The estimation of distance and power of multiple sound sources by combining three-dimensional sound intensity and beamforming

The problem of identifying multiple sound sources occurs in various fields. This study proposes a method for multi-source localization and sound power estimation based on three-dimensional sound intensity (3DSI) measurement combined with high-precision beamforming. First, according to the propagation law of the point source in the free field and 3DSI measurement method, a mathematical model of the sound intensity vector, sound power, and source location in 3D space for multiple sources is derived. The 3DSI components can be measured by 3DSI probes. To reduce the computational cost required to solve the mathematical model, the angles of the sources are estimated via compressive sensing beamforming orthogonal matching pursuit for the method. Moreover, the sound intensity components and angles are used as inputs in the multiple sound source identification model, and the dimensions of the model are significantly reduced. The model was solved to obtain sound source distance and sound power. Two tetrahedral intensity probes and a 16-channel microphone array were used for experiments in a semi-anechoic chamber. The results demonstrate that the method can accurately identify the locations of multiple sound sources and determine the sound power. Considering three sound sources, the maximum angular error is 1.41°, while the maximum distance error is 0.08 m. This method can use a small number of probes to obtain the sound sources spatial position and sound source power, and it improve the resolution and calculation efficiency.