# Developing a Library of Shear Walls Database and the Neural Network Based Predictive Meta-Model
## 3 Artificial Neural Network  
An ANN is inspired by the human brain, in which the neurons are tasked with data processing. By gathering these neurons, the layer is produced, and an ANN may consist of several layers. Neurons are connected by weighted synapse. Finally, the input data exit from the output layer after applying numerical processing on them [23; 24]. [PERSON] [25], [PERSON] [26] and [PERSON] [27] offered fundamentals and extensions of the ANN. Research on the neural network continued until 1985, and [PERSON] et al. [28] proposed multi-layer perceptron (MLP) with back-propagation algorithm. Subsequently, various models and networks were presented and research is still ongoing [29]. A MLP is a type of neural network in which neurons are deployed on more than one layer. An output of \(n\)th neuron in the \(m\)th layer in a generic MLP is determined as:  
\[O_{n}^{m}=f_{n}^{m}\left(\left(w^{(m-1)}\right)^{T}O_{n}^{m-1}+b^{m}\right) \tag{1}\]  
where \(f_{n}^{m}\) is the function of \(n\)th neuron in the \(m\)th layer, \(w^{(m-1)}\) is the weights from \((m-1)\)th to \(m\)th layer, and \(b^{m}\) is \(m\)th layer's bias term. For the last layer, \(n=1\) and \(O_{n}^{m}=\hat{y}\). The objective function for learning process is defined in a way to minimize the mean squared error (\(\text{MSE}=\frac{1}{2N}\sum{(y-\hat{y})}^{2}\)) between the observed value, \(y\), and the estimated one, \(\hat{y}\). This is an iterative procedure by initializing \(w\) value, estimating \(\hat{y}\), and computing the corresponding MSE. If the obtained MSE falls outside the satisfactory range, the initial \(w\) should be updated. The MLP is capable of classification, clustering, and function approximation. With a neural network of three [30; 31; 32; 33] and four [34] layers, and sufficient number of neurons in the hidden layers, nearly any function can be estimated [23; 35]. Usually, a four-layer network requires fewer weights to estimate the functions; however, it introduces more local minima [36]. The ANN is one of popular soft computing techniques in structural engineering and mechanics. Although there is much research and development, on both the theoretical aspects and application, some of the most relevant ones are reviewed in this section. [PERSON] and [PERSON] [37] evaluated the maximum moment of a beam. [PERSON] et al. [38] proposed a method for crack detection in plates using a MLP. [PERSON] et al. [39] evaluated three types of steel beam-column joints. It was observed that the neural network can properly estimate the bending strength of the connection; however, due to differences in the measurement systems, the network had extra error in estimation of the stiffness parameter. [PERSON] et al. [40] provided an estimate of the shear strength of RC rectangular beams by examining the parameters such as concrete strength, reinforcement ratio, thickness, length, and width of the beam. It was observed that the network can estimate the shear strength of concrete beam with acceptable accuracy. More than 96% of the estimated neural network data had absolute error less than 15%, while it was 26% and 23% for UK and US standards estimated data, respectively. [PERSON] et al. [41] evaluated composite shell vibration. It was found that the response from the neural network for all of the loading patterns in the research was nearly identical to the response. [PERSON] and [PERSON] [42] determined the seismic failure in structures. The network inputs were the natural frequency of the structure and shape of the mode, and the output was mass and stiffness. The data were obtained using finite element analysis. The network showed a good performance in prediction of the structural behavior. [PERSON] et al. [43] reviewed the structural failure of the beams using back propagation algorithm. It was observed that the neural network properly predicts the failure of the beams. [PERSON] and [PERSON] [44] predicted the shear strength of the RC beam reinforced with FRP by evaluating 106 experimental data using ANN.