Symmetry constrained neural networks for detection and localization of damage in metal plates

TL;DR

This work investigates symmetry-constrained neural networks for detecting and localizing damage in a thin aluminum plate using Lamb-wave signals collected by a square array of piezoelectric transducers. By representing the multi-sensor measurements as a 4-node graph and enforcing $D_4$-equivariant or near-equivariant architectures, the authors show that symmetry-informed models improve both localization accuracy and robustness under symmetry-breaking conditions. The approximately equivariant network achieves the best mean localization error of $2.58 \pm 0.12$ mm while maintaining over 99% detection accuracy, indicating practical benefits for structural health monitoring under real-world variability. The study demonstrates that incorporating geometric inductive biases reduces data requirements, enhances generalization, and facilitates efficient learning for damage assessment from Lamb-wave data.

Abstract

The present paper is concerned with deep learning techniques applied to detection and localization of damage in a thin aluminum plate. We used data collected on a tabletop apparatus by mounting to the plate four piezoelectric transducers, each of which took turn to generate a Lamb wave that then traversed the region of interest before being received by the remaining three sensors. On training a neural network to analyze time-series data of the material response, which displayed damage-reflective features whenever the plate guided waves interacted with a contact load, we achieved a model that detected with greater than $99\%$ accuracy in addition to a model that localized with $2.58 \pm 0.12$ mm mean distance error. For each task, the best-performing model was designed according to the inductive bias that our transducers were both similar and arranged in a square pattern on a nearly uniform plate.

Figures (20)

• Figure 1: Photo of the experimental apparatus showing the gantry, the aluminum plate, the piezoelectric transducers, and the contact load in addition to the waveform generating oscilloscope and a laptop that runs the code responsible for controlling the gantry.
• Figure 2: Plate schematic for Lamb wave source $S$ in the presence of a contact load at position $L_i$ that redirects waves into receivers $R$.
• Figure 3: A typical uniform initialization of a training set covering $80\%$ of the possible load locations.
• Figure 4: Average full-fidelity received baseline signals for (\ref{['subfig-edge_path']}) waves traversing along an edge connecting two transducers and (\ref{['subfig-diag_path']}) waves traversing the diagonal connecting two transducers.
• Figure 5: Comparison of a baseline signal that propagated along a plate diagonal in the absence of a contact load with a signal corresponding to a damaged state that followed the same flight path. Both signals have been compressed from their raw form by way a high and a low pass filter.