Compressed sensing with nonconvex sparse regularization and convex analysis for duct mode detection

Abstract

Recently, research interests are increasing in mode detection methods based on compressed sensing, as it can reduce the number of sensors required by the classical Shannon-Nyquist sampling theory. This paper proposes a nonconvex sparse regularization method for azimuthal mode detection for aero engine fan noise. The nonconvex sparse regularization is based on the generalized minimax-concave (GMC) penalty, which can maintain the convexity of the sparse-regularized least squares cost function, and thus the global optimal solution can be solved by convex optimization algorithms. The main advantage of the GMC method over conventional compressed sensing method in mode detection is that the GMC method can better recover the mode amplitudes with a small number of sensors. Besides, the GMC method can suppress effectively the irrelated modes induced by the background noise or sensor installation errors. Therefore, the proposed method for duct mode detection can significantly improve the accuracy of the detected modes. Numerical simulations and experimental tests verify the effectiveness of the GMC method in mode detection for aero engine fan noise, and comparison studies show that the GMC method provides more accurate mode detection results than l1 minimization in the category of compressed sensing, as well as traditional mode detection methods.