Fuzzy diversity entropy as a nonlinear measure for the intelligent fault diagnosis of rotating machinery

The entropy-based fault complexity characterization method has garnered significant attention in recent times, owing to its effectiveness and superiority in monitoring the health status of rotating machinery. Due to its high consistency, diversity Entropy (DE) can effectively quantify the irregularity of data and has been widely used in complexity analysis and fault diagnosis. However, the rigorous classification boundary leads to the absence of cosine similarity diversity during DE calculation, which will cause the inaccurate complexity estimation of time series collected from rotating machineries, unable to fully capture subtle changes in the signal, and affecting the accurate representation of fault features. In this paper, fuzzy diversity entropy (FDE) is proposed to solve this problem by incorporating the concept of fuzzy sets during the calculation diversity entropy. FDE employs fuzzy membership degrees as a replacement for the probability of cosine similarity falling into each interval, effectively distinguishing the cosine similarity of the same class that is considered equivalent by DE, and enhancing sensitivity to subtle signal variations. FDE effectively preserves the diversity information in the signal, and entropy estimation is more comprehensive and accurate, reflecting the complex dynamic characteristics of rotating machinery more realistically. Performance of the proposed FDE algorithm is verified by both numerically simulated signals and experimental signals collected from rotating machinery in comparison to original DE algorithm along with state-of-the-art fuzzy entropy (FE) and permutation entropy (PE). Results show that FDE can not only effectively quantify the complexity of rotating machinery time series but also possess low parameter sensitivity and computational cost. Furthermore, the experimental results have verified that FDE can be effectively applied in vibration signal feature extraction and fault diagnosis.