3D sound field reconstruction for the enclosed cavity using the multilayer equivalent sources method

Conventional equivalent source method always models the reflective waves from boundaries using one layer equivalent sources, but how selecting the optimized distance of equivalent sources is diffcult. The proposed MESM (Multiple layer Equivalent Source Method) mainly uses multiple layer equivalent sources to approximate the desired sound field under the assumption that the equivalent sources are sparsely distributed in the external boundary of the space. Firstly, the details of the proposed method are derived. Secondly, the proposed MESM is validated using numerical simulations in a rectangular cavity and measured data in a cabin. The numerical simulation shows that a lower error of 5-10 dB can be achieved with MESM than ESM for the frequencies higher than 600 Hz and a higher error of 5 dB for frequencies lower than 200 Hz. A higher performance can also be achieved by the experimental data.Next, MESM are investigated through the numerical simulations against different conditions. It turns out that the elapsed time by MESM will be about two times of that by ESM. However, a high reconstructive accuracy for the frequency higher than 600Hz can be obtained if the sound field in enclosed space is computed using more sensors, a random distribution of microphones and a lower absorption coeffieint. In addition, the performance of sound field reconstruction will not be almost unaffected by the layer number and the number of equivalent source in each layer.