Reconstruction of Lamb wave dispersion curves by sparse representation with continuity constraints

Ultrasonic Lamb waves are a widely used research tool for nondestructive structural health monitoring. They travel long distances with little attenuation, enabling the interrogation of large areas. To analyze Lamb wave propagation data, it is often important to know precisely how they propagate. Yet, since wave propagation is influenced by many factors, including material properties, temperature, and other varying conditions, acquiring this knowledge is a significant challenge. In prior work, this information has been recovered by reconstructing Lamb wave dispersion curves with sparse wavenumber analysis. While effective, sparse wavenumber analysis requires a large number of sensors and is sensitive to noise in the data. In this paper, it extended and significantly improved by constraining the reconstructed dispersion curves to be continuous across frequencies. To enforce this constraint, it is included explicitly in a sparse optimization formulation, and by including in the reconstruction an edge detection step to remove outliers, and by using variational Bayesian Gaussian mixture models to predict missing values. The method is validated with simulation and experimental data. Significant improved performance is demonstrated over the original sparse wavenumber analysis approach in reconstructing the dispersion curves, in synthesizing noise-removed signals, in reducing the number of measurements, and in localizing damage.