Table 8.

Results interpretation.

Cases	Accuracy (%)
Bi-classification (Undamaged vs. one case of damage)	Concerning the bi-classification problem results presented in Section 5.1 (see Table 5), a different trend in the accuracy behaviour can be noticed between the piezoelectric and accelerometer sensors, as illustrated in Figure 14. In detail, accelerometers generally exhibit a lower variation in both accuracy and standard deviation with the increase in the number of sensors. On the other hand, piezoelectrics show a noticeable dependency on the number of devices, both in terms of accuracy mean value and standard deviation, which decreases significantly with a few more installed patches. This behaviour seems to be explainable by considering the different nature of sensing measurements, the first based on nodal translational motion (which is mostly related to the points where the most relevant motion can be registered), and the other one on the local structural strain (as confirmed by most literature concerning piezoelectric sensors, generally disposed in a dense mesh on the inspected area [10,52], clearly also depending on the adopted SHM method). In general, both devices seem to have reached a “convergence” condition for the accuracy value; hence, the number of considered sensors was deemed optimised for the considered application.
Bi-classification (Undamaged vs. all damage)	The second bi-classification problem addressed in Section 5.1 (see Table 6) analyses the undamaged condition with respect to all other damage configurations. The DNN architecture proved to be able to classify the labels with accuracy higher than 95% in all analysed cases, even if the training dataset is unbalanced between the two classes (i.e., “undamaged” vs. “damaged”). This shows how the proposed approach can discriminate between a “healthy” signal and a damaged one, thus providing the in-orbit system with a reliable damage isolation functionality. Both sensor configurations exhibit comparable performance, with piezoelectrics showing a very similar accuracy for the classification of both high-MSE (labels “1” and “2”) and low-MSE damage (labels “5” and “6”). In this bi-classification case, the accelerometers slightly outperform the piezoelectrics in the case of high-density MSE elements (97% vs. 95%), proving to be more robust to a potentially unbalanced dataset for practical applications.
Multi-label classification	Regarding the multi-label classification problem (see Table 7), for both sensor categories, the class “0” is generally well classified, with piezoelectrics showing better performance for this specific task, with lower cases of false detection (first rows in the confusion matrices in Figure 15 and Figure 16) and limited false alarms (first columns in the confusion matrices in Figure 15 and Figure 16). Most false predictions happen when a single case of damage, i.e., its location, has to be assessed. It should be noticed, however, that failures $I{D}_d=1,3$ $\mathrm{and} I{D}_d=2,4$ are adjacent to each other (in an area of 5 × 10 cm2), which inherently complicates the classification problem in differentiating two very similar dynamic responses to damage. At the same time, failures $I{D}_d=5,6$ induce a lower effect on the system dynamics and are, therefore, less detectable than the others. Moreover, a different classification pattern can be observed between the accelerometer and the piezoelectric approach. The former shows more evenly spread misclassifications among classes “1” to “6”, with slightly worse performance—as expected—when introducing the lower MSE damage $I{D}_d=5,6$, particularly when classifying classes “1” and “5”, and “2” and “6”, which are aligned pairwise along the longitudinal axis y of the panel (see Figure 1). Piezoelectrics, instead, are more challenged by the classification of labels “1” and “2”, and, likewise, “5” and “6”, which are symmetrically placed with respect to the y axis and will likely measure a similar change in rotations at the extremities of the patches (as described in Section 2.2.1). Nevertheless, it should be remarked that the trained networks show good classification performance overall.