圆柱腔低频声场的球谐函数分解及声场再现

Spherical harmonics decomposition and reproduction of a low frequency sound field within a cylindrical cavity

针对圆柱腔低频声场的球谐函数分解,提出了基于移动式球形传声器阵列（简称球阵）测量的空间域直接求解法。利用空间域测量数据,在压缩感知（Compressive Sensing,CS）理论框架下通过一次线性方程组求解,获得整体坐标系下的声场展开系数。首先讨论了感知矩阵的列相关性,比较不同球阵形式及球面采样点数目,不同球谐函数截断阶数以及空间测量位置等的影响。随后在飞机舱室模型内利用文中提出的方法求解声场展开系数,再现腔内水平面的声压分布,并与传统球坐标变换方法做比较。实验结果表明,利用空间域直接求解法,通过球面随机挑选10个采样点的刚性球阵在声腔3个位置进行声场测量,不仅能够有效求解声场展开系数,而且声场再现精度更高,同时计算效率也显著提高。

An efficient method for the spherical harmonics decomposition of a low frequency sound field within a cylindrical cavity using a movable space domain Spherical Microphone Array （SMA） was proposed. By measuring over different positions with the SMA, the sound field coefficients in the spherical harmonics domain with respective to the global origin can be effectively solved under the Compressive Sensing （CS） framework by only one time calculation. Firstly, the column coherence of the sensing matrix was discussed by comparing different configurations of SMA, the number of sampling points, different truncated orders as well as the measurement positions. The proposed method was then validated through an experiment conducted within an aircraft cabin mock-up, and compared with the conventional coordinate translations method. Sound pressures inside the cabin can be well reproduced by the proposed method with a rigid SMA consisting of 10 randomly selected sampling points measured over 3 positions, and higher accuracy of reproduced field can be achieved, meanwhile the computational efficiency has also been greatly improved.