Microphone positioning optimization for conditioning inverse tonal fan noise

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