Localization of acoustical sources rotating in the cylindrical duct using a sparse nonuniform microphone array

The Doppler effect caused by the rotation of turbine fans brings significant challenges to the identification of fan noise sources inside the nacelle. Current methods of rotating source localization inside the cylindrical duct are executed with tough requirements for the microphone array mounted on the duct wall, which includes a fair enough number of microphones and equal-space distribution of each microphone in the azimuthal direction. A methodology based on nonuniform measurements and duct spin modes superposition (NMDMS) is proposed to identify rotating sources with high spatial resolution and few side lobes even near cut-on frequencies, which requires much fewer microphones and no uniform distribution of each microphone in the circumference. The sparsity in the azimuthal domain of the duct field generated by multiple rotating sources is verified theoretically, after which the azimuthal mode in each duct cross-section is reconstructed by the inhomogeneous measurements through the orthogonal matching pursuit (OMP) method. Followed by the identification of mode amplitude in the rotation frame, the sound pressure distribution as well as the axial acoustic velocity distribution on the source plane is reconstructed through duct modes summation. Numerical simulations and experiments are implemented to validate the method. Localization results indicate that rotating sources identification using the proposed method could not only save more than half the microphones without requirements of equal-space distribution but obtain good accuracy of localization and remarkably fewer side lobes.