基于Helmholtz方程最小二乘法的声场重构

对Helmholtz方程最小二乘(HELS)方法的理论进行了研究,提出了一种改进的HELS方法,其基本思想是将辐射声场描述成一系列由球面波函数构成的正交函数的线性组合形式,组合系数通过配置场点的声压来确定.针对HELS方法重建声场过程中矩阵病态和奇异的问题,提出了采用奇异值分解的方法求解组合系数.此外,提出了采用循环迭代的优化方法确定线性组合的项数.这两点改进使得HELS方法更具有普适性、更为稳健.以一脉动球声源为实例,应用改进的HELS方法对其声场进行仿真研究.结果表明,改进的HELS方法是一种非常有效的声场重建算法.

The Reconstruction of Sound Field Using Helmholtz Equation-Least Squares Method

The theory of the Helmholtz equation-least squares(HELS) method was researched,and a modified HELS method was proposed.The HELS method expresses sound field as a series of base functions,which are obtained by the Gram-Schmidt orthonormalization of spherical wave functions.The coefficients associated with these functions are determined by matching the solution of Helmholtz equation to the measured acoustic pressure at measured points.The ill pose and singularity problems were considered,and the SVD method was proposed to determine the coefficients.Also,a loop iteration method was suggested to optimize the number of terms in the series.As a result,the HELS method becomes more robust and flexible.Finally,the modified HELS method was applied,and the sound field of a vibrating spheres sound source was investigated.