## 4 Artificial Neural Networks (ANNs)
Figure 13: Example of a Neural Network Pattern Recognition for damage severity (multi-class classification). \(W\) is the weight and \(b\) is the bias, which are the learnable parameters of the ANN model. The first step in implementing this approach was to define the best way to organize the data as input objects and targets to build a good ANN architecture. Then, since the frequency steps, at the spectra obtained through numerical simulation and after FFT, are the same for all healthy and damaged systems, the amplitudes of each frequency component were used as input attributes for this analysis because these are the features that differentiate each case. The input data are organized in a data table, where each column is an object (a simulation signal) and each row is a dimension of these objects. In this case, each frequency component of the spectrum is considered as a dimension, while the target file is composed of rows of zeros and ones, in which zeros are labels that correspond to the healthy system and ones to the damaged system by using this type of classifier (Figure 14). Hence, this classification problem is used to characterize the system as damaged or undamaged, only. On the other hand, the multi-class classification problem is used to characterize the severity of the damage. This can be achieved due to the one-hot encoding, which is a method that converts the data for better ANN algorithm performance. In this work, categorical variables are converted into unique binary numbers to be used in multiple classifications, defining the healthy system and cases of damage as medium or severe cases. Indeed, to make a classifier algorithm more efficient, transformation of the data characteristics of any entity into vectors of binary numbers is required [63]. In this way, the input file is constructed essentially in the same way as in the previous example; however, the target file is differently created. It is composed of a table in which each column is a unique vector, where the position of the number one represents a class (healthy, medium-level damaged, or severely damaged system), as shown in Figure 15.  
The features of this \"nprtool\" tool are very intuitive, enabling the user to efficiently create a good ANN architecture. While the network is being trained, a percentage of the input data can be allocated to validation and testing. Moreover, the ANN \"nprtool\" automatically mixes data from each healthy and damaged system category to randomize the order of the objects. The system process consists of training, validation, and testing phases. Then, more precise results can be expected since the process is undergoing correction during the training phase and stops when it reaches the minimum error. Additionally, validation can be the factor that stops the process after the network reaches a satisfying accuracy when recognizing an object. To guarantee a sufficient success capability of the trained algorithm, a procedure suitable for the optimization of the ANN structure and  
Figure 14: Example of target file for a classification problem. Figure 15: Example of target file for a multi-class classification problem. the evaluation of its performance in terms of damage diagnosis was used, thus avoiding data overfitting, even given the limited number of examples [54]. Indeed, overfitting occurs when a model learns the detail and noise in the training data. It usually negatively impacts the performance of the model with respect to new data, since the noise or random fluctuations in the training data are learned as concepts by the ANN model. In addition, overfitting tends to be influenced by non-parametric and nonlinear models, which have more flexibility in learning a target function. Thus, ANNs are non-parametric. However, ANNs are practical to use, and the accuracy of neural classifiers is high. In addition, they include parameters to limit and constrain the quantity of details the model can learn to reduce overfitting.