基于波叠加法的非共形近场声全息波函数的构造与选择  

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

作　　者：向宇[1] 石梓玉 陆静[1,2] 吴文军[1,2] XIANG Yu;SHI Ziyu;LU Jing;WU Wenjun(Key Laboratory of Automobile Componentand Vehicle Technology in Guangxi,Guangxi University of Science and Technology,Liuzhou 545006,China;School of Mechanical and Traffic Engineering,Guangxi University of Science and Technology,Liuzhou 545006,China)

机构地区：[1]广西科技大学,广西汽车零部件与整车技术重点实验室,广西柳州545006 [2]广西科技大学机械与交通工程学院,广西柳州545006

出　　处：《振动与冲击》2020年第15期183-192,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金(51775121,51665006)。

摘　　要：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。In the near-field acoustic holography algorithm of the traditional wave superposition method, its integral kernel function usually adopts single-layer potential wave function or double-layer one. When holographic plane and equivalent source plane are non-conformal, these wave functions can easily lead to enhancement of the system matrix’s linear correlation and aggravation of its ill-conditioned state. Most of published studies focus on the regularization of ill-conditioned matrices to obtain better calculation results. Here, firstly the reasons for traditional single-layer or double-layer potential wave functions to cause the system ill-conditioned were analyzed theoretically. Then, a series of ray wave functions with strong directivity were constructed by deducing derivatives of a Green’s function. The single-layer or double-layer potential wave functions used in the traditional wave superposition method were replaced with the ray wave functions constructed here to make the formed system matrix reveal principal diagonal dominant and approximately symmetric, and obtain more accurate and stable calculation results. Numerical simulations were performed for pulsating ball sources, vibrational ones and general ones being able to be superimposed as external sound field of any sound source. Results showed that the proposed high order wave functions’ superposition method can significantly reduce the condition number of a system matrix and make it be well-conditioned in the case of the system matrix of the traditional wave superposition method being ill-conditioned and not able to obtain satisfactory calculation results without Tikhonov regularization;the proposed method is also a regularization means to improve the stability of reconstruction;either traditional single-layer and double-layer potential wave functions or ray wave functions constructed here have their application ranges, advantages and disadvantages, different wave functions should be selected according to different situations to improve computationa

关 键 词：波叠加法 声全息 非共形 射线波函数 

分 类 号：TB52[理学—物理]