# Neuro-symbolic model for cantilever beams damage detection

arXiv: https://arxiv.org/abs/2305.03063 · HTML: https://mlsanity.com/paper/2305.03063/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 37 references that are in the map.
- First posted on arXiv 4 May 2023.

## Builds on (most cited first, 7 of 7)

- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [Deep Learning: A Critical Appraisal](https://mlsanity.com/paper/1801.00631/) (2018)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [Learning Physical Intuition of Block Towers by Example](https://mlsanity.com/paper/1603.01312/) (2016)
- [A Review of Vibration-Based Damage Detection in Civil Structures: From Traditional Methods to Machine Learning and Deep Learning Applications](https://mlsanity.com/paper/2004.04373/) (2020)
- [Can recursive neural tensor networks learn logical reasoning?](https://mlsanity.com/paper/1312.6192/) (2013)

## Built on by (most cited first, 3 of 3)

- [The ethical situation of DALL-E 2](https://mlsanity.com/paper/2405.19176/) (2024)
- [Enhanced Anomaly Detection in Automotive Systems Using SAAD: Statistical Aggregated Anomaly Detection](https://mlsanity.com/paper/2406.08516/) (2024)
- [Sisteme Hibride de Invatare Automata si Aplicatii](https://mlsanity.com/paper/2406.11870/) (2024)

## Abstract (arXiv)

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.