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• The SBL algorithm is used for sound source localization and quantification. • The SBL and IBF algorithms are compared in terms of effectiveness and robustness. • Advantages of SBL at low SNRs, low frequency are validated through experiments. The localization accuracy and acoustic quantification are the leading indicators of acoustic localization. It is difficult to reconstruct the acoustic field completely as the number of sources is larger than the number of microphones. To solve this problem, the sparse acoustic holography under the Bayesian framework is applied to acquire the phase and amplitude distribution of the acoustic field to achieve acoustic source localization. In this paper, a Sparse Bayesian Learning (SBL) algorithm is improved, which can not only perform acoustic localization quickly and accurately, but also quantize the sound source to achieve sparse acoustic holography. To verify the efficiency and robustness of the improved method, simulations and experiments with different sound sources and noise disturbances are performed in this paper to verify the superior performance of the SBL algorithm at low frequencies and low signal-to-noise ratios (SNR). [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]

• 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]