Machine Learning-Augmented DPSM Frameworks for Ultrasonic Field Estimation under Deterministic and Random Wavenumber Variations

Abstract

Ultrasonic field modelling near fluid–solid interfaces is essential for non-destructive testing and evaluation (NDT&E) and structural health monitoring (SHM). Conventional numerical methods, however, are computationally demanding for high-frequency, parametric and stochastic analyses. This thesis develops machine-learning-augmented and stochastic frameworks based on the distributed point source method (DPSM) for efficient and physically consistent ultrasonic field estimation. First, a Neural Green-Distributed Point Source Method (NG-DPSM) is developed using a physics-informed neural network (PINN), which learns the displacement Green’s function (GF) with the closed-form solution as its governing physics. Automatic differentiation provides the gradients needed for stress fields, eliminating rigorous analytical differentiation. NG-DPSM evaluates Green’s functions about sixty times faster than the conventional approach while closely matching DPSM results. Second, a Pix2Pix-based conditional generative adversarial network (cGAN), with a U-Net generator and a PatchGAN discriminator, is trained on DPSM-generated data to predict high-frequency wavefields in isotropic solids coupled with a fluid. Frequency, edge, perceptual and structural similarity index measure (SSIM) losses preserve physical and structural fidelity. The model translates 1 MHz fields into 5 MHz displacement and stress fields within seconds, with SSIM values of 0.86–0.96. Third, uncertainty in elastic constants is modelled by treating the P- and S-wavenumbers as random variables. Closed-form statistical moments of the GF and its gradients are propagated within DPSM to estimate the mean and standard deviation of ultrasonic fields, agreeing closely with Monte Carlo simulations while being 425–473 times faster. Together, these frameworks provide efficient, scalable and uncertainty-aware ultrasonic modelling tools for real-time monitoring and model updating in SHM.