Parametric Doppler correction for wayside array acoustic signal via short-time reconstruction

The trackside acoustic detection system (TADS) plays a vital role in vehicle bearings condition monitoring. However, the inevitable Doppler distortion embedded in collected data will bring considerable difficulties to defect inspection and diagnosis in the system. The distortion elimination approaches mainly achieve spectrum recovery based on time-domain interpolation resampling (TIR) in a data-driven way. These will be further limited by the requirement to signal to noise ratio (SNR) or calculation speed. Considering the principle of wayside acoustic physical model and the benefits of array acoustic in practice, this study proposes an adaptive parametric Doppler correction (PDC) scheme based on short-time reconstruction (STR), including perception modeling, inverse perception optimization and Doppler correction. Firstly, mathematical modeling with multiple perception operators, including acoustic amplitude modulation operator, frequency modulation operator and array time delay operator, a wayside acoustic physical model based on array sensing is established. Secondly, through the corresponding inverse multiple perception operators, a transition signal with frequency-domain energy concentrated is obtained for the optimal moving parameters searching. Thirdly, within short-time sequence segments of the sound source, the real-time position recovery is realized via the proposed STR with formulaic propagation delay compensation. Theoretically, it can be seen that the proposed PDC scheme can simultaneously recover the amplitude, frequency distribution and phase of the Doppler signal, which can be applicable to all wayside acoustic diagnosis scenarios. With the correction analysis of simulation and experimental array defect signals, it can be confirmed that the proposed STRbased PDC scheme is effective for Doppler signal recovery in high fidelity, and has great potential to the real-time diagnosis of TADS.