Dispersion curve recovery with orthogonal matching pursuit

Abstract

Dispersion curves characterize many propagation mediums. When known, many methods use these curves to analyze waves. Yet, in many scenarios, their exact values are unknown due to material and environmental uncertainty. This paper presents a fast implementation of sparse wavenumber analysis, a method for recovering dispersion curves from data. This approach, based on orthogonal matching pursuit, is compared with a prior implementation, based on basis pursuit denoising. In the results, orthogonal matching pursuit provides two to three orders of magnitude improvement in speed and a small average reduction in prediction capability. The analysis is demonstrated across multiple scenarios and parameters.

Multidimensional guided wave dispersion recovery for locating defects in composite materials

“…In previous work, we created sparse wavenumber analysis to extract the wavenumber dispersion curves of an isotropic structure [40,39]. Figure 1(a) illustrates the theoretical dispersion curves of an aluminum panel.…”

“…For isotropic plates, we model Lamb wave (guided waves in an isotropic plate) data Y(ω, r) between two points (i.e., a transmitter and receiver) of distance r and at angular frequency ω by [40,57,39] …”

“…We then use this multi-dimensional dispersion curve to predict, or extrapolate, how guided waves propagate in the anisotropic panel. This process is known as sparse wavenumber synthesis [40,39]. We finally integrate these predictions (i.e., a specific model of wave propagation for the composite) with matched field processing [54,55,37], a model-based localization framework popularized in underwater acoustics [54,55], to locate an active guided wave source.…”

“…We use the physics-based model and sparse recovery to create a multi-dimensional dispersion curve for the composite specimen, illustrating how a guided wave's horizontal and vertical wavenumbers vary with frequency. This process is known as sparse wavenumber analysis [40,39]. We then use this multi-dimensional dispersion curve to predict, or extrapolate, how guided waves propagate in the anisotropic panel.…”

“…A single ultrasonic excitation creates multiple wave excitations (i.e., modes) with distinct, frequency-dependent (i.e., dispersive) velocities [30,31,32]. As a result, many guided wave methods for locating defects in large regions of a structure [33,34,35,36,37] rely on precise knowledge of these complex velocity characteristics [38,37,39,40] or employ approximations of guided wave behavior [33,34] at the cost of accuracy or robustness. For example, the wave envelope (without phase information) is often assumed to have a constant, non-dispersive velocity throughout the structure.…”