Broadband Mode Decomposition of Ducted Fan Noise Using Cross-spectral Matrix Denoising

B1 - Signal processing for noise source location/characterization

In the prospect of classifying ducted fan broadband noise sources, an accurate description of the acoustic pressure field in the duct is required. In this respect, it is possible to compute the cut-on mode amplitudes for each frequency using surface pressure measurements. This study deals with the application of such a mode decomposition technique to ducted fan noise measurements on the broadband part of noise spectra. The originality of the study concerns the microphone cross-spectral matrix (CSM) denoising applied to measurements. It is indeed well known that surface pressure measurements are strongly polluted by the wall turbulent boundary layer evanescent field. A basic but now standard denoising pre-processing consists in removing the CSM diagonal but it raises a non-physical CSM, leading to negative energy values.
In this study, three new denoising techniques are compared:
1/ CSM diagonal reconstruction from the off-diagonal terms given a model coherence function of the acoustic field,
2/ Alternating projections of the CSM onto two convex sets which forces a statistical and spatial structure to the reconstructed matrix,
3/ CSM decomposition into a low rank matrix (carrying the acoustic information) and a sparse matrix carrying the noise information.
The three methods are compared using simulations including additional white noise on a CSM loaded with both correlated and uncorrelated modes.
An accurate computation of the mode amplitude and correlation is obtained even with a -10 dB Signal to Noise Ratio (SNR). After validation, the denoising methods are applied to fan measurements and compared to the noisy matrix case. A standard output of the mode decomposition method is a power spectrum for all cut-on modes.
This work is part of the FRAE research project SEMAFOR.