Guided wavefield reconstruction from sparse measurements

Abstract

Guided wave measurements are at the basis of several Non-Destructive Evaluation (NDE) techniques. Although sparse measurements of guided wave obtained using piezoelectric sensors can efficiently detect and locate defects, extensive informa-tion on the shape and subsurface location of defects can be extracted from full-field measurements acquired by Laser Doppler Vibrometers (LDV). Wavefield acquisition from LDVs is generally a slow operation due to the fact that the wave propagation to record must be repeated for each point measurement and the initial conditions must be reached between each measurement. In this research, a Sparse Wavefield Reconstruction (SWR) process using Compressed Sensing is developed. The goal of this technique is to reduce the number of point measurements needed to apply NDE techniques by at least one order of magnitude by extrapolating the knowledge of a few randomly chosen measured pixels over an over-sampled grid. To achieve this, the Lamb wave propagation equation is used to formulate a basis of shape functions in which the wavefield has a sparse representation, in order to comply with the Compressed Sensing requirements and use l1-minimization solvers. The main assumption of this reconstruction process is that every material point of the studied area is a potential source. The Compressed Sensing matrix is defined as being the contribution that would have been received at a measurement location from each possible source, using the dispersion relations of the specimen computed using a Semi-Analytical Finite Element technique. The measurements are then processed through an l1-minimizer to find a minimum corresponding to the set of active sources and their corresponding excitation functions. This minimum represents the best combination of the parameters of the model matching the sparse measurements. Wavefields are then reconstructed using the propagation equation. The set of active sources found by minimization contains all the wave excitation sources (such as PZT transducers) and scatters, and can therefore be used as an NDE technique. Results are shown for an analytical wavefield as well as for experimental wavefields in an anisotropic specimen with delamination.