基于波叠加法的非共形近场声全息波函数的构造与选择

在传统波叠加法的近场声全息算法中通常采用单层势或双层势波函数作为积分核函数,这类波函数在全息面与等效源面非共形的情况下极易导致系统矩阵的线性相关性增强和病态加重。以往研究多侧重对病态矩阵的正则化处理,以求获得更好的计算结果。从理论上分析了传统单层势或双层势波函数导致系统产生病态的原因,进而通过对格林函数的各阶求导构造出了系列具有较强指向性的射线波函数。利用该系列射线波函数替换传统波叠加法中的单层势或双层势波函数,可以使所形成的系统矩阵呈现主对角占优且近似对称的良态形式,从而可获得更精确、更稳定的计算结果。对脉动球源、振动球源以及可叠加为任意声源外声场的一般球源进行了数值仿真。研究表明:采用高阶波函数叠加法在传统波叠加法的系统矩阵已病态且不使用Tikhonov正则化就无法获得满意计算结果的情况下,能明显降低系统矩阵的条件数,使系统矩阵良态化。因而从这个意义上说,该方法也是一种可提高重建稳定性的正则化手段。同时发现,无论是传统的单层势和双层势波函数,还是射线波函数都各有其适用范围和优缺点,因此在实际使用中应根据不同的情况选择不同的波函数以提高计算稳定性和计算效率。

Construction and selection of nonconformal near-field acoustic holography wave function based on wave superposition method

In traditional wave superposition method for near-field acoustic holography,its integral kernel function usually adopts the single-layer potential wave function or double-layer potential wave function. When the holographic plane and the equivalent source plane are non-conformal, this kind of wave function can easily lead to the enhancement of the linear correlation and the aggravation of the ill-conditioned state of the system matrix.Most studies focused on the regularization of ill-conditioned matrices to obtain better results.Firstly, the reason of ill-conditioned system caused by traditional single-layer potential wave function or double-layer potential wave function was analyzed theoretically. Then, a series of ray wave functions with strong directivity were constructed by calculating derivatives of the Green's function.By replacing the single-layer potential or double-layer potential wave function used in the traditional wave superposition method with the ray wave functions, the resulting system matrix can be principal diagonal dominant and approximate symmetrical form, so the results can be more accurate and stable without using the regularization method.In this paper, the numerical simulation of the conventional pulsating sphere and swing sphere source and the general ball source which can be superimposed as the external sound field of any sound source is carried out. The results show that the superposition method of high order wave function proposed in this paper can significantly reduce the condition number of system matrix and make the system matrix tend to be well-formed under the condition that the system matrix of traditional wave superposition method is ill-conditioned and cannot obtain satisfactory results without Tikhonov regularization.Therefore, in this sense, this method is also a regularization means to improve the stability of reconstruction.It was also found that, weather the traditional single-layer potential wave function and double-layer potential wave function, or the ray wave function constructed in this paper, each had itsapplication scope, advantages and disadvantages. Therefore, different wave functions should be selected according to different situations to improve the computational stability and efficiency.