Improvements in computing capacity have allowed computers today to execute increasingly complex tasks. One of the main benefits of these improvements is the possibility of developing machine learning algorithms, of which the fields of application are extensive and varied. However, an area in which this type of algorithms acquires an increasing relevance is structural health monitoring (SHM), where inspection strategies and guided wave-based approaches make the evaluation of the structural conditions of an aircraft, vessel or building among others possible, by detecting and classifying existing damages. The use of sensors, data acquisition systems (DAQ) and computation has also allowed these damage detection and classification tasks to be carried out automatically. Despite today’s advances, it is still necessary to continue with the development of more robust, reliable, and low-cost structural health monitoring systems. For this reason, this work contemplates three key points: (i) the configuration of a data acquisition system for signal gathering from an an active piezoelectric (PZT) sensor network; (ii) the development of a damage classification methodology based on signal processing techniques (normalization and PCA), from which the models that describe the structural conditions of the plate are built; and (iii) the use of machine learning algorithms, more specifically, three variants of the self-organizing maps called CPANN (counterpropagation artificial neural network), SKN (supervised Kohonen) and XYF (X–Y fused Kohonen). The data obtained allowed one to carry out an experimental validation of the damage classification methodology, to determine the presence of damages in two aluminum plates of different sizes, where masses were added to change the vibrational responses captured by the sensor network and a composite (CFRP) plate with real damages, such as delamination and cracks. This classification methodology allowed one to obtain excellent results by validating the usefulness of the SKN and XYF networks in damage classification tasks, showing overall accuracies of 73.75% and 72.5%, respectively, according to the cross-validation process. These percentages are higher than those obtained in comparison with other neural networks such as: kNN, discriminant analysis, classification trees, partial least square discriminant analysis, and backpropagation neural networks, when the cross-validation process was applied.