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The localization of cyclostationary sound sources is important for rotating machinery noise source identification and fault diagnosis. Cyclostationary sound sources are a special class of nonstationary sound sources, which exhibit periodic changes in statistics. Most of the conventional sound source identification methods are based on the stationary sound source assumption, which do not consider the cyclostationarity of the radiated sound field by rotating machinery. Thus, they are hard to localize the acoustic sources with different cyclic frequencies. In this paper, a novel technique of localizing the cyclostationary acoustic sources with different cyclic frequencies is proposed. First, the cyclostationary conventional beamforming (CSCBF) method is deviated. In CSCBF, the cyclic-cross-spectral matrix (CCSM) is defined considering all the cross cyclic spectral correlation (CSC) between different microphones in the array. The left steering vector and right steering vector are constructed to focus the CCSM on each scanning grid point at a given combination of cyclic frequency and spectral frequency. Then, the high resolution cyclostationary beamforming (HR-CSBF) is further developed to improve the spatial resolution of CSCBF. In HR-CSBF, two linear equations according to the property of CSC is established as the acoustic inverse problems. With the sparse distribution of the cyclostationary sources in the space as the prior knowledge, the iterated Bayesian focusing (IBF) is utilized to obtain a robust and sparse solution in HR-CSBF. Numerical simulations and experiments are conducted to validate the proposed methods. To explore the potential applications of the proposed methods, the localization of high pressure pump (HPP) and rolling bearing with outer-race failure are also used to evaluate the effectiveness of the proposed methods. It turns out that both CSCBF and HR-CSBF can localize the cyclostationary sources with different cyclic frequencies. Compared with CSCBF, HR-CSBF can achieve a higher spatial resolution in the obtained acoustic map. [ABSTRACT FROM AUTHOR]

• A nonconvex GMC penalty is introduced into ESM for acoustic source reconstruction. • The GMC penalty-regularized ESM is solved by an efficient ADMM framework. • The proposed method can improve the reconstruction accuracy and spatial resolution. • The feasibility of the sparsity-enhanced ESM in real scenarios is validated. The Equivalent Source Method (ESM) is a powerful technique for acoustic source reconstruction, which has been widely used in noise control and machinery fault detection. Because the inverse acoustic source reconstruction problem is typically ill-conditioned, regularization techniques are often adopted in ESM to achieve meaningful solutions. Based on the sparse distribution assumption of acoustic sources, sparse regularization can be utilized in ESM to promote the spatial resolution of reconstructed results. Existing sparse ESMs often adopt convex l 1 norm or nonconvex l p norm as the regularization terms. However, l 1 norm-regularized ESM suffers from an insufficient sparsity-inducing problem, which decreases the spatial resolution and reconstruction accuracy. Meanwhile, reconstructed results of l p norm-regularized ESM are often unstable due to multiple local minimas. In this paper, a sparsity-enhanced ESM is proposed, which introduces a nonconvex Generalized Minimax-Concave (GMC) penalty into ESM as the regularization term. The GMC penalty can enhance the sparsity of solutions and simultaneously maintain the convexity of the overall objective function in acoustic source reconstruction. Consequently, the GMC penalty-regularized ESM can improve the spatial resolution and reconstruction accuracy of the reconstructed results. To solve the acoustic source reconstruction problem rapidly, a computation framework based on Alternating Direction Method of Multipliers (ADMM) is derived. Simulation studies indicate that the proposed method can improve the acoustic source reconstruction accuracy in a wide frequency band, compared with existing l 1 and l p norm-regularized ESMs. Two experimental cases further verify that the proposed sparsity-enhanced ESM can effectively reconstruct the acoustic sources with high spatial resolution and reconstruction accuracy at higher frequencies. [ABSTRACT FROM AUTHOR]