Amplitude-based Time-shift Multiscale Feature Fuzzy Dispersion Entropy: A Novel Health Indicator for Aero-engine Fault Diagnosis

Fuzzy dispersion entropy (FuzzyDE) effectively solves the dispersion pattern rounding errors of dispersion entropy (DE). However, distinct pattern characteristics correspond to different properties of dynamic systems. The pattern probability derived from merely counting the number of different patterns imposes limitations on the representation of nonlinear systems by FuzzyDE. To address this issue, this paper presents feature fuzzy dispersion entropy (FFuzzyDE). This approach utilizes the numerical characteristics of dispersion patterns as new indicators for measuring pattern probability, thereby replacing the singular quantification methods of traditional approaches. The fuzzy membership is combined with the characteristics of the patterns to derive the exclusive probability associated with each dispersion pattern. Simulation experiments demonstrate that the feature dispersion pattern construction scheme allows FFuzzyDE to achieve stable entropy values more rapidly across varying data lengths, is sensitive to characteristic changes in frequency-amplitude modulation signals, effectively captures subtle characteristic changes in nonlinear systems, and exhibits excellent noise suppression capabilities. Furthermore, by integrating the amplitude-based time-shift coarse-graining method, FFuzzyDE is extended into the multiscale calculation domain, resulting in amplitude-based time-shift multiscale feature fuzzy dispersion entropy (ATSMFFDE). Two sets of bearing fault damage experiments show that ATSMFFDE can accurately extract bearing fault characteristics, and therefore provides effective health monitoring indicators for Aero-engine bearings.