A boundary element method based near field acoustic holography in noisy environments

In noisy environments, the acoustic wave is complicated and consists of the radiated wave, the incident wave, as well as its scattering wave. Double-layered pressure measurement is introduced to the boundary element method based near field acoustic holography to recover the free field quantities. First, the incoming and outgoing propagation waves are separated by exploring the propagation property of the two waves from their source to the field with the boundary integral equation. Subsequently, the scattering wave is filtered out by considering the boundary condition of the vibrating structure. Further, a measurement on an enclosing hologram is adopted to accurately reconstruct the distribution of normal velocity on the boundary. Two sets of the system of linear equations are built on the double-layered measurements. The Schur complement equation is then applied in conjunction with the Tikhonov regularization method to obtain an optimized reconstruction. Numerical examples are set up for two representative radiators impinged by incident waves. It is demonstrated that the free field normal velocity can be correctly reconstructed even if the signal-to-noise ratio is negative. An experiment is conducted for the cubic radiator to verify the accuracy and potential for the practical reconstruction in a noisy environment.