Accurate sparse recovery of guided wave characteristics for structural health monitoring

Guided wave structural health monitoring systems are often characterized by multi-modal and dispersive propagation media. Accurate knowledge of guided wave characteristics could help to dramatically improve performance, but estimating this information from data is often very difficult. In this paper, we present a methodology, based on compressed sensing, that utilizes ℓ₁-regularized optimization techniques to recover the sparse characteristics of the guided wavefields in the frequency-wavenumber domain. Using simulated guided wave data, we demonstrate the performance of this technique and compare it to a more traditional approach, the 2-dimensional discrete Fourier transform method. We show that, with 10 sensors, our compressed sensing method successfully estimates 1000 points in a wavefield with an average correlation coefficient of more than 0.99 while the 2-dimensional discrete Fourier transform method requires more than 820 sensors to achieve the same performance.