Elastodynamic shape derivative: focus on the sampling of a circular distribution

Abstract

The detection and quantification of defects plays a crucial role in several industries. Assessing the severity enables to schedule maintenance appropriately, optimizing costs and reducing risks. Guided elastic waves are particularly suitable for Structural Health Monitoring applications on thin structures thanks to their long range and high sensitivity. Guided wave tomography, based on an acoustic propagation hypothesis, has been studied over the last decade to quantitatively image defects in waveguides. The acoustic approximation of this family of methods allows fast computation and good estimation of defects for simple geometries such as plates or pipes. However, this hypothesis induces that a single guided mode is considered, without mode conversion, which limits its use to defects larger than two wavelengths in structures close to ideal waveguides. Hence the need of new imaging algorithms for smaller defects in less ideal structures such as pipes with welded supports. We present here an adaptation of the shape derivative method to ultrasounds in order to reconstruct surface defect on structures with complex geometries. The physical model used is the full elastodynamic problem. It allows taking into account all physical phenomena occuring during wave propagation. Iterative methods such as shape derivative are well known to give precise results but at a high computational cost as the method needs to solve the full elastodynamic problem at each iteration, and a sensitivity to local minima, which may prevent convergence toward the true defect. To suppress these two drawbacks, a spectral finite element method is used to reduce the computation and memory costs. The result of acoustic guided wave tomography is also used as a first guess to reduce the number of iterations and the sensitivity to local minima. After explaining the principle of the shape derivative, validations on simulated and experimental data will be presented in this talk.