A Parametrized Reduced Order Model for Rapid Evaluation of Flaws in Guided Wave Testing

Abstract

Data from guided wave propagation in structures, produced by piezoelectric elements, can offer valuable information regarding the possible existence of flaws. Numerical models can be used to complement the attained data for refining the potential for flaw characterization. Unfortunately, evaluation of these models remains computationally expensive, especially for small defects, due to the short wavelength required for detection and, the in turn fine discretization in time and space. This renders realtime simulation infeasible, rendering GWapproaches less attractive for inverse problem formulations, where the forward problem needs to be solved several times. We propose an accelerated computation method, which exploits the properties of guided waves interacting with defects, where an extra band of waves is created, whose phase is differentiated, depending on the location of the flaw (e.g. notch) within the medium. To expedite the actual simulation for the inverse problem, the system is parametrized in terms of the location of the flaw and, in an offline phase, is repeatedly solved to produce snapshots of the systems response. The snapshots are used to create a physics informed interpolation of the solution of the wave propagation problem for different flaw locations. The gained information is then used in an inverse setting for localising the defect using an evolution strategy as a means to stochastic, derivative-free numerical optimization. The method is demonstrated in simulations of a 2D slice of a thin plate.