Iterative high-resolution wavenumber inversion applied to broadband acoustic data

Philippe, F.; Roux, Philippe; Cassereau, Didier

doi:10.1109/tuffc.929

Cited by 14 publications

(4 citation statements)

References 19 publications

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“…Periodic structures or locally resonant systems, also known as metamaterials, have revolutionized the control of waves these last years [1,2]. The main physical properties of these structured media, as for example the opening of band gaps [3,4], the slow wave frequency band [5,6], or the spatial filtering [7], among others, can be directly derived from the complex dispersion relation [8][9][10][11][12]. In addition to dispersive effects, wave attenuation can be caused by factors such as geometric attenuation or intrinsic material loss (e.g., heat or viscous dissipation).…”

Section: Introductionmentioning

confidence: 99%

Complex Dispersion Relation Recovery from 2D Periodic Resonant Systems of Finite Size

2019

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The complex dispersion relations along the main symmetry directions of two-dimensional finite size periodic arrangements of resonant or non-resonant scatterers are recovered by using an extension of the SLaTCoW (Spatial LAplace Transform for COmplex Wavenumber) method. This method relies on the analysis of the spatial Laplace transform instead of the usual spatial Fourier transform of the measured wavefield in the frequency domain. We apply this method to finite dimension square periodic arrangements of both rigid and resonant scatterers embedded in air, i.e., to finite size sonic crystals and finite size acoustic metamaterials, respectively. The main hypothesis considered in this work is the mirror symmetry of the finite structure with respect to its median axis along the analyzed direction. However, we show that the method is robust enough to provide excellent results even if this hypothesis is not fully satisfied. Effectively, a minor asymmetry could be considered as a side effect when the structure is large enough because Laplace transforming the field along the main symmetry directions also implies averaging the field in the perpendicular one. The calculated complex dispersion relations are in excellent agreement with those obtained by an already validated technique, like the Extended Plane Wave Expansion (EPWE). The methodology employed in this work is intended to be directly used for the experimental characterization of real 2D periodic and resonant systems.

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Section: Introductionmentioning

confidence: 99%

Complex Dispersion Relation Recovery from 2D Periodic Resonant Systems of Finite Size

2019

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“…4,7,8 The dispersion of waves propagating through materials is typically interpreted in the context of frequency and wavenumber domain information and obtained from discrete spatiotemporal data via discrete Fourier transforms and related methods. [9][10][11][12][13][14] However, such techniques typically only supply real wavenumber information (or their magnitudes) from twodimensional, discrete, spatiotemporal wave propagation information, such as may be obtained from scanned receiver measurements. Several methods have been proposed to characterize wave attenuation and extract complex wavenumber information; [15][16][17][18][19][20][21][22] however, each has restrictions, as: (i) they are usually based on measurements of wave amplitude decrease with respect to time, [15][16][17][18] (ii) they are iterative methods applied in space, like the modified Prony method, 19 (iii) the number of modes has to be known in advance or a unique mode has to be isolated, [15][16][17]20,21,23 (iv) the modes contributing significantly to the signal are presumed to not interact or overlap with one another, or (v) they must include a third dimension of information, such as would be the case in an experiment with a scanned emitter and a receiver.…”

Section: Introductionmentioning

confidence: 99%

Spatial Laplace transform for complex wavenumber recovery and its application to the analysis of attenuation in acoustic systems

Geslain

Raetz

Hiraiwa

et al. 2016

Journal of Applied Physics

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International audienceWe present a method for the recovery of complex wavenumber information via spatial Laplace transforms of spatiotemporal wave propagation measurements. The method aids in the analysis of acoustic attenuation phenomena and is applied in three different scenarios: (i) Lamb-like modes in air-saturated porous materials in the low kHz regime, where the method enables the recovery of viscoelastic parameters; (ii) Lamb modes in a Duralumin plate in the MHz regime, where the method demonstrates the effect of leakage on the splitting of the forward S-1 and backward S-2 modes around the Zero-Group Velocity point; and (iii) surface acoustic waves in a two-dimensional microscale granular crystal adhered to a substrate near 100 MHz, where the method reveals the complex wave-numbers for an out-of-plane translational and two in-plane translational-rotational resonances. This method provides physical insight into each system and serves as a unique tool for analyzing spatiotemporal measurements of propagating waves. Published by AIP Publishing

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“…Des méthodes à hautes résolutions (HR) sont souvent préférées pour surmonter ces limites (Marcos, 1998). Les modèles autorégressifs (Shang et al, 1988 ;Becker, Frisk, 2006 ;Philippe et al, 2008 ;Le Courtois, Bonnel, 2014a) et les méthodes en sousespace comme MUSIC, ESPRIT (Rajan, Bhatta, 1993) et les Matrix Pencil (Lu et al, 1998, ont montré leur intérêt pour l'estimation des k rm . Cependant, si ces méthodes améliorent la résolution, elles restent sujettes à une plus grande sensibilité au bruit.…”

Section: Introductionunclassified

Estimation modale large bande avec une petite antenne horizontale

Courtois¹,

Bonnel²

2016

Traitement du signal

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L'estimation des nombres d'onde acoustiques présente un grand intérêt pour l'inversion environnementale en milieu petit fond. Avec une antenne horizontale, les nombres d'onde sont calculés par estimation spectrale dans la dimension spatiale. La représentation fréquencenombre d'onde (f −k) est obtenue en concaténant les spectres des nombres d'onde sur plusieurs fréquences. Le plan f − k est particulièrement utile pour la caractérisation des milieux dispersifs. Une méthode d'Acquisition Comprimée (CS pour Compressed Sensing) est proposée pour l'amélioration des performances de l'estimation spectrale spatiale. Le CS est adapté en contexte de propagation modale car le champ acoustique est décrit par un petit nombre de modes propagatifs. Cependant, aux plus hautes fréquences le nombre de modes augmente, la séparation des nombres d'onde devient plus difficile, en particulier lorsque l'antenne est petite. Cet article présente l'utilisation d'une méthode de filtrage particulaire (FP) pour séparer les nombres d'onde sur une large plage de fréquences. La méthode repose sur la physique dispersive, vraie pour tous les guides d'onde, pour suivre les courbes de dispersion avec les fréquences. L'utilisation successive du CS et du FP permet alors la représentation f − k pour des données ne respectant pas les dimensions usuelles pour l'analyse spectrale spatiale. La méthode est appliquée avec succès sur les mesures de l'antenne SHARK (32 capteurs) de la campagne SW06.ABSTRACT. Estimation of the acoustic wavenumbers presents great interests in shallow environments. They provide relevant material to infer the sediment parameters. Using a horizontal array, the wavenumbers are obtained with usual spectral estimation methods in the spatial dimension. The computation of the wavenumber spectra at several frequencies leads to a frequencywavenumber (f −k) diagram, which is appropriate for the characterization of dispersive propagations. In this paper, a Compressed Sensing (CS) method is proposed to improve the separation of the wavenumbers. The CS approach is particularly relevant since only few modes are propagating. However, at higher frequencies the number of propagating mode increases and the wavenumber separation becomes more difficult, especially when using short arrays. This paper introduces a wideband particle filtering (PF) algorithm for the wavenumber tracking. It takes advantage of the dispersion relation which is true in every waveguides. The consecutive use of CS and PF allows computing the f-k representation for array measurements that does not respect the usual requirements of array length. An application on the 32 sensor SHARK array of the SW06 campaign illustrates the whole methodology.

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Iterative high-resolution wavenumber inversion applied to broadband acoustic data

Cited by 14 publications

References 19 publications

Complex Dispersion Relation Recovery from 2D Periodic Resonant Systems of Finite Size

Complex Dispersion Relation Recovery from 2D Periodic Resonant Systems of Finite Size

Spatial Laplace transform for complex wavenumber recovery and its application to the analysis of attenuation in acoustic systems

Estimation modale large bande avec une petite antenne horizontale

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