Inverse Scheme for Acoustic Source Localization using Microphone Measurements and Finite Element Simulations

Kaltenbacher, Barbara; Gombots, Stefan

doi:10.3813/aaa.919204

Cited by 13 publications

(18 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 6. Because of Im(C) ≡ Y , the admissible sets in (12) and (16) are equal and in particular independent of the data.…”

Section: Assumption 2 Let a Topology T And A Normmentioning

confidence: 99%

“…Under the simplifying assumption of unperturbed sound propagation in free space, it basically reduces to a signal processing problem (more precisely, deconvolution with respect to the free space Green's function for the Helmholtz equation) and can be solved by so-called beamforming methods and refined variants thereof, see, e.g., [30,4,36]. In realistic experimental scenarios, more complicated geometries, in particular bounded domains with combinations of reflecting and partially absorbing wall parts need to be taken into account by considering the wave or Helmholtz equation with appropriate boundary conditions as a model, cf., e.g., [16,35].…”

Section: Localization Of Sound Sources From Microphone Array Measuremmentioning

confidence: 99%

See 1 more Smart Citation

Some application examples of minimization based formulations of inverse problems and their regularization

Huynh¹,

Kaltenbacher²

2021

IPI

Self Cite

View full text Add to dashboard Cite

In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing three application examples in this minimization form, namely (a) electrical impedance tomography with the complete electrode model (b) identification of a nonlinear magnetic permeability from magnetic flux measurements (c) localization of sound sources from microphone array measurements. To establish convergence of the proposed regularization approach for these problems, we first of all extend the existing theory. In particular, we take advantage of the fact that observations are finite dimensional here, so that inversion of the noisy data can to some extent be done separately, using a right inverse of the observation operator. This new approach is actually applicable to a wide range of real world problems.

show abstract

“…Remark 6. Because of Im(C) ≡ Y , the admissible sets in (12) and (16) are equal and in particular independent of the data.…”

Section: Assumption 2 Let a Topology T And A Normmentioning

confidence: 99%

Section: Localization Of Sound Sources From Microphone Array Measuremmentioning

confidence: 99%

Some application examples of minimization based formulations of inverse problems and their regularization

Huynh¹,

Kaltenbacher²

2021

IPI

Self Cite

View full text Add to dashboard Cite

show abstract

“…The implemented optimization based identification algorithm is based on a gradient method with Armijo line search exploring the adjoint method to efficiently obtain the gradient of the objective function. Hence, the computational time does not depend on the number of microphones M nor on the assumed number of possible sources N. Further details, about the inverse scheme can be found in [34]. In the current implementation, the finite element (FE) method is applied for solving the Helmholtz equation (24).…”

Section: Fig 5 Ground Plan Of the Room With Source Location (Dimensmentioning

confidence: 99%

Sound source localization – state of the art and new inverse scheme

Gombots

Nowak

2021

Elektrotech. Inftech.

Self Cite

View full text Add to dashboard Cite

Acoustic source localization techniques in combination with microphone array measurements have become an important tool for noise reduction tasks. A common technique for this purpose is acoustic beamforming, which can be used to determine the source locations and source distribution. Advantages are that common algorithms such as conventional beamforming, functional beamforming or deconvolution techniques (e.g., Clean-SC) are robust and fast. In most cases, however, a simple source model is applied and the Green’s function for free radiation is used as transfer function between source and microphone. Additionally, without any further signal processing, only stationary sound sources are covered. To overcome the limitation of stationary sound sources, two approaches of beamforming for rotating sound sources are presented, e.g., in an axial fan.Regarding the restrictions concerning source model and boundary conditions, an inverse method is proposed in which the wave equation in the frequency domain (Helmholtz equation) is solved with the corresponding boundary conditions using the finite element method. The inverse scheme is based on minimizing a Tikhonov functional matching measured microphone signals with simulated ones. This method identifies the amplitude and phase information of the acoustic sources so that the prevailing sound field can be with a high degree of accuracy.

show abstract

“…In this article, DAMAS will always refer to the integral equation (26) and not to the iterative Gau-Seidel method that was suggested in [9] in order to solve the discrete version of (26). The integral kernel ψ is usually referred to as point-spread function (PSF) and defined as ψ(y, y ) = P y , P y HS P y 2 HS = (C * (P y )) (y ) P y…”

Section: Damasmentioning

confidence: 99%

“…Normal equation). The DAMAS problem(26) is equivalent to the operator equationC * C(q) = C * C obs (27)which is the normal equation of the CMF problem(23).Proof. First of all we can multiply(26) by P y which yields the equivalent integral equation C * (C obs ) (y) = Ω P y , P y HS q(y )dy .…”

mentioning

confidence: 99%

Uniqueness of an inverse source problem in experimental aeroacoustics

2020

View full text Add to dashboard Cite

This paper is concerned with the mathematical analysis of experimental methods for the estimation of the power of an uncorrelated, extended aeroacoustic source from measurements of correlations of pressure fluctuations. We formulate a continuous, infinite dimensional model describing these experimental techniques based on the convected Helmholtz equation in R 3 or R 2 . As a main result we prove that an unknown, compactly supported source power function is uniquely determined by idealized, noise-free correlation measurements. Our framework further allows for a precise characterization of state-of-the-art source reconstruction methods and their interrelations.

show abstract

Inverse Scheme for Acoustic Source Localization using Microphone Measurements and Finite Element Simulations

Cited by 13 publications

References 0 publications

Some application examples of minimization based formulations of inverse problems and their regularization

Some application examples of minimization based formulations of inverse problems and their regularization

Sound source localization – state of the art and new inverse scheme

Uniqueness of an inverse source problem in experimental aeroacoustics

Contact Info

Product

Resources

About