Guided-wave inspection switches to sparse measurements: PI-SIREN embeds plate equations in a sinusoidal network and finds a back-side milled notch in experiment
Synopsis
Ultrasonic guided-wave inspection of thin-walled structures usually needs repeated finite-element runs or dense scans to obtain a damage-free baseline. PI-SIREN embeds the coupled elastodynamic equations of Mindlin–Reissner plate theory in the training loss of a sinusoidal-activation network, reconstructing the steady-state wavefield in the frequency domain from sparse measurements without temporal discretization. In the numerical ablation the full optimization pipeline reaches a test error of 0.1037, and in experiment the surrogate serves as the baseline that localizes a back-side milled notch from sparse measurements, whereas comparable plain multilayer-perceptron baselines localize no defect at all.
Interpretation
Guided-wave structural health monitoring can now use a trained physics-constrained network in place of repeated finite-element simulation, supplying a continuous damage-free baseline wavefield that can be evaluated at arbitrary locations. Obtaining such a baseline previously required either computationally expensive finite-element simulation or dense measurements covering all operating conditions, while purely data-driven models struggle to reconstruct the full wavefield from sparse measurements. On aluminum-plate finite-element data, the full optimization pipeline reaches a test relative error of 0.1037, against 0.4932 for the data-only model, 0.2881 for the Adam-only physics-constrained model and 0.1351 for the L-BFGS variant with uniform collocation.
The network takes normalized two-dimensional coordinates as input and outputs three complex surface-displacement amplitudes directly, with rotational fields derived analytically from first-order shear deformation kinematics, so no time dimension or initial conditions are needed. Most physics-constrained networks for guided waves train in the time domain, adding a temporal dimension and known causality problems, while frequency-domain formulations over the coupled spatial fields have been less explored. Training runs in three stages: Adam with randomized collocation resampling, residual-adaptive refinement that concentrates collocation points where residuals are large, and L-BFGS quasi-Newton fine-tuning in double precision; both numerical and experimental data follow this pipeline.
Once the trained surrogate is plugged into a two-stage damage identification pipeline, it localizes a real defect in experimental measurements, whereas comparable plain multilayer-perceptron baselines localize no defect at all. Plain multilayer perceptrons with hyperbolic tangent activations, with or without Fourier feature input embedding, cannot identify damage because their reconstruction errors are too high. The back-side milled notch on the experimental plate is localized by the two-stage pipeline with an error stated as a fraction of the plate diagonal; varying the post-processing smoothing width changes the localization error only slightly, which the authors take as robustness to the kernel-width choice.
Perspective
The demonstrated scope is one EN AW-5083 aluminum plate at a single excitation frequency and material configuration, with a back-side milled notch as the experimental defect; the authors propose extending the framework to anisotropic and composite plate structures as further work.
The experimental global reconstruction error and the interior-region error are both above the synthetic result at the same density; the authors attribute this to optical measurement noise, the mismatch between idealized free-edge conditions and the physically supported plate, and model-form error from the single-frequency plate equations. Localization still succeeds when reconstruction error exceeds the synthetic threshold, so that threshold should be treated as a conservative design guideline.