## 3 Results
### AI Development Description
#### 3.4.1 Fault Detection Network
The objective of this procedure is to select a model that best fits the available data while avoiding overfitting and underfitting. Overfitting occurs when a model fits the training data too closely, capturing noise and losing its ability to generalize to new data. Conversely, underfitting arises when the model is too simplistic to capture the underlying relationships in the data. The standard model selection and error estimation procedure generally follows the following steps:  
* Data Splitting: The available data are divided into training and test (or validation) sets. The training set is used to fit and train different models, while the test set is used to evaluate the performance of the models and estimate generalization error. * Model Selection: Different models with different structures or hyperparameters are chosen, which may vary in their complexity. This may involve selecting different neural network architectures, different machine learning algorithms, or different feature sets. * Training and Cross-Validation: Models are trained on the training set and evaluated on the validation set or through cross-validation. Cross-validation involves dividing the training set into several parts and performing multiple rounds of training and evaluation on different subsets. * Model Evaluation and Selection: Models are compared and evaluated using performance metrics such as mean squared error, accuracy, F1 score, etc. The model with the best performance on the test set or cross-validation is selected. * Generalization Error Estimation: Once the final model is selected, the generalization error is estimated by evaluating its performance on the test set, which contains unseen data during the training and selection processes. The model architecture is grounded in an artificial neural network consisting of one or more hidden layers (defined by 'layers') and a variable number of neurons in each hidden layer (defined by 'neurons'). The flexibility of the network architecture allows for the inclusion of 1 to 3 hidden layers, each featuring a number of neurons ranging from 5 to 50. The search is constrained for the number of layers within a range of a minimum of one layer to a maximum of three layers. The models considered span from a simple neural network to a deeper network with three hidden layers. For the numbers of neurons per layer, exploration covers a range from 5 to 50 for each hidden layer. This encompasses models with varying levels of complexity and the capacity to learn sophisticated representations. Granularity pertains to the number of different values considered for each hyperparameter. In this case, the following parameters are used:  
Figure 4: Neural network for fault detection. * For the number of layers ('layers'), evaluation encompasses three different values: 1, 2, and 3. This provides a reasonable granularity for exploring models of different depths. * For the number of neurons per layer ('neurons'), exploration spans 46 different values, ranging from 5 to 50. This search entails a relatively fine granularity, facilitating consideration of a diverse array of neural architectures with differing representation capabilities. After the training process of the neural network, the regression curves obtained were analyzed, showing the correlation between the targets (x-axis) and the outputs of the system (y-axis). Some examples of regression curves are shown in Figures 5-7. * The network training was conducted with a limited number of cases representing normal operation and fault. To achieve better model adjustment, it is necessary to train the neural network over extended periods under real operating conditions and to simulate abnormal scenarios, such as breakages or collapses, to fine-tune the network's performance. * The optimal sample size for achieving the best network performance was identified as 9 s.
* Networks with 5 to 50 neurons per layer were analyzed. It was observed that using more than 10 neurons per layer did not enhance the network's performance.