  In the last decade, damage detection approaches swiftly changed from advanced
signal processing methods to machine learning and especially deep learning
models, to accurately and non-intrusively estimate the state of the beam
structures. But as the deep learning models reached their peak performances,
also their limitations in applicability and vulnerabilities were observed. One
of the most important reason for the lack of trustworthiness in operational
conditions is the absence of intrinsic explainability of the deep learning
system, due to the encoding of the knowledge in tensor values and without the
inclusion of logical constraints. In this paper, we propose a neuro-symbolic
model for the detection of damages in cantilever beams based on a novel
cognitive architecture in which we join the processing power of convolutional
networks with the interactive control offered by queries realized through the
inclusion of real logic directly into the model. The hybrid discriminative
model is introduced under the name Logic Convolutional Neural Regressor and it
is tested on a dataset of values of the relative natural frequency shifts of
cantilever beams derived from an original mathematical relation. While the
obtained results preserve all the predictive capabilities of deep learning
models, the usage of three distances as predicates for satisfiability, makes
the system more trustworthy and scalable for practical applications. Extensive
numerical and laboratory experiments were performed, and they all demonstrated
the superiority of the hybrid approach, which can open a new path for solving
the damage detection problem.
