# A Deep Learning-Based Approach for the Identification of a Multi-Parameter BWBN Model
## 3 Deep Learning Identification Model  
### The Network Architecture of the Deep Learning Model  
The artificial neural network (ANN) is an information-processing mathematical model established by imitating the brain's neural network structure and function. This method involves a repeated learning and training of the known information, and incudes a scheme for gradually adjusting the learning weights of the neurons to mimic the relationship between the input and the output data. Compared with the traditional GA method, the neural network technique has obvious advantages in dealing with fuzzy data, random data, and nonlinear data, and is especially suitable for large-scale, complex structures and unclear information systems. Deep learning is an artificial neural network structure with multi-hidden layers. Depth usually refers to the number of hidden layers in the neural network structure. Learning is a cognitive process from unknown to known, corresponding to the input and output process in the neural network structure. Deep learning strengthens the ability of feature learning and makes the prediction more accurate by the hierarchical expression of input information and layer-by-layer feature transformation. A multi-layer neural network has excellent feature-learning ability and can learn more essential data features. For the multi-parameter identification problem of the BWBN model, traditional identification methods have better identification performance, but the identification process is complex and needs a large number of calculations. The deep learning model utilized in this work contains multi-hidden layers. By incorporating different activation functions for hidden layers, this deep learning model can handle more complex problems such as identification, segmentation and regression analysis. Obviously, the deep learning model can estimate the model parameters of the BWBN model by making regression analysis on a large number of existing recognition data. The optimal value of parameters can be identified in a simple and direct manner. The comparison with the traditional method is shown in Figure 3.  
The problem of multi-parameter identification of the BWBN model belongs to the problem of multiple vector regression in supervised learning. Since the parameters of the BWBN model are dimensionless, the input parameters of the input layer are also  
Figure 3: Comparison of traditional and present identification method. dimensionless. Herein, the dimensionless parameters provided by the database of PEER include the aspect ratio (i.e., the ratio of shear span to column depth), the axial load ratio, the longitudinal reinforcement ratio, and the transverse reinforcement ratio. The schematic diagram of the neural network structure is shown in Figure 4, the network structure includes one input layer, i hidden layers, i greater than 2, and one output layer. The BWBN model has a wide range of applications. Because this model is a general mathematical model, when it is used in experimental analysis of structural systems, its parameters cannot strictly correspond to the physical parameters of the physical experimental model. Obviously, there is more than one mathematical solution of the BWBN model corresponding to the physical experimental model. Therefore, a double objective optimization function can be constructed to satisfy the following requirements: (a) the parameters of the network model, i.e., weights and hyperparameters of the network model; (b) the corresponding solution of the physical model. The objective function of the network model is the regression evaluation index, which are R\({}^{2}\) and adjusted R\({}^{2}\) (adjR\({}^{2}\)). The evaluation index R\({}^{2}\) can be obtained by:  
\[\text{R}^{2}=1-\frac{\frac{\sum\limits_{i}{{{({{g_{i}}-{y_{i}})}^{2}}}}}}{{ \sum\limits_{i}{{{({{\overline{y}}_{i}-{y_{i}})}^{2}}}}}} \tag{23}\]  
where \(\hat{y}_{i}\), \(\overline{y}_{i}\) and \(y_{i}\) are the predicted value of the test set, the mean value of the test set, and the actual value of the test set.