TITLE:
An Optimization Technique for Inverse Crack Detection
AUTHORS:
Håkan Wirdelius
KEYWORDS:
Inverse Problem, Ultrasonic NDT, Quasi-Newton Algorithm
JOURNAL NAME:
Journal of Modern Physics,
Vol.5 No.13,
July
30,
2014
ABSTRACT:
Any
attempts to apply techniques that are based on indirect measurements of
parameters that are believed to correlate to any material properties (or state)
in an in-line situation must by necessity identify a mathematical model of this
relationship. The most conventional approach is to use some empirically based
model. If the analysis instead is based on an analytical model of a physical
explanation, this trainee period can be minimized and the system is more
dynamic and less sensitive to changes within the chain of production. A
numerical solution to the inverse problem of ultrasonic crack detection is in
this case investigated. This solution is achieved by applying optimization
techniques to a realistic model of the ultrasonic defect detection situation.
This model includes a general model of an ultrasonic contact probe working as
transmitter and/or receiver and its interaction with the defect. The inverse
problem is reduced to minimization of a nonlinear least squares problem and is
performed with a quasi-Newton algorithm consisting of a locally convergent
SVD-Newton method combined with a backtracking line search algorithm. The set
of synthetic data the model is fitted with are generated both by numerical
integration and with the two-dimensional stationary-phase method while the
forward solver in the optimization procedure is based on the latter. In both
these cases, the convergence, in terms of numbers of iterations, is sufficient
when the initial guess is reasonably close.