A Chirp-Rate-Driven Adaptive Window Chirplet Transform and Its Application in Bearing Fault Diagnosis

In this paper, we propose an instantaneous chirp-rate-driven adaptive window Chirplet transform algorithm for the analysis of strong time-varying nonlinear frequency-modulated signals with uncorrelated components. In this approach, the length of the sliding window in the Chirplet transform is dynamically adjusted according to the estimated instantaneous chirp rate of each signal component of an initial time–frequency result from short-time Fourier transform (STFT). A boundary constraint determined from the modal support intervals of the signal is utilized to restrain the allowable searching frequency range of the instantaneous frequency (IF) trajectories and incorporated into a cost-function-based IF extraction method to improve accuracy in the IF estimation. The effectiveness of the proposed algorithm is validated using a simulated nonlinear frequency-modulated (FM) signal with two uncorrelated components, and two sets of experimental bearing vibration signals. It is shown that the proposed algorithm can accurately track the frequency modulation of a strong FM signal dynamically to render an accurate estimation of the IFs and modal amplitudes of a strong FM signal. A comparison study also verifies that the proposed algorithm can produce a better energy-concentrated time–frequency result compared to other commonly employed time–frequency analysis techniques, particularly when the signal is contaminated by noise.