On the in situ estimation of surface acoustic impedance in interiors of arbitrary shape by acoustical inverse methods

Abstract

A method for in situ estimation of the acoustic impedance of surfaces in interiors is introduced in this paper. The key difference with traditional in situ measurement techniques is the use of an inverse acoustic boundary framework which allows us to overcome some geometry constraints from previous methods (such as the planar-surface requirement and placement of microphone arrays). Furthermore, estimation of the acoustic impedance of not only one but all the surfaces is possible provided that local reaction is the predominant effect, and the following parameters are known: geometry of the surfaces, sound pressure at a number of arbitrary points in the interior field and the strength of the sound source. The estimation of the acoustic impedance at each surface is achieved by the solution of an optimization problem formulated from the linear equations of the boundary element method (BEM) applied to the discretized interior boundaries of an interior space. Previous work on similar methods have reported examples with numerical simulations. The work in this paper goes further and numerical examples together with results obtained with experimental data are presented.

Estimating Surface Acoustic Impedance With the Inverse Method

“…There is some procedural analogy to determining acoustic impedance of the interior walls [9,10]. For a sound field generated by a single acoustic source, the boundary element method provides approximate values of acoustic pressure that can be expected in the experimental where p Sx -sound pressure at point x, v Sxacoustic particle velocity at point x.…”

“…where W s , B s -matrices of influence coefficients between two different points at the boundary surface S. Therefore, for the whole system considered there is a set of equations [10] with unknown boundary parameters p S and v S :…”

“…If it is impossible to determine the C -1 matrix, which is inverse to the C matrix, then the exact solution does not exist and the approximate values of v S can be searched for by minimizing the mean-square error (the least squares problem) min ||Cv S -p m || 2 . Another solution of this problem can be sought by applying the singular value decomposition of the C matrix to C = UΣV H [10]. After assuming that the C matrix has m ´ n dimensions, the U and V matrices are orthogonal and have dimensions m ´ m and n ´ n, respectively, the dimensions of the Σ matrix are also m ´ n. By using such an approximation of the C matrix, is possible to determine the inverse matrix by …”

Joint estimation of sound source location and boundary impedance with physics-driven cosparse regularization

“…In practice, one may consult standardized tables of absorption properties of different structures from construction engineering literature (with the need of knowing exactly which materials were used), or to physically measure the acoustic impedance (e.g. [19,20]) of the concerned room, which requires specific hardware setup and calibration. Those two approaches are inflexible when considering different acoustic environments, and possibly inaccurate.…”

Membrane shape and boundary conditions estimation using eigenmode decomposition

“…This problem is widespread in acoustics to measure materials properties for designing absorbers, diffusers, or walls, thanks to different methods like Kundt tubes or reverberant rooms [13,14,15]. Under semianechoic conditions, a simple technique consists in measuring the acoustic reflection coefficient between an incident pulse and its reflection by the considered material [16].…”