Reconstruction of Dispersion Curves in the Frequency-Wavenumber Domain Using Compressed Sensing on a Random Array

Abstract

International audienceIn underwater acoustics, shallow-water environments act as modal dispersive waveguides when considering low-frequency sources, and propagation can be described by modal theory. In this context, propagated signals are composed of few modal components, each of them propagating according to its own wavenumber. Frequency-wavenumber (f−k) representations are classical methods allowing modal separation. However, they require large horizontal line sensor arrays aligned with the source. In this paper, to reduce the number of sensors, a sparse model is proposed and combined with prior knowledge on the wavenumber physics. The method resorts to a state-of-the-art Bayesian algorithm exploiting a Bernoulli–Gaussian model. The latter, well suited to the sparse representations, makes possible a natural integration of prior information through a wise choice of the Bernoulli parameters. The performance of the method is quantified on simulated data and finally assessed through a successful application on real data

Dispersive Grid-free Orthogonal Matching Pursuit for Modal Estimation in Ocean Acoustics

“…In shallow-water environments, the vertical wavenumbers k zm weakly depend on the frequency [9]; the quantity is thus smaller than the other terms of the equation and can be neglected. Dispersive relation has been exploited to track the propagating wavenumbers in the (f-k) diagram in [7] and [8]. We place this work in the continuation of these previous contributions, but in contrast to them, we propose here a method where wavenumbers are not constrained to lie on a discrete grid and that does not require prior knowledge of the modal cut-off frequencies (as in [7]).…”

“…To overcome this problem, we propose to account for the sparsity of the contribution of modes in the spatial spectra. In addition, based on ideas introduced in previous works [7,8], which explicit prior information on both the number of modes expected to propagate at each frequency and their links from one frequency to another, we address mode tracking among spatial spectra at successive time frequencies. Our contribution goes beyond these works : in addition to taking into account physical priors, we propose an algorithm that is free of the constraint of grid search for the wavenumber estimation.…”

Managing Complexity, Uncertainty, and Variability in Guided Wave Structural Health Monitoring

“…We then use sparse wavenumber synthesis to generate a model. These techniques have also been adapted for underwater acoustics [44] and medical diagnostics [45]. Recent advances [44], [46] have also introduced optimization constraints to improve the effectiveness of sparse wavenumber analysis.…”

Accurate Sparse Recovery of Rayleigh Wave Characteristics Using Fast Analysis of Wave Speed (FAWS) Algorithm for Soft Soil Layers

“…Thus, in order to reduce the redundant geophones used in conventional measurements, this paper contributes to this objective by exploring a novel in-site technique based on compressive sensing (CS) to reduce the number of required geophone and measurements for the estimation of surface wave velocity of the subsoil. CS has been applied to recover the multimodal and dispersive properties of Lamb wave from observed data in the laboratory for analysis, reconstruction, and prediction of guided waves [14][15][16][17][18][19][20]. Jiang et al applied CS to ultrasonic computerized tomography to reduce observation times for estimation of a steel tube slab structure [21,22].…”