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The Non-synchronous Measurements (NSM) was proposed to enhance the accuracy of reconstruction and reduce the measurement cost. However, the investigated object of conventional NSM are only sparsely distributed sound sources, and little emphasis placed on the reconstructed accuracy of the spatially extended sound source. In this article, the traditional NSM is further investigated in the spatially extended sound source, and the sound pressure information is reconstructed by Bayesian compressive sensing algorithm (BCS). Firstly, the spatially extended sound source is scanned by moving the rectangular microphone array, and the measurement effects of the array with large aperture and high density are approximately obtained by using NSM technique. Then, BCS is applied to reconstruct sound field by the NSM of sound pressure. The results of numerical simulations provide evidence for the feasibility of applying the proposed investigation to the spatially extended sound source. NSM has advantages in reconstruction accuracy compared with the single measurement. At the same time, the reconstructed sound pressure under NSM can replace the simultaneous measurement (SM) results of multi-array, which avoids the limitation of using reference microphone in increasing the number of channels and spatial layout. The experimental results of the driven steel plate provide additional evidence to support the effectiveness and feasibility of the investigation. • The application problem of the NSM in the spatially extended sound source like the driven steel plate is investigated. • The NSM increases the number of microphones and avoids the limitation of using reference microphone in increasing the number of channels and spatial layout. • The traditional NSM is further investigated in the spatially extended sound source, and the sound pressure is reconstructed by BCS. [ABSTRACT FROM AUTHOR]

• 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]

• Non-stationary noise source localization of permanent magnet synchronous motors (PMSMs) is investigated. • Spatial acoustic maps of PMSMs at a characteristic order can be restored. • Physical insights into the non-stationary noise mechanism of the motors can be revealed. • Experimental results with two industrial PMSMs verify the efficacy of the proposed method. Noise source localization of rotating machinery plays an important role in machinery noise diagnosis and control. Various beamforming methods have been developed for stationary sound source localization. However, for rotating machinery working under time-varying speed conditions, the radiated acoustic signals are typically nonstationary. Under these conditions, characterizing and localizing nonstationary sound sources remains a challenge. Permanent magnet synchronous motors are one of the most widely used rotating machinery in modern industries and often work under variable speed conditions. Herein, the noise source localization problem of motors under time-varying speed conditions was studied. A nonstationary noise source localization method based on the Vold-Kalman filter and time-domain beamforming is proposed to restore the spatial acoustic maps of permanent magnet synchronous motors(PMSMs) at a characteristic order. First, the Vold-Kalman filter is adopted to extract acoustic signals at a characteristic order from the nonstationary measurements using a microphone array. Then, the filtered multichannel acoustic signals are fed into the time-domain beamforming algorithm to obtain the noise source localization result in a characteristic order. Combining Vold-Kalman filter with time-domain beamforming enables the characterization of non-stationary sound sources in the time, spatial, and order domains. The experimental results verify the effectiveness of the proposed method in noise source localization for motors under time-varying speed conditions. In addition, the experimental case with two motors further proves that the proposed method can simultaneously realize noise source separation at different characteristic orders. [ABSTRACT FROM AUTHOR]