Extension of the source localization method SODIX for the determination of partially coherent sound sources

The source localization method SODIX is capable of determining the amplitudes and the directivity of sound sources based on measurements with a microphone array. The source model of the method has recently been extended with fully coherent sound sources which improves the application of SODIX to tonal noise. This paper presents a further extension of the SODIX source model with partially coherent sources in order to overcome residual effects that cannot be correctly modeled with a fully coherent source model, e.g. due to propagation effects that decorrelate the sound field radiated by a sound source for different receiver positions. The extension relies on a parameterization of the source directivities and a compressed-sensing based algorithm in combination with an eigenvalue decomposition of the measured cross-spectral matrix. The extended localization method is applied to simulated sound sources that exhibit different mutual coherence and different source directivities. The results show that only the new source model with partially coherent sound sources is able to resolve the simulated source directivities accurately, when both coherent and incoherent sources are present. Finally, the extended SODIX method is applied to a fan tone from a full-scale outdoor engine noise test. The tone has a rotor-coherent part as well as a relevant part that is not coherent with the shaft rotation of the engine. As can be expected, the incoherent source model is not able to resolve the true directivity of the fan tone, when there is a significant contribution of coherent sound sources. The fully coherent source model improves the determination of the coherent part of the fan tone radiating from the intake into the forward arc and from the nozzle into the rear arc. The partially coherent source model improves the localization results for the contribution of the fan tone that is not coherent with the shaft rotation of the engine. Also, the partially coherent source model determines both the coherent and incoherent sound sources in one calculation. These experimental results are in line with the expectations and prove the possibility to apply the extended SODIX method to engine tones.