## 2 Theoretical Approach
### Artificial Neural Network  
The Artificial Neural Network (ANN) was inspired and developed based on the human nervous system. The ability of ANN to gain knowledge from experience and enhance performance is one of its hallmark characteristics. Recognition, control systems, classification, pattern recognition, and image processing are a few examples of ANN applications. The input layer, hidden layer, and output layer are the three primary parts of an ANN. At each layer, neurons form nodes, which then act as data kernels. The neurons are connected to each other through the associations created using the training parameter (weight and bias). The processing element is connected at each node (or neuron) to synapses, according to neuron's number in the previous processing layer.  
The signalling between neurons in layers is depicted in Figure 1. After receiving input samples, the input layer sends the signal to the hidden layer. The input and output layers are connected with a certain number of neurons in the hidden layer. The connections between each neuron in the previous layers and the subsequent layers depend on the training parameters (weight and bias). Summation and activation functions serve as the foundation for signal transmission.  
The summation function is calculated from the input layer to the hidden layer as the bias, weight ratios, and output signals of the preceding layers (Equation (7)), as follows:  
\[\begin{split}\sum_{i_{2}}^{1}=\sum_{i_{1},i_{  
\[{\rm w}_{i_{3}}^{2}+ ={\rm w}_{i_{3}}^{2}-\frac{\tau\times\partial\chi({\rm w})}{\partial{ \rm w}_{i_{3}}^{2}} \tag{19}\] \[\frac{\partial\sum_{i_{2}}^{1}}{\partial{\rm w}_{i_{1}i_{2}}^{1}} \times\frac{\partial O_{i_{2}}}{\partial\sum_{i_{2}}^{1}}\times\frac{\partial \chi({\rm w})}{\partial O_{i_{2}}}=\frac{\partial\chi({\rm w})}{\partial{\rm w }_{i_{1}i_{2}}^{1}}\] (20) \[\frac{\partial\sum_{i_{2}}^{1}}{\partial{\rm w}_{i_{2}}^{1}} \times\frac{\partial O_{i_{2}}}{\partial\sum_{i_{2}}^{1}}\times\frac{\partial \chi({\rm w})}{\partial O_{i_{2}}}=\frac{\partial\chi({\rm w})}{\partial{\rm w }_{i_{2}}^{1}}\] (21) \[\frac{\partial\sum_{i_{2}}^{1}}{\partial{\rm w}_{i_{1}i_{2}}^{1}} =f_{i_{1}};\frac{\partial O_{i_{2}}}{\partial\sum_{i_{2}}^{1}}= \frac{e^{-\sum_{i_{2}}^{1}}}{\left(1+e^{-\sum_{i_{2}}^{1}}\right)^{2}}\] (22) \[\frac{\partial\sum_{i_{2}}^{1}}{\partial{\rm w}_{i_{2}}^{1}} =1\] (23) \[{\rm w}_{i_{1}i_{2}}^{1}+ ={\rm w}_{i_{1}i_{2}}^{2}-\frac{\tau\times\partial\chi({\rm w})}{ \partial{\rm w}_{i_{1}i_{2}}^{2}}\] (24) \[{\rm w}_{i_{2}}^{1}+ ={\rm w}_{i_{2}}^{1}-\frac{\tau\times\partial\chi({\rm w})}{ \partial{\rm w}_{i_{2}}^{1}} \tag{25}\]  
The Equations (7)-(25) [50; 51; 52] were used to iteratively train the neural network. When the goal or the maximum number of loops was attained, the iteration came to an end.  
In this study, a comprehensive campaign of experimental measurements of the dynamic characteristics were carried out. Natural frequency and mode shape were identified as two dynamic properties of the structure. The results from the measurement experiment were used to update the numerical model. This model would thus have the least deviation from reality. With the updated model, the damage scenarios have been calculated and given as data to train the ANN.  
Figure 1: Architecture for artificial neural networks.