Kernel ridge regression-based chirplet transform for non-stationary signal analysis and its application in machine fault detection under varying speed conditions

The vibration signals of variable speed rotating machines are non-stationary. Time-frequency analysis (TFA) can effectively analyze non-stationary signals in time–frequency (TF) plane and polynomial chirplet transform (PCT) is one of widely adopted TFA methods. In PCT, a vital step is to approximate the instantaneous frequency (IF) of signals through polynomial approximation. However, the solution of polynomial approximation is easily affected by noise or disturbance, which greatly limits the ability of PCT to analyze noisy signals. To solve this issue, kernel ridge regression-based chirplet transform (KRR-CT) is developed to precisely characterize the TF features of non-stationary signals and produce an energy concentrated TF plane. In the KRR-CT, even in the presence of severe noise, a stable solution can be obtained in the approximation step implemented through KRR. Moreover, KRR-CT based iterative algorithm is further constructed for the analysis of common multi-component signals. The efficacy of proposed KRR-CT based iterative algorithm is confirmed by synthetic and real signals, and the feasibility of applying it for machine fault detection is illustrated. The results indicate that the proposed methods can produce a more energy concentrated TF plane and provide more precise IF information for machine fault detection under varying speed conditions than four comparison methods.