Microphone Positioning Optimization for Conditioning of Inverse Tonal Aeroacoustic Problems

The reconstruction of the forces responsible for the tonal noise on fans has been subject of several works on the past years. The inversion of the tonal noise problem is done making use of the transfer function derived from the blade force equation. The condition number of this transfer function matrix plays an important role on the inverse problem reducing the influence of the measurement noise on the final result. This parameter has a direct influence of the problem geometry, thus, an important participation of the measurement positions. With the objective to investigate the influence of the measurements positions and find an optimal measurement grid, several analysis and optimizations are performed. A tonal noise application with optimization of the microphone positions is performed. When comparing these new results with existing results from using classical measurement grids, like hemispherical or arc distributed microphones, a drastic reduction of the conditional number is achieved.