## 3 Feature Selection Algorithms
### Empirical Mode Decomposition
#### 4.2.2 Convolutional Neural Networks (CNNs)  
Convolutional neural networks (CNNs) are maybe the most representative deep algorithm and have been adopted in several application fields of data-based classification and regression problems. A CNN is composed, essentially, of three types of layers according to its function: convolutional layers, pooling layers and fully connected layers. Convolutional layers automatically extract features from the input data through a convolution between input data and a user-defined matrix named filter. Pooling layers reduce the data size, and fully connected layers perform data classification tasks. Several layers can be stacked in the network design architecture, thereby increasing network complexity at the cost of incrementing computation training time and the amount of resources used. CNN networks' inputs consist of n-dimensional training samples, where n can be from 1 to N. Figure 3 shows a convolutional network with an input vector of dimension 1D (128 \(\times\) 1) for a multiclass classification task. These inputs are, in most cases, images according to the classification or regression problem. In structural damage identification, proposals using CNN architectures use 1D acceleration records or 2D data that consist of images or matrices using reshaping methods, signal processing techniques or feature extraction methods. One advantage of using CNN models in SHM systems is that convolutional layers perform the selection of damage-sensitive features automatically. Figure 3: A CNN network example using raw acceleration input data [92]. Input data can be reshaped in 1D or higher dimension vector fashion. Table 9 lists several proposals for SHM applications that employ CNNs. In these proposals, structural responses are captured as acceleration measurements are used. A complete and exhaustive review of SHM systems using CNN and mainly image data can be consulted in [93]. Some relevant limitations of the applications of CNN arise in SHM systems for structural assessment. A large amount of training data are usually required in CNN training to achieve the generalization property of the model, and the structural data of damage states are unavailable in most cases. Moreover, the structural data of damage states in large civil structures are uncommon. A possible solution is to generate damage structural state data from FE models, which is the usual approach in several SHM proposals, as shown in Table 6 However, FE-generated data rely on the accuracy of the FE models, and this also depends on the correct value of the structural parameters that are used for the model. Some of these parameter values are unknown or change over time, so they should be estimated or calculated from experimental data. [PERSON] et al. [51] proposed a structural damage identification method using a time-frequency plot of the acceleration signal. The marginal spectrum was used as the input to a CNN, and the hyperparameters of this network were optimized using PSO, thereby achieving 10% better accuracy than a CNN without PSO. [PERSON] and [PERSON] [94] explored the application of two objective function techniques for the optimal hyperparameter selection of a structural damage identification system using CNN. Their results showed a computational cost reduction of 40%. [PERSON] et al. [95] designed a 1D-CNN to perform multiclass damage identification using bridge vibration data. The random search technique performed hyperparameter tuning to obtain the optimal network architecture. [PERSON] and [PERSON] [96] also proposed a hyperparameter search technique in CNN. These hyperparameters included the subsampling size and the number and size of kernels using a genetic algorithm and a multi-objective optimization technique. Damage-sensitive features were extracted from the automatic signal using a CNN architecture in the damage identification strategy presented by [PERSON] et al. [70], which obtained good performance in damage identification and localization. In [97] [PERSON] et al.