidden_{j}=\sum_{i=1}^{55}w_{ij}I_{i}+\theta_{j} \tag{5}\]  
where \(I_{i}\) is the variable input to the \(i\)th node of the input layer, \(w_{ij}\) is the weight assigned between the \(i\)th node of the input layer and the \(j\)th node of the hidden layer, and \(\theta_{j}\) is the bias assigned to the \(j\)th node of the hidden layer. The result, \(net\_hidden_{j}\), is the weighted sum of all input variables and the bias and is input to the \(j\)th node of the hidden layer.