Zhang Xiao-Zheng, Bi Chuan-Xing, Zhang Yong-Bin, Xu Liang
Institute of Sound and Vibration Research, Hefei University of Technology, 193 Tunxi Road, Hefei 230009, People's Republic of China.
J Acoust Soc Am. 2019 Aug;146(2):1335. doi: 10.1121/1.5123168.
Transient nearfield acoustic holography based on the time domain equivalent source method suffers from the instability that is caused by the use of the time marching scheme. In this paper, the time marching scheme is reformulated to a large iterative scheme. By conducting the eigenanalysis of this large iterative scheme, a necessary condition for stability, i.e., the maximum magnitude of eigenvalues should not be larger than one, can be obtained. Moreover, the causes of instability are analyzed according to the eigenvalues distribution. By virtue of the eigenanalysis, the mechanisms and drawbacks of three previous stabilization methods based on the Tikhonov regularization, the truncated singular value decomposition (TSVD), and the multistep approach are analyzed. To overcome their drawbacks, the classical golden section method is applied to search the regularization parameters and filter parameters based on the necessary condition for stability. Furthermore, the time averaging technique is introduced into the stabilization methods based on the Tikhonov regularization and the TSVD to eliminate the high-frequency oscillation and release the difficulty of searching the filter parameter, respectively. Numerical simulation results indicate that all the improved methods can realize the stabilization of solutions.
基于时域等效源法的瞬态近场声全息术存在因采用时间步进格式而导致的不稳定性问题。本文将时间步进格式重新表述为一种大型迭代格式。通过对该大型迭代格式进行特征分析，可得到稳定性的必要条件，即特征值的最大模不应大于1。此外，根据特征值分布分析了不稳定性的成因。借助特征分析，剖析了基于蒂霍诺夫正则化、截断奇异值分解（TSVD）和多步方法的三种先前稳定化方法的机理和缺陷。为克服其缺陷，基于稳定性的必要条件，应用经典黄金分割法搜索正则化参数和滤波参数。此外，将时间平均技术分别引入基于蒂霍诺夫正则化和TSVD的稳定化方法中，以消除高频振荡并缓解搜索滤波参数的困难。数值模拟结果表明，所有改进方法均能实现解的稳定化。
