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Shock and Vibration
Volume 2018 (2018), Article ID 7303294, 13 pages
https://doi.org/10.1155/2018/7303294
Research Article

A New Method for Determining Optimal Regularization Parameter in Near-Field Acoustic Holography

Jiangxi Province Key Laboratory of Precision Drive and Control, School of Mechanical and Electrical Engineering, Nanchang Institute of Technology, Nanchang, Jiangxi 330099, China

Correspondence should be addressed to Yue Xiao; moc.361@09yxpop

Received 29 September 2017; Revised 17 January 2018; Accepted 24 January 2018; Published 20 February 2018

Academic Editor: Chao Tao

Copyright © 2018 Yue Xiao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Tikhonov regularization method is effective in stabilizing reconstruction process of the near-field acoustic holography (NAH) based on the equivalent source method (ESM), and the selection of the optimal regularization parameter is a key problem that determines the regularization effect. In this work, a new method for determining the optimal regularization parameter is proposed. The transfer matrix relating the source strengths of the equivalent sources to the measured pressures on the hologram surface is augmented by adding a fictitious point source with zero strength. The minimization of the norm of this fictitious point source strength is as the criterion for choosing the optimal regularization parameter since the reconstructed value should tend to zero. The original inverse problem in calculating the source strengths is converted into a univariate optimization problem which is solved by a one-dimensional search technique. Two numerical simulations with a point driven simply supported plate and a pulsating sphere are investigated to validate the performance of the proposed method by comparison with the L-curve method. The results demonstrate that the proposed method can determine the regularization parameter correctly and effectively for the reconstruction in NAH.