Acoustic Mode Measuring Approach Developed on Generalized Minimax-Concave Regularization and Tikhonov Regularization

Investigations on the acoustic modes generated by the ducted fan can provide indispensable guidance for active control of the aero-engine noise. To achieve this, the circumferential pressure of the duct needs to be measured. However, the direct way, mounting a full sensor array (FSA) on the duct wall, requires numerous microphones and leads to a highly complex measuring system. With the introduction of compressive sampling (CS), the azimuthal mode analysis (AMA) can be conducted with much fewer microphones than FSA. In this article, an improved CS-based AMA (ICSAMA) approach is developed to promote the measuring accuracy while the measuring system can be further simplified. To be specific, the
$k$
-sparsity-constrained generalized minimax-concave (GMC) regularization is adopted to estimate the Tyler–Sofrin modes; meanwhile the Tikhonov regularization is employed to estimate the rest nondominant modes. The effectiveness of the proposed approach is verified on a 2.5-stage aero-engine fan rig, where two cases with different rotational speeds are conducted. Advantages of the proposed approach over the classical CS-based one are demonstrated by the experimental results with improved mode accuracy and reduced numbers of microphones. Furthermore, the robustness of the ICSAMA approach is also indicated, which is apparently desired in practical engineering.