Sound source localization of speed reducer with discontinuity of time–frequency energy distribution under non-stationary operating conditions

Speed reducer as a key transmission equipment, its operating state is related to the stability and reliability of the whole mechanical system. On industrial robots, the speed reducers often operate under the non-stationary conditions. The intensity and frequency components of the acoustic signals emitted by speed reducer change. Due to the complexity of the contacts inside the speed reducer and the uncertainty of the sound propagation path outside the reducer, the harmonic components in the acoustic signal are non-stationary and the energy is discontinuous. Therefore, a method combining time–frequency representation, Vold-Kalman filter and slice delay-and-sum beamforming is proposed to localize the sound source of reducers with time–frequency energy discontinuity under non-stationary operating conditions. Firstly, the parametric resampled time–frequency representations of each microphone signal are obtained and aggregated after standardization. Next, time–frequency ridges are extracted from the aggregated time–frequency representation and used as frequency vectors to reconstruct the time-domain signals of each microphone at different orders through the Vold-Kalman filter. Finally, the sound source localization maps of each order are calculated by the slice delay-and-sum beamforming method and all the order localization maps within the same slice are aggregated after standardization to improve localization accuracy. Standardization aggregation fuses the features of time–frequency representations of signals from different channels, improves the continuity of the time–frequency energy distribution, and provides a high-resolution time–frequency representation for accurate extraction of order signals. The effectiveness of the proposed method is verified by numerical simulations of non-stationary sound sources and localization experiment on industrial robot joint.