Sparse recovery of the multimodal and dispersive characteristics of Lamb waves

Abstract

Guided waves in plates, known as Lamb waves, are characterized by complex, multimodal, and frequency dispersive wave propagation, which distort signals and make their analysis difficult. Estimating these multimodal and dispersive characteristics from experimental data becomes a difficult, underdetermined inverse problem. To accurately and robustly recover these multimodal and dispersive properties, this paper presents a methodology referred to as sparse wavenumber analysis based on sparse recovery methods. By utilizing a general model for Lamb waves, waves propagating in a plate structure, and robust l1 optimization strategies, sparse wavenumber analysis accurately recovers the Lamb wave's frequency-wavenumber representation with a limited number of surface mounted transducers. This is demonstrated with both simulated and experimental data in the presence of multipath reflections. With accurate frequency-wavenumber representations, sparse wavenumber synthesis is then used to accurately remove multipath interference in each measurement and predict the responses between arbitrary points on a plate.

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] …”

“…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.…”

“…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.…”

“…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.…”