Prediction of Ultrasonic Guided Wave Propagation in Solid-fluid and their Interface under Uncertainty using Machine Learning

TL;DR

This work tackles structural health monitoring with ultrasonic guided waves in solid-fluid interfaces under uncertainty. It introduces a two-step surrogate framework that first uses Gaussian process regression to predict UGW field patterns and then employs a cascading residual network for super-resolution, all trained on data from a monolithically coupled WpFSI solver. The approach achieves competitive accuracy (SSIM around 0.57–0.61) across multiple inclusion shapes and both material- and geometry-induced uncertainties, while significantly reducing computational costs relative to full multiphysics simulations. The results demonstrate practical potential for real-time damage detection and monitoring in complex fluid-structure systems, with future directions including bi-fidelity strategies to further cut training needs.

Abstract

Structural health monitoring (SHM) systems use the non-destructive testing principle for damage identification. As part of SHM, the propagation of ultrasonic guided waves (UGWs) is tracked and analyzed for the changes in the associated wave pattern. These changes help identify the location of a structural damage, if any. We advance existing research by accounting for uncertainty in the material and geometric properties of a structure. The physics model used in this study comprises of a monolithically coupled system of acoustic and elastic wave equations, known as the wave propagation in fluid-solid and their interface (WpFSI) problem. As the UGWs propagate in the solid, fluid, and their interface, the wave signal displacement measurements are contrasted against the benchmark pattern. For the numerical solution, we develop an efficient algorithm that successfully addresses the inherent complexity of solving the multiphysics problem under uncertainty. We present a procedure that uses Gaussian process regression and convolutional neural network for predicting the UGW propagation in a solid-fluid and their interface under uncertainty. First, a set of training images for different realizations of the uncertain parameters of the inclusion inside the structure is generated using a monolithically-coupled system of acoustic and elastic wave equations. Next, Gaussian processes trained with these images are used for predicting the propagated wave with convolutional neural networks for further enhancement to produce high-quality images of the wave patterns for new realizations of the uncertainty. The results indicate that the proposed approach provides an accurate prediction for the WpFSI problem in the presence of uncertainty.

Figures (13)

• Figure 1: Schematic representation of the WpFSI computational solid domain with a liquid inclusion at time $t=0$ (i.e., the reference domain). Here, $\Omega_s$ represents a solid plate with a fluid inclusion $\Omega_f$ with a common solid-fluid interface $\Gamma_i$. Homogeneous Dirichlet boundaries are defined by $\Gamma_D$ and $f_s$ represent a non-vanishing disc-shaped piezoelectric actuator.
• Figure 2: For the physics model of the WpFSI problem a monolithic coupling in the arbitrary Lagrangian-Eulerian (ALE) framework is used (see Appendix I). Here, $\rho$ is density, $u$ is the wave displacement, $v$ is the wave velocity, $c$ is the wave speed, $\zeta$ is auxiliary variables from mesh motion PDEs model (see Appendix II), ${F}$ is the deformation gradient, ${J}$ is the deformation determinant gradient, and suffixes $"s"$ and $"f"$ are used to indicate the solid and fluid related terms, respectively.
• Figure 3: An example of cross-correlation as performed in (11).
• Figure 4: A typical single layer of convolutional neural network, where the operation in (11) is followed by the application of the activation function and a maxpooling operation.
• Figure 5: A schematic for the local cascading residual neural network used in Step II of the proposed method. Note that this cascade is used inside a global cascade (see \ref{['eq:global_cascade']}).