On the stability of transient nearfield acoustic holography based on the time domain equivalent source method

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.