Neuro-symbolic model for cantilever beams damage detection

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.