## 3 Results
### AI Development Description
#### 3.4.2 Fault Location Network
This approach prioritizes simplicity by employing a single-layer architecture while maintaining flexibility through the exploration of a broad range of neuron values, ensuring a thorough evaluation of the model's capacity to capture patterns and relationships within the data. Figure 9: Neural network (fault location) scheme. In this case, we analyzed the receiver operating characteristic (ROC) curves to illustrate the diagnostic ability of the neural network-based fault detection system as its discrimination threshold is varied. The ROC curve is a graphical representation that plots the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings. * True Positive Rate (TPR): TPR is also known as sensitivity, recall, or probability of detection. TPR measures the proportion of actual positives that are correctly identified by the system. It ranges from 0 to 1 and is plotted on the y-axis. * False Positive Rate (FPR): FPR is also known as the probability of false alarm. FPR measures the proportion of actual negatives that are incorrectly identified as positives by the system. It ranges from 0 to 1 and is plotted on the x-axis. The ROC curve provides a comprehensive evaluation of the classifier's performance across different threshold values. A perfect classifier would have a point in the upper left corner of the ROC space (TPR = 1, FPR = 0), indicating 100% sensitivity and 0% false alarms. Figures 11-13 show the ROC curves obtained from our analysis, demonstrating the effectiveness of the neural network models in distinguishing between normal operation and fault conditions. Figure 10: Neural network for fault location. * Given the limited amount of available data, the ship was divided into zones, and each consumer opening/pipe break was labeled according to its location within these defined zones. To achieve greater precision in fault detection, it is necessary to acquire a substantial amount of data for training the neural network-based algorithm. Figure 11: ROC obtained in training: (**a**) 1 layer and 5 neurons; (**b**) 1 layer and 5 neurons. Training: Scaled conjugate gradient. Figure 12: ROC obtained in training: (**a**) 1 layer and 5 neurons; (**b**) 1 layer and 5 neurons. Training: Levenberg–Marquardt algorithm. Figure 13: ROC obtained in training: (**a**) 1 layer and 5 neurons; (**b**) 1 layers and 5 neurons. Training: Bayesian regularization. * Several different configurations for the neural network (NN) were defined to determine the best training algorithm and the most effective network structure (number of neurons). The training algorithms used included the scaled conjugate gradient, Levenberg-Marquardt, and Bayesian regularization. Networks with one hidden layer, containing 5, 10, 20, and 50 neurons, were trained. * The best results were obtained using Bayesian regularization as the training function. The Levenberg-Marquardt algorithm also produced good results, as it did not require a high number of neurons to perform effectively. The poorest results were obtained with the scaled conjugate gradient method. * It is important to note that the conclusions drawn from these results are based on the premise that the training was conducted with a limited number of training cases, and the identification was performed for relatively large areas of the ship.