Velocity Synchronous Linear Chirplet Transform

Linear transform has been widely used in time–frequency analysis of rotational machine vibration. However, the linear transform and its variants in current forms cannot be used to reliably analyze rotational machinery vibration signals under nonstationary conditions because of their smear effect and limited time variability in time–frequency resolution. As such, this paper proposes a new time–frequency method, named velocity synchronous linear chirplet transform (VSLCT). The proposed VSLCT is an extended version of the current linear transform. It can effectively alleviate the smear effect and can dynamically provide desirable time–frequency resolution in response to condition variations. The smearing problem is resolved by using linear chirplet bases with frequencies synchronous with shaft rotational velocity, and the time–frequency resolution is made responsive to signal condition changes using time-varying window lengths. To successfully implement the VSLCT, a kurtosis-guided approach is proposed to dynamically determine the two time-varying parameters, i.e., window length and normalized angle. Therefore, the VSLCT does not require the user to provide such parameters and hence avoids the subjectivity and bias of human judgment that is often time-consuming and knowledge-demanding. This method can also analyze normal monocomponent frequency-modulated signal.