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.
Highlights
Near-field acoustic holography (NAH) is an effective technique for noise sources identification and acoustic field visualization
The reconstruction stability is a key problem in NAH technology due to the fact that the realization process is ill-posed and the reconstructed results are highly sensitive to signal-to-noise ratio (SNR) [15]
This paper focuses on a new method for determining the optimal parameters of Tikhonov regularization in NAH technique based on the equivalent source method (ESM)
Summary
Near-field acoustic holography (NAH) is an effective technique for noise sources identification and acoustic field visualization. The reconstruction of acoustic quantities of sound sources from near-field measurement data is an inverse problem, which is different from the traditional acoustic radiation calculation. The generalized cross validation (GCV) method [25] and the L-curve method [26, 27] as the posterior strategy are the two most widely used methods for selecting the optimal regularization parameters, both of which have good adaptability in the engineering application. This paper focuses on a new method for determining the optimal parameters of Tikhonov regularization in NAH technique based on the ESM. The minimization of the norm of this fictitious point source strength can be as the criterion for selection of the optimal regularization parameter since the reconstructed value should tend to zero. The numerical simulations are investigated to demonstrate the validity of the proposed method, and the results show that the novel proposed method is able to select the regularization parameter correctly and effectively
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