Compressed Sensing based Radial Mode Analysis of the Broadband Sound Field in a Low-Speed Fan Test Rig

Abstract

A new inverse method for the radial mode analysis of the broadband sound fields in flow ducts is presented combining a Compressed Sensing approach and the eigenvalue decomposition of the sound pressure cross-spectral matrix. The Compressed Sensing method allows the accurate analysis of dominant modes by exploiting the block-structure of the radial mode spectrum and using sparse sensor arrays. The eigenvalue decomposition of the cross-spectral matrix is able to separate incoherent sound field constituents, which are sparse with respect to the in-duct modal spectrum and therefore are suitable for the Compressed Sensing approach. The application of the new method is demonstrated using measured data from a laboratory fan test-rig and the method is validated by comparison with results from a reference method using a full sensor array of 138 sensors. The method's potential to reduce the required number of sensors is evaluated by application of a reduced array with 34 sensors, by which the sound field is subsampled at high frequencies. The separation of incoherent sound field constituents by the eigenvalue decomposition is investigated in detail and its limitations are identified regarding the use of sparse arrays.