Efficient Azimuthal Mode Analysis using Compressed Sensing

Abstract

A new approach for the Azimuthal Mode Analysis (AMA) of over- and subsampled sound fields in flow ducts of turbomachines using circumferential sensor arrays is presented which is based on Compressed Sensing. Compressed Sensing is a framework to solve underdetermined systems of linear equations under the assumption that the solution vector is sparse. In the context of AMA, such sparse mode spectra often occur in the analysis of tonal sound field components generated by rotor-stator interaction. Important features such as stability and accuracy are investigated by analysis of a wide range of simulated and measured pressure data and comparison with commonly applied methods. Also two different optimisation approaches for the design of circumferential sensor arrays are introduced which allows a reduction of the number of sensors for large modal ranges if only a limited number of modes are dominant. Furthermore, the remaining mode amplitudes are estimated exploiting the deconvolution property of the applied Compressed Sensing algorithm.