Parametric Doppler correction analysis for wayside acoustic bearing fault diagnosis

Wayside acoustic system plays a crucial role in monitoring and diagnosing the status of train wheel bearings. However, due to the signal distortion caused by Doppler effect, the diagnosis accuracy will be seriously disturbed. In this manner, this paper proposes a model-driven Doppler distortion self-tuning method in theory, named as parametric Doppler correction analysis (PDCA). Different from traditional methods, such as instantaneous frequency tracking and Doppler distortion sparse representation, the proposed method aims to abstractly construct a physical model of acoustic signal distortion propagation based on Morse acoustic theory, where the acoustic forward propagation model and reverse reconstruction model are simultaneously built. The scheme consists of four basic steps. Firstly, the physical model with amplitude modulation operator and frequency shift operator is described for the distortion process. Secondly, the pseudo transition signal with the characteristics of energy accumulation and no distortion is obtained via a construction of frequency rearrangement operator and amplitude demodulation operator. Then, pseudo Doppler correction (PDC) is presented to solve the frequency distortion of the received signal, where a high energy accumulation for frequency distribution is designed as optimization function. Especially, quasi Newton algorithm L-BFGS is used to realize the adaptive learning for distortion parameters. Finally, through time-domain interpolation resampling (TIR) technique, the corrected signal can be analytically reconstructed with the optimal parameters. Applying the PDCA scheme to simulated signals and experimental signals, its validity is verified. The comparison with the instantaneous frequency ridge extraction approach further indicates the proposed model-driven method can reach a more accurate correction result in a faster and adaptive process.