Monte Carlo solution to the inverse problem of ultrasonic defect characterisation

Abstract

An important problem in the non-destructive testing of materials is the accurate determination of the location, size, shape and orientation of any detected flaws; this is essential for assessing integrity of inspected objects. This thesis presents a novel algorithm wherein recovery of the geometric parameters of flaw captured in pulse-echo ultrasonic inspection data for immersion testing at low angles of incidence is treated as an inverse problem, formulated in terms of directly recovering the underlying physical description of the defect.
The forward problem of modelling the ultrasonic echo signals is given by the Impulse Response Method, a frequency independent numerical solution to the acoustic wave equation. To solve the inverse problem, Markov Chain Monte Carlo methodology is employed as an iterative optimisation strategy, minimising a cost function between observations and a projected model. Modelled flaw parameters are updated stochastically such that they converge toward the true values over successive iterations. The advantages of this approach over standard deterministic algorithms are an ability to circumvent
local minima in the cost function and a means to incorporate a priori knowledge into the solution space. Results are shown for simulated test data, demonstrating convergence of algorithm is achievable regardless of starting condition, thus illustrating the potential of the method.
The proposed method offers the following developments and contributions. The application of Markov Chain Monte Carlo methodology to this particular inverse problem of defect characterisation is unique. Experiments conducted in the latter chapters demonstrate robust convergence of the am proach. The algorithm developed is flexible in its application, in that the
formulation allows for various alternate parameterisations of the problem with minimal structural changes. Furthermore the approach is generic in its application, intended to work for standard observation data, collected utilising standard measurement techniques and apparatus.