Reweighted generalized minimax-concave sparse regularization for duct acoustic mode detection with adaptive threshold

Acoustic mode detection is attached great significance for providing guidance to noise reduction design of commercial aero-engine with high-bypass ratio. Compressive sampling method has been creatively employed in this field due to its notable performance on reducing the number of microphones in acoustic mode measurements. However, the classical ℓ₁-norm regularized compressive sampling model tends to underestimate the dominant mode amplitudes of interest. Moreover, the traditional regularization parameter selection strategy with fixed threshold brings out inefficient and cumbersome work. In this paper, we propose a nonconvex penalized compressive sampling model with adaptive threshold, to seek the sparse and accurate solution of acoustic mode detection from limited measurements, and provide a sufficiently efficient way to adaptively seek the optimal regularization parameter. Firstly, the reweighted generalized minimax-concave (ReGMC) regularization is employed to improve the accuracy of acoustic pressure reconstruction, which feasibly enhances sparsity with maintaining the convexity of the cost function. Secondly, the k-sparsity strategy is introduced to set regularization parameters adaptively. Finally, the applicability of the proposed approach is verified on a multi-stage aero-engine fan test rig. Experimental results demonstrate that the nonconvex ReGMC regularized method outperforms the classical ℓ₁-norm, producing more accurate results in mode detection with fewer measurements and being more robust towards background noise.