Extended dispersion entropy-based Lempel–Ziv complexity: a novel metric for rolling bearing fault diagnosis

Dispersion entropy-based Lempel–Ziv complexity (DELZC) is extensively utilized in fault diagnosis for its exceptional dynamic detection capability. However, DELZC only focuses on converting the signal into symbolic sequences without considering the critical relationship information between the symbolic elements, which inevitably reduces the utilization of valuable information. To solve this issue, extended DELZC (EDELZC) is proposed, which designs the extension sequence to enhance the information representation of symbolic sequences by employing cosine similarity. In addition, EDELZC is promoted to multiscale analysis by integrating with variable-step multiscale coarse-graining processing, termed variable-step multiscale EDELZC (VSMEDELZC). The experiments on simulated signals validate the ability of EDELZC in detecting dynamic changes in complex signals; furthermore, VSMEDELZC is applied to real-world bearing datasets, and the results of experiments show that VSMEDELZC is able to distinguish different fault states more accurately and has the best performance in rolling bearing fault diagnosis compared to other four multiscale complexity metrics.