In industries such as oil and gas, power generation, and chemical processing, the structural integrity of piping systems is crucial for operational safety and reliability. Various factors such as corrosion, erosion, and manufacturing defects can result in a loss of wall thickness, potentially leading to catastrophic failures. Detecting and assessing the integrity of piping systems without causing disruption to operations or compromising their structural integrity is a challenge in asset management and maintenance.
Guided Wave Tomography (GWT) is a promising non-destructive testing (NDT) technique for assessing the integrity of a pipeline by mapping its wall thickness. Using tomographic algorithms that use forward wavefield extrapolators, based on the gradient of the misfit a defect reconstruction can be made. Although the forward model is computationally inexpensive, the currently implemented gradient calculation is costly due to the large number of simulations required for each inversion parameter. This study explores the feasibility of using the adjoint state method for gradient computation in GWT, requiring only a single forward simulation independent of the number of model parameters.
A nonlinear conjugate gradient optimization method is implemented to iteratively update the wall thickness based on the misfit between simulated and observed data. The inversion process makes use of the dispersion curves to establish the relationship between phase velocity, frequency, and wall thickness. The study specifically focuses on the $S_0$ mode, analysing its suitability for complex defect reconstruction. Numerical experiments demonstrate that the adjoint method effectively localizes defects in both noise-free and noise environments, provided that there is a sufficient contrast in the sensitivity kernel between the defect and its surroundings. The technique achieves a resolution of approximately $1$ to $1.5\lambda$, with frequency continuation and multimodal inversions improving reconstruction accuracy. However, challenges arise in handling noise and wall thickness interchanges, which can be mitigated using adaptive regularization strategies.
The results suggest that the adjoint method is a viable alternative to traditional finite-difference sensitivity calculations. Future research should focus on experimental validation with real-world or as noise-free alternative 3D elastodynamic data evaluating the method on complex defect geometries and varying pipe configurations. Finally, the algorithm can be enhanced by integrating Hessian-based optimization techniques, thereby implementing a second-order adjoint method.