Hybrid geometrical full waveform inversion for ultrasonic defect characterisation

Abstract

A hybrid geometrical full waveform inversion (GFWI) method is presented in this article for accurate ultrasonic defect characterisation using a phased array. The proposed method combines two steps: (1) A newly developed multi-mode topological energy method (TEM) is used to provide a high-resolution image for defect classification and a good initial defect model for the second step. (2) A GFWI procedure is executed to reconstruct the defect shape through iteratively reducing the mismatch in waveforms between the measurements and synthetic data from the defect model. The GFWI procedure enables direct inversion of the defect shape by deforming the elements attached at its boundaries from finite element formulation, controlled by the preconditioned boundary gradient. To suppress the cross-talk among different geometrical parameters with distinct units, the BFGS and the subspace methods are implemented together with GFWI, which enables reconstructing defects of various shapes by taking all the wave physics into the inversion automatically. Numerical examples are shown with a volumetric defect, a straight crack, a curved crack and a surface-breaking notch, giving accuracy of defect sizing within fractions of a wavelength. Two experiments using an ultrasonic phased array system further demonstrate the feasibility of this method.