3-D reconstruction of sub-wavelength scatterers from the measurement of scattered fields in elastic waveguides

In nondestructive testing, being able to remotely locate and size defects with good accuracy is an important requirement in many industrial sectors, such as the petrochemical, nuclear, and aerospace industries. The potential of ultrasonic guided waves is well known for this type of problem, but interpreting the measured data and extracting useful information about the defects remains challenging. This paper introduces a Bayesian approach to measuring the geometry of a defect while providing at the same time an estimate of the uncertainty in the solution. To this end, a Markov-chain Monte Carlo algorithm is used to fit simulated scattered fields to the measured ones. Simulations are made with efficient models where the geometries of the defects are provided as input parameters, so that statistical information on the defect properties such as depth, shape, and dimensions can be obtained. The method is first investigated on simulations to evaluate its sensitivity to noise and to the amount of measured data, and it is then demonstrated on experimental data. The defect geometries vary from simple elliptical flat-bottomed holes to complex corrosion profiles.