Reconstruction of transient acoustic field using sparse real-time near-field acoustic holography

Abstract

A sparse real-time near-field acoustic holography method is proposed to precisely and stably reconstruct a transient sound field. By a time-domain impulse response function, a time domain convolution equation between the pressure time-wavenumber spectra on the hologram and reconstruction planes is first established. Then, a smoothed ℓ0-norm optimization algorithm is applied to solve the serious ill-conditioned problem of the inverse process to get the pressure time-wavenumber spectrum of the reconstruction plane. The key part of solving this problem is to approximate replace the discontinuous ℓ0-norm by using a suitable continuous Gaussian function family, and a steepest ascent algorithm is introduced to minimize the continuous function for obtaining the optimal solution. Finally, the pressure time-wavenumber spectra of the reconstruction plane for all wavenumbers at all times are solved, and the corresponding time-dependent pressures are gained by the two-dimensional space inverse Fourier transform. A numerical simulation is conducted to observe the reconstruction capacity of the proposed method. The simulation effect prove that the proposed method can accurately reconstruct the transient sound field, and its reconstruction results are compared to those of the real-time near-field acoustic holography (RTNAH) with Tikhonov regularization and YALL1 modal for verifying the superiority of the proposed method. The YALL1 module utilizes an alternating direction algorithm for solving the ℓ1 minimization problems. Several parameters including the noise, position of the holograph plane and two initialization values are discussed in the simulation. The comparison and discussion results show that the reconstruction effect of the proposed method is much better than those of RTNAH with Tikhonov regularization and YALL1 modal under different parameter configurations. An experiment with a percussive steel plate is implemented for further validating the effectivity of the proposed method.