Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC), Conservatoire National des Arts et Métiers, 292 rue Saint Martin, 75141 Paris Cedex 03, France.
J Acoust Soc Am. 2011 Oct;130(4):2016-23. doi: 10.1121/1.3628339.
This paper presents a different approach to solve the inverse acoustic problem. This problem is an "ill-posed" problem since the solution is very sensitive to measurement precision. A classical way to solve this problem consists in inversing a propagation operator which relates structure quantities (acoustic pressures or gradients) to near-field quantities (acoustic pressures or gradients). This can be achieved by using near-field acoustical holography (NAH) in separable coordinate systems. In order to overcome this limitation, the inverse boundary element method (IBEM) can be implemented to recover all acoustic quantities in a three-dimensional space and on an arbitrary three-dimensional source surface. In this paper, the data completion method (DCM) is developed: the acoustic gradients and pressures are known on a surface surrounding the source, but are unknown on its structure. The solution is given by the resolution of the Helmholtz formulation applied on the empty domain between the two boundaries made by the measurements quantities and the structure of the source. The conventional method applies directly the integral formulation for the empty domain. Another way of solving this Helmholtz formulation can be achieved by splitting it in two well-posed subproblems in a Steklov-Poincaré's formulation. The data completion method allows one to solve the problem with acoustic perturbations due to sources on the exterior domain, or due to a confined domain, without altering the results.
本文提出了一种解决逆声学问题的不同方法。这个问题是一个“不适定”问题，因为解对测量精度非常敏感。解决这个问题的一种经典方法是通过在可分离坐标系中使用近场声全息（NAH）来反转传播算子，该算子将结构量（声压或梯度）与近场量（声压或梯度）相关联。为了克服这个限制，可以实现逆边界元法（IBEM）以在三维空间中并在任意三维源表面上恢复所有声量。在本文中，开发了数据完成方法（DCM）：在源周围的表面上已知声梯度和压力，但在其结构上未知。该解是通过在由测量量和源结构形成的两个边界之间的空域上应用亥姆霍兹公式的分辨率给出的。传统方法直接将积分公式应用于空域。解决这个亥姆霍兹公式的另一种方法是通过将其分裂为两个在斯捷尔洛夫-波诺尔公式中良好定义的子问题来实现。数据完成方法允许解决由于外部域上的源或由于受限域而引起的声扰动问题，而不会改变结果。
