A multistep time-domain plane wave superposition method for stabilizing the reconstruction of the non-stationary sound field

Abstract

Abstract A multistep time domain plane wave superposition method (M-TDPWSM) is proposed to stabilize the reconstruction process of a non-stationary sound field when the measured time-evolving pressure on the hologram plane is used to solve the time-wavenumber pressure spectra on the virtual source plane. Unlike the conventional TDPWSM that performs each solving inverse calculation for only one time step in reconstructing the time-evolving pressure, the proposed M-TDPWSM combines the solving equations at several time steps to form a large matrix equation for once solving inverse calculation. The multistep calculation in the proposed M-TDPWSM not only reduces the total number of the solving inverse calculation for decreasing the accumulation errors, but also changes the element distribution of the inverse matrix to improve the filtering effect. One numerical simulation with an exciting plate is designed to examine the abilities of the proposed M-TDPWSM and the conventional TDPWSM. Several parameters including the position of the virtual source plane, the sampling number in the wavenumber domain, the noise and the number k of the proposed M-TDPWSM are investigated in the simulation. The simulation results attest that the reconstructed time-evolving pressure by the proposed M-TDPWSM at different parameter settings matches well with the theoretical one, but the conventional TDPWSM is sensitive to these parameters and sometimes its solutions are emanative. The proposed M-TDPWSM can suppress the numerical instability of reconstructing the non-stationary sound field and provide a stable solution. An experiment with an impacted planar plate was carried out in a semi anechoic room to further verify the superiority of the proposed M-TDPWSM in improving the stability of the solving inverse process.