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• Oder domain beamforming is proposed for the localization of rotating machineries under variable speed conditions. • A steering vector of order domain beamforming is constructed. Rotating machinery is widely used in the modern industry, which undergoes huge amounts of variable speed working conditions. Localizing the sound sources of the rotating machinery on a specific order is significant to noise source identification and fault diagnosis. The order domain beamforming method (ODBF) is proposed in this paper to localize the source in the rotating machinery at a specific order. Firstly, the measured acoustic array signals are resampled into the angle domain via the key phase signal. Then, the fast Fourier transform is operated to obtain the acoustic pressure on a specific order. Finally, with the derivated steering vector in the order domain, the proposed order domain beamforming method can obtain the acoustic map on the scanning plane to localize the primary acoustic sources of the rotating machinery. The numerical simulation investigates the performance of the proposed ODBF under different cases. The industrial motor noise source identification experiment further verifies the effectiveness of the proposed ODBF. [ABSTRACT FROM AUTHOR]

Identifying acoustic sources with high spatial resolution and precision is significant for machinery noise control. Off-grid compressive beamforming is an effective method for creating acoustic maps with a high spatial resolution. In this study, a two-dimensional off-grid compressive beamforming method via weighted block ℓ 1 norm regularization (WBS-OCSBF) is proposed. The weighted ℓ 1 norm offers a more uniform sparsity penalty compared to the ℓ 1 norm. This method can enhance the performance of off-grid compressive beamforming. Additionally, it is easily implemented on mature linear programming solvers and converges with only a few iterations. Numerical simulations are conducted to analyze the effects of several major parameters on the performance of the proposed method. The simulation results demonstrate the superiority of the proposed method over some traditional methods. The proposed method is then validated using a loudspeaker noises localization experiment. A gearbox transmission system and a transformer are used as two specific objects to explore the industrial application value. The proposed method can effectively localize the gear meshing noise and transformer discharge faults with a high spatial resolution. • Compressive beamforming via weighted Block L1 Norm is proposed in this paper. It enhances the spatial sparsity of the reconstruction results. • Simulation and speaker positioning experiments verify the effectiveness of the method. • Two industrial application experiments proved the potential industrial application value of the method proposed in this paper. [ABSTRACT FROM AUTHOR]