Multiscale Similarity Fuzzy Lempel–Ziv Complexity and Its Application in Bearing Fault Diagnosis

Dispersion entropy-based Lempel-Ziv complexity (DELZC) has been widely applied in the field of fault diagnosis due to its excellent complexity measurement capabilities. However, DELZC neglects the relationships between different patterns and suffers from information loss during mapping, resulting in an inaccurate representation of the signal dynamic characteristics. To address these problems, similarity fuzzy Lempel-Ziv complexity (SFLZC) is proposed. SFLZC comprehensively considers the similarity between patterns at varying intervals through the sigmoid kernel. Furthermore, it mitigates information loss through mapping reduction and precisely represents similarity by employing a fuzzy membership function, thereby enabling accurate characterization of signals. In addition, multiscale SFLZC (MSFLZC) is proposed to measure complexity across different scales, providing more comprehensive information for multiscale analysis. Numerical simulation experiments demonstrate that SFLZC exhibits low parameter sensitivity, high consistency in complexity quantification, strong noise immunity, and reasonable computational efficiency. Experiments conducted on two sets of real bearing datasets confirm that MSFLZC not only surpasses conventional LZC-based metrics and entropy-based metrics but also accurately discriminates different bearing states, which demonstrates its advantages in bearing fault diagnosis.