Global, and Local Optimization Beamforming for Broadband Sources

This paper presents an extension to global optimization beamforming for acoustic broadband sources. Given, that properties such as the source location, spatial shape, multipole rotation, or flow conditions can be parameterized over the frequency, a CSM-fitting can be performed for all frequencies at the same time. A numerical analysis shows that the non-linear error function for the standard global optimization problem is similar to the source's Point Spread Function and contains local minima, but can be improved with the proposed broadband error. Not only increases the broadband optimization process the ratio of equations to unknown variables, but it also smooths out the cost function. It also simplifies the process of identifying sources and reconstructing their spectra from the results. The paper shows that the method is superior on synthetic monopoles compared to standard global optimization and CLEAN-SC. For real-world data the results of broadband global optimization, standard global optimization, and CLEAN-SC are similar. However, the proposed method does not require the identification and integration of Regions Of Interest. Additionally it is shown, that by using reasonable initial values the global optimization problem reduces to a local optimization problem with similar results. Further, it is shown that the proposed method is able to identify multipoles with different pole amplitudes and unknown pole rotations.