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 ${\ell }_1$-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 ${\ell }_1$-norm, producing more accurate results in mode detection with fewer measurements and being more robust towards background noise.

声学模式检测对于为高旁路比的商用航空发动机降噪设计提供指导具有重要意义。由于压缩采样方法在减少声学模式测量中麦克风数量方面的显着性能，因此已在该领域创造性地采用了压缩采样方法。但是，古典${\ell }_{\mathrm{1个}}$-范数正则化压缩采样模型往往会低估感兴趣的主导模式振幅。而且，传统的具有固定阈值的正则化参数选择策略带来了效率低下和繁琐的工作。在本文中，我们提出了一种具有自适应阈值的非凸惩罚压缩采样模型，以从有限的测量中寻求稀疏而精确的声学模式检测解决方案，并提供一种有效地方法来自适应地寻找最优正则化参数。首先，采用重加权广义最小极大凹（ReGMC）正则化来提高声压重建的精度，从而在保持成本函数凸度的情况下，切实地提高了稀疏性。其次，k引入稀疏策略来自适应地设置正则化参数。最后，在多级航空发动机风扇试验台上验证了该方法的适用性。实验结果表明，非凸ReGMC正则化方法优于经典方法${\ell }_{\mathrm{1个}}$-范数，以更少的测量结果在模式检测中产生更准确的结果，并且对背景噪声更加鲁棒。