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Inverse Problem Regularization for the Vibroacoustic Transfer Function Construction Régularisation d'un problème inverse pour la construction d'une fonction de transfert vibroacoustique

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Abstract:

Numerical building of the vibroacoustic transfer function for a structure vibrating in its real environment needs to proceed to the vibroacoustic inverse problem resolution from measured acoustic pressures. These pressures allow actually a density function allocated to point sources on the structure to he calculated. Thus, the obtained function values, coupled with vibratory velocities measured at the same point sources, constitute the data in order to determine the vibroacoustic transfer function. This latter permits the acoustic radiation from the structure on its site to be predicted for any new vibratory state. Our paper presents first and in a short manner, the mathematical formulation establishing the vibroacoustic transfer function construction. Next, the numerical resolution of the inverse problem is detailed. This is typically an ill-posed problem, introduced by a Fredholm integral equation of the first kind. The inversion is carried out with SVD. The regularization process is based on the Miller method using information on the solution and on the measurement errors contaminating the acoustic data. Some numerical simulations and experimental results illustrate the presentation of this regularization test.

French
Dans l'objectif de construire numériquement la fonction de transfert vihroacoustique pour une structure vibrant dans son environnement réel, la résolution d'un problème inverse vibroacoustique à partir de pressions acoustiques complexes mesurées est menée. Les pressions sont en effet utilisées pour le calcul de la fonction densité, affectée aux points sources de la structure. La fonction ainsi obtenue et couplée aux vitesses vibratoires acquises aux mêmes points sources, constitue les données pour déterminer la fonction de transfert vibroacoustique. Son obtention permettra la prédiction du rayonnement acoustique de la structure in situ, suite à une nouvelle acquisition vibratoire. Ce papier présente, tout d'abord et de façon succincte, la formulation mathématique établissant la construction de la fonction de transfert vibroacoustique, puis de façon détaillée, la résolution numérique du problème inverse. Ce dernier est typiquement un problème mal posé, introduit par une équation intégrale de Fredholm de première espèce. L'inversion est menée à l'aide de SVD, et le processus de régularisation est basée sur la méthode de Miller utilisant des informations a priori sur la solution et sur les erreurs de mesure contenues dans les données acoustiques. Des simulations numériques et des résultats experimentaux illustrent la présentation de ce test de régularisation.

Language: French

Document Type: Research Article

Publication date: July 1, 1999

More about this publication?
  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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