Structural health monitoring (SHM) using guided waves requires an accurate description of wave propagation phenomena while maintaining computational efficiency for real-time or large-scale applications. In this work, we investigate a hybrid physics- and data-driven modelling framework based on the shifted Proper Orthogonal Decomposition (sPOD), a model reduction technique specifically designed for transport-dominated phenomena such as propagating wavefronts.

Our current research focuses on extending the sPOD formulation to one-dimensional elastic wave propagation in bounded domains with realistic boundary conditions. A numerical study in a 1D configuration inspired by SHM scenarios is presented as a proof of concept, providing a structured basis for future validation against experimental data and for extensions to two-dimensional guided wave propagation problems.

The proposed academic test case consists of a 1D simulation of a damaged beam subjected to guided-wave excitation. Damage is modeled through a localized reduction of Young’s modulus, and the structure is excited by a tone-burst signal representative of piezoelectric actuation. The study is structured in two stages. In an offline phase, sPOD transport operators are applied to the complete displacement field data from high-fidelity simulations in order to construct a reduced mobile spatial basis adapted to wave propagation phenomena.. In a second stage, measurement data extracted at selected mesh nodes are used to reconstruct the wave field within the reduced-order framework, mimicking sparse sensing configurations. Damage-related features are then investigated through variations in the reduced representation and transport-related parameters of the sPOD decomposition.

The preliminary results obtained with this extension of the sPOD method are promising for future SHM applications for instance to localize corrosion damages in planar metallic structures.

Corrosion and erosion of industrial structures can lead to severe effects for many applications such that leakage or loss in mechanical properties. That is why guided wave tomography methods [1] have been studied over the past years to enable to monitor quantitatively such defects. These methods are usually based on simplifying assumptions, enabling fast computations but needing perfect waveguides. Their application to industrial structures is hence limited. For example, in the case of pipelines, the presence of supports, which are a hot spot for corrosion monitoring, may severely degrade the results of these methods.

In this talk, we present a dynamic shape derivative [2] to circumvent this limitation. This method is a full waveform inversion, considering the full elastodynamic problem to optimize the shape of the structure to reconstruct defects. This kind of methods rely on an iterative inversion, needing to solve several direct problems in the domain of interest. To limit the computational impact, an optimized spectral finite element solver, included in the SHM module of CIVA [3], is used with specific care taken for meshing. The adjoint method is used to limit the number of direct problems to be solved at each iteration. Furthermore, a calibration method has been designed to enable to exploit the multimodal data to the maximum extent.

The method will be exemplified on experimental data and compared to more conventional guided wave tomography. In particular, for pipe-like structures where an unclosed sensor distribution is used to match the geometry, the method significantly increases the resolution of the reconstructed image.

[1] HUTHWAITE, Peter et SIMONETTI, Francesco. High-resolution guided wave tomography. Wave Motion, 2013, vol. 50, no 5, p. 979-993.

[2] ALLAIRE, Grégoire, JOUVE, François, et TOADER, Anca-Maria. Structural optimization using sensitivity analysis and a level-set method. Journal of computational physics, 2004, vol. 194, no 1, p. 363-393.

[3] MESNIL, Olivier, RECOQUILLAY, Arnaud, DRUET, Tom, et al. Experimental validation of transient spectral finite element simulation tools dedicated to guided wave-based structural health monitoring. Journal of Nondestructive Evaluation, Diagnostics and Prognostics of Engineering Systems, 2021, vol. 4, no 4, p. 041003.

With the increasing prevalence of underwater structures and equipment, the demand for structural health monitoring (SHM) of their operational status has grown significantly. Ensuring the integrity of submerged structures poses challenges due to the harsh marine environment and limited accessibility. Current Lamb wave-based monitoring technologies for underwater structures are still underdeveloped. This study focuses on accurately modeling and analyzing guided wave propagation in submerged plates, a scenario in which the solid-liquid interface causes the leakage of wave energy into the surrounding fluid. To characterize wave propagation behavior, we derive characteristic equations based on boundary continuity conditions and solve them to obtain dispersion curves and corresponding modal fields. Furthermore, to quantitatively analyze the complex multimode propagation, we develop a numerical framework to directly extract modal coefficients from full-field data. By utilizing finite element (FE) simulations and a power flow-based matrix inversion method, we successfully evaluate the modal evolution and achieve modal decoupling even in the presence of severe leakage. Numerical solutions and finite element simulations validate the effectiveness of this approach. Key innovations include: (1) A systematic investigation of ultrasonic leaky guided waves in immersed plates; (2) The proposal of an effective power flow-coupling numerical framework for modal coefficient extraction and wavefield reconstruction. This study sheds light on guided wave physics in immersed structures, providing a practical numerical tool for future structural health monitoring applications.

Structural Health Monitoring (SHM) of spacecraft panels increasingly relies on guided ultrasonic waves and numerical twins to detect and localize micrometeoroid and debris impacts in orbit. The fidelity of these numerical models is crucial, since small directional errors in wave propagation can translate into significant localization inaccuracies and biased damage indicators. Smoothed Particle Hydrodynamics (SPH) is particularly attractive for this purpose because it can capture large deformations and fracture resulting from hypervelocity impacts (HVIs), but standard particle layouts in thin plates often suffer from numerical anisotropy, leading to direction-dependent wave speeds and spurious preferential paths.

This work proposes a quasi-isotropic SPH initialization strategy for isotropic plate-like structures, designed to enhance the directional uniformity of guided-wave propagation in support of SHM applications. The approach is inspired by quasi-isotropic laminate stacking, and consists of a deterministic through-thickness layering of particle grids with prescribed in-plane rotations, implemented directly in LS-DYNA without external meshing tools. The method is assessed on three-dimensional aluminum alloy plates, focusing on fundamental S0 and A0 Lamb modes and using an analytical reference model as virtual experiment for pristine plates.

Results show that the quasi-isotropic layout produces nearly circular wavefronts and significantly reduces the variation of group velocity and time-of-flight (TOF) with azimuthal angle, yielding more uniform responses at virtual sensors distributed along the plate. These improvements directly support the construction of high-fidelity numerical twins and physics-consistent datasets for future AI-based SHM algorithms, while remaining fully compatible with SPH-FEM coupling strategies already used for hypervelocity impact analysis.

Guided Wave Testing (GWT) is a cornerstone of nondestructive evaluation and structural health monitoring of critical infrastructure such as pipelines and rails. Due to the dispersive and multi-modal nature of guided waves, their interaction with defects in buried, immersed, fluid-loaded, composite, or welded structures is particularly complex, rendering damage quantification highly uncertain. Physics-based simulations are frequently employed to reduce this uncertainty, yet accurate numerical modeling of wave-defect interactions in such structures continues to represent a major computational bottleneck. Traditional time-step finite element methods, while robust, require extreme mesh densities and infinitesimal time steps due to the ultrasonic nature of guided waves, leading to prohibitive solve times for complex models. This study presents a relevant comparison between these traditional methods included in commercial software and a computationally efficient alternative which performs scattering analyses directly in the frequency domain. We compute the frequency response function (FRF) of a damaged steel pipe using a hybrid semi-analytical finite element (SAFE–FE) approach, with SAFE describing the guided waves and FE modeling the defect region. This approach treats the corrosion defect as a localized scatterer within an infinite homogeneous waveguide, eliminating the need for large spatial domains for the homogeneous part, which often include absorbing boundary layers. The final time-domain signals are obtained via Fourier synthesis, where the FRF is multiplied by the excitation spectrum. Results demonstrate that this methodology is in good agreement with a traditional finite element scheme. More importantly, when parametric studies for defect characterization and machine learning dataset generation are envisaged, the frequency-domain approach yields a reduction in computational overhead by orders of magnitude compared to traditional transient solvers.